Advection and autocatalysis as organizing principles for banded vegetation patterns

We motivate and analyze a simple model for the formation of banded vegetation patterns. The model incorporates a minimal number of ingredients for vegetation growth in semi-arid landscapes. It allows for comprehensive analysis and sheds new light onto phenomena such as the migration of vegetation bands and the interplay between their upper and lower edges. The key ingredient is the formulation as a closed reaction-diffusion system, thus introducing a conservation law that both allows for analysis and provides ready intuition and understanding through analogies with characteristic speeds of propagation and shock waves.Comment: 25

Patterns Selected by Spatial Inhomogeneity

University of Minnesota Ph.D. dissertation.May 2019. Major: Mathematics. Advisor: Arnd Scheel. 1 computer file (PDF); xi, 130 pages.This thesis studies patterns that form in environments with sharp spatial variation. In a uniform environment, spots or stripes typically form with a self-consistent width. This width is taken from an interval around a characteristic value determined by the system. With a dramatic spatial variation, our environments only allow patterns in half the spatial region. This sets up a region of patterns directly adjacent to an area where patterns are suppressed. We show that this environmental inhomogeneity significantly restricts the widths of patterns that may occur in a given system. That is, the length of the interval around the characteristic value is significantly reduced. We examine this phenomenon using a universal partial differential equation model. Reduction techniques from dynamical systems simplify our study to the behavior in a normal form equation (amplitude equation). A difficulty arrises at the location of the discontinuous inhomogeneity; results in the normal form equations on the left and right cannot be directly compared. We construct a transformation of variables that bridges this jump and allows a heteroclinic gluing argument. The explicit form of this transformation determines the widths of patterns that can occur in the inhomogeneous environment

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

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.Comment: 26 pages, 11 figures, 3 tables, 3 appendices with 1 figure; revised Introduction, Sec 1.1, and Discussion; cosmetic changes to figures; fixed typos and made clarifications throughout; results unchange

Anisotropic interaction and motion states of locusts in a hopper band

<p>Swarming locusts present a quintessential example of animal collective motion. Juvenile locusts march and hop across the ground in coordinated groups called hopper bands. Composed of up to millions of insects, hopper bands exhibit coordinated motion and various collective structures. These groups are well-documented in the field, but the individual insects themselves are typically studied in much smaller groups in laboratory experiments. We present the first trajectory data that detail the movement of individual locusts within a hopper band in a natural setting. Using automated video tracking, we derive our data from footage of four distinct hopper bands of the Australian plague locust, <em>Chortoicetes terminifera</em>. We reconstruct nearly twenty-thousand individual trajectories composed of over 3.3 million locust positions. We classify these data into three motion states: stationary, walking, and hopping. Distributions of relative neighbor positions reveal anisotropies that depend on motion state. Stationary locusts have high-density areas distributed around them apparently at random. Walking locusts have a low-density area in front of them. Hopping locusts have low-density areas in front and behind them. Our results suggest novel interactions, namely that locusts change their motion to avoid colliding with neighbors in front of them.</p><p>Funding provided by: National Science Foundation<br>Crossref Funder Registry ID: https://ror.org/021nxhr62<br>Award Number: DMS–1902818</p><p>Funding provided by: Australian Research Council<br>Crossref Funder Registry ID: https://ror.org/05mmh0f86<br>Award Number: LP150100479</p><p>Funding provided by: Australian Research Council<br>Crossref Funder Registry ID: https://ror.org/05mmh0f86<br>Award Number: FT110100082</p><p>Funding provided by: National Science Foundation<br>Crossref Funder Registry ID: https://ror.org/021nxhr62<br>Award Number: DMS–1757952</p><p>See Methods in the associated manuscript: <a href="https://doi.org/10.1101/2021.10.29.466390">https://doi.org/10.1101/2021.10.29.466390</a></p> <p>See also the README file in the associated GitHub repository: <a href="https://github.com/weinburd/locust_trajectory_data">https://github.com/weinburd/locust_trajectory_data</a></p&gt

Anisotropic interaction and motion states of locusts in a hopper band

<p>Swarming locusts present a quintessential example of animal collective motion. Juvenile locusts march and hop across the ground in coordinated groups called hopper bands. Composed of up to millions of insects, hopper bands exhibit coordinated motion and various collective structures. These groups are well-documented in the field, but the individual insects themselves are typically studied in much smaller groups in laboratory experiments. We present the first trajectory data that detail the movement of individual locusts within a hopper band in a natural setting. Using automated video tracking, we derive our data from footage of four distinct hopper bands of the Australian plague locust, <em>Chortoicetes terminifera</em>. We reconstruct nearly twenty-thousand individual trajectories composed of over 3.3 million locust positions. We classify these data into three motion states: stationary, walking, and hopping. Distributions of relative neighbor positions reveal anisotropies that depend on motion state. Stationary locusts have high-density areas distributed around them apparently at random. Walking locusts have a low-density area in front of them. Hopping locusts have low-density areas in front and behind them. Our results suggest novel interactions, namely that locusts change their motion to avoid colliding with neighbors in front of them.</p><p>Funding provided by: National Science Foundation<br>Crossref Funder Registry ID: https://ror.org/021nxhr62<br>Award Number: DMS–1902818</p><p>Funding provided by: Australian Research Council<br>Crossref Funder Registry ID: https://ror.org/05mmh0f86<br>Award Number: LP150100479</p><p>Funding provided by: Australian Research Council<br>Crossref Funder Registry ID: https://ror.org/05mmh0f86<br>Award Number: FT110100082</p><p>Funding provided by: National Science Foundation<br>Crossref Funder Registry ID: https://ror.org/021nxhr62<br>Award Number: DMS–1757952</p><p>See Methods in the associated manuscript: <a href="https://doi.org/10.1101/2021.10.29.466390">https://doi.org/10.1101/2021.10.29.466390</a></p> <p>See also the README file in the associated GitHub repository: <a href="https://github.com/weinburd/locust_trajectory_data">https://github.com/weinburd/locust_trajectory_data</a></p&gt