WASHINGTON, D.C. Z0460
                               CCT17 1983
                                                                      OFFICE OF
                                                               RESEARCH AND DEVELOPMENT
   SUBJECT:   Transmittal of ORD Final Report "Prediction of Ecological Effects
             of Toxic Chemicals:  Overall Strategy and Theoretical Basis for
             the Ecosystem Model"

   FROM:      Erich Bretthauer, Directorial—J-J
             Office of Environmental Processes
              and Effects Research  (RD-682)

   TO:        John Melone, Director
             Hazard Evaluation Division  (TS-769C)

   THRU:      Marcia Williams, Acting Director
             Office of Toxic Substances  (TS-92)

       The attached ORD  research report  (EPA-660/3-83-084) which was
   recently released is  being transmitted to you for your use.  The
   report responds to the Agency's need  for predictive models of toxic
   chemical effects in natural waters.

        The objective of this research was to develop the rationale for a
   prognostic model for  ecological effects of toxic chemicals.  Included
   were efforts to more  clearly define the scope of "ecological effects,"
   to define  the level of resolution needed to permit application of existing
   toxicological measures, to analyze avarRa^U/toxicity data statistically,
   and  to initiate development of a *«y?King model.
        In  this  research  project,  performed under EPA's  Innovative Research
   Program, a  strategy  was  developed for modeling ecosystems to permit
   assessment  of effects  of toxic  chemicals on element cycling and other
   cosystem processes.  Progress also was made in defining ecological
   effects, establishing  model  resolution requirements,  and providing stat-
   Tstical  analysis  of  data on  the LC50 toxicity measure.  The research
   provides a  basis  for continuing work toward a prognostic evaluation model
   for new  chemicals  or those without extensive field data.

   cc:  Greg Grinder, OEPER
        Calvin Lawrence,  CERI




t-""                     Repository Material
                         Permanent Collection
       Prediction of Ecological Effects of Toxic Chemicals:   Overall
           Strategy and Theoretical Basis for  the Ecosystem  Model
                            Ray R. Lassiter
                       Environmental Systems  Branch
                    Environmental Research Laboratory
                          Athens, Georgia  30613
                       Innovative Research Project
                    Cooperative Agreement No. CR808629
                          Principal Investigator
                            James L. Cooley
                           Institute of Ecology
                          University of Georgia
                          Athens, Georgia  30602
                                                         US EfA
                                            Headquarters &,id Chemical Libraries
                                                EPA West Bldg HOS^.T 3340
                                                1301 Constitution Ave NW
                                                  Washington DC 20004
                         ATHENS, GEORGIA  30613


      The information in this document  has been funded  wholly or  in  part by
the United States Environmental Protection Agency under Cooperative  Agreement
No. CR808629 with the University of  Georgia.   It has  been subject  to the Agency's
peer and administrative review, and  it  has been approved for publication as  an
EPA document.


Environmental protection efforts are increasingly  directed  toward
preventing adverse health  and  ecological  effects  associated with
specific  compounds of natural or human origin.   As part of this
laboratory's   research  on   the  occurrence,  movement,
transformation,   impact,   and   control  of   environmental
contaminants, the Environmental  Systems Branch  studies  complexes
of  environmental   processes  that  control  the  transport,
transformation, degradation,  fate, and impact of pollutants  or
other  materials  in  soil  and  water  and develops  models for
assessing exposures  to chemical contaminants.

Concern about adverse environmental  effects of  synthetic organic
compounds has increased the need  for  techniques to predict the
ecological  effects of chemicals entering the  environment as  a
result  of the  manufacture,  use,  and disposal  of commercial
products.  Th is research  is directed toward a new  approach  to
predicting the probable effects  of  toxic  chemicals expressly for
environmental assessment.   The  research was done  under  one  of the
USEPA's  Innovative  Research Projects.   The  research is  continuing
toward providing the capacity  to assess the ecological  effects  of
chemicals particularly on  element  cycling  processes.   Upon
completion it is anticipated  that it will comprise one of the
components in a risk analysis  system.

                             William T. Donaldson
                             Ac t ing Director
                             Environmental Research  Laboratory
                             Athens, Georgi a


It is very difficult  conceptually  to design  a  means by which
effects of toxic  chemicals in natural waters  can  be  predicted.
Part of the difficulty  lies in identifying  exactly what those
effects  are.   Determining the  scale  of the effect of interest  is
a particularly difficult aspect of  the identification problem.
In particular,   it  must  be  determined  whether  the  effect  of
interest  is  expressed  at   the   chemical,  biochemical,
physiological,  individual, population, community or  even larger
scale.  Most experimental studies  are carried out at the finer
scales of  resolution,  whereas most of our ultimate  interest  with
respect to environmental  risk is  at  the coarser  and more
integrated scales.  Experimental studies have been done at the
finer  scales  partly  because they  are  the  scales that can  be
readily handled  experimentally, but  also,  I  believe,  because
there is an implicit  assumption  that  there  are comprehensible
connections  between behavior at the  finer scales and that at the
coarser.   That  is,   it  seems  to  me  that   there  is  a  general
expectation  that inferences  can  be drawn about the  ecological
scale  behavior  and  results  obtained  at the  finer  scales  of
resolution.  The aim of   this study  is to provide a  mechanism for
making  such  inferences.  Specifically, my aim  is  to  predict
behavior  at  the  ecological  level  of organization  based  upon
considerations  at  the  lower  levels.   This report details  my
efforts toward that end.

The project began as  a  result  of  a  proposal  to EPA's  Innovative
Research Program.  Under this  program I carried out two years of
research  at  the University  of  Georgia in  the  Institute  of
Ecology.   Th e  subject   partitioned  naturally  into  two major
subareas,  one  on the  specific representation of the  aquatic
ecosystem and the other  on the specific representation of the
direct  effects of toxicants.  Approximately equal time was spent
on  the  two subprojects.  The  subproject on  representing the
direct effects  did  not  progress as well,  however, as  the
subproject  on ecosystem representation.  For  this  reason the
direct  effects  subproject  is  not reported in  detail.  Only the
rationale for  interfacing the representation  of direct  effects
with  the  ecosystem representation is discussed.

This  report is intended   to convey  two major  sets of ideas and to
give  the  specifics of  one of them.   The  first idea  is  the overall
approach  and its  rationale.  The second  is the   idea on which  the
ecosystem  representation is  based.   This idea  is  that ecosystem
processes can be described functionally as  material and energy
transduction,  and  that  the  embodiment  of  these  functions by
discrete  species  is an  essential feature  of  ecosystems that  must
be represented if ecosystem- 1 ike behavior  is  to be achieved by
the  model.  Relative stability of  processes in the presence of
fluctuations of species carrying them  out  is an example.
Specific  equations  describing  most  of the functional  ecological
processes occupy  most of the  volume of  the report.  The  level of
detail  used in the presentation is intended to  indicate  the  level

of resolution  to  be used and to document the specifics  of  the
ecosystem model as it  will  be  translated  into computer code.

The overall  goal  of  developing the capability  to predict  the
ecological effects of  toxic  chemicals  has not yet been achieved.
On the contrary the difficulty  and magnitude of  the project  are
realized  to  be  greater  than  was  at  first  appreciated.
Nevertheless,  the  potential  to achieve  that goal  still  appears to
be good.  Work has  begun toward a  computer code for  the  mu1ti-
species  ecosystem  model,  and  work  is  continuing  on a  sound
representation of  direct  effects  to  include  the  simultaneous
action of multiple  chemicals.  One major  area of  the ecosystem
representation  that still  needs  further work is  that  of
fermentation,  probably  of  great importance in the  cycling of

The opportunity to  work  for  two years,  relatively  unencumbered,
on this project is  greatly appreciated.   I extend  thanks  to  the
numerous individuals associated with the U. S. Environmental
Protection Agency's Innovative  Research Program and  the  Athens
Environmental Research Laboratory who made it possible for me to
do  this  research.  Among those  individuals,  I am  especially
appreciative of the efforts of  the project  officer,  Dr.  Morris
Levin,  of the  support  of  the  formez  laboratory  director,  Dr.
David Duttweiler,  and of the innovative and untiring effort of
Ms. Connie Shoemaker  to  work out the  institutional arrangements
between the  EPA  and  the University of Georgia. I  thank  Ronnie
Moon and  Bruce Bartell for  drafting  the figures.

The Institute of  Ecology at  the University of Georgia graciously
made  their  facilities  available  to  me  for  the  term  of  the
project.  Dr. James Cooley, Director of  that institute served as
the official principal  investigator  for the  project and  was
helpful  in numerous ways.  To  him  and other individuals at The
Institute I am  appreciative.  Of all individuals who  contributed
ideas  and constructive criticism,  no  one  was  more helpful  than
Mr. Robert  Hermann,  graduate  student  in ecology.   Providing
continuity,   coherence,   and   logical  completeness   to  the
theoretical  basis  for  this modeling  approach was  the  most
important,  difficult, and time consuming part  of  this project.
In  these  efforts  Bob Hermann was  of  inestimable  help  with his
willing  assistance  and  input  through many  protracted,  and
undoubtedly sometimes disjointed,  discussions.  Discussions of
these  and many  related  ideas  in a weekly  seminar  led  by Dr.
Bernard Patten and myself  provided continual  stimulation and
difficult to assess,  but certainly positive,  benefit.

It  is  traditional  for authors  to make a statement of  explicit
assumption of  errors  of omission,  logic,  or  other  sorts.  Such a
statement is more necessary here than usual,  because of  the stage
of  the  research on  which I report.   It  is probable  that  there are
errors,  and, in spite of all the invaluable assistance generously
given me, the errors  are definitely  my  own.

Finally,  this report  officially  is  the  final  report  at  the  end of

the term of the Innovative Research project, but I  intend that  it
be considered to  function  more  as  a  progress  report.   My
admittedly biased assessment of the potential for results of this
project  when successfully completed are  that  it  is of  a  high
magnitude.  It  is  my hope and  intent to add to this  report on the
theoretical basis for the  ecosystem model,  additional  reports  on
the  basis  for  the  ecotoxico1ogy  model,  on  the  design,
implementation,  and  initial  results  from the  working  computer
model, and on results of  experiments  to test predictions of the
mode 1 .


A  strategy  for  predicting  the  ecological   effects  of  toxic
chemicals in aquatic  systems  is  developed.   The  strategy for
obtaining the predictions  is to carry out  a process of several
steps.    The  ecosystem   is  obtained  first  by  specifying
characteristics of the abiotic and biotic  systems.  The biotic
system  is  initially represented by a  large set  of  state  variables
representing potential  species  that  initially  exist  in the
environment. The operating  ecosystem is obtained by selecting
via computer  simulation  the smaller  set  of state variables  that
persist for an  arbitrary  period.   The  resulting  system  is  a
synthetic system.   Any  one  synthetic  system represents  real
systems  only in  a  general way.  Monte  Carlo techniques  are  to  be
used  to  obtain  a distribution of  synthetic  systems  that  persist
for   the  arbitrary  period  in  the  given  environment.
Characteristics  of  a real  system that could  occupy  a  real
environment similar  to  the  one described are  expected to  be
included  in  the  distribution.   Ecological  effects  are obtained  by
comparing  computer simulations that  differ only  in  the presence
or absence of  a toxic chemical along with its direct  effects.

The ecosystem is to  be described  in  the  computer  simulation  as a
set  of  differential  equations  representing  the  biotic and
chemical  species.   Processes  that  occur  in ecosystems are
described  fundamentally  as  energy transductions.   Organisms  are
represented  as reaction systems carrying  out kinetically hindered
redox  reactions  and  using  part of  the  released  energy for
metabolism, activity, and  growth.  Elements  are cycled between
their  oxidized  and reduced  states  via  these biotically  catalyzed
redox  reactions.   The  fundamental distinction  between autotrophy
and heterotrophy is  recognized and their complementary roles  in
element cycles  are represented.  Distinction between the modes  of
ecological  coupling  of micro-  and macroorganisms  is recognized.

Mathematical models  of growth  of autotrophs and heterotrophs are
assimilated or  developed.   The  level  of  resolution  used in these
models  is selected to  permit  coupling  of  toxic  effects by mode  of
action  of  the toxicant.  It is  argued  that  the  relevance of the
synthetic approach  to modeling the ecological effects of toxic
chemicals  depends  upon  the  fidelity  with  which  the  model
processes  represent  real processes; not on an  inherent limitation
of  the approach.

This  report covers  the  period from November  1980 to June 1983,
 and  the work reported  was completed as of February  1983.



Preface  ................................. 1V

Abstract ................................. V11

Figures. ..... ......... ............ « ....... x

Tables  ....... . ........................... x

Introduction ...............................  1

    Nature of Element Cycles and Importance of Considering
      Their Response to Toxicants .....................  2
    Basic Aspects of a Model for Predicting Ecosystem Effects .......  3
    Aquatic Ecosystem. ... .......................  4
    Theory of Ecosystem Structure and Function ..............  4
    Integration of Ecosystem Theory and Toxicity Theory .......  ...  5
    Motivational Basis ..........................  7
    Theoretical Basis ...........  ................  8
    Ecology as the Environmental Pattern of Biochemical Energetics  ....  8
An Ecosystem Model for Element Cycling  ..................  1°

    A Model for Uptake and Feeding Rate with Potential Limitation
      by Simple Saturation Mechanisms ...................  11
    Transport-Limited Chemical Uptake Rate  ................  13
    Autotrophy  ..............................  1 5
    Heterotrophy  .............................  20
    Model Summary.  ..................  ..........  39
Concluding Comments
     Macroscopic Metaview and  Microscopic  Apologia .............  39
     Scale  of Resolution, Reductionism,  Holism,  and Predicted
       Ecosystem Behavior  .........................  41


1   Schematic for redox processes that yield energy useful for              43
   biotic processes

2  Relationships among chemical and biotic  forms of elements               44
   in biosynthesis

3  Variation in terminal electron acceptor  as function of depth            45

4  Diagram of cell in aquatic medium indicating the concentration          46
   gradient surrounding the cell

5  Major components and relationships of autotroph biosynthesis            47

6  Major components and pathways (energy and mass) of heterotrophy         48

7  Categories of organic chemicals                                         49

8  Relationships characteristics of a filter feeding predator              50
   and its potential prey

9  Relationships between characteristics of a pursuing predator            51
   and its potential prey

 Some  reactions used  by chemoautotrophs  for energy                           52


When analyzing the  risks associated with the presence of toxic
chemicals in the environment, one can  be  concerned  with  a  variety
of potential  effects.   Effects  that  are manifested  not  as  a
result  of  direct  toxicity  but  as  alterations  of  the
interrelationships  among  organisms  and with  their chemical  and
physical  environment are  most  difficult  to  evaluate.   Many
possible  effects of  this sort  are  recognized.  Alterations  in
element  cycles, for example, are one  set  of  such  effects worth
considering for their  potential  to change  environmental  levels  of
natural chemicals.   An ecosystem model  representing the  processes
important in element  cycling, if based on fundamental theory,  in
principle  could be  used  to predict effects  on element cycling.
There is   a practical  difficulty,  however,  in  basing  an  operating
model  on  fundamental  considerations.   Element  cycle
transformation  rates  are  rather stable, relative to  fluctuations
typical of  individual populations.  It is nearly  compelling  to
visualize   that  this   stability  arises  from  the presence  of
populations of  several  species  able  to  carry  out  a  single
process.   In this  view  loss or diminution  of a  population  is
followed by  compensating  increases in  one  or more others,  so  that
the function (element  cycle  transformation)  is carried out rather
smoothly  even  in the presence of  extreme fluctuations of  the
individual populations involved.  The  difficulty lies in  finding
an appropriate representation for  a  system, so that  the model
will  exhibit whatever  functional  stability that  results  from
compensation  by  competing species.    In addition  the
representation must  permit the coupling of toxico1ogica 1  and
other effects  to system  components  (species,  chemicals, chemical
pools, etc.)  in such  a  manner  that destabi1ization of  system
functions  will be predicted  when appropriate.   No simple solution
to this problem is apparent.  My  approach  is to describe  the
ecosystem using a system of  differential  equations  for  which  the
associated  state variables represent  population densities  or
chemical  concentrations.   System  functions are fluxes  of
materials  and energy and are  represented by  terms  that couple
these equations.  Several  equations  representing   biotic  species
will each  contain a term representing  a single function  so  that
both compensation and toxico1ogica 1  effects  can be  represented.
Such a model will be  very large, potentially with a few hundred
state  variables.    There  are  associated  methodological
difficulties,  and these  have not been  ignored.  For  this  report,
however,  I  shall not discuss them, so  that  I  may focus on  the
model and  its  theoretical derivation.   Because  of  my intent  for
the  model  to  be  comprised,  in  part,  of the  explicit
representation of   many  species,   all  derivations  of  the
descriptions of interactions will be made with  the  assumption  of
the existence of an  arbitrary number  of species in  the  system.

