Mathematical modelling of dispersal and evolution of life-history traits in biological populations

Abstract

This thesis explores the role of intraspecific variation in a population and how this can affect the overall population dynamics. In particular, we have focused on population dispersal, the evolution of life-history traits and the interface between these two aspects. Through the use of mathematical modelling, we show how intraspecific variation is important to consider for an accurate description of the qualitative and quantitative dynamics of a population. Although intraspecific variation and interaction are widely accepted as being important components affecting the growth of a population, it is only recently that there has been an emphasis on individual heterogeneities affecting dispersal, in most part due to the increasing threat of biological invasions, spread of vector-borne diseases, extinction of heavily harvested populations and the fragmentation of habitats due to climate change. Moreover, although the ecological literature on life-history characteristics, their associated tradeoffs and their evolutionary consequences has a long history, the evolutionary consequences resulting from the interplay of life-history trade-offs are not so clear. The reverse is also true, for an observed qualitative behaviour, it is usually not clear what trade-offs are responsible. This is still the case for many fundamental questions in evolutionary biology, such as "Why do we grow old?", "Why does altruistic behaviour exist?" or "Why do human females regularly live past menopause while chimpanzees do not?". Chapters 2 and 3 examine the role of individual heterogeneity in a population and its effects on the persistence and spread rate of a population. Chapter 4 analyses the stability properties of the solution for the model in Chapter 3. Chapters 5 and 6 examine the evolutionary processes associated with dispersal by including the evolution of a trait that is linked with dispersal and life-history characteristics. Lastly, in Chapter 7 we solely examine the evolution of life-history traits and the evolutionary consequences. Since the inclusion of continuous space or a continuum of heritable trait values acts as an extra dimension, we have used partial differential equations to model the populations being considered in each chapter, with the exception of Chapter 2.