Publication:
Nelson, Michael France, John T. Murphy, Christopher Bone, and Mark Altaweel. “Cyclic Epidemics, Population Crashes, and Irregular Eruptions in Simulated Populations of the Mountain Pine Beetle, Dendroctonus Ponderosae.” Ecological Complexity 36 (December 1, 2018): 218–29. https://doi.org/10.1016/j.ecocom.2018.08.006.
Background
This is by far the largest-scale and most labor-intensive research project that I have conducted. To carry it out, I learned how to program in Java, and gained experience with cluster computing. During the project, I had the opportunity to travel to the Argonne National Laboratory in Ilinois to take advantage of their cluster comuting capabilities. I also got a lot of experience in creative data visualization (in R) and using machine learning algorithms to classify model behavior.
Mountain pine beetles (MPB) are one of the most serious forest pests in western North America. They infest nearly all species of western pines, and must kill their host trees in order to successfully reproduce. Although they are part of the native ecosystem, in recent years there have been unprecedented large epidemics resulting in millions of hectares of dead trees. The mountain pine beetle system also has complex interactions with climate and wildfire.
Figure 1: my first (and last) foray into creating vector art in R. The figure depicts the life cycle of MPBs.
For this project, we created a spatially explicit agent based model of interacting forest patches and MPBs. In the simulation, simulated MPBs dispersed and attempted to attack trees within forest patches. If enough beetles attacked a patch, they were able to overcome the trees’ defenses and reproduce.
Model Variables
In the model, three parameters were varied in order to explore the
parameter space. This resulted in a 3-dimensional parameter space to
explore.
The three variables were:
- Trees per patch: a measure of the relative openness or closedness of the tree canopy.
- Tree vigor: a measure of the ease with which MPBs can successfully overcome a tree’s defenses. Trees could be either vigorous or vigor impaired. This parameter was the proportion of vigorous trees.
- Beetle fertility: a measure of how many offspring each successfully attacking beetle produced.
Simulations
To explore parameter space, 5000 simulations were run, each with a
random value of the three parameters.
Simulations were run for 1000 yearly time steps.
Main Findings
Epidemic Return Interval
Throughout much of the parameter space, recurring MPB epidemics emerged. Depending on the parameter values, epidemics had either regular or sporadic return times.
Figure 5a: The top three rows show a simulation with a regular return interval of about 80 years. The next three rows show a simulation with irregular population eruptions.
A consistent, but complex pattern emerged in the parameter space regarding regular or sporadic epidemic return times. To visualize the results, I classified each run as either regular or sporadic, then used the machine learning technique of support vector machines (SVMs) to characterize the transition surface between regular and sporadic.
Figure 7: Results of the SVM classification surface. This figure shows the parameter space with the transition surface from three different perspectives. Although the pattern of the surface is complex and there are interactions between the three parameters, some general patterns emerge: At high tree densities, epidemics tend to be more sporadic or irregular (you can see this in the top row of slices through 3D parameter space). Regions of high beetle fertility and lower tree vigor tended to show regular epidmic return intervals.
Conclusions
What does this model have to do with reality?
Besides being fun to make, and a great way to learn Java, this model has the potential to inform some management practices. Of the three model parameters, managers can only directly manipulate one: tree density. In the model, the average proportion of the landscape that was in an epidemic state decreased with tree density. This is consistent with managers’ observations that forest patches that have been thinned tend to suffer less kill area than overgrown forests.
Figure 9: This figure shows the average percentage of the forest that was spent in an epidemic state. There are three views through parameter space. If you examine the figure, you can make out a pattern where regions with low beetle fertility and low tree density had the lowest mean epidemic proportion. The region with the highest epidemic proportion (blue surface) was moderately high tree vigor, high tree density, mid to high beetle fertility.