Plenary Address - 1:15-1:55 PM

Random Effects: Present and future

Carl Schwarz

Random effects models have been typically used in capture-recapture settings as an intermediate model between fully time dependent and constant over time models. We review the approaches to fitting these models and discuss the advantages and disadvantages of each. Then extensions of random effect models to incorporate autocorrelation over time, to model classical design-of-experiments random effects, and to model other phenomena will be discussed.


Individual Papers

1:55-2:20 PM

Evaluation of some Bayesian MCMC random effects inference applicable to bird ringing data - Ken Burnham & Gary White

The study design used to evaluate a method of moments random effects analysis for CJS data with per-occasion survival probability as a beta-distributed random variable (Burnham and White, 2002, Journal of Applied Statistics 29:245-264) is herein repeated to evaluate a fully Bayesian MCMC random effects analysis. The design has 5 factors: occasions (t=7, 15, 23, 31), new releases per occasion (u=25, 100, 400), capture probabilities (p=0.4, 0.6, 0.8; no time effects), expected survival probability (E(S)=0.4, 0.6, 0.8; no time effects), and process variation, var(S)=σ2 (s=0, 0.025, 0.05, 0.1). At each of these 432 design points we generated 500 independent (Monte Carlo) data sets. Then MCMC inference was used, based on 1,000 nearly independent samples from the Bayesian posterior for uniform marginal priors on p, E(S) and σ2 (0 to 0.25). We look at properties of point and interval inference on per-occasion S, E(S) and σ2 based on the posterior sample. Some issues considered: coverage of equal tailed versus shortest 95% credibility intervals, and point estimation, especially of σ2 (mean versus mode). The simulations are done, basic results are known. Comparisons to Burnham and White (2002) will be made; the Bayesian approach did well.

2:20-2:45 PM

Testing the additive versus compensatory mortality hypothesis using a random effects model - Michael Schaub & Jean-Dominique Lebreton

We propose a new way to test whether a specific cause of mortality (say cause A) is additive to the remaining mortality or whether it is compensated for by other forms of mortality. In contrary to the existing tests, our approach does not require an independent estimate of the "intensity" that caused mortality due to a specific reason (e.g. hunting effort). It is enough to have ring-recovery data, where the cause of death of the recovered animals is known. First we estimate the mortality probability due to cause A and due to all other causes of death with a time-dependent multi-state model where the states are "alive", "newly dead because of A" and "newly dead because of another reason than A." Second, we test the two opposing hypotheses by using random effects methodology. If the "additive mortality hypothesis" would be true, the correlation between the two mortalities over time is zero. If there would be some form of compensation, there is a negative correlation between the two sources of mortality over time. To extract this temporal correlation from the overall correlation we used random effects model. We illustrate the method with a case study of White Storks, where the two opposing sources of mortalities are natural and electrocution mortality. It appears that the two sources of mortality are partially compensatory in the adults, but additive in the first year birds.

2:45-3:10 PM

Random effects and individual differences: looking for trees in the 'life history' forest. - Emmanuelle Cam, Bill Link, Evan Cooch, Jean-Yves Monnat, & Etienne Danchin.

We investigated the influence of age on survival and breeding rates in a long-lived species Rissa tridactyla using models with individual random effects permitting variation and covariation in fitness components among individuals. Differences in survival or breeding probabilities among individuals are substantial, and there was positive covariation between survival and breeding probability; birds that were more likely to survive were also more likely to breed, given that they survived. The pattern of age-related variation in these rates detected at the individual level differed from that observed at the population level. Our results provided confirmation of what has been suggested by other investigators: within-cohort phenotypic selection can mask senescence. Although this phenomenon has been extensively studied in humans and captive animals, conclusive evidence of the discrepancy between population-level and individuallevel patterns of age-related variation in life-history traits is extremely rare in wild animal populations. Evolutionary studies of the influence of age on life-history traits should use approaches differentiating population level from the genuine influence of age: only the latter is relevant to theories of life-history evolution. The development of models permitting access to individual variation in fitness is a promising advance for the study of senescence and evolutionary processes.

3:10-3:45 PM

Nonidentifiability of population size from capture-recapture data with heterogeneous detection probabilities - Bill Link

Heterogeneity in detection probabilities has long been recognized as problematic in mark-recapture studies, and numerous models developed to accommodate its effects. Individual heterogeneity is especially problematic, in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes. Thus even with very large samples, the analyst will not be able to distinguish among reasonable models of heterogeneity, even though these yield quite distinct inferences about population size. I illustrate the problem using the simple closed population model