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1:55-2:20 PM
Evaluation of some Bayesian MCMC random effects inference applicable to bird
ringing data
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Ken Burnham & Gary White
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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.
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2:20-2:45 PM
Testing the additive versus compensatory mortality hypothesis using a random
effects model
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Michael Schaub & Jean-Dominique Lebreton
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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.
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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.
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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
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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
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