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Inhaltsverzeichnis

Frontmatter

Introduction

Frontmatter

Ecology: An Idiosyncratic Overview

Abstract
The word “ecology” conjures up disparate images. It is part of the rhetoric of political parties, cries for salvation of dwindling species, attempts to increase utilization of renewable resources, determined efforts of scientists to understand our natural world, and blatant commercialization of products from laundry detergents to oil rigs. Aside from its use as an adjective to modify virtually every scientific research field, the jargon “ecologically sound” is used to justify a plethora of so-called development schemes. In daily usage, ecology is regularly confused with environmentalism, and to those in the business community an ecologist may well be considered automatically an obstructionist. Despite all this lack of agreement about definitions, ecology has had a major impact during the past two decades on changing the attitudes of humanity towards our world. Photographs of our glowingly beautiful orb as viewed from the moon notwithstanding, our conscious acceptance of the finiteness and interdependence of processes on this planet is only slowly developing.
Louis J. Gross

Physiological and Behavioral Ecology

Frontmatter

Biophysical Ecology: An Introduction to Organism Response to Environment

Abstract
The direct effects of environmental factors on the physiology and behavior of individuals comprise the building blocks upon which ecology is based. In the reductionist view (Gates, 1980), all ecological interactions may be carried down to the level of the cell and individual through careful analysis of physical and chemical processes. This approach, involving the detailed analysis of the underlying processes in a natural system, is in practice limited by the complexity of biological systems. Interactions may be viewed at levels from the molecular, through tissue, organ, and individual, and beyond to population, community and ecosystem. The viewpoint of biophysical ecology is that general ecological perspectives may be obtained by considering the effects of environments on individuals and that knowledge of processes at this level is critical to understanding the structure of populations and communities. The known results from scientific fields as varied as chemical kinetics, fluid flow, thermodynamics, atmospheric physics, and soil mechanics are applied to structure a cohesive framework for analysing organism response to environmental factors. A great advantage of this framework is that it applies independent of the type of organism, animal or plant, terrestrial, aquatic or arboreal. The same physical principles underly all of nature. In practice, of course, this advantage is ameliorated by the great range of environments which organisms inhabit, each providing its own unique challenges for organism survival.
Louis J. Gross

An Overview of Foraging Theory

Abstract
One of the most active areas of ecological research concerns predation and herbivory. Of interest is how an individual allocates its time and energy in search of food. Animal nutritional requirements vary greatly, not only in quantity, but also in quality, and it is not my aim here to review the variety of feeding mechanisms employed, nor the physiology of alimentary systems and digestion. See Church (1975) and Davenport (1978) for a review of these. Rather, the question of ecological interest is: given certain physiological needs and constraints on feeding, what complex of behavioral traits are employed to meet these needs? My discussion will concern only animals, but analogous questions for plants were mentioned in the chapter on biophysical ecology concerning leaf sizes which maximize photosynthetic gains. Without the behavioral repertoire available to animals, plants respond to the problem of “foraging” for light, water, and nutrients through phenotypically plastic growth forms (Bradshaw, 1965).
Louis J. Gross

Population Ecology

Frontmatter

Population Dynamics in a Homogeneous Environment

Abstract
Ecology, freely translated from the Greek expression, means “the study of the household of nature.” A population is a collection of organisms, usually of the same species, that occupy a prescribed region and function together as an ecological entity. While most populations consist of a single species, the definition of a population is intended to be sufficiently broad to include assemblages of species such as those that can interbreed to produce viable hybrids. Another example might be lichen populations where the algae and fungi are so closely associated that they function as a single species. Population ecology, in the sense meant here, refers to the structure and function of a collection of organisms as an autecological unit and, as such, addresses the more purely biological aspects of ecology.
Thomas G. Hallam

The Formulation of Age-Structure Models

Abstract
Not very long ago, two rash authors wrote that “although age-structure effects frequently influence the quantitative aspects of population dynamics, they are rather seldom responsible for qualitative changes in dynamic behaviour”. Although defensible in the context in which it was written, this assertion admits many exceptions — these are the subject of the present lectures.
R. M. Nisbet, W. S. C. Gurney

Analysis of Age-Structure Models

Abstract
Begin by developing a mathematical model for the growth of a population. Assume that the population is closed to migration, and that only the females are counted. Males are present for reproductive purposes, but are not specifically taken into consideration. In the case of human and other higher species, this makes sense for two reasons. Females know unequivocally who their offspring are; and (more importantly for the purposes of this model) females have a biologically well-defined beginning and end to their reproductive careers.
James C. Frauenthal

Random Walk Models of Movement and Their Implications

Abstract
Biologists long have sought quantitative models to describe the process of dispersal: to aid understanding, to guide experimentation, and to facilitate prediction. The most common such models are of the random walk type, deriving from the assumption that individuals move in a series of discrete steps with probabilities totally determined by positional information. Learning is ignored.
Simon A. Levin

Stochastic Population Theory: Birth and Death Processes

Abstract
Birth and death processes were introduced by Feller (1939) and have since been used as models for population growth, queue formation, in epidemiology and in many other areas of both theoretical and applied interest. From the standpoint of the theory of stochastic processes they represent an important special case of Markov processes with countable state spaces and continuous parameters.
Luigi M. Ricciardi

