386
the thinning response and the size of the individuals
in a crop.
Among the earliest individual-based models in
ecology were models of forests based on the growth
of the individual trees that comprise the forest
stand. These models were developed by quantitatively oriented foresters and were focused from
their inception toward practical issues in production
forestry.
An important subcategory of individual-organism-based tree models that have been widely used
in ecological (as opposed to traditional forestry applications) are the so-called "gap" models (Shugart
and West 1980). The first such model was the
JABOWA model (Botkin et al. 1972; Botkin 1993)
developed for forests in New England. Several gap
models for a wide range of forests (and eventually,
grasslands and savannas) were subsequently developed (Shugart, et al. 1992; Urban and Shugart
1992) for a wide range of locations. The earlier
versions were developed with an interest in using
models for interecosystems comparison (Shugart
1984) and adhered relatively closely to the
JABOWA formulation. More recent models have
diverged, particularly in the addition of spatial
competition among trees, a range of modifications
to allow simulation of a wider range of environmental conditions, and additional biological and/or
physiological mechanisms.
Conclusions
Ecosystem modeling has been treated in this chapter with an emphasis on the historical roots of the
topic and with simple familiar examples of some of
the more common approaches the model development. Ecology has become increasingly quantitative over its recent history, and this has lead to a
"trendy" exploration of a wide array of mathematical approaches in ecological studies. It is important
to realize that the fundamental issues in ecological
modeling go to issues of determining what are the
logical parts of the ecosystem, knowing how these
parts significantly interact, and using this information to posit theories about the nature of ecosystems. The mathematics is in support ofthese larger
and essentially scientific objectives.
The principal examples used in this presentation
have been differential equations used to model the
Herman H. Shugart
interactions of a population or the movement of materials through ecosystems. These examples were
chosen to both demonstrate the dynamics of these
interactions and to illustrate development or analysis of a dynamic model. This chapter was intended
to provide an introduction to some of the considerations in developing ecological models. The
treatment of many important topics in the area of
ecological modeling has been intentionally brief.
There are several texts on the topics of systems and
mathematical approaches in ecology, and several of
these are noted as citations in the text.
References
Allee, w.e. Concerning the organization of marine
coastal communities. Ecol. Monogr. 5:541-554; 1934.
Beltrami, E. Mathematics for Dynamic Modeling. Orlando, FL: Academic; 1987.
Bormann, EH.; Likens, G.E. Pattern and Process in a
Forested Ecosystem. New York: Springer-Verlag;
1979.
Botkin, D.B. Forest Dynamics: An Ecological Model.
Oxford: Oxford Univ. Pr.; 1993.
Botkin, D.B.; Janak, J.E; Wallis, J.R. Some ecological
consequences of a computer model of forest growth.
J. Ecol. 60:849-872; 1972.
Box, E.O. Geographical dimensions of terrestrial net and
gross primary productivity. Radiat. Environ. Biophys.
15:305-322; 1978.
Caswell, H.; Koenig, H.E.; Resh, lA; Ross, Q.E. An
introduction to systems science for ecologists. In: Patten, B.C., ed. Systems Analysis and Simulation in
Ecology. Vol. II. New York: Academic; 1972:3-80.
Cook, RE. Raymond Lindeman and the trophic-dynamic
concept in ecology. Science 198: 109-122; 1977.
Dale, M.B. Systems analysis and ecology. Ecology 51:216; 1970.
DeAngelis, D.L.; Gross, L.J., eds. Individual-Based
Models and Approaches in Ecology: Populations,
Communities and Ecosystems. New York: Chapman
and Hall; 1992.
DiStefano, J,J., III, Stubberud, A.R.; Williams, I.J.
Schaum's Outline of Theory and Problems of Feedback and Control Systems. New York: McGraw-Hill;
1967.
Farquhar, G.D.; von Caemmerer, S.; Berry, J.A A biochemical model of photosynthetic CO2 fixation in
leaves of C3 species. Planta 149:78-90; 1980.
Friend, AD. Use of a model of photosynthesis and leaf
microenvironment to predict optimal stomatal conductance and leaf nitrogen partitioning. Plant Cell Environ. 14:895-905; 1991.
the thinning response and the size of the individuals
in a crop.
