Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids

Helms, S. E., & Hunter, M. D. (2005). Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids. Oecologia, 145(2), 196-203.

Spatial heterogeneity in the environment is ubiquitous, and can affect any number of parameters that drive population dynamics, including fecundity, survival, movement, and competition strength, among others. However, models of population dynamics and easily ignore this heterogeneity, treating each patch as equivalent (or using a mean environmental value). In this paper, Helms and Hunter (2005) ask how variability in plant quality affect population dynamics of insect herbivore populations. In all of their models, the authors simulate ten host plants with differing degrees of density dependence (if b>0, then density dependence is operating). In their simplest model, where one plant displays exponential growth and the others have some degree of density dependence, they find that the entire insect population grows exponentially after some time, even when the average value of b is positive, which would not suggest exponential growth.  The authors then explore the effect of increasing spatial heterogeneity and find that increasing variance in b increases the probability of exponential growth (because the likelihood of having one or more b<0 increases with increasing variance and a fixed mean). Last, by incorporating movement between host plants into the model, the authors show that an equilibrium can be reached even when one plant shows exponential growth, but only when two conditions are met. First, the emigration rate from the exponential plant must exceed its growth rate in order to prevent overall exponential growth. Second, the growth rate at the non-exponential plants must be great enough to prevent extinction (i.e they must display positive growth).

To accompany these models, Helms and Hunter use a model system of aphids growing on Asclepias plants. They measure overall population growth rates and growth rates on individual plants; the results from these measurements confirm that there is a very high probability of finding a plant that supports exponential growth in a group of just ten plants, meaning that the overall population would show exponential growth even when the average b>0. Together, these simple models and model system confirm that population dynamics can depend heavily on spatial heterogeneity. The authors suggest that true variation is likely to increase on a larger spatial scale, making these effects of spatial heterogeneity on population dynamics even larger; further, future studies should explore the role temporal variation in density dependence on a single plant in maintaining equilibria.