Combining capture-recapture data and known ages allows estimation of age-dependent survival rates

Abstract

In many animal populations, demographic parameters such as survival and recruitment vary markedly with age, as do parameters related to sampling, such as capture probability. Failing to account for such variation can result in biased estimates of population-level rates. However, estimating age-dependent survival rates can be challenging because ages of individuals are rarely known unless tagging is done at birth. For many species, it is possible to infer age based on size. In capture-recapture studies of such species, it is possible to use a growth model to infer the age at first capture of individuals. We show how to build estimates of age-dependent survival into a capture-mark-recapture model based on data obtained in a capture-recapture study. We first show how estimates of age based on length increments closely match those based on definitive aging methods. In simulated analyses, we show that both individual ages and age-dependent survival rates estimated from simulated data closely match true values. With our approach, we are able to estimate the age-specific apparent survival rates of Murray and trout cod in the Murray River, Australia. Our model structure provides a flexible framework within which to investigate various aspects of how survival varies with age and will have extensions within a wide range of ecological studies of animals where age can be estimated based on size.

Keywords: Bayesian; age; individual growth; otoliths; state‐space; survival.

Figure 1

Comparison of ages for Murray cod (MC) and trout cod (TC) measured from otoliths versus ages back‐calculated using Equation (3) and the growth parameters estimated from the joint otolith—CMR model. Solid line is the 1:1 line, and segments indicate 95% credible intervals around estimated ages

Figure 2

Estimated ages at first capture for trout cod in Capture–mark–recapture (CMR) data based on (a) a joint analysis of CMR and otolith data and (b) CMR data alone. Each black point represents the mean of the posterior distribution for each individual's age, while horizontal segments indicate 95% credible intervals around that age. Red dots indicate the ages of individual fish estimated from otoliths, and the horizontal dashed line represents Ł _∞

Figure 3

Estimated ages at first capture for Murray cod in CMR data based on (a) a joint analysis of CMR and otolith data and (b) CMR data alone. See Figure 2 for a description of symbols

Figure 4

Density for the posterior distribution of the growth parameters $K_i$, as calculated from otolith data alone (red), CMR data alone (black), and a joint analysis of both (blue)

Figure 5

Estimates of age‐dependent survival rates for trout cod (TC) and Murray cod (MC) based on linear, quadratic, and polynomial models

Figure 6

Relationship between parameters estimated from an age‐specific capture model and true values used to generate simulated data. In the simulated data, both survival and capture probabilities are linearly dependent on age, but in the model, age‐specific rates are given uninformative Uniform(0,1) priors for age‐specific survival and capture probabilities. For survival, detection, and model versus true length plots, each point represents the model estimated value at for each age, while vertical lines indicate 95% credible intervals around each estimate. For length versus age, points represent the simulated data, while the red line indicates the estimated relationship between length and age, based on the von Bertalanffy growth equation

Figure 7

Estimated parameters and simulated data using an age‐dependent survival and capture probability model in which both survival and capture probability are linearly dependent on age. See Figure 6 for an explanation of symbols