  Accurate information on patterns of introduction and spread of non-native
species is essential for making predictions and management decisions. In many
cases, estimating unknown rates of introduction and spread from observed data
requires evaluating intractable variable-dimensional integrals. In general,
inference on the large class of models containing latent variables of large or
variable dimension precludes exact sampling techniques. Approximate Bayesian
computation (ABC) methods provide an alternative to exact sampling but rely on
inefficient conditional simulation of the latent variables. To accomplish this
task efficiently, a new transdimensional Monte Carlo sampler is developed for
approximate Bayesian model inference and used to estimate rates of introduction
and spread for the non-native earthworm species Dendrobaena octaedra (Savigny)
along roads in the boreal forest of northern Alberta. Using low and high
estimates of introduction and spread rates, the extent of earthworm invasions
in northeastern Alberta was simulated to project the proportion of suitable
habitat invaded in the year following data collection.
