| Biological invasion is a main contributor to the loss in biological diversity in the Earth's most sensitive ecosystems, and, along with habitat loss, is one of the greatest threats to endangered species. Due to the serious consequences associated with invasive species, it is important to understand the underlying mechanisms for growth and dispersal so that future invasions might be controlled or even halted before they become firmly established. In this dissertation, we focus attention on the dispersal ability and invasibility of terrestrial plant species. Specifically, the two problems that we address are: (1) develop a mechanistic model to describe wind-driven seed dispersal of terrestrial plant species and (2) develop a mechanistic model to understand the invasive properties of plant communities in a heterogeneous environment.; The model for seed dispersal is formulated as a system of stochastic differential equations. For the analysis of this model we also consider the corresponding Fokker-Plank equation in position and velocity state space. Perturbation techniques and moment closure methods are used to find approximations to the full Fokker-Plank equation in position space only. The leading order approximation to the Fokker-Plank equation is a parabolic partial differential equation and the first order correction is a hyperbolic partial differential. Numerical methods are used to compare the results of the models.; To model the population dynamics of an invasive species, we consider integrodifference equation models in an infinite, one-dimensional heterogeneous environment. To make the analysis tractable, we assume periodicity in the environmental heterogeneity. Using linear stability analysis, we derive conditions for which the trivial solution of the integrodifference equation model is unstable. This condition is directly related to the invasibility of an environment. Next, assuming a traveling periodic wave for the spread of the species, we derive a dispersion relation for the average wave speed. |
