Joint estimation of growth and survival from mark-recapture data to improve estimates of senescence in wild populations

Abstract

Understanding age-dependent patterns of survival is fundamental to predicting population dynamics, understanding selective pressures, and estimating rates of senescence. However, quantifying age-specific survival in wild populations poses significant logistical and statistical challenges. Recent work has helped to alleviate these constraints by demonstrating that age-specific survival can be estimated using mark-recapture data even when age is unknown for all or some individuals. However, previous approaches do not incorporate auxiliary information that can improve age estimates of individuals. We introduce a survival estimator that combines a von Bertalanffy growth model, age-specific hazard functions, and a Cormack-Jolly-Seber mark-recapture model into a single hierarchical framework. This approach allows us to obtain information about age and its uncertainty based on size and growth for individuals of unknown age when estimating age-specific survival. Using both simulated and real-world data for two painted turtle (Chrysemys picta) populations, we demonstrate that this additional information substantially reduces the bias of age-specific hazard rates, which allows for the testing of hypotheses related to aging. Estimating patterns of senescence is just one practical application of jointly estimating survival and growth; other applications include obtaining better estimates of the timing of recruitment and improved understanding of life-history trade-offs between growth and survival.

Keywords: growth; hazard; mark-recapture model; painted turtle; senescence; survival.

Figure 1.

(A) There is a small negative bias in estimates of the rate of senescence (ß₁) in simulated data. The estimated mean values of ß₁ are closer to truth (dotted line) when a growth model is incorporated (open circles). When growth is not included in the model (closed circles), the bias is severe, especially when the proportion of known age individuals is small or when only individuals of a certain age class are of known age. Error bars are +/− 1 SE of the estimates obtained from Markov-chain Monte Carlo simulations. (B) The mean squared error is lower regardless of what percentage and which age classes are known when a growth model is included.

Figure 2.

The (a-b) survival, (c-d) cumulative survival, and (e-f) hazard for male and female Chrysemys picta from populations in Illinois and Wisconsin as they age, starting at the truncation age (year 8). Females are shown with blue and males are shown with red. Shaded areas encompass the 95% credible interval. See text and Appendix S2: Table S3 for the parameter estimates for the models.