One potential difficulty  in  using  a model  comprised of many  state
variables  to represent a  community comprised  of  a large  number  of
species  is  design of  the mechanism for achieving the  coupling
structure  for  trophic  interactions.   The approach   that makes  the
least  demand  on  the underlying  theory is  to  use  a  set  of

predation lates assigned  to  species pairs (the per capita rate  at
which  one  species feeds  on another).  I have  chosen to use  a
different  approach,  however,  in  which feeding  rates aie
calculated from morphological and behavioial  characteristics  and
swimming velocities of predator  and  prey.   It  is presumed  that
these characteristics  could  be determined for individual species.
The  rationale is  that  any  quantity  that  can  be  measured  for
individuals  of  a  species  is  much  more  accessible  than  are
quantities  requiting observation  of  the  interactions  of
individuals  of  two  or  more  species.   Th e  latter  kind  of
measurements will seldom be  available.

All  processes  occur  as  changes  from  disequilibrium  toward
equilibrium conditions.   Biotic  processes  predominantly  occur  as
a result of redoz disequi1ibria.   Plant  photosynthesis  creates
the highest degree of disequi1ibci um by producing both  reduced
carbon  and  the strong  oxidant,  molecular  oxygen.    Aerobic
respiration  is the  converse  process.   In  this same sense
anaerobic  respiration, in which oxidants  other  than  oxygen are
reduced,   and  chemosynthesis  are  converse  processes.
Chemosynthesis is driven by energy  released upon oxidation  of
reduced  forms  of   N,  S,  and  C.   Because  light  drives
photosynthesis and is  available  in aerobic  environments,
photosynthesis and  its converse process, aerobic respiration, can
proceed in  the  same  environments.   Respiration using oxidized
forms  of N,  S, and C,  however,  proceeds  only  in  anaerobic
environments, whereas  the  converse processes (chemosynthetic
processes utilizing  the  same elements) proceed only  in  aerobic
environments.  Thus  for  these  components  of  element  cycles,
reduced forms  of  elements  must  be  transported  into  aerobic
environments for chemosynthesis  and accompanying oxidation of the
elements to  occur.    Completion  of  element  cycles  does  not
necessarily depend  on transport  between  environments, however.
Reduction  of oxidized  forms also occurs during  biosynthesis
regardless  of  the environment.   Most organisms  that  live  in
aerobic environments  can  incorporate  ami no and thiol  groups  into
biomass  by obtaining oxidized  forms  of N  and S  from  the
environment and reducing them  internally.  This  is  assimilatory
reduction  (to distinguish   from  dissimi1 atory  reduction,  the
comparable term  corresponding to  respiration  using electron
acceptors  other than oxygen). Upon  death and decomposition  in
aerobic environments, these  reduced forms  are either  assimilated
directly  or  oxidized via chemosynthesis.   By  these  mechanisms
element cycles are  complete  in  aerobic  environments.

The  relative  importance  of assimilatory  and  dissimilatory
pathways in maintaining local and global  pool sizes  of elemental
forms  is not  clear,  nor is  the importance  of the role of abiotic
processes  or boundary conditions  imposed  by  geological  and
meteorological  factors  relative  to  biotic  factors.    If,  in
principle,   these  factors are included, however,  it  is  fair  to

say  that  element  cycling  is  responsible  for  pool  sizes  of
geochemica 1s.    These  include  the atmospheric  gases,  the
composition of the oceans,  and the earth's soils.  The remarkable
stability of  these  characteristics over geological  time scales
(1) probably  is  indicative of  the  robustness of  the component
processes (perhaps due  largely  to  functional compensation arising
from  species  diversity).   No comparative analysis of  the role of
biotic versus  abiotic processes  in element cycling  has been made,
but the number  and  importance of processes known to be  carried
out by organisms  leaves no doubt  that the characteristics of the
earth depend on  the  continuation of  biotic processes  at about the
level  that   they  are  presently  occurring.   Large  scale
introduction of  new xenobiotic chemicals into the  biosphere is a
practice  that  has been occurring for only a short  time.   Whether
the robustness that  apparently  has been  exhibited over geological
time  will continue in the presence of  these chemicals is not
known.   It is  prudent,therefore, to make the  effort  to  consider
potential changes in element  cycling,  to make it  possible to
identify  conditions that  might  lead  to serious  results,  and,
equally  importantly,  to  provide an estimate  of  the  probability
that  the  change  will occur.


The  importance  of  the  ecosystem  concept  is  to account  for
phenomena that   result  from  the interaction  of smaller  scale
entities,  such  as physical   factors,  chemicals,   species
populations,  and  functional groups  of populations.   Examples are
concentrations  of chemical  nutrients,  population densities of
component  living  species,  various  rate  related  measures  such as
productivities,  and less  easily quantitated concepts  such as
community structure.  When these  phenomena are  viewed in the
context of the whole ecosystem,  i.  e.,  not  in  an   experimentally
controlled situation,  they  are  often referred  to as whole system
phenomena.  Predicted ecosystem effects,  as I shall refer  to
them,  are standardized  differences in  whole system phenomena
between  a system in its  undisturbed state and  its state in the
presence  of a quantity of a particular  toxic  chemical.   Effect
can be quantified only  against  normal  functioning;  thus predicted
ecosystem effect can  be  made only  by contrasting  the predicted
affected state to the predicted  normal  state.

In predicting  an effect,  the same conditions  are assumed for the
normal  as  for the affected state, except that  for the  affected
state  the added presence  of a  toxicant is  assumed.  Predicted
ecosystem effect is,  therefore,  conditional.  Utility  will depend
both  on the theoretical  basis  of the model  and on  the relevance
of the conditions selected  for  the conditional mode  analysis.
The theoretical   basis  in  the underlying disciplines  of   physics,
chemistry,  and  biology,  and the  less  structured  discipline of
hierarchial organization of the system  representation is  quite
obviously a scientific question.  Discussion  of  the  theoretical
basis  occupies the bulk of  this  report.  That  the manner  in  which
questions are asked of  the model is  also a problem for science is

less obvious.  The problem of identifying,  at  least  to  my  own
satisfaction,  the kinds  of   questions  that one can  logically
expect  to answer was  a  necessity  for  carrying out  this research.
I shall discuss  this  question  also  later  in  this report.


To  predict  effects  of  toxic  chemicals  in  aquatic  ecosystems
several items are required.  The most  fundamental item  is  a  clear
definition  of  what  effects   are  to  be  predicted.   The  term
"aquatic ecosystem"  must be defined specifically for  the  present
purposes.  As used in the assessment  of  ecological effects, the
term  can have  one  of  two possible  meanings.   It can  mean  a
particularly defined aquatic  ecosystem (a  single instance),  or  it
can mean a  range of defined aquatic ecosystems  so that the
effects of the toxicant over  the  range of  systems can be referred
more generically  to  "the  aquatic  ecosystem."  In either  case  the
term is used in  conjunction with predicted ecosystem effects and,
when so used, refers  to  the set  of  attributes that  represent  the
aquatic  ecosystem in the theoretical  model. That  is, one  needs
to  realize  that use of "the  aquatic  ecosystem" in conjunction
with   this  model refers not to  a  physically  identifiable
environment, but to a set of  attributes that  relate  abstractly  to
a  set  of attributes of  real  systems.    The  more substantial
problem,  however,  is  the  provision  of  theory   of  ecosystem
 structure  and   function  at   a level  of resolution  to permit
observation of  the  effects.    Integration  of information  on
 toxicity  of  chemicals  to  aquatic organisms  to  the  same  level  of
 resolution  is a  necessity. Finally, not  only must  both ecosystem
 theory  and toxicity  theory be  organized  at  the level  of
 resolution  to permit observation  of the effects, but each must  be
 organized  to interface with  the  other  in  a model to make  the
predictions  of  effects.


 Structure and function are inseparable  in  ecology.  Structures
 enable functions.  It is my assumption that  there is parsimony of
 structure  and  behavior  in  biotic  systems (an  assumption  in
 keeping with the principle of Ockam's razor):  structures do not
 exist  without  function.  Generally,  this  is   a  reasonable
 assumption,  because  power  is required  to maintain structures, and
 the competitive  advantage  is held  by  organisms  without the added
 burden  of  useless  structures.    In  the  theory  of  ecosystem
 function  proposed here  the power  demand  is  calculated as the net
 cost of  carrying out  the  functions.  It is assumed  that there are
 no overhead costs  for maintaining structure,  except structure
 that   is  used  in obtaining  energy,  survival,   or  reproduction.
 These  assumptions are in keeping with  the  overall  assumption of
 pars imony .

 Much  theory exists  in  ecology,  in the generic sense of theory.
 This  theory is diffuse,  and  it  has not  been assimilated at the

level of resolution that is useful for a theoretical model  for
predicting  ecosystem effects of toxic chemicals, at least not  in
the vein of the model  discussed here.  The major effort  in this
research,   therefore, has  been  to  assimilate a  theoretical basis
for  the model.   In  doing  so I  have held to the  parsimony
hypothesis.   The  level  of  resolution  is  such  as   to  permit
information on  mode of action  to be used when it is available.as
well as to  permit  more general statistical measures  of  toxicity
to  be  used.  The  ecosystem  theory  that  is the basis  of this
theoretical model uses concepts from  chemical  thermodynamics  (in
much  the   same  way  as  they  are   used  in  biochemistry),
biochemistry, physiology, population  dynamics,  and  limnology.   A
biophysical approach is  used to derive  relationships  so  that  the
resulting model  equations are written  primarily at  the population
level,   with terms of   the equations calculated  using  expressions
reflecting  underlying  physiology,   biochemistry,   etc.,   all
constrained by  mass and  energy accounting.   Because  reference is
made to these  finer levels in the describing equations, system
effects at  these  levels  also can be explored.


Theory  developed or assimilated  in  this  research is primarily
ecosystem theory.  As noted, however,  the  ecosystem theory  has
been expressed  so  as  to  permit  the application  of   various
toxicity measures.   Translation  of  LC50  values  to  effects on
death rates  in  this model has  the usual accompanying difficulties
of   interpreting LD5Q  values as  rates  and  the  additional
difficulty  of extrapolation to very low concentrations.  Whatever
the assumed interpretation and  extrapolation mechanisms,  the
method  of  application  of toxicity  measures will be influenced by
the approach taken  in  the model to  represent  ecosystem processes.
This approach  is  to  represent processes or functions  as  being
carried out by  a group of populations differing from each other
in  various  ways, one  of  which  is  their susceptibility to a toxic
chemical.   The model  does  not  represent  particular  existing
species, but instead the model  parameters  are in  the  range of
analogous  values  expected for  existing  species  that carry out  the
process that  is represented.

A fundamental  assumption that amounts to  a principle  for  this
modeling  approach  is  the  basis  for  this  non-specificity of
 representation.  Simply  stated, I  assume that element  cycling  and
most other  macroscopic properties  of ecosystems  derive  from
 interactions  of organisms as  they obtain  useful energy via modes
 of  metabolism  suited to the  energy  sources.  These  modes of
metabolism, unlike species,  are   common  to diverse  environments
 ENERGETICS).   I view  a  particular biotic community simply  as a
 complement of  species populations  that  are able  to  exploit  the
 energy sources, grow  and  reproduce in a  particular  environment.
 This-is not,  I  think,  an  extreme  view.   However,  in  a similar
 sense, for the  model  to  be  operational,  computer algorithms  are
 required  to  select  coexisting  species  as  represented  in  the

model.  These ace selected in the context of a given environment
representation.  It  will be  impossible  foe  this  environment  to
tepcesent  precisely any  real  environment,  and by  virtue  of
selection  of  species  representations  as  a  function  of  the
environment  descriptors,  the  species representations will not
represent specific real organisms.   For that matter, no one  teal
environment can be said to represent precisely  any other  one, yet
many organisms are common to  widely  different  environments.  Over
time  intervals  relevant to selection processes, environments are
not  isolated and selection  occurs  over  all   communicating
env iionments.

Derivation of the species  representations, while not  representing
particular species,  to  maintain  a  credible  level of  reality, will
use  available  information on  appropriate existing organisms.
Discussion of these matters,  however,  is very  premature,  because
the  working  program is far  from complete.  The main ideas  to
derive  from  the comments are  that  this model is  not directed
toward  any specific  system representation,  that on  the contrary,
a  fundamental  assumption  is  that  the macroscopic  system
properties  such as  element  cycling  do  not depend  on any such
specificity,  and that perturbations  (as by  a  toxic chemical)  on a
biotic  community  in a particular  environment  will  result  in
characteristic alterations to the unperturbed  behavior  (see  also

From  a preliminary analysis on  several  compounds,  considering all
species  together,  toxicity can be represented by an asymmetric
frequency distribution in which no  taxonomic  relationships above
the  species  level are  apparent.  That  is,  if  the  frequency  of
occurrence of LC50 values (Criteria  Documents Data Base  2,3) are
plotted, the  distribution is  unimodal  and skewed  such  that there
is a low frequency  tail at relatively highLC5Q  values.   If one
then  identifies  the  species  occurrence in this distribution,  no
pattern  associated  with  taxa  higher  than  the species level  is
apparent.  These analyses  are highly tentative, however,  and
another  analysis  with a  much larger data base is beginning.
Assignment  of  toxicities   to  the   model  populations with
probability reflecting  the frequency distribution  appears  to  be a
reasonable approach.  In any case there is no basis to expe'ct a
close match between measured toxicities and the explicit  needs  of
any  ecosystem model, and  therefore,  no specific parameterization
of  a model  can  be  expected.   Use  of  toxicity  information,
therefore, will require  that  some  rationale  be  employed;  that
employed here is to  assign toxicities to the model  as nearly  as
possible to match  the  measured fzequency distribution.  Use  of
this rationale,  in general, will be  limited by  data availability,
particularly for  assignment   of  behavioral  effects  such  as
variation in  hunting or escaping efforts.


