Early Life History and a Modeling Framework for Lobster (Homarus Americanus) Populations in the Gulf of Maine

Beginning in the late 1980s, lobster (Homarus americanus) landings for the state of Maine and the Bay of Fundy increased to levels more than three times their previous 20-year means. Reduced predation may have permitted the expansion of lobsters into previously inhospitable territory, but we argue that in this region the spatial patterns of recruitment and the abundance of lobsters are substantially driven by events governing the earliest life history stages, including the abundance and distribution of planktonic stages and their initial settlement as Young-of-Year (YOY) lobsters. Settlement densities appear to be strongly driven by abundance of the pelagic postlarvae. Postlarvae and YOY show large-scale spatial patterns commensurate with coastal circulation, but also multi-year trends in abundance and abrupt shifts in abundance and spatial patterns that signal strong environmental forcing. The extent of the coastal shelf that defines the initial settlement grounds for lobsters is important to future population modeling. We address one part of this definition by examining patterns of settlement with depth, and discuss a modeling framework for the full life history of lobsters in the Gulf of Maine.

Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.