Among the earliest individual-based models in
ecology were models of forests based on the growth
of the individual trees that comprise the forest
stand. These models were developed by quantitatively oriented foresters and were focused from
their inception toward practical issues in production
forestry.
An important subcategory of individual-organism-based tree models that have been widely used
in ecological (as opposed to traditional forestry applications) are the so-called "gap" models (Shugart
and West 1980). The first such model was the
JABOWA model (Botkin et al. 1972; Botkin 1993)
developed for forests in New England. Several gap
models for a wide range of forests (and eventually,
grasslands and savannas) were subsequently developed (Shugart, et al. 1992; Urban and Shugart
1992) for a wide range of locations. The earlier
versions were developed with an interest in using
models for interecosystems comparison (Shugart
1984) and adhered relatively closely to the
JABOWA formulation. More recent models have
diverged, particularly in the addition of spatial
competition among trees, a range of modifications
to allow simulation of a wider range of environmental conditions, and additional biological and/or
physiological mechanisms.
Conclusions
Ecosystem modeling has been treated in this chapter with an emphasis on the historical roots of the
topic and with simple familiar examples of some of
the more common approaches the model development. Ecology has become increasingly quantitative over its recent history, and this has lead to a
"trendy" exploration of a wide array of mathematical approaches in ecological studies. It is important
to realize that the fundamental issues in ecological
modeling go to issues of determining what are the
logical parts of the ecosystem, knowing how these
parts significantly interact, and using this information to posit theories about the nature of ecosystems. The mathematics is in support ofthese larger
and essentially scientific objectives.
The principal examples used in this presentation
have been differential equations used to model the
Herman H. Shugart
interactions of a population or the movement of materials through ecosystems. These examples were
chosen to both demonstrate the dynamics of these
interactions and to illustrate development or analysis of a dynamic model. This chapter was intended
to provide an introduction to some of the considerations in developing ecological models. The
treatment of many important topics in the area of
ecological modeling has been intentionally brief.
There are several texts on the topics of systems and
mathematical approaches in ecology, and several of
these are noted as citations in the text.
References
Allee, w.e. Concerning the organization of marine
coastal communities. Ecol. Monogr. 5:541-554; 1934.
Beltrami, E. Mathematics for Dynamic Modeling. Orlando, FL: Academic; 1987.
Bormann, EH.; Likens, G.E. Pattern and Process in a
Forested Ecosystem. New York: Springer-Verlag;
1979.
Botkin, D.B. Forest Dynamics: An Ecological Model.
Oxford: Oxford Univ. Pr.; 1993.
Botkin, D.B.; Janak, J.E; Wallis, J.R. Some ecological
consequences of a computer model of forest growth.
J. Ecol. 60:849-872; 1972.
Box, E.O. Geographical dimensions of terrestrial net and
gross primary productivity. Radiat. Environ. Biophys.
15:305-322; 1978.
Caswell, H.; Koenig, H.E.; Resh, lA; Ross, Q.E. An
introduction to systems science for ecologists. In: Patten, B.C., ed. Systems Analysis and Simulation in
Ecology. Vol. II. New York: Academic; 1972:3-80.
Cook, RE. Raymond Lindeman and the trophic-dynamic
concept in ecology. Science 198: 109-122; 1977.
Dale, M.B. Systems analysis and ecology. Ecology 51:216; 1970.
DeAngelis, D.L.; Gross, L.J., eds. Individual-Based
Models and Approaches in Ecology: Populations,
Communities and Ecosystems. New York: Chapman
and Hall; 1992.
DiStefano, J,J., III, Stubberud, A.R.; Williams, I.J.
Schaum's Outline of Theory and Problems of Feedback and Control Systems. New York: McGraw-Hill;
1967.
Farquhar, G.D.; von Caemmerer, S.; Berry, J.A A biochemical model of photosynthetic CO2 fixation in
leaves of C3 species. Planta 149:78-90; 1980.
Friend, AD. Use of a model of photosynthesis and leaf
microenvironment to predict optimal stomatal conductance and leaf nitrogen partitioning. Plant Cell Environ. 14:895-905; 1991.