The motivation  for  this  research  project  was  the perceived need
to be able  to assess  probable ecosystem  effects, particularly
effects  on  the  cycling  of major elements,   resulting from the
introduction of a toxic chemical.   Such  a  capability would be
most  useful if  it  were prognostic and  able  to be used  in an
exploratory mode in  search of generalizations about  expected
effects.  Planning  research  to develop such  a  capability is an
exercise in  matching the  possible  forms of theoretical prediction
with  potentially useful questions.  As a  result of  indulging in
such  an  exercise I  drew the  following conclusions about  some
reasonable  forms of useful questions, and what basis  exists to
support research toward  providing  answers  to such questions using
predictive models.

    Questions   relating  to  effects  on   identifiable  existing
    species  in  specific environments cannot  be answered by a
    synthetic,  predictive ecosystem model.

    It  is  feasible  to  answer  questions relating  to  probable
    effects on  ecosystem functions,  given the  following
    conclusions that a  basis  exists for a model of  ecosystem
    functioning  and  effects   of   toxic   chemicals  on  the
    funct ioning.

        Enough  is known of  physical, chemical, biochemical,
        microbial,  macro-organism  biology,  etc.,  to  support
        virtually any level  of underlying  process description.

        Enough  is known of  ecological relationships  to provide a
        basis for structural  relationships  in  addition to those
        implied by the underlying  process  descriptions.

It  is hypothesized (rathex  than concluded)  that  there  is no
dependency of system  function  on  presence of  particular species
(as already  discussed)  nor  on species diversity. Capacity of a
system to carry  out  a process  smoothly  while populations involved
in  the  process  are stressed  by  a toxicant,  however,  depends
entirely upon species diversity.  The additional hypothesis is
made  that  capacity for  compensation increases at  a decreasing
rate  as diversity increases.  There is, therefore, dependency on
the presence of  species  to  carry  out each function,  and there is
dependency  on a minimal degree of diversity within each function
to  permit  compensation by   non-susceptib1e  populations  for
reduction in population levels of species  susceptible to toxic
chemicals.  The  importance  of  this latter  hypothesis to modeling
the  functional  behavior of   ecosystems  using  a multispecies
representation,  is  that it is possible to represent  ecological
processes using  a limited number of species, if  it is true.


Following  these  ideas,  a  theory of  ecosystem function was
assimilated and wotk  towatd a  functioning model  based on the
theory  is  in progress.  The theory is not  new in its entirety,
but   it   does   contain   original  elements.   Perhaps  mote
significantly,   it departs  from  both holistic  and  reductionistic
views.    It  departs  from  the   traditional  holistic view by
attempting  to  synthesize system  properties using a  biophysical
integration of finer scale components to the level required  to
represent  the  system.   It  departs  from the reductionist  view  by
concentrating on the ecosystem as  the object to be represented
and by virtue  of interest  in processes whose behavior cannot  be
considered  to  be a function of  any single  system component.

This  theory like every theory of macroscopic  phenomena,  is  based
upon  phenomenologica 1  models  of its fundamental  components.   In
an attempt  to  give the  theory a greater predictive  capability,  I
have  selected as fundamental  components, models  representing
energy  transduction at  the biochemical  level. In these models
organisms  are considered  as  reaction   systems  that  catalyze
energy-rich,  kinetically hindered redox reactions and,  in  the
process, use part of  the  reaction energy  for biosynthesis  and
mechanical  work.   Ultimately,   population  rates  of  change result
from the biochemical  models  based upon  redox  chemistry.
Ecological  interactions  result  from dependencies  among  organisms
for  elements  from which to form biomass  and for  compounds  to
serve as  oxidation and reduction reactants  to provide energy.   To
maintain the  identity  of all organic   compounds  that  could  serve
as  chemical nutrients  or  as energy   substrates in the working
model would be an impossible computing problem.

To  overcome this  problem,  organic  chemicals  are aggregated into
classes  that are ecologically relevant.  The underlying  theory  is
worked  out elsewhere (4) and does  not  depend  on  this aggregation.
Toxic chemicals  interfere with  the processes  by  which  organisms
obtain  or  use  energy or  elements.   Thus  this  theory  of  ecosystem
function is based upon fundamental conceptual  components that are
models   of real  components  that  respond to  toxic chemicals.
Integration of toxicology  at lower resolution,  such as  altered
probability  of death as  obtained from reported  LC5fl  values,  can
also be  used  directly  without  reference  to  the  fine  scale
phenomeno1ogical models.


ECOLOGICAL MODES  OF  METABOLISM.  Disequilibria that drive biotic
processes  are  in two  forms:  light  and chemical.   Organisms that
use  light induced disequi1ibria are phototrophs,  and  those that
utilize  chemical  are  chemotrophs  (5,6)   Phototrophy  and
chemotrophy  refer  to the  source  of  energy,  i.  e., whether the
free energy    is  derived  from  photochemical  or  biochemical
reactions.  In either case the electron donor  (reducing agent)
can  be   either  inorganic or organic (lithotrophy or organotrophy

with the prefix photo-  or chemo-) making  a  total  of  four major
classes of  energy  metabolism.

Figure  1  is  a  schematic of  the processing  of  energy.   For
biosynthesis  the  source of carbon can be either CO2  or  organic
compound (autotrophy or heterotrophy).  Combining the modes of
energy metabolism with the modes  of biosynthesis, eight
categories  are formed,  all eight  of which exist in nature along
with  variations  on these major  categories.   For the  initial
theoretical  development,  it  will  suffice to consider  only three
of the major categories:  photo1ithoautotrophy,  chemo1ithoauto-
trophy, and chemoorganoheterotrophy.   Because there will be no
risk  of  confusion,  I  shall  refer  to these  categories  by  the
shortened  terms, photoautotrophy,  chemoautotr ophy ,  and hetero-
trophy.  I  shall further subdivide  the latter category   into
macroheterotrophy  and  microheterotrophy,  and  microheterotrophy
further into categories  reflecting the electron acceptor used.  I
shall  refer  to   these  latter  categories  occasionally  by  the
coarser terms, oxymicroheterotrophy  and anoxymicroheterotrophy.

Figure 2 is  a  schematic of biosynthesis  at  the  ecological  scale.
Figure 3 indicates the spatial  and  energetic  relationships of
microheterotrophy as a function of presence of potential  terminal
electron  acceptors.    Although  too  complex   to   represent
graphically, a composite of Figures  1,  2, and 3  provides  a rather
complete, but abstract,  scheme for element cycling.

ECOLOGICAL ENERGETICS.   Energetics  is  simply  a term  for
thermodynamics  as applied  to the  analysis of  biological
processes.   Biological  processes, like all  processes,proceed
only when conditions of disequilibrium exist.  More specifically,
biochemical  mechanisms  proceed by  transfer  of  electrons  and
associated energy  to form,  primarily,  ATP  and NADPH (or NADH).
ATP  is the  universal mediator of biochemical reactions;
NADPH  and NADH  are the  major  biochemical  reductants.   Processes
 in which  these  compounds  participate  are   subcellular,   yet
processes  by  which they are  formed and in which they are used are
of utmost  relevance at  the  ecological  level  of organization  and
of great utility  in theoretical  ecology.  This  is  so  because  the
macroscopic  patterns  in which they occur  are  interpretable,  not
 at the cellular, individual, or population level  --  but only at
 the  ecological  level  of organization.   That  is, the existence  of
 a particular  mode of metabolism,  for  example -- chemoautotrophy,
 is a phenomenon that   can be explained only  with reference  to
 ecological  processes.

These  processes  are interactions  of biotic and  abiotic components
 that create and  maintain environments  suitable  for  particular
 modes of energy metabolism.  Organisms  can sustain a mode  of
 energy metabolism in an environment only if  the reaction on  which
 this  metabolism  depends  is  thermodynamically favored  (exergonic)
 in that environment.   Specifically, organisms cannot  maintain
 physiological  conditions  that permit  a  net  derivation of energy
 from biochemical processes  unless the  net  of  those  processes   is

exeigonic in their  environment.  This fact can be used as a major
organizing  principle for theoretical  ecology.   It provides the
basis for calculation of  potential modes of energy metabolism for
given environmental  conditions without  reference  to organisms.

The Gibbs  free energy function  is  the appropriate measure for
such calculations  because  it is a measure of the useful work that
can be extracted from the energy of a  reaction,  and it refers to
conditions  of constant  temperature  and pressure,  but  allows
volume to vary  (as,  for  example, occurs in a biotic process that
results  in  the  evolution of  a gas).   These are  conditions most
appropriate to biological systems.   Such calculations are not of
energy budgets as  such.   Calculations  for energy budgets usually
consider  that energy is  conserved (in  keeping  with the first law
of  thermodynamics)  and  accountable when  all  system  gains and
losses are  considered.  Conservation  of energy,thus,  refers to
conservation of the  sum of all forms of  energy.  Energy that can
be  used  by  biotic   systems  is  the  Gibbs  free  energy  for the
specific energy yielding reactions,  such as the oxidation of
organic compounds  with sulfate as the  terminal electron acceptor.

The useful energy that can be extracted from these processes is  a
function of the concentrations  of the reactants  and products.
Hence,  ecologically  relevant calculations  for the  amount of
useful energy that  can be derived  from chemical  reactions are
functions  of the  conditions  of  the environments in  which the
reactions  occur,  and,  hence,  very definitely not  subject to
conservation laws.  In contrast,  however, mass conservation  is  a
principle that is  useful  for  theoretical ecological computations.
In  fact  in the  ecosystem  model mass  conservation  is the
fundamental  principle  for    accounting  that  permits  the
calculation of the  Gibbs  free energy.   This comes about because
mass  conservation  is used directly as  the  accounting principle
for calculating chemical  quantities including  concentrations, and
the Gibbs  free  energy  function  for chemical  reactions is
dependent on concentrations  of reactants and products.


An  ecosystem model for element cycling  is necessary for
predicting  effects  of  toxic chemicals on  cycling processes.
Morowitz (7) has shown that  flow of energy through a  system  from
a source to a  sink  will  necessarily result in cycling in steady
state  systems.  Ecosystems approximate  steady state systems  that
are far from  equilibrium,  a  condition that  is  associated
necessarily  with  structure   (8).    The  model  presented here
represents ecosystems  as   open  systems  that  are far  from
thermodynamic  equilibrium.  The degree of  approximation to  steady
state,  however,  is  not  explicitly  assumed,  but  rather, the
ecosystem  is  represented as  a  dynamic  system.  This  is done
because  interest is in alterations  in the rate of cycling, not

just in whether  elements  cycle.   The  fundamental basis for  this
model  can be  stated  rather  simply,  but  the details  of these
fundaments will occupy the next  several pages.

The organisms  that carry  out  the  ecological  modes  of metabolism
comprise  the  structures  that are  necessary for element cycle
transformations.  For  each mode of  metabolism,  stability  is
maintained in part by diversity  among  the populations in their
response  to external factors.   As  a  consequence  of diversity,
compensatory  changes  occur, resisting fluctuations in  the  fluxes
of  materials  and energy that  result  from  element  cycle
transformations.  There  is  a high degree of similarity  at  the
biochemical level within each mode  of metabolism.   Diversity
exists  in  morphological   variation and is  expressed  in
physiological  and  behavioral  differences.   The  development  that
follows  is based on  the  foregoing  assumptions  of   biochemical
similarity and morphological diversity within metabolic modes.

The derivations  and equations  that  follow,  while comprising  the
greatest part  of this report,   should  not be  considered  to  be  the
most important part.  They constitute  my rationale  for  the  way to
express,  ultimately  in  a  computer  model,  the hypotheses  and
working assumptions already discussed.  In attempting  to  develop
a predictive model for aquatic  systems without relying  on  the
specifics  of any  one system,  it has become  apparent that
traditional views of ecology present a barrier to the development
of ecological  theory.   These traditional views, utilizing  natural
history and taxanomic approaches, have overemphasized,  I believe,
differences among  ecosystems  to the  exclusion of  theoretical
approaches that do not assume from  the  outset the  primacy  of
importance of  specific  taxa.   This  is not to  claim that  the
approach  put  forth here has,  indeed,  overcome these barriers to
the extent that  a general  ecological theory will  result.  Indeed,
the approach that I present  is  also  highly complex,  dependent
upon  as  yet  unsupported hypotheses,  and  upon computational
capabilities  that could be very difficult  to  achieve.  What  I  do
claim,  however,  is that the viewpoint  taken, which  is  more  akin
to that of  microbial ecologists,  is  a valid one,  and I  should
hope  that if  it does not  lead directly to  the  goal of a model
capable of  predicting ecological  effects,  perhaps indirectly  it
will contribute  to another approach that will.


Every  organism must cope  with  two problems,  obtaining  energy and
obtaining  elements  from which to form  biomass.   Photoautotrophs
potentially  are  limited in  their  energy supply  rate by light
availability because of  light attenuation by various  agents in
water.  For all microorganisms,  obtaining chemicals from  the
environment  is  a  process of  molecular  uptake  of  chemicals
dissolved in water. There  is a concentration gradient from the
bulk water concentration to  the  concentration localized at  the
cell boundary.   The  gradient  is  generated  when  the  cell  removes
dissolved material  from the water at  a rate  that  is  competitive

with  diffusional replenishment  of  the matetial at the external
cell  bound a c y .

These  localized  concentrations can  limit  the energy supply rate
as  well  as the  rate of  supply  of elements for  biosynthesis.
Mac r ohe t e r ot r ophs either move through the water  or move water
past  themselves  to obtain  food.  Mobile organisms use  energy for
evasion of  predators.  In these activities  the power to overcome
drag  can account for a considerable fraction of the total power
expenditure.  For  large aquatic animals food supply for  energy
and biosynthesis must be  maintained in an environment that is
fluctuating with  respect to  food  supply   and  pressure  from
predators.   In  the  following the  supply  rate  of energy  and
materials will be considered for  each  of the metabolic modes, and
a resultant expression  for population rate of change will  be
ob t ained .

