Population dynamics is the study of how and why populations of animals change in distribution and abundance. Thus, the aims of the science of population dynamics are twofold: to document the empirical patterns of population distribution and change, and to determine the mechanisms underlying those observed patterns. Population dynamics data typically have rich and complex spatio-temporal patterns. Modern and flexible statistical methods are needed to describe these patterns, and for the sound estimation of parameters in realistic mathematical models of spatio-temporal population dynamics. Of particular importance has been the development over the past decade of modern computational statistical methods, such as Markov chain Monte Carlo (McMC), that enable rigorous parameter estimation for more realistic models. The work as reported in this thesis has evolved around three case studies, each involving a long-term data set of estimated abundance's of a species at different locations over time, and a specific set of questions of interest: 1) Linking the spatio-temporal variation in recruitment of the Atlantic puffin (Fractercula arctica) to the spatio-temporal variation in densities of nesting herring gulls (Larus argentatus ) and lesser black-backed gulls (Larus fuscus) within the Isle of May natural nature reserve. 2) The use of flexible statistical tools to investigate coincident changes in the spatial and temporal dynamics of cyclic populations of field voles (Microtus agrestis). 3) Investigating the metapopulation dynamics of water voles (Arvicola terrestris) in the Scottish uplands using stochastic patch occupancy models. In each case study, the central aim was to formulate mathematical models that describe the spatio-temporal dynamics of the animal populations, and to develop and investigate the uses of flexible statistical methods that can be used to inform these models using the data.