Bayesian analysis allows 'forward' dynamical models from ecological theory to be incorporated directly into statistical models. This procedure is useful because ecological models are the best available representations of the processes that give rise to ecological data. Prior information is often available for ecological models' parameters, and posterior inferences of those parameters are biologically meaningful.

However, when viewed as priors on the space of relationships between past and future system states dynamical models tend to be relatively restrictive, as many ecological systems can plausibly be modeled in several different ways. Placing nonpara metric Gaussian process priors on rate functions captures more of the range of plausible dynamics and allows inference of the rate functions.

This dissertation introduces two Bayesian methods for such inference. The first method is applicable to relatively complete models for multispecies dynamics, but is computationally expensive. This method is used to infer the functional response from a classic predator-prey dataset. The results contribute to the discussion of ratio-dependence in predator attack rates: the inferred functional response is prey-dependent at low predator densities and ratio-dependent at higher predator densities.

The second method is much cheaper and easier to implement, but is relatively assumption-bound. This method is applied to fishery datasets, and optimization and forecasting for resource management are found to become more difficult as a result of the model uncertainty expressed by the nonparametric prior. New management tools based on local dynamics are proposed to address the difficulties.

The dissertation concludes by presenting software that allows users to construct and fit a wide range of probability models involving Gaussian processes using a directed acyclic graph-based Bayesian model specification language. Use of the software requires conceptual understanding only, as opposed to familiarity with Gaussian process-related algorithms.