Abstract
The theory of dynamic systems originally evolved in the engineering sciences for designing complex mechanical and electronic systems from their basic component parts. It has since found increasing usage by military, economic, and industrial strategists, and more recently by biologists, as a method for gaining insight into the structure and function of complex systems. In this first chapter I will outline some of the elementary concepts and principles of dynamic systems theory as a prelude to our investigation of population dynamics. I have tried to avoid engineering jargon as much as possible and have freely modified some of the more rigorous concepts to suit the particular needs of population ecology, hopefully without losing the original intent. My aim has been to use the theory to gain a better understanding of population dynamics and management and, thus, I have glossed over or ignored much of the formality and detail (references to more technical treatments are given in Note 1.1 at the end of this chapter).
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Notes
Positive Feedback—A General Systems Approach to Positive/Negative Feedback and Mutual Causality edited by J. H. Milsum, published by Pergamon Press, New York, 1968, is a compilation of works that examines the philosophical, historical, and technical aspects of dynamic systems theory, and its application in the biological and social sciences, in a manner comprehensible to the general scientific community. It is this little book (only 169 pages) which first introduced me to control theory, and it is responsible, in large part, for my writing this book.
Biological Control Systems Analysis by J. H. Milsum, published by McGraw-Hill Book Company, New York, 1966, is a much more technical treatment of dynamic systems theory for the advanced student. Although it is largely concerned with physiological systems, some population concepts and their control theory analogues are introduced. The general reader may find Chapters 1 and 2 a useful, if rather technical, introduction to dynamic systems and their control.
Feedback Mechanisms in Animal Behavior by D. J. McFarland, published by Academic Press, New York, 1971, is, as the title indicates, mostly concerned with the application of control theory to behavioral systems. However, a lucid introduction to the elements of control theory is presented in Chapters 1 and 2.
We often tend to draw rigid distinctions between the arts and sciences when such distinctions are fuzzy, at best. Many scientists spend much of their time in what can only be described as artistic endeavors. This is particularly true of those involved in the analysis and synthesis of natural systems. The artist uses concrete materials to construct an abstract model of something that exists in his mind. Likewise, the systems analyst uses concrete scientific information to construct an abstract model of how he thinks the system works. The model is his conception and, therefore, its resemblance to reality is only as good as his facts and his innate abilities to synthesize those facts into a model of the system. The scientific method called the “hypothetico-deductive” (H-D) approach involves the validation, or better invalidation, of the conceptual model (see Stephen Fretwell’s book Populations in a Seasonal Environment for a nice summary of the H-D philosophy applied to ecological problems; the book was published in 1972 by Princeton University Press as part of their series entitled Monographs in Population Biology). Because the “art” of constructing abstract models rests on knowledge and insight concerning the nature of the system being analyzed, it is important that biological models arise in the minds of experienced and intelligent biologists. In the past, however, many biologists, although able to see the picture, were unable to paint it because they were unfamiliar with the tools—mathematics. Consequently incomplete or inaccurate pictures were often painted by those who were—the mathematicians. Fortunately this scene is slowly changing as biologists learn how to use the mathematical tools and mathematicians become students of biology.
The “Game of Life” was first reported in the Mathematical Games section of Scientific American vol. 223, no. 4, October 1970. Since then it has become a popular game amongst schoolchildren as well as professors of mathematics. The game can be accessed through most computer systems, usually under the code name LIFE. For those who have access to a computer, I heartily recommend that you invest a few hours playing the game to obtain a feel for the rich variety of dynamic behavior that can result from the application of even the simplest rules in a feedback structure. However, beware! People have become addicted to this game and withdrawal may be painful.
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© 1981 Alan A. Berryman
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Berryman, A.A. (1981). A Brief Look at General Systems. In: Population Systems. Population Ecology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7325-2_1
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