Spiral waves in population density distributions of invasive pests in warm-temperate deciduous forest ecosystems

Abstract

Globally, forests are increasingly being affected by invasive alien pests, some of which have caused wholesale destruction of trees. Recent research suggests that, in the United States, large-scale forests have been invaded by an astonishing number (> 450) of tree-feeding pests. Invasive alien pests always induce cascading ecological effects, leading to harmful socioeconomic consequences; however, the prevention and control of invasive alien pests in forests have been facing significant challenges worldwide. Here, we studied theoretically the control of invasive nonnative pests in warm-temperate deciduous forest ecosystems by their natural enemies (biological control), and controlled them to an extent that ecosystems can bear. We obtained a novel type of spiral wave in the spatial distribution of population density, and also observed a transition phenomenon between spiral wave and anti-spiral wave, which is explained by a mathematical analysis. Specifically, the formation of this type of spiral wave is attributed to the directional transformation of states between the period-5 orbits under the impact of diffusion transport. And the transition phenomenon is caused by changes of relative positions of the period-5 orbits in phase space. Moreover, we also found a novel type of instability of spiral wave, which includes a birth-growth-death process of spiral fragments. The findings provide possible regularities in the process of biological control of invasive alien pests in the complex and changeable forest ecosystems, which may guide actual biological control projects.