Integrated survival analysis using an event-time approach in a Bayesian framework

Using incidental mark-encounter data to improve survival estimation

Obtaining robust survival estimates is critical, but sample size limitations often result in imprecise estimates or the failure to obtain estimates for population subgroups. Concurrently, data are often recorded on incidental reencounters of marked individuals, but these incidental data are often unused in survival analyses.We evaluated the utility of supplementing a traditional survival dataset with incidental data on marked individuals that were collected ad hoc. We used a continuous time-to-event exponential survival model to leverage the matching information contained in both datasets and assessed differences in survival among adult and juvenile and resident and translocated Mojave desert tortoises (Gopherus agassizii).Incorporation of the incidental mark-encounter data improved precision of all annual survival point estimates, with a 3.4%-37.5% reduction in the spread of the 95% Bayesian credible intervals. We were able to estimate annual survival for three subgroup combinations that were previously inestimable. Point estimates between the radiotelemetry and combined datasets were within |0.029| percentage points of each other, suggesting minimal to no bias induced by the incidental data.Annual survival rates were high (>0.89) for resident adult and juvenile tortoises in both study sites and for translocated adults in the southern site. Annual survival rates for translocated juveniles at both sites and translocated adults in the northern site were between 0.73 and 0.76. At both sites, translocated adults and juveniles had significantly lower survival than resident adults. High mortality in the northern site was driven primarily by a single pulse in mortalities.Using exponential survival models to leverage matching information across traditional survival studies and incidental data on marked individuals may serve as a useful tool to improve the precision and estimability of survival rates. This can improve the efficacy of understanding basic population ecology and population monitoring for imperiled species.

Surrogate rearing a keystone species to enhance population and ecosystem restoration

Translocation and rehabilitation programmes are critical tools for wildlife conservation. These methods achieve greater impact when integrated in a combined strategy for enhancing population or ecosystem restoration. During 2002–2016 we reared 37 orphaned southern sea otter Enhydra lutris nereis pups, using captive sea otters as surrogate mothers, then released them into a degraded coastal estuary. As a keystone species, observed increases in the local sea otter population unsurprisingly brought many ecosystem benefits. The role that surrogate-reared otters played in this success story, however, remained uncertain. To resolve this, we developed an individual-based model of the local population using surveyed individual fates (survival and reproduction) of surrogate-reared and wild-captured otters, and modelled estimates of immigration. Estimates derived from a decade of population monitoring indicated that surrogate-reared and wild sea otters had similar reproductive and survival rates. This was true for males and females, across all ages (1–13 years) and locations evaluated. The model simulations indicated that reconstructed counts of the wild population are best explained by surrogate-reared otters combined with low levels of unassisted immigration. In addition, the model shows that 55% of observed population growth over this period is attributable to surrogate-reared otters and their wild progeny. Together, our results indicate that the integration of surrogacy methods and reintroduction of juvenile sea otters helped establish a biologically successful population and restore a once-impaired ecosystem.

Filling in the gaps in survival analysis: using field data to infer plant responses to environmental stressors

Elucidating how organismal survival depends on the environment is a core component of ecological and evolutionary research. To reconcile high-frequency covariates with lower-frequency demographic censuses, many statistical tools involve aggregating environmental conditions over long periods, potentially obscuring the importance of fluctuating conditions in driving mortality. Here, we introduce a flexible model designed to infer how survival probabilities depend on changing environmental covariates. Specifically, the model (1) quantifies effects of environmental covariates at a higher frequency than the census intervals, and (2) allows partitioning of environmental drivers of individual survival into acute (short-term) and chronic (accumulated) effects. By applying our method to a long-term observational data set of eight annual plant species, we show we can accurately infer daily survival probabilities as temperature and moisture levels change. Next, we show that a species' water use efficiency, known to mediate annual plant population dynamics, is positively correlated with the importance of "chronic stress" inferred by the model. This suggests that model parameters can reflect underlying physiological mechanisms. This method is also applicable to other binary responses (hatching, phenology) or systems (insects, nestlings). Once known, environmental sensitivities can be used for ecological forecasting even when the frequency or variability of environments are changing.

Using expert knowledge to incorporate uncertainty in cause-of-death assignments for modeling of cause-specific mortality

Implicit and explicit use of expert knowledge to inform ecological analyses is becoming increasingly common because it often represents the sole source of information in many circumstances. Thus, there is a need to develop statistical methods that explicitly incorporate expert knowledge, and can successfully leverage this information while properly accounting for associated uncertainty during analysis. Studies of cause-specific mortality provide an example of implicit use of expert knowledge when causes-of-death are uncertain and assigned based on the observer's knowledge of the most likely cause. To explicitly incorporate this use of expert knowledge and the associated uncertainty, we developed a statistical model for estimating cause-specific mortality using a data augmentation approach within a Bayesian hierarchical framework. Specifically, for each mortality event, we elicited the observer's belief of cause-of-death by having them specify the probability that the death was due to each potential cause. These probabilities were then used as prior predictive values within our framework. This hierarchical framework permitted a simple and rigorous estimation method that was easily modified to include covariate effects and regularizing terms. Although applied to survival analysis, this method can be extended to any event-time analysis with multiple event types, for which there is uncertainty regarding the true outcome. We conducted simulations to determine how our framework compared to traditional approaches that use expert knowledge implicitly and assume that cause-of-death is specified accurately. Simulation results supported the inclusion of observer uncertainty in cause-of-death assignment in modeling of cause-specific mortality to improve model performance and inference. Finally, we applied the statistical model we developed and a traditional method to cause-specific survival data for white-tailed deer, and compared results. We demonstrate that model selection results changed between the two approaches, and incorporating observer knowledge in cause-of-death increased the variability associated with parameter estimates when compared to the traditional approach. These differences between the two approaches can impact reported results, and therefore, it is critical to explicitly incorporate expert knowledge in statistical methods to ensure rigorous inference.