Thursday, January 26, 2012

Predicting the future ... its harder than it looks.

Brenda Molano-Flores and Tim Bell just published a paper in Biological Conservation that uses count based PVA and linear regression models to evaluate the effects of climate change on an endangered plant.
Land managers primarily collect population counts to track rare plant population trends. These countbased data sets are often used to develop population viability analysis (PVA) to project future status of these populations. Additionally, practitioners can use this count-based data to project population size changes under different climate change scenarios at both local and regional levels. In this study we developed a count-based PVA for a population of the US federally endangered Dalea foliosa, using annual census data (1997–2008), to determine extinction probability (Pe) at 50 and 80 year time points. We determined which weather variables best explained variation in count data and population growth rate using linear regression. Lastly we projected population size for the population location at 50 and 80 years using forecasted temperature and precipitation from 16 climate change models under three emission scenarios. Count-based PVA indicated a Pe of 0.2% at both 50 and 80 years. However, these estimates of Pe have large confidence intervals, so persistence is not a certainty. Most variation in population size was explained by snowfall (R2 = 0.786, p < 0.001). Population size projections varied greatly among the 16 climate models due to widely varied weather projections by the models, but little differences were found among emission scenarios for most models. The low Pe projected by count-based PVA represents an estimate based on current conditions remaining the same. However, climate models indicate that current conditions will change over the next century. In particular, mean February temperatures are projected to increase by approximately 2 C. The majority of the models using climate change predictions projected population decline, suggesting that the studied population may not be protected against extinction even under low emissions scenarios. This study demonstrates the usefulness of collecting count-based data and our contrasting results from count-based PVA and climate projections indicate the importance of combining both count-based PVA and climate change models to predict population dynamics of rare and endangered species.
Um. Maybe. Let's see, where to start ...

I have to take issue with one of their primary conclusions from the PVA:
... by using a count-based PVA, we were able to determine that the Midewin D. foliosa population is most likely doing fine as long as the current conditions persist.
 Here is their Table 1

They base their conclusion on the low mean probability of extinction at 50 and 80 years. However, look at the confidence limits - extinction probabilities over 80% for this population are plausible!  They admit this in their abstract (see above): "...persistence is not a certainty." No! Never! They did not provide enough information on how they calculated Pe, but I assume from the parameters they are using the density independent model in Morris & Doak (2002). That model does not include demographic stochasticity, and the quasi-extinction threshold of 5 individuals is much lower than the 20 individuals or more recommended by Morris and Doak to avoid pernicious effects of demographic population size. So their Pe estimates are biased low, already.
OK, so a dodgy choice of assumptions on the PVA, but nothing earthshattering. However, I was really interested to see how they incorporated predicted climate change into this forecast - this is a bit like the holy grail of single species population dynamics right now. So I was stunned to see that they used a linear regression of past population size on past temperature and precipitation to project average population size in 2050 as a function of predicted climate conditions! Their "projection" didn't use a population model at all! I think the implied logic must look like this: There is a stationary statistical relationship between mean temperature in February and population size, estimated under current climate conditions. This relationship remains in place until 2050, at which point the model is used to project an average population size as a function of an average temperature from a new climate regime. At least they could have calculated confidence limits from their regression. Even then they have way under estimated the degree of uncertainty in future population size given a non-stationary environment. Although I am not against extrapolating with predictive models, it seems like this approach stretches the bounds of credibility too far.
They conclude that they have contrasting results from count based PVA (everything is fine) and their regression model (imminent disaster) - but how can they conclude this? One is predicting Pe and the other is predicting mean population size? Apples and oranges or am I just being persnickety? 
I'm not even going to talk about model selection by doing 900 correlations without correcting Type I error rates.
Why didn't they use their regression of mean lambda on weather to conduct simulations in a non-stationary environment?
They also claim that this demonstrates the utility of count based survey data. Hm. Nope, not convinced. Without an objective and some alternative management options there is no way to tell if count based survey data is sufficient.
PS: See my later reflections on what they did right

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