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: The focus of this dissertation was the estimation of theoretical reference levels such as K, the environmental carrying capacity, and MNPL, the maximum net productivity level, for three fishes off Southern California and for the northern fur seal (Callorhinus ursinus) population of St. Paul Island, Alaska. The estimation techniques were based on computer modeling of historical population trends. The assessment of these theoretical reference levels for nature populations is fundamentally important to the development and testing of concepts in theoretical ecology and population dynamics. In the first study, maximum-likelihood estimates of pre-exploitation biomass were made for the white seabass (Atractoscion nobilis) and the yellowtail (Seriola lalandei) by assuming that development of corresponding commercial fisheries led to a shift in size distributions of these fishes, as indicated by records of the Avalon Tuna Club, Santa Catalina Island, California. Pre-exploitation biomass for Southern California populations of both these fishes was estimated to be about 20,000 tons. The pre-exploitation biomass of the giant sea bass (Stereolepis gigas) was estimated to be 1300 tons. Due to insufficient natural history information, this estimate was based on commercial catch records only. In the second study, estimates of theoretical reference levels for the northern fur seal population of St. Paul Island were based on computer simulations of pup production from 1912 to 1970, repetitive simulations were used to construct frequency distributions of estimates for MNPL, K, the number of pups born at MNPL and K, and the ratio MNPL/K. These distributions serve as a measure of the confidence that can be placed in single estimates of reference levels, and thereby provide a general context within which these reference levels can be evaluated. The final study of this dissertation investigated the pelagic migration of northern fur seal pups. Results indicated that initial migration paths for these pups are more widely dispersed than previously assumed. This information contributes to the understanding of northern fur seal life histories. A fuller understanding of life history information will eventually facilitate more accurate modeling of northern fur seal population dynamics. (DBO)