| Summary: | The use of mathematical modelling as a tool for investigating selected topics in conservation
biology is the focus of this thesis.
A continuous system of partial and ordinary differential equations model the age structured
population dynamics of a cohort of endemic, threatened New Zealand North Island
brown kiwi, Apteryx mantelli. Critical predation and recruitment rates of immature birds are
estimated. Stoats, Mustela erminea, are the main predator of immature kiwi. A refinement
to the model allows the calculation of acceptable stoat densities. In order to reduce stoats
to this critical density, a linear system of ordinary differential equations, representing an
acute secondary poisoning regime, is solved. An optimal secondary poisoning scheme, which
minimises the number of prey poisoned and the amount of poison used, is found. The minimum
area required for pest control is estimated by simulating the dispersal of sub-adult kiwi
using a discrete random walk approach. Simulations and a discrete age structured model are
used to investigate pulsed management strategies for both kiwi and kokako, Callaeas cinerea
wilsoni. Finally, a two dimensional discrete random walk is generalised and a continuous
diffusion equation is derived. A diffusion equation is incorporated into a S1 R (Susceptible,
Infected, Recovered) model representing the natural spread of Rabbit Haemorrhagic Disease
from a point source in rabbit, Oryctolagus cuniculus cuniculus, populations. The speed
for the virus, dependant on certain model parameters, is found and the minimum initial
population density, below which the wave of infection will not travel, is estimated.
All specific models discussed throughout the thesis are generic by nature and can be
applied to a diverse range of subjects.
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