One dimensional nonlinear difference equations have been used to model population growth. The standard biological models have the interesting characteristic that
they display global stability if they display local stability. Various researchers have sought
a simple explanation for this agreement of local and global stability. Here, we show that
enveloping...
A long running problem in mathematical biology is the prediction of extinction events, a specialized case of the larger global stability problem found in differential equations and dynamical systems theory. A central technical question is how to introduce the randomness observed in real ecological systems not accounted for in deterministic...
Stock assessments use statistical models and empirical data to re-create the population dynamics of a stock in order to provide estimates of biomass and fishing mortality rates to inform fisheries management. Fish stocks are not uniformly distributed across spatial regions, but stock assessments typically ignore stock spatial structure, for the...
We model a fish population in a spatial region comprising a marine protected area and a fishing ground separated by an interface. The model assumes conservation of biomass density and takes the form of a reaction diffusion equation with a logistic reaction term. At the interface, in addition to continuity...
In this research a model is developed to predict population for relatively
rural areas experiencing rapid economic development. Of the many
ways to predict population size, in this research a "demographic-economic"
model is chosen for use. The economic variables which aid in projecting
population are total employment, and net changes...
To protect and restore environmental quality, efficient and effective conservation policies are needed. Designing policies require a sound understanding of the contributions of natural endowments to economic vitality, and the performance and impacts of conservation programs. This dissertation consists of three essays, and addresses several issues relevant to these two...