It is usually  assumed that the uptake  rate  of  dissolved chemicals
by microorganisms is  best described  by a rectangular hyperbola as
first  proposed  for  microbial processes  by  Monod (9).   Such a
description can  be rationalized by any one  of  several specific
mechanisms.   All  such processes  appear  to have  a common
characteristic,  however,  y_Lz^., a saturable  component.  In this
respect  many  such processes exist,  not  all  associated  with
microorganisms,  and not  all of  which are biotic  processes.
Molecular  sorption to particles is frequently described by the
Langmuir isotherm, which,  although  not  a  rate description,  is a
rectangular hyperbola.    In  this instance the  saturable component
is the surface of the particle,  or  at least  the capacity of the
surface for the  sorbate.  The  feeding  of fishes was described in
much  the same way by Rashevsky  (10)  and  the feeding  of  insect
predators  by Holling  (11),  the saturable component being the gut
capacity in Rashevsky's  analysis  and  available time in  Rolling's.
Specifics  of such processes will be discussed in the appropriate
sections.  The model is  so  generally  applicable that it will be
useful to indicate its  derivation prior to  specific uses.

The model consists of a  description of  each  of  two simultaneous
processes:   obtaining material (filling  the  saturable  component)
and  removing material  (restoring or  emptying  the  saturable
component).   The  rate of  obtaining  is proportional to  the degree
of unsaturation  (S-x) and to  the concentration of  the material
being  ob t ained (s) :

The rate  of  change of material associated  with  the  saturable
component is the difference between the rate  of  obtaining  and the

rate of emptying,  the  latter  being  proportional  to the quantity
of material  associated  with  the  saturable component:
                  at -   a
In the above, y  is  the  material being  obtained, x is  the  same
mateiial  in  the  saturable  component, S is  the  capacity of the
saturable  component,   and  kQ  and  k£  are  rate  constants  for
obtaining and emptying,  respectively.

For large populations over  time intervals long  with  respect to
characteristic   times   for  the  two processes,   the  degree  of
saturation will  reach a stable value,  implying that the rate of
emptying is  equal to the rate  of obtaining.   Thus
f rom which
                   X =•
Substituting into equation 3  gives  the  expression  for  the rate of
obtaining material when the processes are at a steady  state:

Even  though  microorganisms move, it is not clear what  stimuli
result  in the  movement,  what  terminates  movement,  whether
movement  ceases upon  reception of  other  stimuli,  etc..  There  is
difficulty, therefore,  in  representing activity of microorganisms
as a  function of their energetic  needs.   It is more convenient  to
consider  activity  as part  of  the  fundamental  metabolism  of
microorganisms.  As noted one aspect of microorganism  physiology
that  is a  result of size and the related absence o f mo r pho 1 o g i c a 1
features  for feeding is the uptake of dissolved chemicals  from
the environment. For  very  small  organisms  viscosity  of water  is
high  enough  that movement results in little  advantage  in  terms  of
increased  food availability.   Diffusion  and other mixing
processes,  threrefore,  are important  in  bringing  food to the
organ i sm  (12,  13).

The  rectangular  hyperbola  is  assumed to  be the  appropriate
description  of  uptake  of dissolved chemicals  from  the

environment.   Depending upon char ac t ei i s t i cs of  the  environment
and the organisms,  depletion of the chemical  in the immediate
vicinity  of  the  cell surface can  reduce  the uptake rate below
that expected  when  depletion  is not considered.   Pasciak  and
Gavis  (14,  15)  and Gavis  and  Ferguson (16) analyzed this problem.
Their model  for  the influence of  local depletion of dissolved
chemicals  on uptake rate accounts for the effects of  cell  size
and shape.   If  s is replaced  by Cu ,  the concentration of  the
chemical  at  the  cell boundary,  ana S by M,  the  capacity of  the
cell membrane  for  the chemical  in moles  cm   ,  then equation 6
represents a flux onto  the cell  membrane (Figure 4).   This  flux
can also be described in  terms  of Fick's first law:

                Jb  = -

where J ^ is the flux at the cell  membrane. D is  the diffusivity
of  the  chemical   in  water  (cm2  sec   ),    C  is   the  bulk
concentration,  R  is  the  cell  radius, and conversion to moles  cm
hr    requires  the  conversion factor, 3.6.   The flux  to a
spherical  cell  is equation 6  multiplied by 4  R  :
When the two expressions for the flux into the cell (equations 5
and 7) are equated, a quadratic  in Cu is obtained.  Pasciak and
Gavis (14) write  this equation in non dimensional form as


where  Cu = kuCu/k|,  C  =  kuC/kj,  and  P =  14.4  RD/ku.  Cb  is
available via  the quadratic formula and r e s ub s t i tu t i on of the
above .

To account for cell geometries other than spheres, Pasciak and
Gavis  (15) modified the above results  to  represent oblate and
prolate spheroids (disks and spindles).   This  is  accomplished by
multiplying  P  by a shape factor  that is  a  function of  the
eccentricity  of  the  cells (eccentricity is  a measure of  the
relationship  of  the  major and  minor  axes).   For  a   complete
description and  derivation see Pasciak and Gavis (15)  and  their
refer ence s .

This  description of  the   uptake  process  is  rather   general,
permitting uptake to be  represented  for  any  micr roor gani sm  that
uses  dissolved  substances.  It does  not provide,  however,  a
description  of  uptake by aufwuchs or benthic  communities.   This
is  easily accomplished by  a  development  similar  to  the  one
described above,   but using  a  rectangular  coordinate  system.   In
this solution  the concentration  at  the  surface  of  the  community
depends upon  the  thickness  of the unstirred layer adjacent to the


surface.   Accuracy  of  uptake  calculations  depends strongly upon
knowledge of the thickness  of  this layer.


Phot osynthe t i c production of biomass and G>2 coupled with  aerobic
respiration form a  complete element  cycle.  Respiration  in  light
and diffusion limited  environments depletes O^, ,  and  consequently
other oxidizing agents are used.   These conditions are usual  in
deep waters,  organically  rich  waters,  wetlands  and  soils.  Each
oxidizing  agent,   like  O2 , participates  in  a  cycle  that   is
complete.  These  redox  cycles, mediated biologically for  the
elements of interest  here (C,  O, N, P, and  S) ,  form the basic
structures  of  the  biogeochemical  or  element   cycles.
Chemoaut o t r ophs obtain energy  from oxidation  of  reduced  inorganic
compounds,  usually with  G>2  as  the oxidizing  agent  (terminal
electron acceptor, TEA).   Elements  that  are  reduced during
anaerobic  respiration  are oxidized   during  chemo au t o t r ophy ,
thereby  completing  the cycle.   These processes occur  in  different
environments,  however, and therefore transport  is a key  process
in  the cycles and potentially  is the limiting step.

Most  chemoautot r ophs   are  gram  negative bacteria of pseudomonad
related genera   (17)  and  are,  therefore,  prokaryotes.
Photoautot rophy is  carried out  predominantly by  green  algae  and
cy anoba c t e r i a.  Green algae  are  eukaryotes  and cy anob ac t e r i a ,
prokaryotes.   It might  be expected that extreme diversity  of
biochemical  function  exists among  such diverse kinds  of
organisms.    In regard  to energy metabolism  and biosynthesis
(Figure  5),  however, there  is  little diversity.   The  Calvin  cycle
is  the mechanism  for  fixation of CO2  and production of  hexoses
(17)   Lehninger   (18)  gives  the  following  reaction   for
biosynthesis  in photoautot r ophs :
Here  (CH2O)  refers to 1/6 of a hexose. The  degree to which the
reaction  is  favored  thermodynami c al ly can be seen by  decomposing
it  into  its  three  component  reactions.
                                                  =  -7-3
                                                  *  /l4'8

When the standard free energies are used  the net  free  energy  for
the reaction is -12.12.  Under  physiological  conditions, however,
the reaction is probably  even  more favorable.  An indication of
this can be obtained by introducing only the free energy of  ATP
hydrolysis  (-12.5  kcal   M"1)  reported by  Burton  (19).   This
increases the tendency of the  reaction  to proceed (AG(v»)= -27.72).
The analogous reaction for chetnoautot r ophi c  bacteria  differs only
in the use  of  NAD+ and NADH rather  than NADP+ and NADPH  (17).
The energetics  are approximately the same.

Diversity  of  autotrophy  lies  neither  in energy metabolism  nor
biosynthesis  but  in the  sources of  energy:  light  for  the
phot oauto t r ophs and a very  large  variety of redox reactions  for
the chemoautot r ophs.  Table  1 gives several  of  the  reactions used
by chemoau t o t r ophs as energy sources.

strategy that I  have adopted for  representing autotroph growth is
similar  for  both  pho t o au t o t r ophs  and chemoau t o t r ophs .  Energy,
whether light or chemical, and chemicals for biosynthesis have to
be obtained separately.  Therefore,  energy or  any  element  can
limit  the  growth  rate   at  a  given  time.   My  strategy  is  to
calculate  the  growth rate that could be sustained on  the supply
rate of each required factor  (element or energy),  if no other
factor  were  limiting.   That  is, given  the concentration  or
density  of a resource,  the  rate at which it can be obtained  and
used  assuming  that  nothing  else  limits  the use  rate  is
calculated.  This produces  a  set  of potential  resource limited
growth  rates.   The actual  growth rate is  then taken to be  the
minimum  of  this set.

Suspended substances reduce  light  by  shading  and  dissolved
substances by frequency selective  sorption.   The Bee r -Lambe r t  1 aw
expresses  the  reduction  in  intensity  with depth  (or  mean  optical
path)  as  a function  of  a  situation  specific  attenuation
coefficient, £  :
                           = -el

 Units  of  the rate are E absorbed m ~ 2  of  surface area m"   depth
 day'1,  the  units  of  I  are  E  m~2 day"1, and of the characteristic
 attenuation  coefficient,  £,  are m'1.  Steele  (20) proposed an
 equation for the rate  of  photosynthesis  as  a function  of  light

where pm  is the maximal  rate of photosynthesis, ceached when the
light intensity  is Im.  Equations 11  and  12  can be  combined for
the tate  expected at any depth,  etc.,  when the parameters aie
known .

Bannister (21) developed  production  equations  in terms  of  a
parameter that  is  mote closely related  to  the  biochemical
processes of  energy  gathering and utilization, 0k> the maximal
quantum yield.  Bannister's  analysis was carried out in terms of
productivity, M(C)  m'^day"1.    It  perhaps  would be a  purer
analysis  to express the  quantum  yield  in terms of  electron moles
E~ ,  and  to work  in  terms of  electron  equivalents throughout the
model.  At this point, however,  it would  introduce an extra and
apparently unnecessary  step,  and so  I  shall use Bannister's
analysis  including his  units.  He  used  three  separate light  curve
equations. Because it  includes  the  pho t o i nh ib i t i on effect, I
shall use Steele's equation (20,  21)  as equation  12 above.  The
derivation is  given here in  abbreviated form.

Reduction  of  light with  depth can be  partitioned  into reduction
by each of the causal  components.  Reduction rate  by  suspended
algae  is  caused  primarily by  the absorption of  light  by the
cellular  pigments. The  molar  adsorption rate  is

with units of  E absorbed m~3day~1  (actually to be in keeping with
the units of the derivative  with respe
better  be expressed  as  E m~*  of su
the units of the derivative with respect  to depth the units might
                                      rface day   m"1  of  depth).
Normally productivity is measured in g(C) m'^day"1 or equivalent.
Division  by  12  converts  to  moles.   Th e  quantum yield is
expressible as the  ratio of  the molar  productivity to the molar
adsorption  rate,  with units  of  M(C)  E"  , and an explicit
expression for the  quantum yield  can be  obtained  by  substituting
from equations 12 and 13.
                       '  C$ =-  f*>e	7-               
                       ?  ^     12 r   ix   A
                                 •X. J-W Kft. f*
As light  intensity approaches  zero,  saturation  effects on  the
photopigments  disappear  and  the  quantum yield  approaches  a
max imum:

This quantity  theoretically is a constant, its value in natural
waters  being  approximately 0.06  (21)  or  0.07  (22)  in  units of
M(C)  E'1 absorbed.   Substituting  for I  in  equation  12  and
integrating with  respect  to  depth  gives  the  total  photosynthesis
rate per unit  surface area.   Further substitution for  pm  (from

equation 15) and foe £ in terms of the  light  attenuation  factors
provides the total  photosynthesis rate in terms of parameters and
the chlorophyll concentration,  A.   If  this  rate  is  integrated
over time,  production is obtained.   To do so  requires that IQ be
written as  a time dependent light flux.   This  can be approximated
in several  ways, but is not represented  here.

The quantity that is needed  for  the simulation approach taken
here  is the  dep t h- i nt eg r a t ed photosynthesis  rate of  carbon
assimilation, considering no  limiting factors  besides  light.  Two
depths  are  of interest: either a given depth  as, for example, is
of interest  when a volume element  of particular  dimensions is
considered, or  the compensation depth given  by the depth at which
the light  compensation point  is  reached.  In  either  instance the
applicable  equation for photosynthesis rate  is

in  which  L  is  the  fraction of the  incident light that is
transmitted through the element,  and  is  given  by

If  z'  is  a fixed  depth,  equation  17  can be  used,  but if  z*
represents the compensation  depth,  then the  light level, I1,  at
the compensation depth  must  be specified, and L  is calculated
directly  as L = I'/Im.

Equation 13 is the primary equation for  calculating  1 i ght- 1 imi t ed
rate of growth of pho t oauto t r ophs .   In  simulation calculations  it
may  prove  convenient  to express  the  rate  as a  quantity per
volume,  rather  than  per surface  area.   This  is a  simple
multiplication of the quantity ,  p-p,  by the  applicable surface
area to which the total  applies.

