Modeling Stratified Diffusion in Biological Invasions.
Reviewed 09/16/11
In keeping with the authors way of laying out their paper, I will review this paper in a 'header with sub-headers and points' fashion. If we envision that invasion can occur by two basic types of dispersal, short-distance (SD) and long-distance (LD), how do we model each dispersal contribution over time, in conjunction with its relationship to the other dispersal type?
The authors detail four examples of invaders and their range expansion over time. The selected species represent a range of continents for invasion, species type, and method of introduction and dispersal.
1) A small mammal (muskrat) invasion shown to have a linear increase in area invaded over time. Dispersal mostly SD. Invasion occurred from a single focal point.
2) A bird (starling) with a bi-linear, or biphasic invasion. Invasion initially occurred from a single focal point, with scattered overwintering birds later providing important points for range expansion.
3) A beetle (weevil) with a completely non-linear, accelerating expansion of range invaded over time. Typical dispersal is by short distance swimming through rice paddies paired with rare long distance flying events.
4) A grass (Bromus) with a non-linear, accelerating expansion over time. Had multiple early foci due to human-mediated dispersal that ended in the late 1800's.
The authors qualitatively classified invasion into three temporal phases: an establishment phase with low density and/or population count levels, an expansion phase of area invaded, and a saturation phase. The establishment phase noted in the examples could be due to two possibilities, the difficulty for establishing populations at low densities or a difficulty for human detection of invader populations at low densities. The Expansion Phase was further classified by the authors as either linear (Type 1), biphasic (Type 2), or accelerating (Type 3). All of which had matches with the selected example species.
Three main model types were detailed by the authors, mostly focusing on the expansion phase of the invasion for simplification purposes. A homogenous environment and a radial spread of the invasion front for each focal colony was assumed. Interactions with native species and patchy habitats were ignored. The three basic models discussed were:
One based on SD dispersal and establishment time. The second on scattered colonies, where multiple foci of colonies are apparent at the start of the invasion, with little radial overlap of the invasion front stemming from each colony. The third and final model looked at a primary colony that created secondary colonies via LD dispersal, where there was significant coalescence of smaller growing secondary colonies with the, also expanding, primary colony of invaders.
The authors did a fairly decen tjob of outlining their models in a very structured fashion. After the outline and boundary conditions of each model was given, they were fit to preexisting data from the example species, outputting fitted terms for the empirical sets. Importantly the authors also detailed colonization success of LD- propagules. For their models they input three basic ways to look at colonizer success rates. The rate could equal some constant value for all colonies and all LD dispersal events. Or a linear increase with the radius of the colony is possible, this assumes that LD dispersal only occurs at the edges of any given colony. Finally a quadratic increase of LD dispersal success by the radius of the originating colony; this assumes that the number of LD migrants is proportional across all areas of the originating colony. All three had their equivalents in the example species. However the authors also point out that the colonization success is not necessarily limited to these three examples. A Type 3, "Accelerating Invader Expansion", response can be achieved as long as the success of new colony establishment from LD dispersal events is greater than linear.
I believe that the patch dynamics of the environment, biotic interactions of the invader, and the differential colony growth at the expense of density increases would be interesting future aspects to analyze within this modeling framework.
On a slightly off-course train of thought I was also left thinking how invasion and disease emergence are similar and different in their modeling approaches.
No comments:
Post a Comment