Life tables

Zoo and wild population life tables were compiled from the Species360 database and literature, respectively (see Lemaître et al.14 for more details). Concerning free-ranging populations, publications containing life-tables from semi-captive populations were excluded to allow a strict comparison between captive and free-ranging populations. For 25 species, we collected several life tables from the same or different populations. When available, we gave preference to life tables obtained from longitudinal data. When several life tables of a given quality were available, we averaged them. When life tables were given in months or not with an integer of years, a standardization was made to obtain the survival at each integer age. For 9 species, the total number of individuals followed or considered was not given in the focal study. In such cases, we arbitrarily assumed that 100 individuals were considered per sex (close to the median value of the number of individuals alive at 1 year of age in the life tables we used). For wild life tables with a known total number of individuals (N = 50 species), the lowest was found for females of Mustela vison for which the life table only included 30 individuals, and the highest is observed for males of Oryctolagus cuniculus with a total of 9,020 individuals (Supplementary Table S1). For captive populations, we only used extinct cohorts of animals for which the sex and both birth and death dates were known, implying that animals were born in captivity. Extinct cohorts were defined as all cohorts born before a given year, which is determined as 2013 minus three quarters of the maximum longevity recorded for the species (Supplementary Table S1). As in captivity the sex ratio could be biased due to the culling of some young males during the first year for management issues (mostly in ruminants), we only computed parameters when at least 25 individuals for each sex of each species were alive at 1 year of age to get accurate estimates of age-specific survival. We finally obtained a dataset of 52 species for which data for both females and males were available, with one additional species with male-only data (leading to 53 species in males) and 6 additional species with female-only data (leading to 58 species in females) (Supplementary Table S1). For both captive and wild populations, we made the same calculations to obtain exactly comparable life tables. For visual comparison only, we included data from females of the two elephant species26,27 and sex-combined data from the common hippopotamus21 in the resulting data plots but did not include them in the analyses, as their data did not correspond to the data selection criteria stated above.

Metrics of survival

To measure species- and sex-specific patterns of survival and actuarial senescence in captive and free-ranging populations, we used four distinct but complementary metrics: the longevity, the baseline annual mortality, the age at the onset of actuarial senescence and the rate of actuarial senescence (see Fig. 1. for a graphical display of these metrics). The longevity was extracted from species-specific life tables for both males and females and for both captive and wild populations (Supplementary Table S1). We defined longevity as the age at which 90% of individuals from the initial cohort (alive at 1 year of age) had died (Fig. 1). This allows avoiding spurious estimates due to the exceptionally long life of a few individuals15. However, this trait (called ‘longevity’ hereafter) is not a direct measure of senescence because it does not include any explicit information about age-dependent decline in survival. For other metrics, we first measured the logit-transformed age-specific mortality from a given life table. We thus constrained survival of 1 to be equal to 0.99, and we fitted a Generalized Additive Model to obtain the age-specific mortality curve. Since both theoretical and empirical evidence reveal that actuarial senescence does not start prior to the age of sexual maturity28,29, the onset of actuarial senescence was defined as the age at which the annual mortality rate was the lowest between the age at sexual maturity and the age at which 90% of individuals from the initial cohort have died (Fig. 1, Supplementary Table S1). The age at sexual maturity (in years) was collected for each sex and each species from a specific literature survey (Supplementary Table S2). The baseline mortality for each sex of each species and for both captive and free-ranging conditions was defined as the annual mortality observed at the age corresponding to the onset of senescence (Fig. 1, Supplementary Table S1). The baseline mortality at the onset of actuarial senescence corresponds to the lowest mortality observed for a given sex, species, and environment (i.e. wild or captive) between the age at sexual maturity and the age at which 90% of individuals from the initial cohort have died. The rate of senescence was measured as the slope of the linear regression of survival (on a log scale) on age computed between the age at the onset of senescence and the age at which 90% of individuals from the initial cohort have died (i.e. our measure of longevity)30 (Fig. 1, Supplementary Table S1). For short-lived species and life tables with a small sample size, we used the age at which at least 5 individuals of a given sex were still alive instead of the age at which 90% of the initial cohort was dead, both to achieve unbiased estimates due to the too few years lived by short-lived species, and to avoid estimating survival from less than 5 individuals. All estimates are reported in Supplementary Table S1 and displayed on Fig. 2 and Supplementary Figures S2–S4.

Comparative analysis

To avoid biased assessment of the variation in survival patterns between captive and free-ranging populations, we controlled all the analyses for the non-independence between species due to shared ancestry using ‘Phylogenetic Generalized Least-Squares’ (PGLS) models31. A phylogeny was built for the 59 species (Supplementary Figure S1) using the phylogenetic super-tree of mammals published by Bininda-Emonds et al.16,32. Survival and senescence metrics were compared between free-ranging and captive males and females using linear models. Longevity and the onset and rate of actuarial senescence metrics were log-transformed, while baseline annual mortality was logit-transformed prior to any analysis. In a first part, the results of which are displayed in the main text, we analyzed the relationship between the metric measured in zoos (dependent variable) and the corresponding metric measured in wild populations (independent variable). A higher (for longevity and onset of senescence) or a lower (for baseline mortality and rate of senescence) value in captivity indicates that the focal species performs better in zoos. In a second part, we tested whether the quality of demographic estimates in the wild (i.e. measured from longitudinal or transversal studies) and species body mass (log-transformed) influenced the relationships between captive and wild metrics. Survival and senescence patterns are strongly associated with body mass33. Typically, larger species live longer18 and show a lower rate of senescence34 compared to small species, and have a slower pace of life35. To assess whether the patterns we report held when accounting for size differences among species, we included log-transformed body mass as a covariate in our models in a secondary analysis. We collected information about sex-specific mean adult body mass from the literature for each species analyzed (Supplementary Table S2). Therefore, for each of the four survival or senescence metrics in zoos and for a given sex, the full model included the corresponding wild metric and mean adult body mass as covariates, and the two-way interaction between the wild metric and data quality (as a fixed factor using longitudinal data as the reference). We then reduced the model by testing nested models by likelihood-ratio tests (LRT) so that the final model only included variables with statistically significant effects. A total of 3 nested models were tested for each of the metrics analyzed (Supplementary Table S3). A G-test was performed in each case. Models including the interaction between data quality and the wild estimates were never selected, whatever the survival or actuarial senescence metric considered (Supplementary Table S3). This suggests that quality of the wild demographic estimates did not influence the relationship between zoo and wild metrics. Moreover, we observed that body mass influenced zoo metrics in the same direction as the pace of life (Supplementary Table S4), leaving the patterns unchanged, whether including body mass in the models or not. All of these results are provided in Supplementary data (Supplementary Tables S3 and S4). For ruminant species, it has been shown that grazer species (whose natural diet consists mainly of grass) perform better than browser species (whose natural diet consists mainly of leaves or twigs) in captivity, in terms of survival and actuarial senescence9,14. In a complementary analysis, we therefore took this pattern into account and corrected the four survival and senescence metrics by including the percentage of grass in the natural diet of each ruminant species in the model. For all ruminant species, survival and senescence metrics were then adjusted for 60% (median, N = 27) of grass in the natural diet. However, results remained remarkably similar with or without this correction (Supplementary Table S5). All analyses were performed with R version 2.14.036 and parameter estimates are given with the 95% confidence interval.