# Spatially explicit dynamic N-mixture models

## Abstract

Knowledge of demographic parameters such as survival, reproduction, emigration, and immigration is essential to understand metapopulation dynamics. Traditionally the estimation of these demographic parameters requires intensive data from marked animals. The development of dynamic N-mixture models makes it possible to estimate demographic parameters from count data of unmarked animals, but the original dynamic N-mixture model does not distinguish emigration and immigration from survival and reproduction, limiting its ability to explain important metapopulation processes such as movement among local populations. In this study we developed a spatially explicit dynamic N-mixture model that estimates survival, reproduction, emigration, local population size, and detection probability from count data under the assumption that movement only occurs among adjacent habitat patches. Simulation studies showed that the inference of our model depends on detection probability, local population size, and the implementation of robust sampling design. Our model provides reliable estimates of survival, reproduction, and emigration when detection probability is high, regardless of local population size or the type of sampling design. When detection probability is low, however, our model only provides reliable estimates of survival, reproduction, and emigration when local population size is moderate to high and robust sampling design is used. A sensitivity analysis showed that our model is robust against the violation of the assumption that movement only occurs among adjacent habitat patches, suggesting wide applications of this model. Our model can be used to improve our understanding of metapopulation dynamics based on count data that are relatively easy to collect in many systems.

## Keywords

Abundance Dail and Madsen model Demography Hidden Markov model Metapopulation dynamics Movement## Notes

### Acknowledgements

The research was funded by Research Work Order 91 (G11AC20327), from the US Fish and Wildlife Service to Colorado State University through the US Geological Survey Colorado Cooperative Fish and Wildlife Research Unit. The findings and conclusions in this article are those of the authors and do not necessarily represent the views of the US Fish and Wildlife Service. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the US Government.

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