The Mathematics of Conservation

Invasive species eradication seems like a pretty straightforward affair. You have a foreign species lurking around your neighborhood, pushing native species out of their natural niches, altering complex food webs, and generally throwing off the already tenuous balance of the ecosystem in question. It is pretty clear you need to remove your disruptive newcomer as soon as possible, and so the only complication is finding the right chemical to douse it in, right? Well, not quite. As most graduate students or professionals will tell you, the majority of ecology and conservation eventually boils down to higher math and statistics. A recent paper from Carnegie Mellon University published in this week’s Proceedings of the National Academy of Science exemplifies that fact.

The paper proposes a new statistical model for simulating dispersal of an exotic species over time and uses it to analyze the growth and management of the red fire ant invasion in Brisbane, Australia. The model opts for an “agent-based” format, where individual nests interact autonomously to simulate their synergistic effects within the system. Using previously collected data from the eradication program, which has run from 2000 to the present day and is Australia’s largest eradication effort to date, they determined the probability that a given nest was detected, was treated, or managed to both survive and found a new nest elsewhere. These probabilities were then fed into a statistical model which would simulate expansion of the invasion across the Australian continent.

This agent-based approach is unique in that it abandons the typical grid-based structure of mapping out nests and expansion. This allows for a more nuanced approach as each nest found and recorded by the eradication program can be taken into consideration. It also allows for inclusion of human error in detection methods. This is one of the more complex issues facing studies such as these, as inferring how complete or accurate a survey is can be incredibly difficult, especially when locked into a grid-based analysis. By using an agent-based model though, each nest was evaluated as a possible source of new, unidentified nests.

 A system like this would help conservationists to evaluate the effectiveness of an eradication or management program as it progresses. From there, they can reassess their objectives and methods depending on the trajectory the invasion seems to be traveling along.

Studies like this really highlight precisely how complex conservation science is. The paper itself reads much like a statistics textbook, with extensive formulae, a small library of variables, and discussions of the intrinsic flaws in varying preceding methods. It is very easy to see conservation as a discipline defined by field surveys and national park restoration projects, but it is work like this that allows those efforts to maximize their impact on the environment. Detailed statistical mapping of progress allows for more an approach specifically tailored to the unique progression an invasion presents with. These complicated mathematical gymnastics lend weight to those methods by helping to ensure that the work being done is as effective as possible and being done in those areas where it is most necessary. Even wiping out fire ants can be an incredibly intricate affair whose success is driven less by manpower than by numbers.

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