The Role of Modeling in Monarch Butterfly Research and Conservation

Models are an integral part of the scientific endeavor, whether they be conceptual, mathematical, statistical, or simulation models. Models of appropriate complexity facilitate comprehension and improve understanding of the variables driving system processes. In the context of conservation planning decision-making or research efforts, a useful model can aid interpretation and avoid overfitting by including only essential elements. Models can serve two related, but different purposes: understanding and prediction of future system behavior. Predictive models can require several iterations of refinement and empirical data gathering to be useful for conservation planning. Models with less predictive ability can be used to enhance understanding of system function and generate hypotheses for empirical evaluation. Modeling monarch butterfly systems, whether it be landscape-scale movement in breeding habitats, migratory behavior, or population dynamics at monthly or yearly timeframes, is challenging because the systems encompass complex spatial and temporal interactions across nested scales that are difficult, if not impossible, to empirically observe or comprehend without simplification. We review mathematical, statistical, and simulation models that have provided insights into monarch butterfly systems. Mathematical models have provided understanding of underlying processes that may be driving monarch systems. Statistical models have provided understanding of patterns in empirical data, which may represent underlying mechanisms. Simulations models have provided understanding of mechanisms driving systems and provide the potential to link mechanisms with data to build more predictive models. As an example, recently published agent-based models of non-migratory eastern North American monarch butterfly movement and egg-laying may provide the means to explore how different spatial patterns of habitat, habitat quality, and the interaction of stressors can influence future adult recruitment. The migratory process, however, has not been addressed with agent-based modeling. Using western monarch migration as an example, we describe how modeling could be used to provide insights into migratory dynamics. Future integration of migratory models with non-migratory and population dynamics models may provide better understanding and ultimately prediction of monarch butterfly movement and population dynamics at a continental scale.