Stochastic Population Theory: Diffusion Processes

Abstract
In the previous contribution we discussed birth and death processes as models of populations subject to random growth. There, the population size at each instant was represented as a discrete random variable labeled by the considered instant. Since the probabilistic description was characterized by a straightforward integration, we purposely avoided spending time on definitions and mathematical preliminaries. However, it is sometimes convenient to model population growth by continuous differential equations and by their stochastic counterparts. This implies that the population size at each instant can be any nonnegative real number or else a continuous space-continuous time stochastic process. It is to be stressed that this is evidently an approximation which, however, may prove useful in making inferences about global properties of the population dynamics such as stability, extinction, etc.
Luigi M. Ricciardi

Communities and Ecosystems

Frontmatter

Community Dynamics in a Homogeneous Environment

Abstract
Populations do not exist as isolated entities in a physical environment. They interact with other biological populations on a regular long term basis and, because of these interactions, often coevolve as an ecological unit. An assemblage of two of more biotic populations is called a community. The simplest structure, one composed of two species, and the possible interactions between these two components will be discussed first. These would not be considered communities in the classical ecological literature, but I will be consistent in using this term whenever species interactions are involved.
Thomas G. Hallam

Interacting Age Structured Populations

Abstract
Both the study of interacting species without age structure and single species with age structure have had a long history in theoretical ecology, beginning with studies in the “golden age” of ecology (Scudo and Ziegler, 1978) by Lotka and Volterra. Only much more recently have there been studies on the dynamics of interacting, age structured models. Such models can quickly get extraordinarily complex, so in this review I will concentrate on the simplest models.
Alan Hastings

Population Models and Community Structure in Heterogeneous Environments

Abstract
Until recently, the bulk of the extensive mathematical literature in ecology ignored the role of spatial heterogeneity. There were exceptions, for example the classic work of Skellam (1951); but despite much earlier developments in the related areas of epidemics (Brownlee, 1911) and genetics (Fisher, 1937; Haldane, 1948), it has only been in the last few years that theoretical studies in ecology have begun to take account of the fundamental importance of geographic distribution. Recent reviews of the subject may be found in Levin (1976a, b).
Simon A. Levin

Stochastic Community Theory: A Partially Guided Tour

Abstract
This chapter is intended as an introduction to the biological questions, mathematical analyses, and biological conclusions of stochastic models for multispecies assemblages. Because of the large number of topics and models, little attention is devoted to detailed analysis of particular models. Instead, I attempt a survey of the key ideas and provide references for further study. The presentation is organized according to the mechanism(s) creating the probabilistic effects. Three classes are considered:
1.
Demographic stochasticity (or “within-individual variability”, Chesson, 1978) - Whether or not God plays dice, individuals who are apparently identical have different life lengths and produce different numbers of offspring. Integer-valued stochastic models are typically used to investigate the consequences of this variation.
 
2.
Environmental stochasticity - Environments vary unpredictably through time in ways that affect all individuals equally. Most analyses of the consequences begin by introducing random variation into the parameters of a standard deterministic model. This produces stochastic difference and differential equations with continuous ranges.
 
3.
Combined demographic and environmental stochasticity - In general, both sorts of variation are always present. However, there are relatively few attempts to analyze their joint consequences.
 
Michael Turelli

A Theoretical Basis for Modeling Element Cycling

Abstract
Elements that comprise the major portion of biomass (C, H, O, N, P, and S) exist in many different forms. Molecules of these forms are transient, appearing when converted from one form and disappearing when converted into another. Many of the transformations involve changes in oxidation-reduction (redox) state. For the most part these transformations proceed very slowly by abiotic chemical reactions. Organisms, however, possess enzyme systems that both catalyze the reactions and couple them to cellular biochemistry, producing energy for chemical and mechanical work (synthesis and movement). Element cycle transformation rates depend upon the concentration of organisms as well as upon concentrations of reactants, but generally, biotically-catalyzed rates are orders of magnitude faster than corresponding abiotic chemical reaction rates.
Ray R. Lassiter

Applied Mathematical Ecology

Frontmatter

Bioeconomics and the Management of Renewable Resources

Abstract
Within the past decade many economists have become interested in natural resource models which simultaneously consider economic flows (such as cost and revenue) and population dynamics. Resource management is often cast as a problem in dynamic optimization where the management objective may be to maximize the present value of net benefits subject to the stock adjustments which result from growth, natural mortality, and man’s harvesting activities. When the resource in question is a plant or animal, capable of regeneration, these resource models are called bioeconomic models.
Jon M. Conrad

Population Biology of Microparasitic Infections

Abstract
Much, though not all, of the material in my chapter has already been published in journals that are likely to be as accessible as this book. There is a constant temptation to repeat oneself in print; with the aim of avoiding this temptation, I have kept most of my presentation to the bare bones, adding flesh in those places where the work is not already published or where new avenues of investigation seem to me to be ready for study. The emphasis here is on the mathematical development of the subject; various kind of applications are discussed in the light of available data elsewhere (and references are given to these works, without repeating the presentation here).
Robert M. May

Backmatter

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