To enhance our study of ecology, the intersection between mathematics and biology becomes increasingly evident and important. Mathematical analysis provides new insights to ecological data, while ecological context can help explain those insights. Specifically, there is often a need for estimation of basic demographic parameters (e.g. birth and mortality rates) for animals of multiple species. This detailed analysis increases our knowledge of the species under study and may show how seasonality, climate change, or other ecological factors may affect their demographic parameters. One method used to estimate various population parameters is Cormack-Jolly-Seber (CJS) modeling, which estimates information about the life history of organisms from their trapping history. Though software for these models exists, we chose to write our own programs to ensure a more customizable and transparent implementation. In this project, we have written scripts in the language R to find CJS estimates of the demographic parameters for various species from a small mammal community in South Texas, USA, recorded in a dataset that was donated by collaborators. Going forward, we hope to use the results of this CJS model to parameterize mathematical models of ecological interactions between species. By taking both of these approaches, we link differential equations-based population models to probability-based models, which together provide more information about the community under study than either could alone.
