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Project description: Capture-recapture data are commonly collected and modelled for the study of wildlife populations (McCrea and Morgan, 2014). Existing capture-recapture models typically assume independence between individuals, with no network structure. Hence, the probability of capture, survival, or movement of particular individuals is assumed to be unaffected by events occurring to other individuals, or actions of these individuals, in the same population. The assumption of independence between individuals gives rise to likelihood functions that are simple products of probabilities of individual capture histories.

However, animal populations are structured by interaction networks among individuals and many species tend to live in social groups that result in these interaction networks differing from random (Wey et al., 2008; Pinter-Wollman et al., 2014; Krause et al., 2015;). In these cases, probabilities of certain events involving particular individuals might be related to their position in the social network. For example, individuals that are strongly connected in a network may be more likely to be captured at the same event. However, network relationships may also result in covariation in survival, or associated traits, between individuals. For example, the spread of directly transmitted infectious diseases will be linked to network structure and this could result in social covariance in survival if infection elevates mortality. Therefore, the survival probability and capture histories of individuals in the same network are expected to change according to the histories of all individuals in that network.

Moreover, there may an additional level of clustering, with certain networks, which are in close proximity for example, affecting each other, maybe to a less, but still not negligible extent. Additionally, it is possible that network structure changes over time, with network membership, and as a result network behaviour, also changing over time. Capture-recapture models offer a possibility of modelling network structure, while accounting for changing membership over time.

A wide range of statistical social network models have been developed, especially within sociology, and are increasingly applied across a range of fields (Cranmer et al., 2017; Silk et al. 2017). However, no such modelling approach exists for capture-recapture data. Ignoring a potential network structure, and hence ignoring dependence between individuals in the same network or dependence between linked networks, may lead to biased estimates of demographic parameters of interest, such as survival probability. Further, incorporating network structure within existing capture-recapture models offers a statistical framework to understand longer-term network dynamics that is more robust to turnover in membership than many existing statistical models of networks.

The project will develop network models for capture-recapture data, motivated by a long-term data set on badgers. The European badger Meles meles is a medium-sized carnivorous mammal widely distributed across the Western Palearctic. In high density populations badgers live in territorial social groups, and individuals interact frequently with other group members and much more rarely with individuals from neighbouring groups (Weber et al. 2013 Current Biology). One such high density population in South West England has been studied using mark-recapture methods for over 40 years providing a unique long-term demographic dataset ideally suited to investigate the questions outline above (McDonald et al., 2018). Capture-recapture models (e.g. McDonald et al., 2016) and social network approaches (e.g. Weber et al., 2013, Silk et al. 2018) have been used to provide valuable insights into this population, but have yet to be combined within a single approach. Therefore, this project offers an important opportunity to gain a new understanding as to how social interactions relate to key demographic processes.

Although the project is motivated by a capture-recapture data set, the methods developed and applied will be more generally applicable to the study of network data. Given the size and complexity of the available data set, the developed methods will need to be scalable to large data sets, making them even more appealing and relevant in the study of network data.

References

Cranmer, S. J., Leifeld, P., McClurg, S. D., & Rolfe, M. (2017). Navigating the range of statistical tools for inferential network analysis. American Journal of Political Science, 61(1), 237-251

Krause, J., James, R., Franks, D. W., & Croft, D. P. (Eds.). (2015). Animal social networks. Oxford University Press, USA.

McCrea, R. S., & Morgan, B. J. (2014). Analysis of capture-recapture data. CRC Press.

McDonald, J. L., Robertson, A., & Silk, M. J. (2018). Wildlife disease ecology from the individual to the population: Insights from a long‐term study of a naturally infected European badger population. Journal of Animal Ecology, 87(1), 101-112.

Pinter-Wollman, N., Hobson, E. A., Smith, J. E., Edelman, A. J., Shizuka, D., De Silva, S., … & Fewell, J. (2013). The dynamics of animal social networks: analytical, conceptual, and theoretical advances. Behavioral Ecology, 25(2), 242-255.

Silk, M. J., Croft, D. P., Delahay, R. J., Hodgson, D. J., Weber, N., Boots, M., & McDonald, R. A. (2017). The application of statistical network models in disease research. Methods in Ecology and Evolution.

Silk, M. J., Weber, N. L., Steward, L. C., Hodgson, D. J., Boots, M., Croft, D. P., … & McDonald, R. A. (2018). Contact networks structured by sex underpin sex‐specific epidemiology of infection. Ecology letters, 21(2), 309-318.

Weber, N., Carter, S. P., Dall, S. R., Delahay, R. J., McDonald, J. L., Bearhop, S., & McDonald, R. A. (2013). Badger social networks correlate with tuberculosis infection. Current Biology, 23(20), R915-R916.

Wey, T., Blumstein, D. T., Shen, W., & Jordan, F. (2008). Social network analysis of animal behaviour: a promising tool for the study of sociality. Animal behaviour, 75(2), 333-344.

Applicants should have a good degree in statistics, mathematics, computer science, or related subjects with a strong numerical component. They should be comfortable working with data and learning new methods, determined, and interested in engaging with the practical applications of their research.

Supervisors

The supervisory team brings together multidisciplinary expertise covering statistics and ecology.

Dr Eleni Matechou and Dr Xue Wang, University of Kent
Dr Matthew Silk, University of Exeter

Eleni gave a seminar on the 15th of March 2017 as part of the Ecology, Evolution and Environment seminar series at the Department of Animal and Plant Sciences, University of Sheffield.

Title: Modelling phenology for marked and unmarked populations

Abstract: In this seminar I will discuss fairly recent models for capture-recapture and for count data that enable us to estimate, among other things, phenology of wildlife populations. The methods explored will include classical as well as Bayesian parametric and non-parametric approaches. They will be demonstrated using data on breeding great crested newts, migrating reed warblers, bivoltine butterfly species , bumblebees from the citizen science scheme BeeWalk as well as data on anglers in Norway.