Energy is obtained  for  chemo au t o t r ophy  by  uptake  of  reduced
inorganic  chemical  species  and  of  oxygen  as  an oxidizing  agent,
and by  carrying out  the  redox reaction.  Both the  chemicals  that
are used  for  the  energy  reaction and  those  that  are  used  in
biosynthesis are  obtained  by uptake  through  a  gradient.
Therefore the concentration at  the cell membrane  can  be the
limiting factor  (equation 8).  The chemical  that  is  used  as the
electron  donor  in  the  energy  reaction can  also  be used as  a

substrate for biosynthesis.  Foe  example  in nitrifying bacteria
the following reaction is  used  for  energy:
Ammonia  is  also used for synthesis.   It  must be  supplied at a
rate that is commensurate with the other needs of growth,  and
therefore,  the  rates at which  it is required for  energy and for
synthesis each  need to be calculated  and compared to the other
needs.   Equations  9 and 10 apply equally well to all  autotrophs.
From these  equations it can be seen that  three moles of ATP and
two  of  NADPH are  required  to  synthesize  one  mole  of carbon.
Using standard  free energy values, this  requires  that at least
126.9 kcal  be  supplied  via  the above reaction  (equation  18).
Assuming  38% efficiency  (the  same as is often calculated for
photoauto t r ophs  (23)  and heterotrophs (18), 334 kcal from about 5
moles of NH4+ must  be  released   (a  quantum  yield of 0.2 M  carbon
synthesized M"1 NH^+ utilized  for  energy).  A quantum yield of
0.2 was  observed by Gunderson  and Mountain  (24).   It can be seen
that for energy to be a non  limiting commodity,  ammonia must be
obtained at five times the rate of  obtaining CO, and at 3 1/3 the
rate of obtaining  O 2 .  Th e same kinds of calculations apply to
each of  the energy reactions indicated in  Table  1.

comparisons are valid if  autotroph  growth is resource limited, a
situation  that  is  expected  in   all  but  unusual  transient
conditions.   Energy and all  chemicals  can be present  transiently
in abundant  supply.  Under these conditions  growth is limited by
some  inherent  i n t r a c e 1 1 ul a r  property.   Growth  rate  is then
maximal, and the condition is  transitory  because the populations
that are growing maximally  increase rapidly until  some resource
again becomes limiting.   I shall assume that  the minimum  of the
maximum uptake rates, as limited by membrane transport,  is the
growth  limiting factor  for  autotrophs.  That  is, the maximal
growth  rate that  is  achieved  under  these  conditions  is  the
minimum  of  the  growth  rate  that would be  achieved maximally for
each of  the required resources.   By  this  assumption it  is not
necessary  to provide a separate growth model for  this special
case, because  it  is calculated naturally  as the limit  of the
general  case.

The general case  of growth  is  the  minimum  of the growth rates
that  would  be  achieved  on  each  of   the  required  resources.
Elemental composition of  the organisms  has  to be considered when
calculating  these  minima,  however.   One way  to accomplish  this is
to reference each  of  the  rates to  the  carbon assimilation rate.
If the organism's  elemental composition is C£NnP S$l then the
ratio of nitrogen  to carbon  is n/c, nitrogen  is required at only
n/c dC/dt,  and thus the minimum of  dC/dt  and c/n  dN/dt would be
the  expected growth  rate  if  either  carbon  or  nitrogen were
limiting (here  and in the following equation dC/dt and  dN/dt are

used to  indicate the uptake rates  of  C  and N).   In  general  the
growth rate is given by


Each of the  rates  of  assimilation  is  described by  an  equation
like equation 5.


Heterotrophs derive  both  energy and  biomass  from a  complex
mixture  of  chemicals.   Some  fraction of  this  mixture  is
essentially  indigestible.   The remainder  is  hydrolyzed  to small
compounds and  further broken down to small monomers (7) Some of
the monomers are used as reactants for  energy  production  and some
for biosynthesis.   Essentially  any  of  the monomers can be used
for energy,  but  in biosynthesis discrimination among  monomers
must occur so that  biomass  specific  to  the particular heterotroph
can  be synthesized.    This general scheme  characterizes  the
metabolism  of  both m i croheterotrophs and macroheterotrophs .
Microheterotrophs,  of course,  deal with  the complex organic
mixture extracellularly first, then  after it is broken down into
soluble compounds,  absorb  it and use it for energy and  synthesis.
Excretion of products  that  cannot be  used for  energy  or  synthesis
is an  important process for microheterotrophs.  Macroheterotrophs
consume complex  organic mixtures  either  as other organisms or as
detritus, and  the  whole process  of  digestion and metabolism is
carried out  internally.  Elimination  of  indigestible  material and
breakdown products that cannot  be used for  energy or  synthesis
are both  important  processes for macroheterotrophs.

description  of  the growth  and energy metabolism  of  heterotrophs
is a simplification, whose  purpose is to  establish the  categories
of organic chemicals  that  I shall employ to represent  growth of
heterotrophs.   In keeping  with  the  overall  objective  of
representing ecological processes  that  are important in  element
cycling,  the growth model  will  be a function  of the supply rate
of each of  the  important elements.  As already discussed these
processes  are  driven  by redox disequilibria,   created by
photoautotrophy  and  providing continual  input to the respiratory
(redox)   processes carried out  by  heterotrophs  in  obtaining
energy.   The model for  calculating growth rate consists  of  three
parts.  One  is  the component  for  partitioning  of  food  into power
supply and biomass synthesis.  A second is  the ca 1culation of
power  demand.   The other  is  the  calculation of  food consumption
rate  in terms  that permit  calculation of  power  supply  as  well as
the  supply  rate  of food components  whose composition  is  similar
to  that of  the  consumer.

consumption,  power  consumption,  power  production,   and
biosynthesis  are rates.   The problem faced by heterotrophs is to
obtain food at a rate  so  that  the  power  produced from it
satisfies   the  power  demand  of  obtaining   food  and  escaping
predators  plus  the  basic power  demand  of  life processes  and
repair  with  enough  remaining  power  and  materials  to support
growth.  Figure 6 gives  the scheme for accounting the  energy and
materials  in  partitioning the food intake rate into power output
and  biosynthesis.    The  scheme   refers  most  directly  to
macroheterotrophs,  but  it  is applicable  to microheterotrophs if
food is considered to consist of dissolved organic  chemicals and
elimination of the indigestible  fraction is  ignored.  Figure 7
shows  the  assumed relationships of  the  categories  of organic
chemicals  in  the aquatic  system.  Processes and states  inside the
dashed line occur inside  microbial cells.

The  object  of  the  model  is  to calculate  growth  rate  of  a
heterotroph  population.   This  is  accomplished in several  steps.
Composition of the  food is compared  to  the  composition of the
heterotroph so that  the  rate  of  consumption  of  two  food
components   can be calculated.   The  two components are biomass-
1 ike (referenced as pool  1  in  the  following) and non biomass-like
(pool 2).   (The term "pool" should be  interpreted  to indicate a
dynamic quantity characterized  by varying  elemental  composition
as the  composition of food  varies.) In  the  overall model,  the
free energy content  of  total food at  any time  is known via an
accounting  chain.   The   free  energy  content of  each  pool is
calculated as part  of the function of this model as is  discussed
below.  This  provides  the power  supply  via each of the  two pools.
The disposition of the pools  is determined by comparison to the
power  demand,  and growth  rate is   immediately available  as  a
result  of  this comparison.   The specifics  of the process  are
given below  in the sequence of the descriptive overview presented
in this paragraph.

The  process  of  partitioning  food  into  power   supply  and
biosynthesis  is  developed  in  the  following  in  terms  of
macroheterotrophs.   The  situation  for  microheterotrophs is
simpler  in one aspect because  of the  representation  as  lumped
categories of the organic  chemicals  on  which  they  feed.   The
development  for  macroheterotrophs  can  be   applied  to
microheterotrophs by considering the categories of  organic in
place of the  species of prey.   But in  another  aspect it is  more
complex.   Macroheterotrophs  use a  single  electron  acceptor,
oxygen, whereas microheterotrophs   use a whole  series of them.
Use of the term "energy  content" is to  be  interpreted as  the  free
energy of   the reaction  between a chemical serving as an  electron
donor and  another  chemical serving  as an  electron  acceptor.  In
much of  the following the  electron acceptor is assumed to be
oxygen and no single chemical  will  serve as  electron donor, but
rather  electrons  will  derive from  a  mixture  of   chemicals,
comprised  of  the biomass of  higher organisms.  In this  situation

also,  I  shall use  the  term "energy  content."   A discussion  of
energetics with electron acceptors other than oxygen will  follow
the  section on food partitioning.
The food intake rate (Mass t'1
                               consumer'  )
                               i s
where  i  indicates  a  source  of  food  (prey  population  or
environmental pool  of  chemical),   and  j  identifies  the predator.
The  overall  elemental  composition  of  an  organism  (or  of  a
chemical pool can be represented  for  the  elements  of  concern  as

where the upper case letters  symbolize  the  elements  as  usual,  and
the lower case letters represent  the  mole numbers of the  elements
with  which  they  are associated.   Let  nik represent  the mole
number of element k,  species  i,  and w^  represent  the gram  atomic
weight  of  element  k.  Then  the  fraction of food mass obtained
from prey species  i comprised of  element  m is
              I.   -   0»
               1 mi     W"
   that the rate of consumption of element m in the  mixed  food  is
Th e average
i s the set
molar rate
                           consumption  of  elements by consumer  j
	 0_ , .
3 1
Division  of each of the elements of  this set by the mole number
of  the consumer for the  corresponding  element  gives another  set,
the least value of which  corresponds to the element of  the food
which  is  in  least  supply  relative to  the composition of  the
consumer.   A set of mole numbers  for the composition of  the  food
normalized to  the  element  in  least supply  can be obtained by
dividing  the  elements of  the  set of molar consumption rates
(equation 24)  by  the  rate  for  the element  in  least supply.  A
similar set can be  obtained  for  the consumer  by  dividing  the mole
numbers of  the  consumer  empirical formula by the mole number of

the element  in  least supply.  Then the food
into the  two  pools.   The noimalized empirical
be t ept esent ed as
                                             can be partitioned
                                             formula of food can

and,  because  pool
r epr es ent ed as
                     1 is  like  consumer biomass,  it can  be
                CON   PS
                 «j   •*    "a  P
In the above  formulae, the subindez  F  indicates that  the  mole
numbers are for the food,  and  the  subindez  j  indicates that  those
mole numbers are for pool 1 which  is like  consumer  j.  Pool 2
component  constitutes the remainder  of  food.   Its mole numbers
are the difference between the mole  numbers of the  food and of
pool 1 :
Now the rate of consumption of  the  two pools can be calculated.
First let n^;  represent the mole number  of  element j  in pool  k.
Conservation requires  that

The fraction
                food that  is  pool  k  is

                       4         «*
and the rate of consumption of  pool  k (k = 1  or  2)  is
                  ir '   _
                  1       -
If the free energy  content of food is known, then it too can be
partitioned.   Morowitz  (7)  discussed  some of the  problems of
using  free energies of biological materials and  concluded that
enthalpy  (heat content)  values are useful  approximations.  There
are  other approaches  to  this problem that could yield better
approximations, but that  problem will be left,  and I  shall merely
assume at  this  time  that  free  energy  values  are available.

The  free eneigy  content of  food can  be  obtained  if  the free
energy content of  individual  food  items  is  known:

 GC ^ is the free energy content  of  species  i.

During the process of digestion of the food to monomers, a small
loss of free  energy occurs, the polymer bond energy, AG^.  The
free  energy of  pool  1 is  the  same  as  the  free energy  of the
consumer  less  the free energy loss of depo 1 ymer i za t i on,  4Gm* =
AG • - AGj.  Pool 2 free energy is the remainder less  the  energy
loss of depolymer izat ion:  AGm2  =  (SFjj AGp  -  FI AG,:)/F,  - AGd.
The power  supply  from  the two pools  can  now be  calculated.  From
pool 1 it  is
where  B-  indicates the mass of an individual  of  species j, and
f r om pool 2 it is
Describing  the  way that  this  free energy is used to produce ATP
and NADPH requires a model of  cellular biochemistry.  I assume
that discrimination between the two pools occurs, so  that pool 2
is used  preferentially  for  energy  and pool 1  as  material for
biosynthesis.   Power demand,  Pfl  is taken  to be the  sum of the
energy expense  rates for  maintenance,  repair, motility of hunting
and escaping, and  other  activities  associated  with feeding.  If
the power demand is greater than power production from pool 2,
then pool 1  is used as needed.  If the power demand is less than
power production from pool 2,  then  pool  2 remainder is  converted
into new biomass  at  at  rate  determined by the uptake of the
necessary  inorganics   to  achieve the  consumer's  elemental
composition or  it  is  converted  into  storage   compounds.   The
remainder,  in  excess  of  the rate  of conversion by  these
processes, is eliminated.  Four distinct cases arise  as  a result
of the comparison of the  power supply and demand:

     Case 1:    pool 2 power supply  > power demand  for  activity
               plus synthesis  of pool  1  into consumer  biomass:

                                                    <        (34)

     Case  2:    pool  2  power supply  >  power demand  foe  activity
               but  < power  demand  for  activity plus  synthesis
               of pool  1  into consumer biomass:
     Case  3:    pool  2 power supply < power demand for activity,
               but  pool 1 + pool  2  power supply  > power  demand
               for  activity:

Case 2:    pool  2 supplies  the power demand of activity plus
          patt  of  the power demand  of  synthesis.   The growth
          rate  on  pool  1 monomers  sustained by power derived
          f r om pool 2  is
          Power to synthesize  the  remainder of pool 1 must
          derive  from pool  1,  itself.   The remainder of
          powe r in pool 1 is
          Thus, the growth rate sustained by the  remainder
          of pool  1 is

                      jx »&&?-,.- P.)
          The net growth  rate  is  the  sum of the two, which
          after simplification  is

Case 3:   pool 2 is insufficient to supply the power demand
          of  activity,  so  pool   1  is  diverted  at  the
          necessary rate.  The power  available from pool  1
          remainder is

                                              :          (44)
          The growth rate that  is  sustained on  pool  1
          remainder is
Case 4:   the power obtainable from the total food  is less
          than  the  activity power  demand.   It  is  assumed
          that   the  consumer  continues   to  attempt
          to  carry  out  normal  activities  of  feeding,
          escaping,  etc.,  at the  expense of body mass. The

               net  effect  to  the  whole  population  is a  loss
               of biomass,  expressible as a negative growth rate:

                                                 '           (46)

The growth rates calculated above   (equations 38, 43, 45, and 46)
use values for  power  production rate  and  power  utilization rate,
in  addition to  the  patterns  of  physiological  processes  and
biomass composition.   Power is  used at  the  cellular  level, but it
can be accounted most  easily at higher levels  of  organization.
Power is required for biosynthesis, hence the accounting point is
in  the  model for biosynthesis, i^.  £_^, in the  above  equations
describing growth.  There  are two other major categories of power
demand.   One is the basic metabolic  demand.  The  other  is  the
demand  due  to  motile  activity.   This  latter  demand  is  more
readily  accounted  at   a  higher hierarchial level,   the  power
required to move a  body through a liquid medium. Power  production
rate  is a  function  of  the composition of the  food,  and of the
rate  at which  it  is  obtained.   Hence,   a  description  of  the
feeding process is an important part of the model,  because  in its
development the basis will be obtained  for calculating  power
supply, supply  of materials for biosynthesis, motile activity for
obtaining  food, and  motile activity  for escaping  predators.  In
addition  loss  rates  caused by  predation are obtained by simple
rearrangement of the equations  for  feeding.

FEEDING BY MACROHETEROTROPHS.   Macroheterotrophs capture  discrete
food  particles by one  of  two  general means.   Either they feed
upon  all  particles  encountered that are  within  the  size range
that  they  can handle,  or  they  select and capture individual  food
particles by explicit overt action.  I  shall refer to organisms
characterized by the  former behavior  as  filter  feeders and to
those by  the latter  as  pursuit  feeders.

