Post provided by Eleni Matechou
To celebrate the 10th Anniversary of the launch of Methods in Ecology and Evolution, we are highlighting an article from each volume to feature on the Methods.blog. For Volume 4, we have selected ‘Estimating age‐specific survival when age is unknown: open population capture–recapture models with age structure and heterogeneity’ by Matechou et al. (2013). In this post, the authors discuss the background and key concepts of the article, and changes in the field that have happened since the paper was published seven years ago.
At the time I was studying for my PhD, there was a lot of interest within the Max Planck Institute for Demographic Research (MPIDR) on modelling senescence for wildlife populations, which is challenging because ages of individuals in the wild are typically unknown. During the Euring 2007 conference (Dunedin, New Zealand), Professor Shirley Pledger presented a new open–population model for capture–recapture data that allowed for retention probability to be a function of the unknown time spent at a migration stopover site.
Although the biological application was slightly different, the conceptual link between this work and our aim to model senescence was immediately obvious, and we thought the approach might work if we could overcome two challenges:
- Sampling at stopover sites tends to start before individuals arrive at the site, so Shirley’s model assumed that the time the individuals have spent at the site before the start of the study is negligible. However, when modelling senescence, individuals can be born before the start of the study, and for species with long lifespans individuals can be born many years before we start sampling the population. Therefore, we needed the model to account for that to obtain reliable estimates of age–dependent survival probabilities (i.e. the probability an individual of age ‘a’ survives to age ‘a+1’). We achieved that feature by back–tracking possible birth times of individuals and providing a new formula (equation 2 in our paper) for calculating the proportion of individuals that were new arrivals, i.e. births, in the years before sampling started.
- The seminal paper by the then director of MPIDR Professor Jim Vaupel, highlighted the need to account for individual heterogeneity in survival when modelling senescence to avoid erroneous conclusions, such as survival probabilities that appear to increase with age. Additionally, using simulation, we found that unaccounted for heterogeneity in capture probability can also bias our inference on age–dependent survival probabilities. Therefore, we extended Shirley’s stopover model to account for heterogeneity in both survival and capture probability (equation 3 in our paper).
I was lucky enough to have the opportunity to work alongside Shirley in Wellington (New Zealand), for a few months after the end of my PhD, which is when we completed this work. We fitted the new model to capture–recapture data on possums in New Zealand, provided by Dr Murray Efford, with whom we exchanged many interesting ideas. Some possums were of known age but we did not take this information into account for this work to demonstrate how the model can be used to estimate age–specific survival probabilities for individuals of unknown age.
Our findings suggested that survival probability is lower for individuals aged 1, then it increases for ages 2 to 4, and it decreases after that age, with annual survival probability lower than 50% for all ages over 12. This pattern has been observed for several species in the past, including birds, deer and sheep, but demonstrated for the first for individuals of unknown age.
Since the article…
Since our article was published, there has been a lot of work in the field and several open–population models, for capture–recapture and other types of data, have been proposed. While the term “stopover model” was originally established in the context of modelling the movement of organisms through migration stopover sites, it is now widely used to mean a model that allows for the estimation of survival probabilities as functions of unknown age. Examples include Bayesian stopover models, stopover models within a Hidden Markov model framework as well as novel Bayesian non-parametric models for a single site and year or multiple sites and years.
These new developments have tended to focus less on senescence and more on migration stopover case studies, similar to that originally considered by Shirley. An exception is our very recent work demonstrating the use of Polya Tree priors for modelling open populations. In one of the case studies in this paper, we show how we can back–track the times of birth to estimate age–specific survival probabilities using ring–recovery data when only some of the individuals are of known age.
Understanding age-specific survival, and how this might change over time, is a vital aspect of contemporary ecology in a world subject to climate warming. This is why models for estimating age–specific survival probabilities when age is unknown (or the equivalent for stopover data) remain of interest and new modelling approaches are still being developed for this purpose.
Find out about the Methods in Ecology and Evolution articles selected to celebrate Volumes 1-6: