In all fields of science today, data are collected and theories are developed and published faster than scientists can keep up with, let alone thoroughly digest. In ecology the fact that practitioners tend to be divided between such subdisciplines as aquatic and terrestrial ecology, as well as between popula tion, community, and ecosystem ecology, makes it even harder for them to keep up with all relevant research. Ecologists specializing in one sub discipline are not always aware of progress in another subdiscipline that relates to their own. Syntheses are frequently needed that pull together large bodies of information and organize them in ways that makes them more coherent, and thus more understandable. I have tried to perform this task of integration for the subject area that encompasses the interrelationships between the dynamics of ecological food webs and the cycling of nutrients. I believe this area cuts across many of the subdisciplines of ecology and is pivotal to our progress in understanding ecosystems and in dealing with human impacts on the environment. Many current ecological problems involve human disturbances of both food webs and the nutrients that cycle through them. Little progress can be made towards elucidating the complex feedback relations inherent in the study of nutrient cycles in ecological systems without the tools of mathematics and computer modelling. These tools are therefore liberally used throughout the book.
Cybernetics, a science concerned with understanding how systems are regulated, has reflected the preoccupations of the century in which it was born. Regulation is important in twentieth century society, where both machines and social organizations are complex. Cybernetics focused on and became primarily associated with the homeostasis or stability of system behavior and with the negative feedbacks that stabilize systems. It paid less attention to the processes opposite to negative feedback, the positive feedback processes that act to change systems. We attempt to redress the balance here by illustrating the enormous importance of positive feedbacks in natural systems. In an article in the American Scientist in 1963, Maruyama called for increased attention to this topic, noting that processes of change could occur when a "deviation in anyone component of the system caused deviations in other components that acted back on the first component to reinforce of amplify the initial deviation." The deviation amplification is the result of positive feedback among system components. Maruyama demonstrated by numerous examples that the neglect of such processes was unjustified and suggested that a new branch of cybernetics, "the second cybernetics," be devoted to their study.
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
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