2.4 Estimating survival probabilities
Radio-tracking data were aggregated into encounter histories of biweekly intervals. The encounter histories were used in a Cormack–Jolly–Seber (CJS) mark–recapture model estimating biweekly survival while controlling for variation in detection probability and individual variability (Lebreton et al. 1992; Kéry & Schaub 2012).
Because our key interest was to quantify seasonal differences in survival, our survival model included a fixed intercept for each of the four seasons (summer, autumn, winter, spring), as well as fixed effects to account for the mass and sex of each fledgling (Tschumi et al. 2019), and whether the fledglings came from broods that were provided with supplementary food (Perrig et al. 2017). We also included a fixed effect that explored whether duration of snow cover could explain variation in survival. Because body mass and size were highly correlated, and the variables age and body size did not affect survival in preliminary explorations, we retained the most parsimonious combination of variables (Hooten & Hobbs 2015), and neither age nor size were retained in our survival model. We fitted three models to include the variables body mass and supplementary feeding in three alternative model formulations: either by affecting survival only in the immediate post-fledging period (Perrig et al. 2017), or by allowing body mass and supplementary feeding to affect survival in every season over the first year of life (Catitti et al. 2022; Nägeli et al. 2022; Mainwaring et al. 2023).
To estimate detection probability, we included temporal variation in tracking effort as an explanatory variable due to the unequal tracking efforts across years and tracking periods. We specified that detection probability was zero during four intervals when no tracking effort occurred. For the remaining intervals we estimated two distinct detection probabilities, one for those six biweekly periods with reduced effort in winter 2009 and 2010, and another for the remaining 80 periods with full tracking effort. We also included a random individual effect to account for residual variability in detection probability among individuals. Because severe winter weather may not only affect survival, but may also lead to temporary escape movements to more benign areas (Sonerud 1986; Mysterud 2016; Gura 2023), we included the same snow cover variable that we assumed to affect survival also for detection probability to account for possible temporary emigration and low detection probability during severe winter weather.
We used a Bayesian approach for inference to include existing prior information on the survival probability of little owls (Schaub et al. 2006; Le Gouar et al. 2011; Thorup et al. 2013). We fit the models in software JAGS v. 3.3. (Plummer 2012) called from R 4.1.3 (R Core Team 2023) via the ‘runjags’ library (Denwood 2016). We used a mildly informative prior for the biweekly survival probability (beta distribution with α = 95 and β = 10) given previous information on little owl survival (Le Gouar et al. 2011; Thorup et al. 2013), and a similarly informative prior for the detection probabilities during occasions with normal (random uniform 0.7 – 1) and reduced effort (random uniform 0.3 – 0.9). We used vague normally distributed priors for all other parameters, and conducted a prior sensibility test to ensure that biologically plausible survival estimates resulted from our prior distributions (Banner et al. 2020). We ran three Markov chains for 3,500 iterations each, discarded the first 200 iterations and used every sixth iteration for inference. Convergence of the three chains for all monitored parameters was visually inspected using trace plots and tested using the Gelman–Rubin diagnostic (Brooks & Gelman 1998) to confirm that all parameters had an R-hat of < 1.02. We implemented posterior predictive checks to assess the goodness-of-fit of the survival model (Gelman et al. 1996; Kéry & Schaub 2012; Conn et al. 2018), and confirmed that there was no evidence for a lack of fit (Bayesian p-value = 0.427). Code to replicate these analyses can be found at https://github.com/Vogelwarte/LittleOwlSurvival and in the Supplementary Material.
We present median parameter estimates (β ) for covariates on the logit scale with 95% credible intervals. We also present posterior estimates of biweekly survival probability with 95% credible intervals for each of the four seasons based on birds of average body mass that did not receive supplementary food as nestlings. To facilitate interpretation and comparison with other survival estimates, we calculated season-specific survival by raising biweekly survival to the power of the length of each season (summer: 4 periods, autumn: 6 periods, winter: 10 periods, spring: 6 periods). To predict survival in severe winters, we used the maximum length of intense snow cover periods during our study to decompose the 10 winter periods into 2 periods with extreme snow cover, 3 periods each with high and intermediate snow cover, and 2 periods without snow cover (resulting in 43% of 140 winter days experiencing snow cover), and we multiplied the respective survival probabilities to estimate overwinter survival. To estimate annual survival, we multiplied the four seasonal survival probabilities, which represents the annual survival probability from 1 July to 30 June of the following year. To visualise what proportion of juveniles survived over the first year of life, we simulated the proportion of 100 juveniles of average body mass that survived 26 fortnightly periods from one summer to the next by multiplying the number of live birds by the fortnight-specific survival probability. We present this proportion for four scenarios, namely for birds that did and did not receive supplementary food as nestlings during either a mild or a harsh winter.