Predator-prey modelling involves computationally simulating predator-prey relationships which are observable in nature. Predator species hunt and consume prey species, forming an ecosystem where the population sizes of the various species are interdependent. The models take the form of mathematical equations, where a set of coupled equations model the effect that predator and prey species have upon each other, with the modelling either taking place on a continuous or discrete time basis. Generally to date, the majority of research into the modelling of predator-prey ecosystems has concentrated on a single predator species interacting with a single prey, especially in the case of discrete time implementations. Historically, the modelling of large scale multiple species predator-multiple prey ecosystems would have been too computation ally intensive to be modelled. As computers have increased in power, the execution of these larger ecosystems has become possible. This thesis investigates large discrete time multiple species predator-prey models with the introduction of mutation amongst the various predators and prey species that occupy it. It consists of three main studies. First it was necessary to model and discuss a discrete time multiple species predator-prey model without mutation. This was achieved by the modification and execution of a discrete time single predator- single prey model taken from current literature. A focus here is placed on the number of surviving species when executing the multiple species model for a varying numbers of initial predators and prey species (between 2 and 10,000 species), and the effect of the control parameters varying upon them. Two main studies are undertaken. Firstly the unimodal discrete time map that governs the prey dynamics is varied, with this it was shown that the choice of unimodal map has a great effect on the survival of the predator and prey species. Secondly a study into the effect of predation strategies, which define how the predator hunts the prey species, is presented. Each strategy is outlined and conclusions are drawn comparing each strategy, assessing how effective each of them are in allowing predator and prey species survival in the model. The next step was to detail how mutation could be introduced into the ecosystem, with a Coupled Map Lattice (CML) approach being identified. The second study details the dynamics of this CML without predation. A focus was placed upon a CML where the parameters are linearly scaled across the set of maps. The number of maps in the CML is varied between 10 and 10,000, Comments are made upon how changing the mutation rate affected the dynamics of the CML and conclusions are drawn upon how the number of maps within the CML impacts upon these dynamics. Finally the Finally the two studies are merged, attaining and presenting a multiple species discrete time predator-prey model with CML based mutations amongst the various species that occupy the ecosystem. Again various unimodal maps are usedfor the underlying dynamics of the prey species, and different predation strategies are utilised. The system is first observed in a simple form, with a single predator and multiple mutating preys, and then in more complex form , with both mUltiple mutating predators and multiple mutating prey. Conclusions are drawn on how varying the parameters govern the underlying behaviour and survival of the species within the various models. It is observed, that in such a complex system, with both multiple mutating predators and multiple mutating preys, a large range of non-linear dynamics are possible.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:665505 |
| Date | January 2014 |
| Creators | Mullan, Rory |
| Publisher | Ulster University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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