Patch selection behaviour in the presence of environmental constraints

Habitat selection behaviour is the primary way in which organisms are able to regulate encounters with their biotic and abiotic environment. An individual chooses an area that best meets their current needs, particularly regarding safety and the presence of high-quality food. Several physical aspects of the environment can make it difficult for individuals to assess the relative habitat quality of the areas available, thus leading to suboptimal habitat selection. In this thesis, I investigated the way in which two aquatic habitat constraints - obstacles to movement between patches and turbidity - affected the ability of fish to make optimal patch choices, using threespine stickleback Gasterosteus aculeatus as a model species. Laboratory experiments showed that when movement between patches was hindered by increasingly challenging obstacles, groups of stickleback did not move as freely between the patches, and thus had greater deviations from the predictions of the Ideal Free Distribution (IFD). I also demonstrated that, unlike other species, stickleback do not use turbid environments to avoid predator detection. A trend was seen towards avoidance of a turbid food patch regardless of risk level, although this was not statistically significant. As expected, the stickleback avoided feeding in the presence of a predator regardless of water clarity. Overall, I found that both turbidity and movement constraints can have significant impacts on patch use and distribution in the threespine stickleback. Both turbidity and ease of transit will impact the distribution of ecologically important species like the threespine stickleback, and therefore should be taken into account when studying habitat selection in the wild.

Empirical likelihood based longitudinal studies

In longitudinal data analysis, our primary interest is in the regression parameters for the marginal expectations of the longitudinal responses; the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly for correlated discrete outcome data. Marginal modeling approaches such as generalized estimating equations (GEEs) have received much attention in the context of longitudinal regression. These methods are based on the estimates of the first two moments of the data and the working correlation structure. The confidence regions and hypothesis tests are based on the asymptotic normality. The methods are sensitive to misspecification of the variance function and the working correlation structure. Because of such misspecifications, the estimates can be inefficient and inconsistent, and inference may give incorrect results. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its characteristics and asymptotic properties. We also provide an algorithm based on EL principles for the estimation of the regression parameters and the construction of a confidence region for the parameter of interest. We extend our approach to variable selection for highdimensional longitudinal data with many covariates. In this situation it is necessary to identify a submodel that adequately represents the data. Including redundant variables may impact the model’s accuracy and efficiency for inference. We propose a penalized empirical likelihood (PEL) variable selection based on GEEs; the variable selection and the estimation of the coefficients are carried out simultaneously. We discuss its characteristics and asymptotic properties, and present an algorithm for optimizing PEL. Simulation studies show that when the model assumptions are correct, our method performs as well as existing methods, and when the model is misspecified, it has clear advantages. We have applied the method to two case examples.