The derivation for  uptake and feeding given in equations  1-5
follow the  general  pattern of  Rashevsky's (10)  derivation of
stationary  state feeding rate for  fishes.   His work was motivated
by  Ivlev's  (25) studies on the  feeding of  fishes.  Ivlev's model
for fish feeding is widely used in  mathematical  models  of systems
that  include feeding  by   large consumers. It  was derived as  a
formal  mathematical  expression that fitted  his  data.   Rashevsky
derived his model from assumptions about  the way that fishes
feed.   Part of his  purpose was to  present a  stationary state
analysis  based on Ivlev's model, which described  the  feeding of
of  fishes  as a  function of the  density of  food.   Ivlev's  equation
was of the form
 where R is  the food eaten per experiment (a fixed time), Rm is
 the  maximum  feeding rate for the fixed time, BW  is the biomass


density of prey (mass per  volume),  and  z  is  a  fitted constant.

Rashevsky's  derivation of  an equation comparable to Ivlev's began
with the statement that  the feeding rate  (F) equals the encounter
rate  (E)  times  the  probability  that  the  prey is  eaten if
encount er ed  (P):

                            F  = E  P                          (48)

The encounter rate  is  derived by assuming  that the  predator
sweeps out  a right circular cylindrical volume  as it  swims in
search of food.  The encounter rate  is then the product of this
volume per  time and  the  density  of prey in  the  volume,  r vB,
where  r  is  the radius  of the  cylinder, v  is  the  swimming
velocity,  and B is  the mass  of  the prey  per volume  of water.
Rashevsky took the probability  of  consumption given an  encounter
to be  proportional to the unfilled gut capacity,  an assumption
exactly equivalent to that made in  equation  1.

The latter  assumption  is credible for situations in  which the
saturable component is  filled  via  mechanisms  that  operate
passively,  such  as the  adsorption  of dissolved chemicals onto  a
microbial cell membrane.  Where the component  is filled  by  active
processes,  however,  such as the  filling of a fish's  stomach by
active feeding,  it  is  not clear  that  the rate  of   filling is
necessarily  proportional  to  the  unfilled  capacity.   If  the
probability  that  an individual  consumes  a  prey increases as
unfilled  stomach  capacity  increases, but not  linearly,  then  this
model  better  approximates the  feeding of  a population where  there
is  a   distribution  of  the extent of  filling  than  it  does an
individual's feeding.   Ivlev's  fits  of  the model  to  data
indicated   no   discrepancy  from  the  model  of  direct
proportionality,  however,  and  therefore,  the  point  is  more
cautionary  than substantial. The point should  simply be  borne in
mind  that it  is not necessary for a higher organism to reduce its
feeding rate  to  the fraction of  its  maximum  that  corresponds
exactly to  the fraction  of unfilled stomach capacity.  In  this
particular  regard  the model of Rashevsky and  the  models  that are
developed here are  not necessarily based  upon an unassailable
as sump t i on.

The encounter  rate is

                               •^    i _*^~
                      *  TT

where r is the encounter  radius,  v  is  the  swimming  velocity,  and
M  is the biomass density as in Ivlev's model.  The probability
of consumption of  prey  given  an encounter is
    P -
where M$  is  the capacity  of  the  stomach, M  is the quantity  of
food in the stomach, and c is a constant of proportionality.   If
the  probability  of  consumption is   1  when  the  gut  is  empty  (M
= 0) then  the proportionality constant,  c,  is MS-I.  Thus  the
feeding rate  is
F  =
                    Trr"vC>,  <,   'M  ')              (Ji>
Feeding  rate,  F,  is  the  same as the  rate  of  change of stomach
content,  dM /dt if the experiment is done over a short  enough
time  interval  that stomach  emptying  can  be ignored  (there  is  no
loss  term).   Integrating  and putting M  = 0 when  t  =  0,  the
stomach content is
  Mfl =  M,  (l -
For Ivlev's  experiment,  t  =  tf,  the fixed experimental length,  so
that the constant,  z,  of  Ivlev's model is equivalent to TIT  vt£/M
of  Rashevsky's.   As  noted  by Rashevsky  (10),  Ivlev's  model
applies  only  to  the phenomenon of  feeding  as  a function  of
concentration of  food.   That is, it  does not  take into account
other factors that  affect  feeding, such  as stomach  emptying rate.
It is not suitable, therefore,  for use  in a model  in which time
intervals  are long enough  that  the  other  factors  become
impor t ant .

For  a population  considered  over  a  time interval that  is  long
compared to the characteristic times  for  stomach  filling  and
emptying,   the  mean food  intake  rate  equals  the  mean stomach
emptying rate,  i.  e. T  steady  state feeding is achieved:

where k  is  the stomach emptying  rate constant.  The feeding rate
is  obtained  by  rearranging  Equation  53  so  that  kM  is expressed

in  terms that  do not  include  the  stomach content,  M  ,  and
recalling that at  steady  state  feeding,  feeding  rate  equals the
stomach emptying rate,  or

               _     kMsB,,
               F  -T*T7^
                            •t- L->^
Note that this equation is  of  the same form  as  Equation 5, and
that its equivalent components  are  int er pr e t abl e  similarly.

To the extent  that  this model  represents the main  features of
pr edat or -p r ey interactions  in  aquatic  systems  it has a property
that  is very  useful,  it  permits  complete  specification of
predator-prey interactions  as  a function  of  the  characteristics
of the individual  predator  and of  the population densities of
predator  and prey.   That  is, no  species specific,  pairwise
interaction  coefficients  are needed.   Immediately,  however, one
rejects that  pr edat or -prey  interactions   involve  characteristics
of  the  predator  and  not  the  prey.   In  the  following  a  more
detailed derivation of  predator-prey models is made for two major
ecological  modes of feeding by  aquatic organisms, filter  feeding
and pursuit  feeding.    In these models characteristics of both
predator and prey  are incorporated  while   retaining  the
characteristic that no  interaction coefficients are  required.

FILTER FEEDING.  Consumers that feed i nd i s c r imi nan t 1 y upon all
organisms  that they  encounter  that  are  within the  size range
possible for  them  to  feed  upon  are  grouped here under  filter
feeders.   It  is  assumed that they move through  the water creating
a disturbance front detectable  by prey  with suitable sensory
organs.  Some of  these prey  are able to escape and  some are
captured.  The scheme  for this  type  of feeding  is  given  in Figure
8.  If  a prey organism  swimming  at velocity  v  swims normal to
the path  of   the oncoming  predator,   reaching the edge  of the
encounter  cross section,  the distance  P- r,  before the predator
swimming at velocity v  swims  the encounter distance  s^,  then the
prey escapes;  else it  is captured.  All distances, T ,  such  that

are escape  distances.   All prey inside  the  radius,  (,  at the
point  of  encounter  with  the  disturbance  front preceding the
predator  are  captured.   The  feeding  rate   of an  individual
predator feeding on a  single prey of population density, M,  is

The  first  of the  two  forms  of  F,  although somewhat  more
cumbersome,  is preferable,  because  it  groups  quantities  together

that are properties of the predator alone.  Hence,  in  dealing
with several prey populations  and  one  predator  these quantities
are constants.   They are the  factor,  kM , and the  whole first
term in the denominator.  The  second of  the  two forms indicates
that the effective  rate  that  the predator hunts  is dependent upon
both predator  and prey.  That is in  the  first the volumetric
search  rate  is fT/*2 vc, but in  the  second the comparable  term is
fCt*vc,  a smaller  quantity  that  is  a  function of  both  predator and
prey because *P is a function of the swimming  velocities  of  both.
The expression  for  feeding by  predator  j  on  n  prey populations is
          FL-  =              _,	•                     <">

                      •4;  *  />>lrVBl-
PURSUIT FEEDING.  Consumers that  swim  at  one velocity  while
searching for prey, then pursue the prey  at  another velocity  are
referenced  here  as  pursuit  predators.   Figure  9  gives   the
schematic  for  this  mode  of  food  gathering.   The  searching
velocity of the  predator is v  •.   The  distance  at which  the
predator can detect prey is taken here to be a constant that  is
characteristic of the predator, sdj.  It can be made a function
of  water  clarity  or  even  a  function  of  prey size  or  other
characteristic  without  major  change  in  the  form of   the
derivation.   Upon detection  both predator  and prey begin swimming
at  the  pursuit  velocity,  vpj.  and  flight  velocity,  V£if
respectively.   The duration  of  the  pursuit,  t  •:,  is  given  by

The prey's distance of the flight,  «£—, is given by

                 <                                           (59)

                 S*-'J  =  V*;  V^3
It  is  arbitrarily assumed that prey that  escape swim the same
distance  as  prey  that  are captured,  and similarly for predators.
Another arbitrary (but necessary  for simulation)  function was
developed (but not discussed in detail  here)  to calculate  the
probability of escaping  pursuit predators.   Essentially  it  is
assumed that  the  probability  of  escape  is  greater,  the  closer  is
vf •  to v  •.  That is  if  the prey can swim nearly as  fast  as  can
the  predator,  there  is a  high probability  of escape.

As  with  filter  feeders   the  effective  rate  that  the pursuit
predator  hunts  is  a  function  of both predator  and  prey.
Gerritsen  and  Strickler (26)  developed  a model  for predation that
depends on  both  predator and  prey cruising  velocities.  This

model  is  equivalent to the effective hunting rate,  the rate of
encounters while hunting:
             Aij ~  " *dj  ^  '   3^    J                     (60)

where u = min(v  -,  v •),  w = max(vc£,v  •),  and  vcj  and v •  are
the cruising  velocities of prey i  and predator j,  respectively.
The rate of encounters while hunting  is greater  than the  feeding
rate, because pursuit  feeders  spend their  time  in two ways,
searching  and pursuing.    (In  general  I  shall  aggregate  all
activities  involved  in  feeding into  pursuing,  i. e.,  pursuit,
capture,  handling,   ingestion.    First,  however,  it   is  less
cumbersome  to develop the model  in  terms  of  overall  rate of
encounter,  then later  to  introduce  the probabilities of  pursuit
given encounter and of capture given pursuit.)

In  parallel  to  the  phenomenon of  partitioning  a  saturable
component  into filled  and unfilled portions, a  pursuit  predator
partitions  time into searching  and  capturing:

            F*; = (Tc + T,,)"1                                (61)
              j      s     p'

where  F j  is  the  encounter  rate, TS is  the mean time spent
searching  per encounter,  and T  is  the mean  time spent pursuing
per  encounter.  More specifically  the  mean  search  time  per
encounter and the mean pursuit  time per encounter are

where R— is the relative frequency of  the  ijtn encounter:
After rearrangement the encounter  rate can be  written  as

                                      l;J^''                   (64)
Unlike  the  expression  (Equation 57)  for  filter  feeders,  the
components  of  Equation 64 are  not as simple dimensionally  as  is
desirable  for  ease  of interpretation.  The terms  of  the
denominator  each  represent  an  encounter  rate,  the  first  relating
to  pursuits  and  the  second  to  detections of  prey  while  the

pcedatot is searching.   If the equation is rewritten by dividing
both  numerator  and denominator  by  the  sum of  the  velocity
differences,   the  "half  saturation"   term becomes  simply  the
detection distance  for  an  encounter, a  form that  is  perhaps  more
easily  interpreted. Without exhausting  the possible ways  that
the equation could  be  rewritten  in  search  of  a  form  that is  most
readily int erpr e t abl e ,  it  is  apparent  that the components of the
expression are functions of  characteristics of  both  predator and
prey  to a greater  extent  than are  the  comparable components of
Equation  57.    It  is  therefore comparably more  difficult  to
separate the components of the equation in such a manner that it
is as easily interpreted.

To  complete  the model  for  pursuit  predation,  the  effect  of
stomach filling must be incorporated.   In  the general  expression
for  the  limitation  of  feeding rate by stomach filling  (Equation
51), the probability of feeding was taken to be proportional to
remaining  stomach  capacity.   A  similar assumption is made  here.
The encounter  rate  times the  probability of  encounter  for pursuit
feeders  is  the  encounter  rate,  F  , as developed  above times the
probability of  feeding  given  an encounter,  (Ms=  - Mgj)/Msi-  At
steady  state feeding this  rate equals  the  stomach emptying  rate,

Rewriting to remove  terms  involving  the  variable, M  •
                                                  6 J
Equations  57 and 66 are expressions  for  feeding rate of the two
major  ecological  modes of  feeding by  mac r ohe t e r ot r ophs .   By
parameter variation they can be made  to  describe  a  wide variety
of behavior by these types of organisms. For example, Equation
66 can be made to describe the feeding of an ambush  predator by
noting  that  the  cruising velocity of such  a predator is zero,
which reduces  the  expression for the volumetric  search rate to
aii = frsdi   ci'  ^n  additional consideration  is  the feeding of
ma c r ohe t er o t r ophs  in  communities  in   which  there  is  a  wide
disparity  in sizes of the organisms present.  Introduction  of a
factor  in the numerator of both equations to account  for the size
window  within  which  feeding occurs overcomes  the  potential
problem for  an operating model.  The function  that  I have  used
expresses  the probability  of  ingestion as a  function of  prey
size.   I shall  not  describe  it  in  detail  in  this  report.

Expressions  can  be  obtained for  mortality occurring  in a
population as  a  result  of consumption by populations of filter
and pursuit feeding predators,  and for power  used in moving about
in the activities of  feeding  and  escaping being  fed upon.

MORTALITY CAUSED BY  PREDATION.  The mortality rate experienced by
a population  is the sum  of  the  mortalities  caused by  all  the
predators.   The quantity,  therefore,  is obtained by  summing  the
rates over all predators.  One approach is  to consider  that  the
mortality  caused  by  a  predator  population,  j, on a prey
population,  i, is  the total  feeding  rate  of the  predator
multiplied by  the  fraction  that the  specific  prey population
comprises  of  the total prey encountered  by the predator.   The
appropriate fraction,  however,  is not  simply the prey population
mass divided by total prey mass  of all species.   The appropriate
expression is obtained by using the  encounter radii, T;
Fot pursuit  feeders  essentially  the  same  approach is  used,  except
that encounter  rate  constants  (equation 60) are used  as weighting
factors.   The resulting  expression  is
where ni-   is the  mortality rate  to population i caused by
pursuit feeders.

to move around in  a viscous fluid nominally is porportional  to
the third power  of  the velocity  of movement:

where GJ is the drag coefficient,  O is  the density  of  water,  A is
the appropriate  area of the moving organism,  and  V is velocity.
The drag coefficient, Cj, is not  a constant,  however, but  is  a
complex function of  velocity.  In  practice Cj  has  to  be measured
as a function of the velocity (or the  Reynolds number) for  each
shape  (13).  This difficulty of operation will not be discussed
further  here.   Instead,  it is   assumed that  equation  71  is
sufficient  to develop the  ideas  for the model,  thereby  deferring
this operational  difficulty until   the  time when  parameter  values
are sought  for the model.

