Zusammenfassung: Age-classes in crayfish populations can be determined from size-frequency data provided 4 tents are adhered to only crayfish collected from areas of rock substrate are used; trapping are excluded; species do not have longevities exceeding about 4 yr; and most importantly, sample sizes are greater than about 200. Studies that have failed to follow these guidelines have met with limited success in dissecting mixed frequency distributions. Further, 3 validation procedures must be undertaken: temporal replication within molting events to measure the precision of both data collection and size-frequency analysis; corroboration with known-age crayfish from either field recaptures or laboratory molt increments; and concordance with independent analysis of the mean size at onset of sexual maturity. When these checks support the size-frequency results, population age composition and analyses of rates of growth or mortality can be considered reliable.

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)