Modeling invasive plant spread: The role of plant-environment interactions and model structure.
Reviewed: 09/23/11
The modeling of invasive spread has a long history in ecology. However the accuracy and ecological relevance of many models developed to predict this spread have often been unrealistic in terms of analytical input or accurate outputs. This paper attempts a comparison between the classic reaction-diffusion (R-D) models of invasive spread and the spatially-explicit, individually-based (SEIB) variety that the authors develop here. RD models are simple, requiring only population growth rate and diffusivity. SEIB models have the benefit of incorporating age structure, stochasticity, environmental heterogeneity, and various plant attributes into the model. SEIB models are also more equipped to look at spread patterns and not just rates.
The authors look at the invasion of South African fynbos communities by pine tree species by developing a 2-D modeling space composed of 100m2 grids arrayed in a 150x400 pattern. Pine species begin along one edge of the environment, representative of a Pine-tree plantation. The model is set up so that only one tree can exist inside a grid at a time, which is supposed to represent the natural canopy cover of the species; however the modelers include a simulation experiment looking at the size of these grids and how it affects the success of the model as a test of sensitivity. The authors used several factors to determine how individuals would spread in the SEIB model, including adult survival after fires, fecundity, dispersal distance, age at reproductive maturity, and time between fires. These same factors and there assumptions were used to calculate values for population growth and diffusivity in the R-D model, though none able to be explicitly incorporated into that simple model. These five factors were crossed in a factorial simulation experiemnt to give 32 factor combinations, replicated 10 times.
Both the R-D and SEIB models predicted similar mean rates of spread, though the range was much larger for the SEIB model. This makes sense as SEIB is designed to incorporate stochasticity into the model. Both models also found that adult survival after fires was not important to any of the response variables tested, indicating that because the models were designed to only allow for new or open territory to be invaded, the amount of "virgin" territory far outpaces the rate of new grids recycled back into the system after adult mortality. The SEIB model was also able to test for interactions between various factors. For example, the simulations showed that a short fire interval increased recruitment for fast maturing populations, but caused mortality for slow maturing ones. These ecologically relevant facts would have been undetectable using the R-D model. This leads to one of the key benefits of this model according to the authors, the ability to determine which factors in a community are the most relevant for study and further empirical investigation. Different factors were also shown to have varying degrees of relevance for different response variables such as bare mean spread or density of the invasion focus.
The model does come with certain caveats however. The mean distance of dispersal was modeled as a negative exponential model that was cut off after 1km distance from parent. This ignores any potential for long distance dispersal events. Model improvements could easily be obtained by feeding in better data on dispersal distributions for the pine trees or whatever invasion is being modeled. The size of the grid used for the experiment is also vary important. For this system, the tree canopy acts as the ecologically relevant factor determining grain size and the total number of grids tested was 60,000 (150x400) due to size limitations in the simulation. Results showed that the grid size did alter the outcome of all or most of the response variables and the importance of the factors in the invasion spread; though the authors did not test any grid sizes smaller than their main grid of 100m2, they did test several higher ranges. It is of note that if the size of the grid were to be drastically reduced in order to be more relevant for smaller invader species, say grasses or fungi, limitations in the ability of the model to handle a high number of grids may be limited. Meaning that for smaller species, the SEIB model may not be able to look at a very large swath of total landscape, reducing the usefulness of the model.
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