Effects of fish density distribution and effort distribution on catchability

The effects of fish density distribution and effort distribution on the overall catchability coefficient are examined. Emphasis is also on how aggregation and effort distribution interact to affect overall catch rate [catch per unit effort (cpue)]. In particular, it is proposed to evaluate three indices, the catchability index, the knowledge parameter, and the aggregation index, to describe the effectiveness of targeting and the effects on overall catchability in the stock area. Analytical expressions are provided so that these indices can easily be calculated. The average of the cpue calculated from small units where fishing is random is a better index for measuring the stock abundance. The overall cpue, the ratio of lumped catch and effort, together with the average cpue, can be used to assess the effectiveness of targeting. The proposed methods are applied to the commercial catch and effort data from the Australian northern prawn fishery. The indices are obtained assuming a power law for the effort distribution as an approximation of targeting during the fishing operation. Targeting increased catchability in some areas by 10%, which may have important implications on management advice.

Decision-theoretic designs for dose-finding clinical trials with multiple outcomes

A decision-theoretic framework is proposed for designing sequential dose-finding trials with multiple outcomes. The optimal strategy is solvable theoretically via backward induction. However, for dose-finding studies involving k doses, the computational complexity is the same as the bandit problem with k-dependent arms, which is computationally prohibitive. We therefore provide two computationally compromised strategies, which is of practical interest as the computational complexity is greatly reduced: one is closely related to the continual reassessment method (CRM), and the other improves CRM and approximates to the optimal strategy better. In particular, we present the framework for phase I/II trials with multiple outcomes. Applications to a pediatric HIV trial and a cancer chemotherapy trial are given to illustrate the proposed approach. Simulation results for the two trials show that the computationally compromised strategy can perform well and appear to be ethical for allocating patients. The proposed framework can provide better approximation to the optimal strategy if more extensive computing is available.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.