Hastings A. et al. (2005). Ecology Letters.

"The spatial spread of invasions: new developments in theory and evidence."

Reviewed 09/08/11

Hastings et al. begin with a historical perspective on spread models, particularly the uni-spatial model developed by Fisher (1937). In this model the rate of species spreading over time is related to the sum of population growth in that spot/time and the displacement/relocation to that spot. The model assumes a number of important factors, among them are environmental homogeneity and that the growth rate of the population is high when the density is low. Mean age and variance for species reproduction and dispersal are also not directly incorporated into model parameters. Many newer models have been developed over the years that attempt to address one or more of these problems.  
It seems that one of the big limitations in modern theoretical understandings of invasive spread is the lack of data on long-distance dispersal events. Does the probability distribution for dispersal resemble a normal curve, or is a distribution with a tail necessary for modeling? This questions also addresses how invasion is thought of, in terms of being a multi-point origination of invasion due to rare long distance establishment events, or does invasion move as a front across landscapes.
The authors present regression models as an alternative to parametrizing life history models (pop. growth rate and Dispersal). Some of the benefits of regression models are their ability to give Confidence Intervals for invasion spread in space and time, assuming studies report standard errors, and that generalized linear models can be used. They do however require a lot of data in order to make accurate future predictions.
One of the things that I found intriguing about this article was the seeming lack of agreement across studies about whether invasion should be conceptually/literally modeled as stochastic, oportunistic, or deterministic. Does invasion occur randomly, do species respond to environmental and biotic stimuli that open up new opportunities, or do they actively seek or avoid certain habitats? It is of course possible that this framework is unique to every species or life-history type. This question was not headlined by the authors, though they did make reference to the different types in their paper.
I found the section on evolution in invasives also very interesting. Is phenotypic plasticity, or the ability to acclimate to a large variety of environments, a necessary trait for an invasive, or does local adaptation also play a key role after those medium to long range dispersal events? I think this type of thinking is analogous to other theoretical arguments in global change ecology. Though I suppose that invasion, or the switch to invasion, may become more and more linked with global change in the future. Species that are introduced in a new area and those that are facing environmental pressures to expand their ranges share many theoretical questions in common.