Factors Influencing Soay Sheep Survival

Abstract

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population signi®cantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to in¯uence survival signi®cantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also ®tted. The only covariate which is found to in¯uence survival signi®cantly is the type of horn of ®rst-year female sheep. There is a substantial variation in the recovery probabilities over time, re¯ecting in part the increased effort when a population crash was expected. The goodness of ®t of the model is checked by using graphical procedures.

Analysing Mark–Recapture–Recovery Data in the Presence of Missing Covariate Data Via Multiple Imputation

“…An individual history is most easily expressed in the form of the combination of an encounter history (whether an individual is observed at each capture event) and covariate history (the weight of the individual at each capture event). For example, consider the following history of an individual first observed as a lamb in 1991 and recovered dead in 2000: 199119921994199519961997199819992000 The second line corresponds to the encounter history, where "0" denotes the individual is not observed, "1" the individual is observed, and "2" the individual is recovered dead. Thus this individual was initially captured and marked in 1991, recaptured in 1992, 1995 and 1997 before being recovered dead in 2000.…”

“…To incorporate additional individual heterogeneity in the survival probabilities, φ, we specify the survival probabilities as a function of individual time-varying continuous covariates (Catchpole et al 2000(Catchpole et al , 2004Bonner and Schwarz 2006;King et al 2006King et al , 2008King et al , 2009). We consider a single covariate, for simplicity, but the method can be immediately extended to multiple covariates (see Sect.…”

“…Previous classical approaches for obtaining parameter estimates in the presence of individual covariates have included removing individuals for which there are any missing covariate values (Catchpole et al 2000, for only time-invariant individual covariates); the trinomial approach using a conditional likelihood (Catchpole et al 2008); and discretisation methods, either coarsely (Nichols et al 1992), which discards significant information, or finely (Langrock and King 2013). For further discussion of these (and additional approaches) see for example Catchpole et al (2000) and Langrock and King (2013).…”

“…For further discussion of these (and additional approaches) see for example Catchpole et al (2000) and Langrock and King (2013). Alternatively, a Bayesian data augmentation approach has been proposed (Bonner and Schwarz 2006;King et al 2006King et al , 2008 forming the joint posterior distribution over the model parameters and unobserved covariate values.…”

Temporal variations in English populations of a forest insect pest, the green spruce aphid (Elatobium abietinum), associated with the North Atlantic Oscillation and global warming

“…Cod (Gadus morhua L.) recruitment in the North Atlantic increased during the sustained negative phase of the NAO index in the 1960s and then recruitment decreased during the more positive phase of the NAO index in the 1990s with water temperature as the most likely controlling factor (Parsons and Lear, 2001). Soay Sheep (Ovis aries L.) populations on Hirta, part of the St Kilda archipelago, Scotland, appear to be influenced by precipitation in March (Catchpole et al, 2000). Red Deer (Cervus elaphus L.) in Norway are affected by the NAO before birth, with warmer winters resulting in smaller birth size than those born following cold winters (Post et al, 1997).…”