Landscape and forest structure at moose mortality sites on Isle Royale National Park. A LiDAR based assessment

Landscape structure and heterogeneity play a potentially important, but little understood role in predator-prey interactions and behaviourally-mediated habitat selection. For example, habitat complexity may either reduce or enhance the efficiency of a predator's efforts to search, track, capture, kill and consume prey. For prey, structural heterogeneity may affect predator detection, avoidance and defense, escape tactics, and the ability to exploit refuges. This study, investigates whether and how vegetation and topographic structure influence the spatial patterns and distribution of moose (Alces alces) mortality due to predation and malnutrition at the local and landscape levels on Isle Royale National Park. 230 locations where wolves (Canis lupus) killed moose during the winters between 2002 and 2010, and 182 moose starvation death sites for the period 1996-2010, were selected from the extensive Isle Royale Wolf-Moose Project carcass database. A variety of LiDAR-derived metrics were generated and used in an algorithm model (Random Forest) to identify, characterize, and classify three-dimensional variables significant to each of the mortality classes. Furthermore, spatial models to predict and assess the likelihood at the landscape scale of moose mortality were developed. This research found that the patterns of moose mortality by predation and malnutrition across the landscape are non-random, have a high degree of spatial variability, and that both mechanisms operate in contexts of comparable physiographic and vegetation structure. Wolf winter hunting locations on Isle Royale are more likely to be a result of its prey habitat selection, although they seem to prioritize the overall areas with higher moose density in the winter. Furthermore, the findings suggest that the distribution of moose mortality by predation is habitat-specific to moose, and not to wolves. In addition, moose sex, age, and health condition also affect mortality site selection, as revealed by subtle differences between sites in vegetation heights, vegetation density, and topography. Vegetation density in particular appears to differentiate mortality locations for distinct classes of moose. The results also emphasize the significance of fine-scale landscape and habitat features when addressing predator-prey interactions. These finer scale findings would be easily missed if analyses were limited to the broader landscape scale alone.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.