Gene flow across landscapes is accomplished by gravity, wind, water, and animals. These transport processes are increasingly studied using dynamic, spatially explicit models. The purpose of this talk is to provide an overview of these models and discuss there potential applicability to studying gene flow in fragmented and managed forests.

 In the most general sense, it is useful to distinguish two classes of spatial models: "object" models, which track discrete spatially referenced features floating in space (e.g. habitat islands), and "field" models, which divide continuous space into smaller elements and assign a value to each element. Most spatially explicit models in ecology are field models that utilize a 2- or 3-dimensional lattice to represent landscape properties such as elevation, vegetation, location of organisms, etc. Movement across such grids is usually modeled by local rules. Examples of field models include cellular automata, discrete reaction diffusion models, and cellular networks. Object models are sometimes used to represent individual animals or populations for individual-based models and metapopulation models, respectively.

 There are several different data structures for representing spatio-temporal dynamics (e.g., image sequences, polygons with a vector of temporal attributes for each polygon). Modern GIS systems now provide some useful spatial analytical capabilities relevant to modeling gene flow (e.g., distance and neighborhood analyses, diffusion models, path cost analysis), but are still very limited for dynamic modeling, which is instead usually performed using specially designed research software. Generic issues in the use of spatial dynamic models include: defining the spatial extent, resolution, and time step for the model, treatment of boundary effects, and movement/connection rules (e.g., rules governing the relationship between diagonal cells on a square grid).

 Among physical transport processes, modeling movement of water is well developed and a variety of programs are available to model both surface and subsurface flow at spatial scales from local to continental. Wind transport models have mainly been developed to represent larger scale atmospheric processes, although landscape models have also been developed to study urban microclimate, valley and land-sea wind systems, and local snow and sand transport. These wind models are generally computationally very intensive and require extensive parameterization. Simpler models have been developed based on surface aerodynamic resistance and fetch that could be useful in studying local gene flow in rugged or heterogeneous terrain.

 Spatially explicit diffusion models have been used to study a variety of biological processes, for example, biological invasions, seed dispersal, and disease spread. Animal movements have been simulated using simple diffusion and cellular automate models, as well as more complex, spatially explicit individual-based models and metapopulation models, some of which require large-scale computing resources. Simpler approaches to studying gene flow among animal populations include analysis of topography, vegetation, or other surface features to calculate path costs for varying dispersal routes as a way of modeling likely patterns of animal dispersal on complex landscapes.

 My sense is that spatially-explicit models represent an as yet relatively untapped set of tools which could be used to study gene flow in continuous versus fragmented landscapes. Even relatively simple applications of widely available GIS software could be useful for managing and visualizing gene flow data as well as for some simple modeling procedures. There are obvious opportunities here for collaboration between geneticists measuring gene flow in the field and landscape ecologists with expertise in dynamic spatial models.