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5.6.4 Analysis of the Microtus Data

For illustration, we provide a reanalysis of the Microtus data under model M0, using the model specification given in Panel 5.5. The R instructions for carrying out this analysis are provided in the Web Supplement.

We augmented the data set with M — n = 5G all-zero encounter histories. The posterior distributions for p and N are shown in Figure 5.3, where we see that the posterior mass of N piles up around G, consistent with our previous finding that the MLE of N occurred on the boundary N = n. In fact, Pr(N < 58) « G.986 (recall that n = 56 individuals were captured). The posterior mean of p is G.63, and the (2.5, 97.5) percentiles of the posterior are (G.57G, G.687).

Panel 5.5. WinBUGS model specification for the reparameterization of Model M0 that is induced by data augmentation.

Figure 5.3. Posterior of N and p for the Microtus data under model Mo, analyzed in WinBUGS using data augmentation.

5.6.4.1 Model Extension: Behavioral Effects

One good reason to use data augmentation for the analysis of closed population models is that it allows us to avoid dealing with the unknown sample size parameter N. Instead, models are converted to zero-inflated logistic-regression type models, and most model extensions can be implemented without additional difficulty (beyond that required for Model M0). We illustrate that point here using the Microtus data, following Royle (2008a).

We noted previously that the traps were baited with corn. This raises the possibility of what is usually referred to as a behavioral response where we might expect detection probability to increase after initial capture because individuals will return for an easy meal (it could also work the other way around - capture being the Microtus equivalent of being abducted by aliens).

We consider here the classic behavioral response 'Model Mb' (Otis et al., 1978), as well as a model suggested recently by Yang and Chao (2005) allowing for a short-term behavioral response (what they referred to as an ephemeral response). The classical model (the 'persistent' behavioral response model) supposes that previous capture might increase or decrease an individual's probability of capture. If we let xij = 1 if an individual was captured prior to sample j, then the model can be formulated as a logistic-regression type model for the Bernoulli observations yij, provided that N is known. The ephemeral response of Yang and Chao (2005) extends this model to include an autoregression term in the model, so that individual detection probability is influenced by capture in the previous sample. This broader

Table 5.7. Analysis of the Microtus data under the behavioral response model of Yang and Chao (2005).

parameter

mean

sd

2.5%

median

97.5%

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