‘Supplementary information on methods used to model adult survival available on Nature’s World-Wide Web
site (http://www.nature.com):
Data were first fitted to an overall model. A model with time dependence separately for each sex in both survival
and capture probabilities (s*t , ps*t , where  is the survival probability, s the sex, t the year, and p the capture
probability) was considered as a biological starting point. The fit of this model to the data was tested using the
RELEASE software (Test 2 and Test 3; Burnham et al. 1987). Model (s*t , ps*t), fitted the data poorly (Test 2 +
Test 3, χ²114 = 330.801, P < 0.001). A large part of this χ ² statistic was explained by Test 2.Ct (χ ² 36 = 171.699, P
< 0.001), indicating a “trap-dependence” effect on capture (Lebreton et al. 1992, Pradel 1993). Capture
probability at year y+1 was higher for individuals captured at year y than for individuals not captured at year y,
indicating "trap-happiness" (Pradel 1993). To ignore trap-dependence would lead to a severe underestimation of
the apparent survival probabilities (Pradel 1993). Consequently a model with trap- and time-effects was fitted
numerically on a logit scale. A trap-dependent effect was denoted by m (Sandland and Kirkwood 1981) and
model (s*t , ps*t*m) was tested versus model (s*t , ps*t). An additive effect of m and t on capture probabilities was
also tested. A goodness-of-fit test accounting for trap-dependence on capture was calculated by considering only
the components of Test 3 and Test 2.Cm but the model still fitted the data poorly (χ ²78 = 159.101, P < 0.001).
Test 3.SR also explained a significant part (χ ²28 = 117.573, P < 0.001) of total χ ². Following Lebreton et al.
(1992), we denoted by a2 a two age-classes dependent effect and tested model (a2*s*t , ps*t*m) versus model (s*t ,
ps*t*m). A goodness-of-fit test accounting for both trap and age-dependence on capture was calculated considering
only the components of Test 3.Sm and Test 2.Cm. This model fitted the data (χ ² 50 = 41.528, P = 0.797). Thus,
model (a2*s*t , ps*t*m) was used for the modelling of survival and capture probabilities
Model selection followed the step-down strategy suggested by Lebreton et al. (1992). Capture probabilities were
modelled first to retain as much power as possible for tests of survival parameters. Akaike Information Criterion
(AIC) and likelihood ratio tests (LRT) were used to select the most appropriate model (Lebreton et al. 1992).
AIC is defined as AIC = DEV + 2×np, where DEV represents the deviance (-2ln(L)), L the likelihood of the
model evaluated at the maximum likelihood estimates, and np the number of separately estimable parameters in
the model. AIC values were used to select which model is most parsimonious in terms of providing an adequate
description of the data with the smallest number of model parameters. Lower AIC values indicate “better”
models. As a general guideline, AIC values differing by >2 are a good indication that the model with the lowest
AIC value is preferable, whereas models with AIC values differing by <2 are fairly similar in abilities to describe
the data in a parsimonious manner, regardless of the magnitudes of the AIC values. Because it is an objective
optimisation function, the AIC avoids the increased risk of Type I errors resulting from multiple statistical tests
between models (Lebreton et al. 1992). Model estimates of survival and capture probabilities tend to have
relatively large sampling variances that reduce the power of tests that use these estimates. Because LRT
commonly have low power between non-parsimonious models used at the beginning of the model selection
procedure, we used a significance level of P  0.15 to increase the power of the LRT (Lebreton et al. 1992).
Parameters that may explain time-variation in survival were then examined using the capture-mark-recapture
data set over the 1982-89 period when data were simultaneously available with adult survival (before 1982, no
physical data were available). The 1982-89 data set was used to test the effects of physical parameters on
survival. Model (s*t , ps*t) fitted the data (Test 2 + Test 3, χ ²22 = 27.505, P = 0.193). Model selection indicated
that model (s + t , pt) had the lowest AIC. Yearly variation in adult survival was then modelled as a function of
SST (s + SST , pt), SIE (s +SIE , pt) and SLP (s + SLP , pt) using AIC for model selection. To assess the effects of
these covariates we compared constant and time-dependent adult survival (Gaillard et al. 1997). The total
amount of variation due to time dependence was calculated as the difference in deviation between the time
dependent and constant survival models. The amount of variation accounted for by covariates was similarly
calculated. This difference is equivalent to an overall sum of squares in ANOVA. The proportion of variation
accounted for by covariates was calculated using analysis of deviance (ANODEV : White & Burnham 1999).
This corresponds to the proportion of explained variation and is comparable to a squared correlation coefficient
(Schemper 1990).
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(Birkhäuser Verlag, Basel, 1993).
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Gaillard, J.-M. et al. Early survival in roe deer: causes and consequences of cohort variation in two contrasted
populations. Oecologia 112, 502-513 (1997).
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