Systems Ecology

Mathematics can be used to accurately explain and predict many natural occurrences. Systems ecology is the study of the structure and function of ecosystems by using mathematics to model ecological processes ranging from climate patterns and precipitation cycles to nutrient and energy transfer. Systems ecology is a synthesis of two more general disciplines: ecology and general systems theory. Ecology is the study organisms and their response to each other and their organic and inorganic environment. The concept of systems is fundamental in ecology (hence the term "ecosystem"). A system consists of different parts interacting with each other to produce emergent properties, which cannot be attributed to any one part of a system, but only as a result of the interactions. Much of the understanding of systems comes from general systems theory. First proposed by Ludwig Von Bertalanffy in the 1960s, general systems theory aims to apply rules to all kinds of systems, in all fields of research. When general systems theory is applied to the study of ecology, attention is shifted from populations of organisms to the complexity of the systems in which they live. This is largely achieved through applications of graph theory and modeling.

Overview

Simple diagrams used in systems ecology, such as the food web shown in Figure 1, apply methods of graph theory to estimate the transfer of a resource (nutrients, energy, etc.) within a system. Rather than giving precise numerical data, they typically help to visualize flow. To understand the specifics of the systems, mathematical modeling is a great tool.

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Perhaps the most essential tool in the study of systems ecology, models aim to simulate or help visualize occurrences in the natural world, usually on a much smaller scale. Most model frameworks are created by collecting and analyzing data. In the case of systems ecology, multivariate statistics play a huge part in determining how to construct a model, as there can be any number of variables involved in an ecological system. Likewise, there are any number of different kinds of systems in a single ecosystem. For example, nutrient cycles, climate patterns, and energy flow can interplay in virtually any environment, which can lead to countless sources of variation in a system, and therefore different emergent properties. By estimating the probability of possible events occurring within a system, statistics can be used to predict the most likely outcomes.

When constructing models, researchers must constantly compare the data they expect to see based on theory with the empirical data they actually observe. Nature does not conform to computer models, and experiments should not be treated as such. Any instances where the predicted data and observed data do not match up must be studied thoroughly to understand where the differences arise and to account for them. With an everchanging natural environment, systems ecology is a constantly improving study that must rely on graphs and models to explain and predict natural occurrences.

Bibliography

Jørgensen, Sven Erik. Introduction to Systems Ecology. Boca Raton, FL: CRC, 2012.

Odum, Howard T. Ecological and General Systems: An Introduction to Systems Ecology. Niwot, CO: U of Colorado, 1994.

Otto, Sarah P., and Troy Day. A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Princeton, NJ: Princeton UP, 2007.

Ricklefs, Robert E., and Rick Relyea. Ecology: The Economy of Nature. N.p.: Freeman, 2013.

Yi, Lin. General Systems Theory: A Mathematical Approach. New York: Springer, 2013.