Bayesian Estimation of the Distribution Function of the Poisson Model

This paper presents the Bayes estimators of the Poisson distribution function based on complete and truncated data under a natural conjugate prior. Laplace transform of the incomplete gamma function and the Gauss hypergeometric function have been employed in order to overcome the intractability of the integrals. Numerical examples from biosciences are given to illustrate the results. A Monte Carlo study has been carried out to compare Bayes estimators under complete data with the corresponding maximum liklihood estimators.     

Fisher information matrix of the Dirichlet-multinomial distribution

In this paper we derive explicit expressions for the elements of the exact Fisher information matrix of the Dirichlet-multinomial distribution. We show that exact calculation is based on the beta-binomial probability function rather than that of the Dirichlet-multinomial and this makes the exact calculation quite easy. The exact results are expected to be useful for the calculation of standard errors of the maximum likelihood estimates of the beta-binomial parameters and those of the Dirichlet-multinomial parameters for data that arise in practice in toxicology and other similar fields. Standard errors of the maximum likelihood estimates of the beta-binomial parameters and those of the Dirichlet-multinomial parameters, based on the exact and the asymptotic Fisher information matrix based on the Dirichlet distribution, are obtained for a set of data from Haseman and Soares (1976), a dataset from Mosimann (1962) and a more recent dataset from Chen, Kodell, Howe and Gaylor (1991). There is substantial difference between the standard errors of the estimates based on the exact Fisher information matrix and those based on the asymptotic Fisher information matrix.     

Moving south: effects of water temperatures on the larval development of invasive cane toads (Rhinella marina) in cool‐temperate Australia

The distributional limits of many ectothermic species are set by thermal tolerances of early‐developmental stages in the life history; embryos and larvae often are less able to buffer environmental variation than are conspecific adults. In pond‐breeding amphibians, for example, cold water may constrain viability of eggs and larvae, even if adults can find suitable thermal conditions in terrestrial niches. Invasive species provide robust model systems for exploring these questions, because we can quantify thermal challenges at the expanding range edge (from field surveys) and larval responses to thermal conditions (in the laboratory). Our studies on invasive cane toads (Rhinella marina) at the southern (cool‐climate) edge of their expanding range in Australia show that available ponds often average around 20°C during the breeding period, 10°C lower than in many areas of the toads’ native range, or in the Australian tropics. Our laboratory experiments showed that cane toad eggs and larvae cannot develop successfully at 16°C, but hatching success and larval survival rates were higher at 20°C than in warmer conditions. Lower temperatures slowed growth rates, increasing the duration of tadpole life, but also increased metamorph body mass. Water temperature also influenced metamorph body shape (high temperatures reduced relative limb length, head width, and body mass) and locomotor performance (increased speed from intermediate temperatures, longer hops from high temperatures). In combination with previous studies, our data suggest that lower water temperatures may enhance rather than reduce recruitment of cane toads, at least in areas where pond temperatures reach or exceed 20°C. That condition is fulfilled over a wide area of southern Australia, suggesting that the continuing expansion of this invasive species is unlikely to be curtailed by the impacts of relatively low water temperatures on the viability of early life‐history stages.     

Far from home: responses of an American predator species to an American prey species in a jointly invaded area of Australia

Far from their native ranges in the Americas, two invasive species come into contact in Australian waterbodies. Cane toads (Rhinella marina) fatally poison many anurophagous predators, whereas eastern mosquito fish (Gambusia holbrooki) voraciously consume anuran larvae. As cane toads spread south along Australia’s east coast, they are colonizing areas where mosquito fish are abundant. What happens when these two American invaders encounter each other in Australia? We tested the responses to toad tadpoles of mosquito fish from populations that were sympatric versus allopatric with cane toads. Toad-sympatric fish generally ignored toad tadpoles. Toad-allopatric fish initially consumed a few tadpoles, but rapidly developed an aversion to these toxic prey items. The laboratory-reared progeny of toad-allopatric fishes were more likely to approach toad tadpoles than were the offspring of toad-sympatric fishes, but the two groups learned toad-avoidance at similar rates. Thus, mosquito fish show an innate aversion to cane toad tadpoles (perhaps reflecting coevolution with North American bufonid taxa), as well as an ability to rapidly learn taste-aversion. Our comparisons among populations suggest that several decades of toad-free existence in Australia caused a decline in the fishes’ innate (heritable) aversion to toads, but did not affect the fishes’ capacity to learn toad-avoidance after an initial exposure. Any impact of mosquito fish on cane toads thus is likely to be transitory. The rapid (<100-year) time frame of these shifts (the initial weakening of the fishes’ response during toad-allopatry, and its recovery after secondary contact) emphasizes the dynamic nature of faunal responses during biological invasions, and the interplay between adaptation and phenotypic plasticity.     

Dietary Diversity and Food Selection in Hanuman Langurs (Semnopithecus entellus) and Purple-Faced Langurs (Trachypithecus vetulus) in the Kaludiyapokuna Forest Reserve in the Dry Zone of Sri Lanka

Understanding how ecological differences between sympatric species lead to coexistence is a fundamental question in primatology. Evidence for intraspecific dietary variation in colobines suggests that findings from a single study site may not be generalizable to other sites. Previous comparative studies of Semnopithecus entellus and Trachypithecus vetulus showed that S. entellus used seasonal plant parts more frequently than did T. vetulus. We examined whether these different food selection strategies can be generalized to explain the species' coexistence at a novel study locality. We collected dietary data for two groups of Semnopithecus entellus and one group of Trachypithecus vetulus between July 2008 and June 2009. We examined the monthly percentage of time devoted to feeding on specific dietary items in relation to their availability, compared the dietary niche breadth of the two species, and quantified the distribution and abundance of resources to examine the potential for intragroup and interspecific competition. Seasonal plant parts accounted for >90?% of the diets of both species and there were no significant differences in monthly dietary breadth or in the monthly proportions of time allocated to feeding on fruits, immature leaves, or mature leaves between the two species. Both species fed on fruits and flowers according to their availability, and most plants preferred by both primate species were relatively rare and clumped in distribution. Such resource distributions are suggested to promote both intragroup and interspecific competition. The food selection strategies of these two primate species are more similar at our study site than at previous study sites, and suggest that these species employ different strategies to facilitate coexistence at different sites.