Statistical Methods for the Joint Analysis of Spatial, Sparse or Missing Ecological Data

To mitigate biodiversity loss, we need to understand the environmental and demographic causes of changes in the distributions and abundances of species. Bird populations are in a continual state of flux; these fluctuations can be explained by changes in vital rates, such as survival and productivity (breeding success). This thesis is the result of three different ecological projects for which we have developed statistical methods that combine different types of data together. In particular, in this thesis we describe, implement, and develop statistical models that can be applied to different types of ecological data such as census, ring-recovery, and capture-recapture data. In the first project we use data from the British Trust for Ornithology (BTO), which has developed an extensive historical data set of the total number of birds ringed in Britain and Ireland, dating back to 1909. However, until 2000 the data were submitted by ringers in paper form. The way in which such archival data were collected and stored means that the total number of birds ringed in different age categories is difficult to obtain. Bird survival changes with age, with younger birds being more vulnerable. Missing information on the age at ringing compromises our ability to understand historic variation in survival rates. We examine suitable methods and propose a new model for enhancing the use of such data. Using blackbird (Turdus merula) and sandwich tern (Thalasseus sandvicensis) data we show the rigour of our model in estimating unknown age proportions for different species, allowing the BTO and other European institutions to fully utilise their historical data. Bi-parental care is crucial in the reproduction success of the little auk (Alle alle) which we study in the second project. For this species, typically, the female deserts the brood before the male does. Hypotheses which considered that females left the nest earlier in order to increase their remating success or to secure their good body conditions have been rejected. As a result, a biological explanation for this unusual trait has not been found yet. We investigate whether the length of time that females stay in the nest in a given breeding season may have an impact on their survival probability in the period following breeding. We combine capture-recapture data from two sites and use sparse continuous covariates data to study if the survival of the female little auk is affected by the time spent in the brood guarding the chicks. Animals are affected by local environmental conditions that vary with space. In the third project, we incorporate detailed local spatial information, such as geographical coordinates and land cover type data, into an spatially-explicit integrated population model. This involves supplementing census data with ring-recovery data to study demographic rates, while also incorporating detailed local spatial information into integrated population models. Bird count data are typically modelled at large scales using state-space models. In classical analysis, the time-series likelihood component has traditionally been approximated using a Kalman filter methodology, which is computationally efficient but relies on the assumption of the suitability of Gaussian approximations.

Rather than one single nation-wide time-series of counts, spatial census data consist of multiple time-series associated to specific locations. These data are particularly challenging

to model because of the presence of very small counts at some locations, which violates the Gaussian assumption of the Kalman filter. To address this issue, we consider hidden Markov

models, which are ideally suited to the analysis of very small counts, as their validity does not rely on Gaussian approximations. Both methodologies, the Kalman filter and hidden

Markov models, are combined in a flexible algorithm which adapts to the varying sample sizes at different locations-it is therefore able to accommodate data sets of different sizes

for many bird species. We illustrate our methods using starling (Sturnus vulgaris) data.