Monday, October 24, 2011

The need to include parameter uncertainty

One of the themes in Population Viability analysis that's been echoing around for a bit is the distinction between sampling variability and environmental variability in vital rate estimates. For instance, if you measure reproductive output for Piping Plovers over 5 years, the variance in reproductive output includes two components - variation between years due to environmental and biotic differences, and pure sampling error due to the fact that you can only measure reproductive output for a sample of nests. Conor McGowan and coauthors have a nice article in the latest issue of biological conservation "Incorporating parametric uncertainty into population viability analysis models", which directly demonstrates the dramatic impact of failing to distinguish between these two sources, and/or to incorporate both of them. Here's the "killer figure":
The top two panels are what you get if you either A) separate temporal and sampling variance, but ignore sampling variance, or B) leave sampling and temporal variance combined as "process variance". The bottom panel shows the impact of separating temporal and sampling variance, and then using them independently in the predictions. The expected trajectory isn't much different. But the variance in the trajectory is much, much bigger in case C. I saw this exact same pattern in regional models of Piping Plover and Interior Least Tern prepared for the USACE on the Missouri River:
This is the distribution of population sizes in 2015, forecast under the "Business as usual" habitat selection strategy, and including sampling variability in the vital rate parameters. The vertical red bar indicates the Recovery Plan target, which is met less than 50% of the time. The trouble with these predictions is that they end up including POSITIVE trajectories as well as negative ones. This tends to make them controversial, because obviously plovers can't increase in the absence of substantial modifications to their habitat, they're threatened. They have to decrease. Don't they?

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