We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation.
Long-term monitoring of endangered species abundance based on acoustic recordings has not yet been pursued. This paper reports the first attempt to use multi-year passive acoustic data to study the impact of the Deepwater Horizon oil spill on the population of endangered sperm whales. Prior to the spill the Littoral Acoustic Demonstration Center (LADC) collected acoustic recordings near the spill site in 2007. These baseline data now provide a unique opportunity to better understand how the oil spill affected marine mammals in the Gulf of Mexico. In September 2010, LADC redeployed recording buoys at previously used locations 9, 25, and 50 miles away from the incident site. A statistical methodology that provides point and interval estimates of the abundance of the sperm whale population at the two nearest sites is presented. A comparison of the 2007 and the 2010 recordings shows a decrease in acoustic activity and abundance of sperm whales at the 9-mile site by a factor of 2, whereas acoustic activity and abundance at the 25-mile site has clearly increased. This indicates that some sperm whales may have relocated farther away from the spill. Follow-up experiments will be important for understanding long-term impact.
When nonrandom segregation of marker haplotypes from parents to offspring is detected, leading to an increased parental haplotype sharing by affected offspring, an association between the disease and the marker loci is often inferred. In this paper, we provide the uniformly most powerful test for testing nonrandom segregation, and compare the power of this test with another test that is available in the literature. Other statistical properties of the two tests are also discussed. Further, since nonrandom segregation can result from linkage of the disease and marker loci, when the hypothesis of random segregation is rejected, it is of interest to estimate the underlying parameter assuming linkage. We provide an estimation procedure.
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