Zusammenfassung: For several decades, aquatic ecologists have debated differing viewpoints on the factors that control ecosystem productivity. Much of the controversy centers on the interpretation of empirical relationships between factors that limit the amount of energy transferred among trophic levels in aquatic ecosystems. The primary statistical tool used has been regression analysis, but such models often fail to explain a substantial portion of the variability observed. The suggestion has been made in the literature of aquatic ecology that regression models may be inappropriate, and that limiting factors may be better related to the maximum rather than mean response. Statistical models that account for the large variability in relationships between limiting factors and response variables at higher trophic levels and shift the focus from description of expected values to description of upper boundaries have not been developed. The goal of this project was to develop statistical models for the relationships between limiting factors and the maximum output of biological processes. A number of models may be formulated, one of the primary being Y sub(i) – gamma x sub(i)U sub(i) + sigma epsilon sub(i), where gamma > 0, U sub(i) similar to iid Beta ( alpha , beta ), the x's are considered fixed values on the real line, and the error terms, epsilon sub(i), are centered iid random variables. This model describes a triangular array of points lying between zero and a straight line with positive slope, a data pattern seen numerous times in the ecological literature. The response variable Y is an identifiable mixture of the random variable U, with the model representing a situation in which Y is observed but U is unobserved. Maximum likelihood estimates for the parameters ( alpha , beta , gamma , sigma ) may be computed using the EM algorithm. Estimation is based on maximization of the expected full-data likelihood where the expectation is taken with respect to the conditional density of U given Y. A portion of the dissertation is devoted to the confirmation of asymptotic properties as the response variable, Y sub(i)'s, are not identically distributed. A set of conditions depending on the identically distributed error terms is given for consistency and asymptotic normality of MLE's. The model specific conditions are met by a number of error densities. (DBO)

Zusammenfassung: Increasing numbers of students now study natural resource and environmental economics at undergraduate level, and this interest in the subject has been matched by a corresponding expansion in the number of textbooks and other learning material available for use. Unfortunately one very important aspect of natural resource economics which is often not adequately dealt with in the undergraduate literature concerns the question of dynamics: how rapidly will a resource become exploited, and what time path will it follow? These issues are particularly relevant to the management of renewable resources such as fish stocks whose survival depends on factors such as the rate of entry and exit by the exploiting firms, and the ability of the resource to recover from the effects of intense harvesting. The fault of most textbooks stems not from a failure to cover the question of dynamics, but rather that the treatment is often too advanced or mathematical for the majority of students. Computers can make a useful contribution to our understanding of the dynamics of natural resource exploitation, and in this example the case of marine commercial fishery exploited under 'open-access' conditions is considered. The quantitative assessment of environmental contaminants is a complex process. It involves nonlinear models and the characterization of variables, factors, and parameters that are distributed and dependent each other. Assessments based on point estimates are easy to perform, but since they are unreliable, Monte Carlo simulations have become a standard procedure. Simulations pose two challenges: They require the numerical characterization of parameter distributions and they do not account for dependencies between parameters. This paper offers strategies for dealing with both challenges. The first part discusses the characterization of data with the S-distribution. This distribution offers several advantages, which include simplicity of numerical analysis, flexibility in shape, and easy computation of quantiles. The second part outlines how the S-distribution can be used for hierarchical Monte Carlo simulations. In these simulations the selection of parameter values occurs sequentially, and each choice depends on the parameter values selected before. The method is illustrated with preliminary simulation analyses that are concerned with mercury contamination in king mackerel (Scomberomorus cavalla). It is demonstrated that the results of such hierarchical simulations are generally different from those of traditional Monte Carlo simulations.