This dissertation describes novel applications of Monte Carlo and Markov chain
Monte Carlo (MCMC) techniques to statistical inference in problems from the
field of conservation genetics.  The inference problems are motivated by issues
arising in the conservation and management of trout and salmon. The first half
of the thesis deals with estimating effective population size and related
quantities from temporally spaced samples of genetic data.   A likelihood
function for organisms with discrete generations is developed, based on the
Wright-Fisher model and a hidden Markov chain formulation.  Importance sampling
methods for computing this likelihood are presented and applied to published
data on {\em Drosophila}.  Some modeling assumptions implicit in the use of the
Wright-Fisher model are detailed, and a new model for genetic inheritance,
based on a P\'{o}lya urn scheme, is presented and characterized.  Methods are
developed using this model for the MCMC estimation of the likelihood or
posterior probability for the effective size of a population or for the ratio
$\lambda$ of the per-generation number of effective breeders to census breeders
in a population.  The P\'{o}lya urn model forms the basis for a probability
model of allele frequency change conditional on $\lambda$ in salmon
populations.  Specifying this model in terms of a large  directed graph
simplifies the application of a single-component Metropolis-Hastings algorithm
for computing the posterior distribution of $\lambda$.  The method is applied
to genetic data simulated upon the census counts of a threatened salmon
population in Idaho, demonstrating that the method allows precise estimates of
$\lambda$ with such data.  

The second half of the thesis focuses on approaches to inference within
populations of recently-hybridized populations.  First, I extend the methods of
\citeN{Pritchardetal2000} to allow inference of pure and admixed categories of
individuals in structured populations.   Finally, I develop methods based on
explicit modeling of recent hybridization and evaluate the potential for using
genetic data to distinguish $\F_1$, $\F_2$ and backcrossed hybrid categories
among sympatric, hybridizing populations.