Estimating survival in continuous space from mark-dead-recovery data – Towards a continuous version of the multinomial dead recovery model

Understanding spatially varying survival is crucial for understanding the ecology and evolution of migratory animals, which may ultimately help to conserve such species. We develop an approach to estimate an annual survival probability function varying continuously in geographic space, if the recovery probability is constant over space. This estimate is based on a density function over continuous geographic space and the discrete age at death obtained from dead recovery data. From the same density function, we obtain an estimate for animal distribution in space corrected for survival, i.e., migratory connectivity. This is possible, when migratory connectivity can be separated from recovery probability. In this article, we present the method how spatially and continuously varying survival and the migratory connectivity corrected for survival can be obtained, if a constant recovery probability can be assumed reasonably. The model is a stepping stone in developing a model allowing for disentangling spatially heterogeneous survival and migratory connectivity corrected for survival from a spatially heterogeneous recovery probability. We implement the method using kernel density estimates in the R-package CONSURE. Any other density estimation technique can be used as an alternative. In a simulation study, the estimators are unbiased but show edge effects in survival and migratory connectivity. Applying the method to a real-world data set of European robins Erithacus rubecula results in biologically reasonable continuous heat-maps for survival and migratory connectivity.
 
Keywords: Mark-recovery data, Mixed binomial point process, Observation process, Spatially continuous survival estimation, Thinned point process
 
Understanding spatially varying survival is crucial for understanding the ecology and evolution of migratory animals, which may ultimately help to conserve such species. We develop an approach to estimate an annual survival probability function varying continuously in geographic space, if the recovery probability is constant over space. This estimate is based on a density function over continuous geographic space and the discrete age at death obtained from dead recovery data. From the same density function, we obtain an estimate for animal distribution in space corrected for survival, i.e., migratory connectivity. This is possible, when migratory connectivity can be separated from recovery probability. In this article, we present the method how spatially and continuously varying survival and the migratory connectivity corrected for survival can be obtained, if a constant recovery probability can be assumed reasonably. The model is a stepping stone in developing a model allowing for disentangling spatially heterogeneous survival and migratory connectivity corrected for survival from a spatially heterogeneous recovery probability. We implement the method using kernel density estimates in the R-package CONSURE. Any other density estimation technique can be used as an alternative. In a simulation study, the estimators are unbiased but show edge effects in survival and migratory connectivity. Applying the method to a real-world data set of European robins Erithacus rubecula results in biologically reasonable continuous heat-maps for survival and migratory connectivity.
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Understanding spatially varying survival is crucial for understanding the ecology and evolution of migratory animals, which may ultimately help to conserve such species. We develop an approach to estimate an annual survival probability function varying continuously in geographic space, if the recovery probability is constant over space. This estimate is based on a density function over continuous geographic space and the discrete age at death obtained from dead recovery data. From the same density function, we obtain an estimate for animal distribution in space corrected for survival, i.e., migratory connectivity. This is possible, when migratory connectivity can be separated from recovery probability. In this article, we present the method how spatially and continuously varying survival and the migratory connectivity corrected for survival can be obtained, if a constant recovery probability can be assumed reasonably. The model is a stepping stone in developing a model allowing for disentangling spatially heterogeneous survival and migratory connectivity corrected for survival from a spatially heterogeneous recovery probability. We implement the method using kernel density estimates in the R-package CONSURE. Any other density estimation technique can be used as an alternative. In a simulation study, the estimators are unbiased but show edge effects in survival and migratory connectivity. Applying the method to a real-world data set of European robins Erithacus rubecula results in biologically reasonable continuous heat-maps for survival and migratory connectivity.