Parameterizing probabilities for estimating age-composition distributions for mixture models

When estimating parameters that constitute a discrete probability distribution {pj}, it is difficult to determine how constraints should be made to guarantee that the estimated parameters { pˆj} constitute a probability distribution (i.e., pˆj>0, Σ pˆj =1). For age distributions estimated from mixtures of length-at-age distributions, the EM (expectationmaximization) algorithm (Hasselblad, 1966; Hoenig and Heisey, 1987; Kimura and Chikuni, 1987), restricted least squares (Clark, 1981), and weak quasisolutions (Troynikov, 2004) have all been used. Each of these methods appears to guarantee that the estimated distribution will be a true probability distribution with all categories greater than or equal to zero and with individual probabilities that sum to one. In addition, all these methods appear to provide a theoretical basis for solutions that will be either maximum-likelihood estimates or at least convergent to a probability distribut

Distribution and potential bioeffects of atrazine in coastal waters

Estuaries provide critical nursery habitat for many commercially and recreationally important fish and shellfish species. These productive, diverse ecosystems are particularly vulnerable to pollution because they serve as repositories for non–point-source contaminants from upland sources, such as pesticide runoff. Atrazine, among the most widely used pesticides in the United States, has also been one of the most extensively studied. There has not, however, been a specific assessment of atrazine in marine and estuarine ecosystems. This document characterizes the presence and transformation of atrazine in coastal waters, and the effects of atrazine on marine organisms. Review of marine and estuarine monitoring data indicate that atrazine is chronically present in U.S. coastal waters at relatively low concentrations. The concentrations detected have typically been below acute biological effects levels, and below the U.S. EPA proposed water quality criteria for atrazine. While direct risk of atrazine impacts are low, uncertainty remains regarding the effects of long-term low levels of atrazine in mixture with other contaminants. It is recommended that best management practices, such as the use of vegetative buffers and public education about pesticide use, be encouraged in the coastal zone to minimize runoff of atrazine into marine and estuarine waters.

An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.