Effect of temporal and spatial noise colour in insect outbreak frequency

Abstract

Insect outbreaks are a common multicausal population phenomenon that is characterised by a fast growth of the population, followed by an equally sudden collapse in a relatively short period in the manner of an excitable system. If the outbreaking insect is herbivorous or attacks trees or plants as a part of its life cycle, this phenomenon causes a major impact on the plant’s population. As a consequence, outbreaks are a major cause of vegetation loss and tree mortality in ecosystems. Among the several causes of outbreaks, climatic/environmental variation is one of the most important. For example, droughts can weaken plant defences making them more susceptible to insect herbivore attacks. As the climatic-driven effects on plant populations are correlated to time and space, not only the type of variability but also its magnitude, are of key importance for the appearance of this phenomenon. In theoretical studies, noise colour is usually used as a proxy to represent the variability of forcing external variables, such as climate. In this study, we conducted a series of simulations using a spatially explicit model to analyse the effect of combining several types of spatial and temporal environmental noise colours (red, pink, white, blue, violet, and grey) on the frequency of outbreaks. We found that the frequency of outbreaks increased with the autocorrelation of noise. The combination of spatial and temporal white noise showed a low-risk scenario, while pink noise had a much higher frequency of this phenomenon. However, the combination of spatial grey noise (a noise composed of both low and high frequencies), with temporal low-frequency noise, resulted in all simulations causing severe outbreaks. We suggest two explanations for this. On one hand, the presence of high-frequency noise gave the herbivore the ability to percolate through refugees caused by the low-frequency noise; and, on the other hand, low-frequency temporal noise gave the herbivore time to kill all simulated host plants.