Estimating spatially variable and density-dependent survival using open-population spatial capture-recapture models

Open-population spatial capture-recapture (OPSCR) models use the spatial information contained in individual detections collected over multiple consecutive occasions to estimate occasion-specific density, but also demographic parameters. OPSCR models can also estimate spatial variation in vital rates, but such models are neither widely used nor thoroughly tested. We developed a Bayesian OSPCR model that not only accounts for spatial variation in survival using spatial covariates, but also estimates local density-dependent effects on survival within a unified framework. Using simulations, we show that OPSCR models provide sound inferences on the effect of spatial covariates on survival, including multiple competing sources of mortality, each with potentially different spatial determinants. Estimation of local density-dependent survival was possible but required more data due to the greater complexity of the model. Not accounting for spatial heterogeneity in survival led to positive bias in abundance estimates (up to 10% relative bias). We provide a set of features in R package nimbleSCR that allow computationally efficient fitting of Bayesian OPSCR models with spatially varying survival. The ability to make population-level inferences of spatial variation in survival is an essential step towards a fully spatially-explicit OPSCR model that can disentangle the role of multiple spatial drivers on population dynamics. Open Research statement code to reproduce the analysis is available on github; https://github.com/Cyril-Milleret/Public/tree/master/SpatialSurvivalOPSCR

mortality, each with potentially different spatial determinants. Estimation of local density-23 dependent survival was possible but required more data due to the greater complexity of the 24 model. Not accounting for spatial heterogeneity in survival led to positive bias in abundance 25 estimates (up to 10% relative bias). We provide a set of features in R package nimbleSCR that 26 allow computationally efficient fitting of Bayesian OPSCR models with spatially varying 27 survival. The ability to make population-level inferences of spatial variation in survival is an 28 2 essential step towards a fully spatially-explicit OPSCR model that can disentangle the role of 29 multiple spatial drivers on population dynamics. and applied (Chandler et al. 2018). However, the performance of models that estimate spatially-49 variable survival has not been thoroughly tested and their potential remains under-exploited.

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Estimation of spatially varying vital rates is a key step in the development of OPSCR models 51 3 (Royle et al. 2014) as it will lead to a better understanding of the processes driving the spatial 52 distribution of individuals (Pulliam 1988).

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At their core, OPSCR models account for imperfect detection by using an observation process 54 which assumes that an individual's probability of detection is a function of distance from its 55 activity center (AC) (Borchers andEfford 2008, Royle et al. 2014). The location of individual 56 ACs is a latent quantity and is a representation of the center of the individual's home range.

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AC locations are a key quantity of OPSCR models as they allow the estimation of density and 58 inter-annual movement. AC locations also provide the spatial information necessary to 59 characterize the environment in which individuals are located, and therefore its influence on 60 survival (Chandler et al. 2018).

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Density itself can be a key driver of survival (Gaillard et al. 2000). The study of density-62 dependent survival has often been limited to estimating the average population response to 63 variation in overall population size through time (Bonenfant et al. 2009). However, variation 64 in density is a spatiotemporal process and individuals within the population may not experience 65 the same density. OPSCR models, by estimating spatio-temporal variation in density, offer a 66 unique opportunity to study density-dependence in survival at the local scale while accounting 67 for variation and uncertainty in both density and survival within a unified framework.

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Here, we present a Bayesian OPSCR model that accounts for spatial variation in survival as a 69 function of spatial covariates (e.g., characteristics of the landscape, resources availability) and 70 density. We model survival using a hazard rate formulation to allow inferences on spatial 71 variation in competing risks of mortality (Ergon et al. 2018). We quantify model performance 72 by simulating OPSCR datasets under a wide range of scenarios. In addition, we quantify the 73 consequence of ignoring spatial heterogeneity in mortality for OPSCR inferences. All

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• If zi,t-1 = 2, individual i can survive with probability and remain zit=2. If it does not 113 survive, it can either die due to culling and be recovered (transition to zi,t=3) with 114 probability hi, or die from other causes without being recovered (transition to zi,t =4) 115 with probability wi, so that zi,t ~ dcat(0, , hi, wi), where Φi = 1−hi −wi.

Ignoring spatial heterogeneity in mortality 212
To evaluate whether ignoring spatial variation in mortality leads to biased parameter estimates, 213 especially abundance (̂), we fitted all simulated datasets described above with OPSCR models 214 that assumed constant survival across space and time. As in the earlier simulations, we fitted 215 models with two competing risks for the deterministic spatial covariate scenarios and a single 216 cause of mortality for the density dependent scenario.   228 We summarized the posterior ̂ for each parameter and each simulation using relative error of   , table 3-6). Across all scenarios, the effect of spatial covariates on mortality cause 252 with no dead recovery information ( ) was more challenging to estimate, with lower precision 253 (approx. 2 times larger CV) than ( ℎ ) (Fig 1.C, Appendix 1, table 3-6).  255 Across the 100 replicated datasets, 86 models reached convergence and showed no 256 identifiability issues (Appendix 2, table 13). We detected a 13% positive relative bias in 0 257 and but coverage was >92% for all parameters (Figure 2 A, table 14).

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We described and tested an OPSCR model that explicitly models and estimates spatial variation  One of the main advantages of SCR models is that they can estimate spatial variation in density. 285 We showed that OPSCR models can simultaneously estimate local density and its effect on 286 survival. This has the advantage that the uncertainty in both the number of individuals alive