Not-so-scary maths and extinction risk

27 08 2009
© P. Horn

© P. Horn

Population viability analysis (PVA) and its cousin, minimum viable population (MVP) size estimation, are two generic categories for mathematically assessing a population’s risk of extinction under particular environmental scenarios (e.g., harvest regimes, habitat loss, etc.) (a personal plug here, for a good overview of general techniques in mathematical conservation ecology, check out our new chapter entitled ‘The Conservation Biologist’s Toolbox…’ in Sodhi & Ehrlich‘s edited book Conservation Biology for All by Oxford University Press [due out later this year]). A long-standing technique used to estimate extinction risk when the only available data for a population are in the form of population counts (abundance estimates) is the stochastic exponential growth model (SEG). Surprisingly, this little beauty is relatively good at predicting risk even though it doesn’t account for density feedback, age structure, spatial complexity or demographic stochasticity.

So, how does it work? Well, it essentially calculates the mean and variance of the population growth rate, which is just the logarithm of the ratio of an abundance estimate in one year to the abundance estimate in the previous year. These two parameters are then resampled many times to estimate the probability that abundance drops below a certain small threshold (often set arbitrarily low to something like < 50 females, etc.).

It is simple (funny how maths can become so straightforward to some people when you couch them in words rather than mathematical symbols), and rather effective. This is why a lot of people use it to prescribe conservation management interventions. You don’t have to be a modeller to use it (check out Morris & Doak’s book Quantitative Conservation Biology for a good recipe-like description).

But (there’s always a but), a new paper just published online in Conservation Letters by Bruce Kendall entitled The diffusion approximation overestimates extinction risk for count-based PVA questions the robustness when the species of interest breeds seasonally. You see, the diffusion approximation (the method used to estimate that extinction risk described above) generally assumes continuous breeding (i.e., there are always some females producing offspring). Using some very clever mathematics, simulation and a bloody good presentation, Kendall shows quite clearly that the diffusion approximation SEG over-estimates extinction risk when this happens (and it happens frequently in nature). He also offers a new simulation method to get around the problem.

Who cares, apart from some geeky maths types (I include myself in that group)? Well, considering it’s used so frequently, is easy to apply and it has major implications for species threat listings (e.g., IUCN Red List), it’s important we estimate these things as correctly as we can. Kendall shows how several species have already been misclassified for threat risk based on the old technique.

So, once again mathematics has the spotlight. Thanks, Bruce, for demonstrating how sound mathematical science can pave the way for better conservation management.

CJA Bradshaw

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