A  heterotroph does not swim at   constant speed,  so its power
demand is  a variable.   I  assume  that  a he t er o t roph1 s  time  can be
partitioned into four kinds  of  activities:   searching,  pursuing,
escaping,  and inactivity.  (Filter feeders do  not  pursue,  so for
them  this fraction  is  zero.)   If  every  individual  in  the
population  behaves in  this  way,  and  the   behavior  is  not
synchronous, nor  correlated  time-wise,  then  an alternate  view is
that  the   fractions refer  to the fractions  of  the  population
engaged  in the four  activities  at any time.   I have not  taken
into account  a time  fraction spent in  reproductive activities as
would  be appropriate for  higher  organisms.  There is, however,
allowance  for energy  of  reproduction  in the  cost  of biosynthesis
rationale  for accounting  power   expenditure  for reproductive
activities could possibly  begin  by partitioning  the power  that
now is allotted to growth into a portion for  activities  associated
with  reproduction  (nesting,  migrations,  etc.) and a  portion for
population growth.  Unfortunately, no  means  is  apparent  to  me at
this time  by  which to rationalize this partitioning,  and a great
deal  of  research  would necessarily  precede  such a model.   It


would be necessary to determine whether  any  relationships
for example, between power availability  and  the  elaborateness of
reproductive behavior.   As represented in the present model,  any
unaccounted activity will  result  in  calculation  of  growth  rates
greater than could be attained  in  reality.

To obtain the fractions, I have assumed  that  an  organism's  first
priority  is  self  preservation.  Therefore  the  fraction of time
spent escaping predators  can  be  calculated   independently of  all
the other fractions,  and the other  fractions  simply  partition  the
remaining time.  A given organism  can be  subject  to  predation by
both filter  feeders and pursuit  feeders.   The  fraction of time
spent escaping predators,  in general, will be a  function of both
types of  predation.  The  fraction of time remaining  for feeding
after  escaping predators,  in  general,  will  alter  feeding
behavior,   and  equations  57  and 66  must  be   correspondingly
corrected to account for this  effect.

Calculations of  these  fractions  of  time make  use of  the
relationships already  developed.   When all ramifications  are
considered, however, they are  more tedious  than  is worthwhile  for
presentation in  this  report.    Therefore they  will not be
presented in detail.   Instead  the  general approach  taken in
obtaining the derivations will  suffice.

The  fraction of  time spent in an activity  is the time per unit
(or event) of that activity times  the zate of occurrence of  that
activity.  Thus the  fraction of time spent  escaping  predators  is
the  time per  escape times the encounter rate.   (Naturally,  the
actual  calculation is  far  more involved.   For  example,  one
complication  is  that  the fraction of  time spent  fleeing  is
calculated  as  the  difference  between the fraction of time  spent
being  pursued and  the  fraction  of  time spent  being captured,
because  the  power used by those  that are captured is irrelevant
to the surviving  population.)  After the fraction of .time  spent
escaping,  f£,  is  accounted,   the remaining time,  ft,  is
partitioned into feeding  and  inactivity.   The  expressions  for
feeding are corrected for reduction  in available time by  escaping
predators by noting that stomach  emptying occurs  at  the same rate
regardless of the predation  pressure,  while feeding itself is
limited  to  the  remaining time.   The  power required  for  the
activity  is  obtained  by multiplying  the  velocity of  swimming in
each activity by  the  fraction of  time  spent  in  each activity  and
using equation 71 for organism j  in the  following form

where  f^j is the  fraction of time spent in the kth  activity by
organism  j, and v^-  is  its velocity  in that  activity.

At  this  point  power   supply  via feeding,   power   demand as  a
function  of  activity, and  disposition of  the elements comprising
the  food are  all  calculable   for  heterotrophs using  the

relationships developed.  One additional aspect of metabolism
needs to be  considered  foi  theoretical  completeness,  so  that a
closed system of equations can be developed to represent element
cycling.   That aspect  is  the  use  of  different oxidizing  agents  as
terminal electron acceptors in the  energy metabolism carried  out
by all heterotrophs.

represent  organic  chemicals  in a  general way  as sources  of
materials for energy and synthesis,  it is  necessary  to group  them
into  categories.  Criteria  for establishing  these categories
include similarity of elemental  composition, energy content,  and
the way  in which organisms  use them.   These criteria do  not
specify  the  level  of  resolution,  however,  and  in  the  final
analysis the categories  will be  selected  through  experience with
attempts  to  match several possible  categorization  schemes with
the other model  components to achieve  the  results  with reasonable
economy.   An initial scheme  is  presented  in Figure 7.  In  this
scheme  the  categories   are  particulate  organic matter  (POM),
refractory organic matter (ROM),  digestible organic  matter  (DOM),
soluble  organic  matter  (SOM),  itself  consisting of   two
components:  biomass-like monomers (BOM) and non-biomass-1 ike
monomers  (NOM).   POM receives input from  organism deaths,  molts,
egesta,  etc.  The  distinction  between  ROM  and DOM  is purely
categorical, i.  e. f  no   process  separates  ROM from DOM.   DOM,
however,  is  readily hydrolyzed  by  exoenzymes  of microorganisms
into SOM, whereas ROM is only very slowly solubilized.  SOM is
absorbed  by  the  organisms,  and  separation  into  BOM and NOM
occurs.   (This is also a categorical distinction  as discussed in
the  section  on  partitioning  of   food  into  power supply  and
biosynthesis.)  This  categorization scheme  reflects  the mode  of
biological   utilization  more  explicitly  than  similarity  of
composition or  energy   content.   It is  possible  that for  the
latter criteria  additional categories  will be  required.   It might
become  necessary,  for  example,  to represent CH4 ,  acetate,  or
other  specific  categories  of chemicals  that are  important  in
microbial  systems  for  the  model to reflect certain  aspects  of
their dynami c s.

As organisms oxidize organic chemicals  for  energy,  there  is a
sequence of utilization  of electron acceptors  that corresponds to
the variation in  redox  potential  for  the  reactions  (4,  27).  That
is, a preferred electron acceptor is used until  it is  depleted,
then  the  next preferred form  is  used,  and so  on.  O2 is used
first,  followed  by NO,"1  and  NO2"1,  SO4"2,  and CO,.  Other
oxidants  are also  usea, such  as other  forms of  sulfur.   The
interesting point of this sequence  is  that the  preferred sequence
is  in the  order of  the  energy  released in  the reactions.
Oxidations of organic  compounds  using  the  more  preferred electron
acceptors result  in  greater  energy  yield than  reactions  using  the
less preferred.  It is unlikely  that  this reflects  any chemical
necessity (4), but more  likely  reflects  the  competitive  advantage
accruing to organisms that use the  more highly productive  energy
sources.   This sequence  of  reactions  will be  expressed  wherever

transport or  regeneration of electron  acceptors is slower than
their use by organic decomposition.  In natural systems, it is
expressed temporally in highly eutrophic systems  and spatially as
vertical stratification in  systems with  highly  organic  sediments,
such as  wetlands and many water bodies.

The  use of  ozidants  in  sequence  can be  represented  by  the
assumption  that  the  strongest oxidant  present  is  used.  The
problem that then remains is  that  of  calculating  the energy yield
appropriate to  the oxidant  that  is  being  used.  One  direct
approach  to this problem is that  suggested  as  appropriate by
McCarty (4), the use of half  reactions  and equivalent  weights as
described in elementary chemistry texts, and as  is  commonly used
in biochemical calculations (28, ch.  17).   If this approach is
taken  the standard free energies of the half  reaction of their
reduction (at  pH  7, and unit  activity  for the other reactants),
per  equivalent  weight  of  the  oxidants   is  in  the  order
corresponding  to the sequence of their  utilization.   An exception
to this is nitrite, whose value for  AG°(w)  is higher than  that of
O,. It is  not  clear whether this apparent  reversal in tendency  is
a  consequence  of adaptation of  the  organisms  that use  nitrite as
an electron  acceptor  or  of the peculiar  relationship  of  nitrite
to nitrate.  That  is,  nitrite is  formed as a product  of nitrate
reduction and is  available as a reactant, therefore,  only after
nitrate is  reduced.

For  the  scheme  for   representing  organic  matter  to  be used
effectively,  an  accounting  algorithm must be  applied  to  enforce
the  conservation of mass.  The  algorithm  that  is applied  here  is
in  outline  the  following.   Each of the  categories  of  OM  are
treated as  state variables, except that  POM is not represented  as
a  separate  state variable,  but rather  as a  sum  of DOM  and ROM.
Fractions of  the various  sources of detritus are  refractory  to
hydrolysis  and are  therefore  ROM.  The  remainder  is DOM.   DOM  is
lost  through  hydrolysis  to  soluble  compounds,  SOM,  which in  turn
is lost via uptake  by  microorganisms.    As  discussed above,   the
subsequent  processes  are as  represented for macroheterotroph
metabolism.   Conservation  of  mass in this model,  however, has  a
more  specific  meaning.   The  elements  of concern  must be
individually  conserved.   This  is accomplished by accounting  the
concentration of  the  elements in each of the pools.  The rules
given  above then apply to  the individual elements.  The pools  are
treated  in  many respects as  a  single type of  molecule with mole
numbers proportional  to  the  concentrations of  the elements.
(Except that  for  computations using  the Gibbs  free energy, it  is
not  assumed that  the  concentration  of  the  molecule as a reactant
is  that  of  the whole pool.   See Energetics  above.)

The  above procedures  will  guarantee conservation of mass, but  to
calculate  the  energy  yield  from reaction  with the  various
oxidizing agents  requires  an  additional algorithm.  The  oxidants
are  represented  as  half  reactions in which an  electron equivalent
of  the oxidant plus an electron  (hence  electron  acceptor) yields
a  reduced  form of  the element.  A complementary  half  reaction is
required for  the electron  donor,   a molecule  from  one  of  the


categories  of  organic matter.  This  can easily be done (but  is
not  discussed here).   Of more difficulty is  the problem  of
obtaining  the  appropriate  free energy  for  this  half reaction.
The approach to be taken initially is to use a conservation  rule
for heat  of combustion with oxygen  so that  the  energy of the
pools  is  accounted  dynamically.  When calculating  the energy
yield  for  reaction with another  oxidizing  agent,  the reaction
with oxygen will  be  replaced by an equation for  the  appropriate
reaction by first removing the  half reaction for oxygen  and  then
substituting   the  half  reaction  for  the  oxidizing  agent  of


The above  several sections  summarize  a complete and  theoretically
rationalized  basis for a  multi-species, yet  functionally
oriented,  ecosystem model.   It  yet remains  for this theory  to  be
implemented into  a  working computer  model.   Further  work  is
needed to  provide   a  basis   for describing  physiological,
behavioral, population  level,  and  other specific effects with a
comparable  degree of  theoretical rationale.  It  is quite  possible
that this work will  require  yet additional work  on the model  as
pr esent ed.

                       CONCLUDING COMMENTS


The futility of the reductionist method for studying systems has
often  been argued convincingly.  Early  in this  report I  noted
that I have departed from both the holistic and reductionistic
approach.   Yet it has not surprised  me to  find  that many  with
whom I have discussed  these  ideas have gained the impression that
this research  is  extremely  reductionistic.   They have  noted that
it  is reductionistic  to attempt to understand a natural system by
studying its parts in  detail,  and  that  this approach  to ecology,
historically has failed.  They have  further noted that my  work
bears  a strong resemblance  to  that  approach.  There  is a  great
philosophical  and  operational  difference,  however,  between this
model  and  the  reductionistic  approach.

This model  is  indeed constructed of   fine  scale  components.   But
in  contrast to the failures  to comprehend natural  systems through
comprehensive  study  of  their  parts,   I  expect   to  obtain
predictions at the ecological scale.   The reason  for optimism can
be  explained by  contrasting  the comprehensibi1ity  of  natural and
engineered systems.   Engineered  systems  are  understood
essentially as  well as their  component  parts  are understood,
because  they  have been  explicitly  designed  and constructed.
Oftentimes  models  are constructed  of  mathematical  analogs  of  the
component  parts  and  coupled in a way  considered  to be analogous
to  the  way that  the  engineered system is built.  The model  is
itself  an  engineered  system,  built  in  strict  analogy to the
physical engineered  system.  It is intended that  the model  output


represent  the  system level  behavior of the engineered system.
The degree to which  the  model  behavior  actually  represents  that
of  the physical  system  depends  upon the  closeness of  the
analogies  between the systems,  which in turn depends  upon the
skill  of   the  modeler.   There is  no  question  of  whether  any
failure of the model  to  describe  the physical  system's  behavior
is  due to inherent   impossibility  of  obtaining  system  level
behavior from a model constructed  of mathematical analogs to fine
scale  physical components.

All coupled models,  including the one  discussed in this report,
are  engineered  systems.   At  issue  is  whether  this  model's
behavior  will  represent,  to any  useful   extent,  behavior  of
natural systems.  Specifically not at issue, as argued  above,  is
whether system behavior can result  from a  model constructed of
fine scale components.  As  with models  of engineered system, the
extent to which model  behavior  will  represent natural  system
behavior will depend  upon  the  closeness of   the analogies between
model  components and  physical couplings.

Physical  ecosystems  are comprised  of  a virtual  infinitude of
components.   It is  patently obvious  that  it  is  impossible to
study  or  represent all  of them.   But  even  if  it  could be done,
one  would have  a representation  of  only  a  single  ecosystem.
Patterns  of  ecosystem behavior for broad categories  of systems
are recognizably similar, even if not predictably  so.  There is
structural and  functional  similarity that apparently emerges, in
the  presence  of  significant  diversity of system  components.
Analogously, a system model,  if  constructed of  components that
well  represent the processes  that occur in a type of  ecosystem,
can be  expected to exhibit  functional behavior  similar to  that of
the  system type whose  components  are  represented, despite the
unavoidable misrepresentations   of  the greatest majority of
species present  in physical  ecosystems.

The  manner  in  which  I  anticipate  that   this  model's  system
behavior  will  represent  real system behavior is best explained in
terms  of  three macroscopic,  testable hypotheses about this model
and  its  relationship  to  natural  system  behavior.    It  is my
hypothesis  that  it   will  be  possible to  find  comp1ements of
species representations (sets of attributes)  that will coexist
for very  long  times  (not necessarily asymptotic coexistence),  and
further  that among such coexisting complements  that there  will be
a high  degree of  similarity of  process  rates.   That  is,   I
hypothesize  that  there  may  be many nearly  stable  model
communities  that could  occupy a model   environment, but  that  one
will  not  be  able to discriminate  among them merely by  considering
differences in process  rates.  Further, I  hypothesize that  the
predicted  ensemble  average  ecological  effect  of  a  specific
 toxicant  will  not differ  distinguishab1y  among such  coexisting
complements.   A  connection with reality is needed  for  these
results to be considered  predictions, and the final hypothesis
provides  this  connection.  I hypothesize  that one will  not be
 able  to  discriminate between  measurements  on processes  occurring
 in a  real system and analogous values  of processes as calculated


by  this model,  including  the  ecological  effects of  toxic
chemicals,  provided that the teal system's boundary  conditions
can be  well represented in the model.   This latter  provision
recognizes  that uncertainty in boundary conditions  can limit the
capability  to  discriminate  between  the  predictions  and
observations.    Laboratory  ecosystems  hold  some  promise  of
overcoming   this  potential  limitation  by  permitting control over
boundary conditions  so  that they  can be represented  in  the model.

