Microbial communities associated with animals and plants (i.e., microbiomes) are implicated in the day-to-day functioning of their hosts, and there has been an explosion of research on them. Much of this research has focused on surveys of microbial diversities across a variety of host species, including humans, with a view to understanding how these microbiomes are distributed across space and time, and how they correlate with host health, disease, phenotype, physiology and ecology. Fewer studies have focused on how these host-microbiome associations evolve. In this dissertation, we develop a computational agent-based frameworks for modelling the long-term evolution and short-term dynamics of microbiomes within a population of hosts. Our frameworks allow different ecological processes and evolutionary forces to directly or indirectly affect microbiome composition. By incorporating a Wright-Fisher or Moran genealogical population model, we combine host phylogeny with microbiome assembly to consider the shared evolutionary history between hosts and their microbes. We also incorporate how hosts acquire their microbiomes, and how the environmental microbial community available to the hosts is assembled under both neutrality and selection. Under the selective models, we allow selection to operate on both microbes and hosts and observe how microbial diversities are gradually shaped by this evolutionary feedback between hosts and microbes. Furthermore, host population division and dispersal limitation are taken into account for our short-term neutral models. Our results indicate that the extent of parental contribution to microbial availability from one generation to the next significantly impacts the diversity of microbiomes over both long-term and short-term periods: with greater parental contribution, microbiome diversity within hosts tends to decline while microbiome diversity between hosts tends to increase. We also show that the implementation of selection further depresses microbial diversities and the comparison between host level and microbe level selection suggest that the evolutionary pressures directly acting on microbes is more dominant in shaping microbial diversity patterns. Finally, we show that host population division and dispersal limitation under high host contribution further shape the diversity patterns by elevating microbiome differences between hosts and depressing microbial diversity within hosts.
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