Avoiding unintentional eviction from integral projection models.

Integral projection models (IPMs) are increasingly being applied to study size-structured populations. Here we call attention to a potential problem in their construction that can have important consequences for model results. IPMs are implemented using an approximating matrix and bounded size range. Individuals near the size limits can be unknowingly "evicted" from the model because their predicted future size is outside the range. We provide simple measures for the magnitude of eviction and the sensitivity of the population growth rate (lambda) to eviction, allowing modelers to assess the severity of the problem in their IPM. For IPMs of three plant species, we found that eviction occurred in all cases and caused underestimation of the population growth rate (lambda) relative to eviction-free models; it is likely that other models are similarly affected. Models with frequent eviction should be modified because eviction is only possible when size transitions are badly mis-specified. We offer several solutions to eviction problems, but we emphasize that the modeler must choose the most appropriate solution based on an understanding of why eviction occurs in the first place. We recommend testing IPMs for eviction problems and resolving them, so that population dynamics are modeled more accurately.