The stability-diversity-complexity debate has persisted as a central focus of theoretical ecology for half a century. The debate concerns the deceptively simple question of whether there is a causal relationship between the complexity and/or diversity of biological communities and their stability. Historical analysis of the debate shows that conflicting claims different studies seem to support indicate an underlying lack of conceptual clarity about the three concepts. The problem of defining these concepts is thus at the debate's core, and finding adequate definitions is one objective of the dissertation. The absence of consensus about how ecological stability should be defined, for instance, reflects uncertainty about what properties of a community should be considered its stability, resulting in studies that suggest conflicting conclusions based on different senses of the concept. For this reason, some philosophers have claimed that proposed definitions of ecological stability are incompatible and that the concept is itself problematic. I argue, however, that three unproblematic concepts are jointly sufficient and individually necessary for ecological stability. Another issue concerns whether the mathematical concept of Lyapunov stability utilized in physics adequately defines ecological stability, as many theoretical ecologists assume. I argue that it does not because it cannot adequately represent perturbations against which community stability must be assessed. The project of defining these particular concepts raises a more fundamental issue: what adequacy criteria should definitions in general satisfy? Against the prevailing view that definitions must preserve meaning exactly, I argue there are good reasons to require definitions preserve only similarity of meaning with the defined concept. Following Carnap, I call such definitions 'explicative'. The prevailing view is clearly unproblematic if the definitional goal is simply to clarify the actual meaning of concepts. It is problematic, however, if the objective is to provide normative guidance about concepts. Concepts play an indispensable role in the acquisition of knowledge. As such, definitional modifications of our conceptual apparatus should be evaluated by epistemic advantages or disadvantages they procure. I argue the advantages afforded by an explicative definition --such as enhancing precision, testability, theoretical unification, etc.-- justify forgoing strong similarity with the concept being defined.

This thesis studies how structure and energetics influence complex food web dynamics. In Chapter 1, I approach the question by studying a simple food web model that can be modified to include different structural and energetic features. In Chapter 2, I study stability and food web properties in assembled webs that are structured by body-size restrictions and a generalist-specialist tradeoff. The results of both chapters suggest that structure and energetics must be considered to understand food web dynamics. In Chapter 1, I find that food web structure can be modified by weak and strong energetic flows and stabilize dynamics through asynchrony. In Chapter 2, I find that food web assembly with different assemblages of generalists or specialists leads to structures that have corresponding differences in the stability and properties of food webs. Hence, my thesis reexamines the relationship of complexity and dynamics from a topological and energetic framework.

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Quantitative habitat models of wildlife-habitat relationships are developed to formalize our current understanding about an ecological system. A habitat association model is one of these models that is useful for answering questions about how the habitat is occupied, how much growth habitat is required by the animal, or how the animal selects its food and habitat. Radio telemetry is adopted as a technique for studying home range and habitat use. The major objective of a radio telemetry study is to collect behavioral or demographic data in order to be able to estimate population parameters for home range and habitat selection. A radio telemetry study is a kind of multinomial experiment. The Logistic Regression Model is often used for estimating the relationship between animal activities and the habitat characteristics of the location used (animal preference). However, this model is not a good model for the telemetry data. Under this model, the slope parameter estimate becomes lower and farther from the true value as the Average Habitat Quality (AHQ) increases, with Diversity fixed. The Multinomial Model is better suited to telemetry data. Using the Logistic Regression Model, a habitat association study can be conducted in conjunction with adaptive cluster sampling. In terms of the variance of the regression parameter estimate, adaptive cluster sampling is better than simple random sampling. Adaptive sampling plans are also satisfied for habitat association analysis with imperfect detectability. / Graduation date: 1995

Matrix difference equations have been used to model the discrete time dynamics of a variety of populations whose individual members have been categorized into a finite number of classes based on, for example, age, size, or stage. Examples of such models include Leslie's age-structured model and the Usher model, a size-classified model which has been applied to trees, corals, sea turtles, copepods, and fish. These matrix difference equations can incorporate virtually any type of nonlinearity arising from the density dependence of fertility and survival rates and transition probabilities between classes. Under a fairly general set of assumptions, it can be shown that the normalized class distribution vector equilibrates, and thus an asymptotic or limiting equation for total population size can be derived. In this research we assume the existence of a dynamically modeled resource in limited supply for which the members of the species compete, either exploitatively or through interference. The existence and stability of population size equlibria or cycles is then studied by means of bifurcation theory. Several biological considerations are addressed, including the Size-Efficiency Hypothesis of Brooks and Dodson, the effects of changes in individual physiological parameters on the size and competitive success of a species, and the effects of delays on the viability of a species.

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Calow (1983) realized that differences between parasites and their free-living relatives can be explained by the differences in nutrient richness. I propose a model that is based on Calow's idea which identifies the relative position of different trophic strategies (e.g. predation, grazing, parasitism and others) based on (1) the differences by which consumers arrive at their intrinsic rate of growth, and (2) the ecological impact they inflict on their hosts. I hypothesize that trophic interactions can be clarified if a parameter is included that takes into account the host's/prey's fate in the interaction. Moreover, this model suggests specific trophic evolutionary pathways (TEPs) between each strategy, and suggests that some pathways are more likely than others. In particular, parasitoidism is believed to be a highly derived strategy, and the TEPs presented in the model suggest parasitoidism could have arisen from either a predator-like or a typical-parasitic ancestor. Though the trophic categories determined by the model seem intuitive, this approach does provide, apparently for the first time, an objective, mathematically and ecologically useful basis for classifying animal trophic relationships. / Graduation date: 1998

Multivariate statistical techniques were applied to the development of habitat suitability models for the Mt. Graham red squirrel, an endangered species. A digital map data base and a geographic information system (GIS) were used to support the analysis and provide input for two logistic multiple regression models. Squirrel presence/absence is the dichotomous dependent variable whose probability the models pretend to predict. Independent variables are a set of environmental factors in the first model, and locational variables in the second case, where a logistic trend surface was developed. Bayesian statistics were then used to integrate the models into a combined model. Potential habitat losses resulting from the development of an astronomical observatory were assessed using the environmental model and are found to represent about 3% of currently available habitat.