If these hypotheses  are  borne out,  and  calculational difficulties
can be overcome,  then this model  will  provide a  synthetic means
of  predicting  ecosystem  effects.   If  they  are  refuted,  the
results will suggest other  hypotheses.


The  third   hypothesis   is  the critical   one.   Underlying  this
hypothesis  is  the premise that interactions of  the equations will
be analogous to interactions  among real ecosystem components.  In
fact the results of  any  ecosystem model must depend upon the same
premise, regardless of  whether they are considered  reductionistic
or  holistic.   The  equations  of  any  model must  bear  some
relationship to  the  system components that they represent.  The
degree of resemblance  is  dependent on  the correspondence  of the
level  of resolution to the resolution of  the  components of the
natural  system components of interest,  and  on the  skill  with
which these components  have been selected and described.  If  a
fine scale  of  resolution is selected,  a model  is apt  to be called
reductionistic, or  conversely, if  coarse,  then holistic.   But is
the  difference  between  reductionism and  holism merely   a
quantitative  difference  in  scale  of resolution?   I would argue
that scale  of resolution is not  even relevant  to the  distinction
between the two  views.   If one  is  interested in  studying the
response of processes  or entities as  a function of the level or
intensity  of   various  influences,  where  the  uncontrolled
fluctuations  of the system have been "reduced" to  an acceptable
level,  then the view is r educ t i on i s t i c .  If, on the other hand,
one is  interested in processes  or entities  that  take on their
special  characteristics  as  a result  of  the direct and indirect
influences  of  other  system components, then the view is holistic.
Moreover, taking  a  holistic  viewpoint  does not necessarily admit
a coarse scale  of resolution.  The scale of resolution dictated
by  the processes  and entities of  interest, whether   the viewpoint
is  reductionistic or holistic.

There  is  no intent for  this model  to  reproduce  the detailed
behavior of a  real physical system  in  such a manner that one
could  identify  the behaviors  of  real   living  species  in the
results.  What is intended  is  that  this model be  an analog of
aquatic systems,  in the sense that system behaviors  that  cannot
be attributed  to individual biotic species,  i. e^.,  whole  system
properties, are indistinguishable  from results  of the  same
kinds  of  behaviors  of  natural  systems  with similar boundary

conditions.  The  possibility that such results  can  be obtained
depends on the  choice of processes to represent,  the  adequacy of
the description of those processes over the operating range,  and
the application of constraints  (conservation  laws,  thermodynamic
and kinetic principles)  in  a manner  that  is  analogous to
constraints  on  natural  systems.

All results  of a  system model  must  necessarily be viewed as
system level results.  There are  two categories  of system level
results,  however.   One  is  the sort  that could also be measured in
a reductionistic way  in a  controlled  experiment,  for example  -- a
chemical  reaction,  but whose  peculiar  characteristic  in  the
system context results from system  interactions.  The  other is
the sort  that  cannot  be observed  in a reductionistic way, because
it does not  exist  apart from the system.   An element cycle is an
example of such a  result,  and measurement  of  the  flow of  material
around an  element cycle  loop  is an  example of  a system level
measur ement.

The distinction  is  not  as  great  as  it  might at  first  appear,
however,  because  of  the possibility  of interpreting the  former
sort  of   result  as  indicative  of   the  latter.   Patterns of
interactions  are new  macroscale  phenomena that  arise  via the
existence of  the system,  but  they  can be  observed only at the
scale of  observation  possible  for   the  observer.    Thus
measurements  of  chemical  reaction rates in  the  system can be
observed  and used to infer  behavior of the whole pattern of the
element cycle  in  which it participates.   It  is not  inconceivable
that  some sort of  observation could be made at  the scale of the
pattern  itself.  It is  characteristically human to perceive and
discriminate  among  patterns,  but it  is  quite another  level of
difficulty  to quantify objectively patterns of  behavior  in  a
manner  to permit  discrimination  among behaviors  of  ecosystems.
If the capacity  for  this sort  of perception and discrimination
among ecosystem  behaviors  is  to be  developed,  it would appear
that  models of  about the  complexity  of that  described here would
be valuable in the endeavor.

       Energy Processing Cycle
A Chemolitho- w
\ 	 	 	 9

^ Anoxychemo— k
Figure 1. Schematic for redox processes that yield energy useful
        for biotic processes.  Elements cycle between reduced
        and oxidized forms.

? f
Reduced Chem.
Forms in Biomass
Production of

O.M. fc
Reduced Chem.
Forms in O.M.
                 excretion, etc.)
 Inorganic Forms
 Reduced Chem.
Forms in Biomass
                    Production of O.M.
                                       Inorganic Forms
                                        Inorganic Forms
Reduced Chem.
 Forms in O.M.
Figure  2.  Relationships among chemical and biotic  forms of
          elements in biosynthesis.

               aerobic,  C02 + H20	> Org
         Higher Organisms, Food Web, Microorganisms
           Org +  02	> C02 +  H20,  AG° = -25.5
                   anaerobic, N03 present,
                 - > N02 + C02 + H20,  AG°
             N02 - > N2 + C02 + H20,  AG°
       Org + S0|
          anaerobic, no N03 present,
                 S0|~ present
                 H2S + C02 + H20,
= -1.7
                 anaerobic, no N03  present,
                no SOf" present, C02 present
             (C02) + H20 - > C02  + H20, AG°
= -1.1
Figure 3.  Variation in terminal electron acceptor  as function
          of depth.

                                           \     C  (in bulk fluid)
                                       7*	Cb (at cell  surface)
Figure  4.  Diagram of Cell in aquatic medium indicating the concentration
          gradient surrounding the cell.

         Autotroph Biosynthesis
                  ADP + P	> ATP
                  NADP	> NADPH
Figure 5.  Major components and relationship of autotroph biosynthesis.

               Power Output
o AGd(loss)
                        (AGp - AGd)
     AGD (cost)
                                     (AGC - AGd)
                                •C02 + H20
                                                  TCA cycle
                                                             N & S input, function
                                                              of pool Z synthesis
Figure 6.   Major components and pathways  (.energy and mass) of heterotrophy.

        Organic Matter
            Dead organisms,	
             molts, egesta

Figure 7.  Categories of  organic chemicals (P=particulate,
          R=refractory,  D=digestible, S=soluble, B=biomass-
          like, N=non-biomass-like)

     Filter Feeding Schematic
Figure 8.  Relationships characteristics of a filter feeding
          predator and its potential prey that determine
          probability of capture.

         Pursuit Feeding  Schematic
        vc] s predator search velocity
                     Table 1

Some reactions used by chemoautotrophs for energy
Reaction Free Energy
kcal/M( substrate) kcal/eq.wt. (substrate)
HS~ +
S° +
HS~ +
S° +
•2 +
H2 +
H2 +
CH4 +
+ 1 .5 O, = NO.," + 2 H+ + H-,0
^ A &
+ .5 O2 = NO3~
2 02 = S042~ + H+
5/2 O2 + H2O = S042~ + H+
+ 2 02 + H20 = 2 S042~ + 2 H+
+ 1/2 02 = S042-
8/5 N03~ + 3/5 H+ = S042~ 4- 4/5 N2 + 4/5 H2O
6/5 NO3~ + 2/5 H2O = S042" + 3/5 N2 + 4/5 H+
2/5 N03 + 2/5 H+ = 1/5 N2 + 6/5 H2O
1/4 SO42~ + 1/4 H+ = HS~ + H2O
1/2 CO2 = CH3COOH + 1/2 H2O
2 O2 = CO2 + 2 H2O
S0.2~ + H+ = CO, + HS~ + H-.O
-21 .79


1.   Ehhalt,  P.  H.  The  Atmospheric  Cycle  of Methane.  Tellus
    26:58 - 70 (1974).

2.   Skucnick,  J.   Risk/Concentration  Estimates for Aquatic  Life
    by Species Within  Pollutant. Appendix: Acute  Criteria
    Documents  Data  Base.   SRI  International,  Menlo  Park
    California,  307 p (1980).

3.   JRB  Associates,  Inc.   User  Documentation for  Criteria
    Documents Data Base.   JRB Associates,  Inc., McLean,  Virginia
    (1980) .

4.   McCarty, P.  L.  Energetics and Bacterial  Growth.   J.n:  Organic
    Compounds  in Aquatic  Environments,  S.  J. Faust  and  ].  W.
    Hunter,  Eds.,  Marcel  Dekker,  Inc.,  New York,  p 495 -  529
    (1971) .

5.   Docile, H.  W. Bacterial  Metabolism,  2nd  Ed.   Academic Press,
    New York, 738 p (1975).

6.   Fenchel,  T.  and  T. H.  Blackburn.    Bacteria and Mineral
    Cycling.  Academic  Press, London,  225 p (1979).

7.   Morowitz,  H.  J.    Energy  Flow  in  Biology,   Biological
    Organization as a  Problem  in Thermal   Physics.  Academic
    Press, New York,  179 p  (1968).

8.   Nicolis,  G.   and   I.  Prigogine.    Se 1 f-Organization  in
    Nonequi1ibrium Systems.   From Dissipative Structure to  Order
    through Fluctuations.   John Wiley and Sons, New  York,  491 p

9.   Monod,  Jacques.   Recherches sur  la  Croissance des Cultures
    Bacteriennes.  Hermann  et Cie, Paris  (1942).

10. Rashevsky,  NF.  Some Remarks  on the Mathematical  Theory of
    Nutrition  of Fishes.   Bull.  Math.  Biophys.   21:161  -  183
    (1959) .

11. Holling, C.  S.  The  Functional Response  of  Predators  to  Prey
    Density  and Its Role in Mimicry  and Population  Regulation.
    Mem. Entomol. Soc.  Can. 45:1  - 60  (1965).

12. Purcell, B. M.  Life at  Low  Reynolds  Numbers.  Am. J.  Phys.
    45:3 - 11 (1977).

13. Vogel,  S.   Life  in  Moving Fluids.   The  Physical Biology of
    Flow.  Willard Grant Press,  Boston, 352 p (1981).

14. Pasciak, W.  J.  and J.  Gavis.  Transport  Limitation  of
    Nutrient Uptake  in  Phytoplankton.   Limnol. Oceanogr.   19:881
    - 888 (1974).

IS.  Pasciak,  W.  J.  and  J.  Gavis.  Transport Limited Nutrient
    Uptake Rates  in Di.t_y_lum br_i£ht_we.ll.jLi_.   Limnol. Oceanogr.
    20:604 -  617  (1975).

16.  Gavis, J.  and  J.  T.  Ferguson.   Kinetics  of  Carbon Dioxide
    Uptake  by Phytop 1ankton  at  High  pH.    Limnol. Oceanogr.
    20:211 -  221  (1975).

17.  Schlegel,  H.  G.   Mechanisms  of Chemo-autotrophy.   in:  Marine
    Ecology.  A Comprehensive,  Integrated  Treatise on Life  in
    Oceans and Coastal Waters.   O.  Kinne,  Ed.,  John Wiley  and
    Sons,  New York,  p 9 - 60 (1975).

18.  Lehninger, A.  L.   Biochemistry.  The Molecular  Basis  of Cell
    Structure  and  Function,  2nd.  Ed.  Worth Publishers,  Inc.  New
    York,  1104 p  (1975).

19.  Burton,   K.   Energy  of Adenosine  Triphosphate.   Nature
    181:1594  - 1595  (1958) .

20.  Steelc,  J. H.  Environmental  Control  of Photosynthesis   in the
    Sea.  Limnol.  Oceanogr.   7:137 -  150  (1962).

21.  Bannister,  T.  T.   Production  Equations  in Terms  of
    Chlorophyll Concentration,  Quantum Yield,  and Upper Limit  to
    Production.  Limnol.  Oceanogr.  19:1  -  12  (1974).

22.  Dubinsky, Z. and T. Herman.  Light Utilization Efficiencies
    of Phytopiankton  in  Lake Kinneret  (Sea of Galilee).   Limnol.
    Oceanogr.   21:226 - 230  (1976).

23.  Clayton,  R.  K.   Photosynthesis:  Physical   Mechanisms  and
    Chemical  Patterns.  Cambridge Univ. Press,  New York, 281 p
    (1980) .

24.  Gunderson, K. and C.  W.  Mountain.  Oxygen  Utilization  and pH
    change  in  the   Ocean  Resulting  from  Biological  Nitrate
    Formation.  Deep Sea  Res.   20:1083  -  1091  (1976).

25.  Ivlev, V.  S.  Experimental Ecology of  the Feeding of  Fishes.
    English Trans,  by D. Scott.  Yale Univ.  Press, New  Haven,
    302 p (1961).

26.  Gerritsen, J. and  J. R.  Strickler.  Encounter Probabilities
    and Community Structure in Zooplankton:  a Mathematical  Model.
    J. Fish.  Res.  Board Can.  34:73 - 82  (1977).

27.  Stumm,  W. and  J.  J.  Morgan.   Aquatic Chemistry.   An
    Introduction  Emphasizing Chemical  Equilibria in Natural
    Waters.    John  Wiley and Sons, New York,  780 p (1981).

28.  Lehninger,  A.   L.   Principles  of Biochemistry.    Worth
    Publishers, Inc., New York,  1011 p (1982).

                                   TECHNICAL REPORT DATA
                            (Please read laarucnons on the reverse before completing)
                                                            3 RECIPIENT'S ACCESSION NO.
                                                           S REPORT DATE
Prediction of Ecological Effects of Toxic Chemicals:
Overall Strategy  and Theoretical Basis for  the
                                                           6 PERFORMING ORGANIZATION CODE
                                                           8 PERFORMING ORGANIZATION REPORT NO
   Ray R.  Lassiter
   Environmental Research  Laboratory
   U.S.  Environmental  Protection Agency
   College Station Road
   Athens GA 30613
                                                         10. PROGRAM ELEMENT NO.
                                                         11 CONTRACT/GRANT NO.

   Environmental Research  Laboratory—Athens GA
   Office of Research  and  Development
   U.S.  Environmental  Protection Agency
   Athens GA  30613
                                                                            •RIOO COVERED
                                                         14. SPONSORING AGENCY CODE
         A strategy is  developed for modeling ecosystems to permit assessment of effects
   of toxic chemicals on element cycling and other  ecosystem processes.   The strategy
   includes use of multi-species representations  of biotic communities and mathematical
   descriptions of the  processes that are important in aquatic ecosystems.  Direct
   effects of toxicants are assigned to the species comprising the biotic community
   in a manner suggested by available toxicological  information.  Effects are calculated
   as the difference between selected measures of processes from unaffected systems and
   systems affected by  the presence of a toxic chemical.  Ecological effects calculated
   in this manner are considered to be heuristically useful.
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EPA Form 2220-1 (9-73)