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The importance of census times in discrete-time growth-dispersal models

Dispersal has been the focus of spatial ecology for a few decades. What should be a proper theoretical framework for understanding and modelling of dispersal processes remains a controversial issue though. Integrodifference equations (IDE) model the spatial dynamics of a population with distinct growth and dispersal stages in their life cycle. Depending on the stage observed, the equations take on different forms, only one of which is usually studied in the literature. Here we reveal that while these different forms are mathematically equivalent, the biological conclusions drawn from the different forms may differ considerably. We provide a summary of similarities and differences and point out the greatest potential caveats when applying IDE.