Part A studies the optimal strategies of seed germination problems where the population has a class structure under a fluctuating environment . In particular, a multidimensional age-class model is studied using a dynamical programming method. Numerical results about the so-called optimal stochastic strategy which consists of information about previous environmental states are computed. Comparing the optimal stochastic strategy with the optimal population-based strategy shows that the optimal stochastic strategy is highly effective in genera.l. A potentially useful diffusion approximation for the seed germination problem is also derived with numerical results. For part B, a multi-dimensional Moran model is studied using a diffusion approximation approach. The scaling limit and corresponding governing stochastic partial differential equations (SDEs) are derived. An expansion method is used to approximate the stationary distribution of the SDEs. An approximation formula for the effective migration rate is then derived.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682366 |
| Date | January 2015 |
| Creators | Xu, Yiyang |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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