Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry

PLoS Comput Biol. 2020 May 4;16(5):e1007820. doi: 10.1371/journal.pcbi.1007820. eCollection 2020 May.

Abstract

Locusts are significant agricultural pests. Under favorable environmental conditions flightless juveniles may aggregate into coherent, aligned swarms referred to as hopper bands. These bands are often observed as a propagating wave having a dense front with rapidly decreasing density in the wake. A tantalizing and common observation is that these fronts slow and steepen in the presence of green vegetation. This suggests the collective motion of the band is mediated by resource consumption. Our goal is to model and quantify this effect. We focus on the Australian plague locust, for which excellent field and experimental data is available. Exploiting the alignment of locusts in hopper bands, we concentrate solely on the density variation perpendicular to the front. We develop two models in tandem; an agent-based model that tracks the position of individuals and a partial differential equation model that describes locust density. In both these models, locust are either stationary (and feeding) or moving. Resources decrease with feeding. The rate at which locusts transition between moving and stationary (and vice versa) is enhanced (diminished) by resource abundance. This effect proves essential to the formation, shape, and speed of locust hopper bands in our models. From the biological literature we estimate ranges for the ten input parameters of our models. Sobol sensitivity analysis yields insight into how the band's collective characteristics vary with changes in the input parameters. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations. We thus demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands. This work suggests that feeding behaviors should be an intrinsic part of future modeling efforts.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animal Migration / physiology*
  • Animals
  • Australia
  • Behavior, Animal / physiology
  • Feeding Behavior / physiology*
  • Grasshoppers / physiology*
  • Grassland
  • Models, Biological
  • Models, Theoretical
  • Natural Resources / supply & distribution
  • Plague
  • Population Density

Grants and funding

All authors were supported by the Mathematics Research Communities Program of the American Mathematical Society in 2018 under National Science Foundation grant DMS-1321794 (http://www.ams.org/programs/research-communities/mrc). All authors were supported by the Institute for Advanced Study Summer Collaborators Program (https://www.math.ias.edu/summercollaborators). JW is supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship grant DMS-1902818 (https://www.nsf.gov/funding/pgm_summ.jsp?pims_id=5301). WCS was supported by a Simons Foundation Grant #585322. AJB was also supported by a Simons Foundation Grant #317319 (https://www.simonsfoundation.org/grant/collaboration-grants-for-mathematicians/). Funding for open access to this research was provided by the University of Tennessee’s Open Publishing Support Fund. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.