New paper: ‘A Bayesian model of metapopulation viability, with application to an endangered amphibian’

f1000005.jpgLast night Diversity and Distributions published our latest paper, in a special issue entitled ‘Risks, Decisions, and Biological Conservation’.

The paper – co-authored by Mick McCarthy, Michael Scroggie, Kirsten Parris and John Baumgartner – describes an occupancy-based approach to metapopulation viability analyses that I think will prove a valuable extension to standard occupancy modelling.

Here’s the back story. In the early 2000’s, Darryl MacKenzie struck ecological gold by developing and publishing an occupancy modelling approach that accounts for imperfect detection. Darryl’s 2003 paper (co-authored with the gurus at the Patuxent Wildlife Research Center) was particularly influential. That paper describes a modelling approach that can be used to estimate the probabilities of extinction and colonisation for a given species using multi-season occupancy data, with the bonus of accounting for imperfect detection. But perhaps most mouth-watering for ecologists was the ability to model the probabilities of extinction and colonisation as functions of site- and landscape-level covariates (things like patch area, quality and connectivity) using standard regression techniques. Doing so allows hypotheses about the drivers of extinction and colonisation to be tested while accounting for imperfect detection.

Our paper builds on this functionality. What we’ve done is effectively tack on the ability to simulate extinction and colonisation dynamics for a given species based on the models of extinction and colonisation that result from Darryl’s approach. That is, we’ve developed a means of running occupancy-based metapopulation viability analyses using these models. We provide code for doing this in the Supplementary Material (see also my Code and data page).

It’s a fairly simple process conceptually. One fits a multi-season occupancy model to their particular dataset, estimates the effects of patch area, quality etc. on the probabilities of extinction and colonisation, extracts the parameters of the extinction and colonisation models, and then simulates the extinction and colonisation dynamics (and hence changes in occupancy) for a particular metapopulation according to these parameters. All that’s required for the simulations are measures of the relevant covariates for each site, and the initial occupancy status of each site.

The cool thing is that one can explore, using these simulations, how the metapopulation will respond to particular management scenarios. You can take away particular patches to represent habitat loss, you can tweak patch characteristics to represent habitat enhancement or degradation, and you can even add in new patches to see how habitat creation affects metapopulation viability. We do just that in the paper – examining the effect of habitat loss and creation on metapopulation viability for the endangered Growling Grass Frog (my particular muse….).

Now, in case Andrew Royle or Marc Kéry are reading, I best now tell you that we in fact used their 2007 Bayesian state-space version of Darryl’s approach. In a move that will surely see them breeze through the pearly gates, Royle and Kéry not only put in the hard-yards developing and publishing the Bayesian approach, but provided code to do it too.

The nifty thing about the Bayesian version is that it provides the opportunity to propagate uncertainty in the effects of patch characteristics on extinction and colonisation through to the simulations. I’ll leave it to the paper to explain how, but what we end up with are probability distributions for the metrics of metapopulation viability that not only encompass uncertainty due to the stochasticity of the modelled dynamics, but also from uncertainty in the parameters of the extinction and colonisation models.

That’s the approach in a nutshell. If you’d like a copy of the paper but can’t get through the paywall, just drop me a line and I’ll email it through. Otherwise, go forth and simulate!

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