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.