I present three independent studies linked by one high level theme. Traditionally, theoretical ecology has studied population dynamics from the level of the population. This approach requires a number of assumptions, of which two, a large number of individuals living in a well-mixed space, are key components of the resulting population dynamics. These two assumptions are often mutually exclusive. That is, it is rare to find a population made up of a large number of individuals who also live exclusively in a homogeneous spatial environment. I combine two alternate model formulations, Stochastic Birth-Death (SBD) models and Spatially-Explicit Individual-Based models (SEIBMs) with experimental techniques the more traditional analytical models to investigate the effects of these two assumptions.
In Chapter 1, I introduce the implications of the addition of SEIBMs to the "toolkit" of the ecological modeler.
In Chapter 2, I use a SBD model to test the assumptions necessary for an analytical model that was fitted to an experimental time series. I show that the analytically derived model is far too stable (as measured by persistence) to represent the real system. I then demonstrate that it is statistically impossible to differentiate between the analytical model formulation and an alternate model formulation in the presence of demographic stochasticity.
In Chapter 3, I use an analytical model of a host-parasitoid system as a baseline for development of a SEIBM metapopulation model. I demonstrate the application of verification and validation techniques to some unique spatial patterns caused by a combination of a refuge effect, a slow dispersing host, and a fast dispersing parasitoid.
In Chapter 4, I introduce a continuous-time continuous-space SEIBM. I use this model to in conjunction with a SBD model to analyze of the properties of the Lotka-Volterra predator-prey equations in the presence of space and discrete individuals. I show that spatial patterns can arise from local interactions between individuals in the absence of spatial heterogeneity. I also show that these patterns can be either stabilizing or destabilizing with respect to well-mixed space. Finally, I demonstrate that the experimentally measured "functional response" cannot be represented as a analytical function in the presence of these spatial patterns.
My Research