Reducing matrix population models with application to social animal species

Stage-structured matrix models are commonly used to inform management decisions for species with complex life cycles. These models require information on the number or proportion of individuals in each stage. However, complex life cycles, such as those in species exhibiting a complex social organization, can make these data difficult to obtain. The discrete time structure of matrix models makes them reducible, meaning that full models can be simplified by removing some stages. We illustrate the method by reducing the life cycle of wolf (Canis lupus) on which culling and conservation plans often lead to controversial debates. Starting from a 4-stage matrix incorporating social stages, we obtained several reduced models of increasing simplicity all showing similar demographic outcomes to the full model. We found that asymptotic growth rates of reduced models were in close agreement with empirical data. Our approach can offset the lack of information on individual stage abundance and therefore be valuable when using matrix models for wildlife management when data on certain stages are sparse.