Perturbation analysis has long been an essential part of any modeler’s toolbox. Until recently the vast majority of perturbation analyses for structured population models were conducted within the well-developed framework of matrix models with discrete stage classes. For organisms with population structure that can be described by continuous trait values (e.g. size, biomass), Integral Projection Models (IPMs) provide a compelling alternative approach. As IPMs are essentially high-resolution matrix models, perturbation approaches developed for matrix models remain largely applicable. However, the regression-based framework of IPMs expands the set of values that can be perturbed, and the continuous nature of state variables used to structure the population can demand careful consideration in certain cases. I use a literature survey, simulated data, and field-collected data of a perennial plant to (1) review and compare different perturbation approaches for IPMs, (2) introduce a new method for perturbing size transition probabilities in order to better understand the relative importance of growth versus retrogression, and (3) highlight areas where researchers should be particularly careful and critical when conducting perturbation analysis.
Results/Conclusions
When perturbing size transition probabilities (given survival) it is essential to account for interdependence among values within matrix columns so as to maintain the sum of the size-specific transition probabilities. An existing approach effectively counter balances any perturbation via a change to the probability of stasis. I show that this method is inappropriate as it introduces a second perturbation to the distribution of transition probabilities. This amplifies the sensitivity/elasticity values associated with growth or retrogression, depending on the distribution of size transition probabilities relative to stasis. I introduce an alternative perturbation approach that accounts for size transition interdependence while maintaining the relative proportions of non-target transitions. Life Table Response Experiment (LTRE) analysis highlights important differences in this approach regarding the importance of growth vs. retrogression compared to existing methods. Another important result is that elasticity values associated with perturbations to the state variable (e.g. the mean of the future size distribution) can be strongly impacted by the scale of measure. For example, a proportional change in rosette diameter is not the same as a proportional change in rosette area (or log area). This can result in substantially different elasticity values for growth versus survival or fecundity given the same dataset.