Plant population responses to fluctuating herbivory: An approach for obtaining stochastic elasticities to the mean and variance of species interactions

Background/Question/Methods

Many insect populations vary dramatically in abundance from year to year, and as a result, the damage to plants caused by herbivorous insects can vary remarkably as well. Recent applications of demographic modeling to assess the long-term effect of herbivores on plant population dynamics have used deterministic approaches; other analyses have focused on decomposing the multifaceted effects of interactions into the separate contributions of different individual rates (deterministic or stochastic life table response experiments). Neither approach asks directly what effects could be expected from changes in mean levels of herbivory or in its variability, such as might be expected in a fluctuating and shifting climate. Stochastic elasticities separate the influence on long-term population growth rate of changes in the mean from effects of changes in the variability of individual demographic rates. I bring these methods to bear on herbivory, which can affect many vital rates simultaneously and in different ways in different years, in order to calculate stochastic elasticities to the mean and to the variability of herbivory. This approach adds valuable information to the demographic interpretation of species interactions, and uses data from the same long-term experimental designs as previous analyses.

Results/Conclusions

Stochastic elasticities measure the effect on the stochastic growth rate of changes to the time-dependent population projection matrix. Although frequently used to assess the effects of changes to individual matrix elements, elasticities can take into account changes to multiple elements. In order to assess the effects of a treatment which affects multiple rates, we must determine how the different rates change together. For each vital rate that changes due to herbivory in any year (assessed using comparison with herbivory-exclusion plots), I regress the changes due to herbivory across years on the change in the most variable rate. I calculate the stochastic elasticity to the mean of herbivory computationally, using multiple simultaneous perturbations: the perturbation applied to the most variable vital rate is a standard against which perturbations to other rates are relativized using regression coefficients. To calculate stochastic elasticities to the variability of herbivory, in each year I perturb each affected vital rate in proportion to its deviation in that year from its mean in the absence of herbivory. I illustrate the approach and calculations using published data on a perennial grassland herb, Primula veris.