|dc.description.abstract||Evolution frequently plays out over ecological timescales. Local adaptation
under the joint action of evolutionary and ecological processes frequently leads to
novel outcomes, as is evidenced by the theoretical work on adaptation at species'
borders. However, to date this body of work does not have a theory for the effect
of stochastic processes on local adaptation.
The primary goal of this thesis is to show that demographic and genetic fluctuations can significantly impact upon local adaptation. In addition, the
effect of polygenic evolution is also analysed. Specifically, three types of models
First a deterministic mainland-island, subject to hard directional selection,
maladaptive gene flow and density regulation is solved for two different trait
architectures: an explicit multilocus trait and a quantitative trait. The
maladaptive and adaptive steady states can be bistable. This depends on the
underlying architecture of the trait, as well as locus number and ploidy. Sourcesink
structure can emerge, accompanied by a novel, upper critical threshold above
which maladaptation occurs. The most favourable condition for local adaptation
occurs for few loci and low migration.
Second, a stochastic version of the mainland-island model is analysed as a
diffusion process. This is the central premise of the thesis and is explored by
examining properties of the stationary distributions of both trait architectures,
and the first-passage properties of the single locus case. It is found that across a
range of migration rates that depend on locus number and migrant polymorphism,
local adaptation may be reversed or escape from maladaptation becomes possible
at varying transition rates. The diffusion model is compared to a similar discrete
model. The continuous model is in good qualitative agreement with the discrete
Third, the stochastic model is generalised to the infinite island model, which
evolves deterministically. Under deterministic dynamics a range of equilibria
are possible, depending on whether habitat size varies or is fixed. Multilocus
dynamics restrict the conditions for polymorphism. Stochastic dynamics can have
potentially detrimental consequences for the persistence of the island population
when drift is strong.
The relevance of the stochastic model to border populations is discussed.
Although the diffusion process imposes severe constraints on the permissible
parameter ranges, it is still able to provide a good qualitative understanding
of the impact demographic and genetic
fluctuations have on local adaptation.||en