6 research outputs found
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
How Emergent Social Patterns in Allogrooming Combat Parasitic Infections
Members of social groups risk infection through contact with those in their social network. Evidence that social organization may protect populations from pathogens in certain circumstances prompts the question as to how social organization affects the spread of ectoparasites. The same grooming behaviors that establish social bonds also play a role in the progression of ectoparasitic outbreaks. In this paper, we model the interactions between social organization and allogrooming efficiency to consider how ectoparasitic threats may have shaped the evolution of social behaviors. To better understand the impacts of social grooming on organizational structure, we consider several dynamic models of social organization using network centrality measures as the basis of neighbor selection. Within this framework, we consider the impact of varying levels of social grooming on both the group structure and the overall ectoparasitic disease burden. Our results demonstrate that allogrooming, along with ongoing dynamic social organization, may be protective with respect to both the timing and the magnitude of ectoparasitic epidemics. These results support the idea that ectoparasitic threat should not be considered a single evolutionary factor in the evolution of host social systems, and may have operated in different ways depending on the broader ecology of the host-ectoparasite interaction
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Analysis of coupled reaction–diffusion equations for RNA interactions
We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffusion of the RNA interactions, respectively, with the most complex one being the full coupled reaction-diffusion equations. The simplest system consists of ordinary differential equations (ODE) modeling the chemical reaction. We present a derivation of this system using the chemical master equation and the mean-field approximation, and prove the existence, uniqueness, and linear stability of equilibrium solution of the ODE system. Next, we consider a single, nonlinear diffusion equation for one species that results from the slow diffusion of the others. Using variational techniques, we prove the existence and uniqueness of solution to a boundary-value problem of this nonlinear diffusion equation. Finally, we consider the full system of reaction-diffusion equations, both steady-state and time-dependent. We use the monotone method to construct iteratively upper and lower solutions and show that their respective limits are solutions to the reaction-diffusion system. For the time-dependent system of reaction-diffusion equations, we obtain the existence and uniqueness of global solutions. We also obtain some asymptotic properties of such solutions
Analysis of coupled reaction–diffusion equations for RNA interactions
We consider a system of coupled reaction-diffusion equations that models the inter-action between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reac-tion, nonlinear diffusion, and coupled reaction and diffusion of the RNA interactions, respectively, with the most complex one being the full coupled reaction-diffusion equa-tions. The simplest system consists of ordinary differential equations (ODE) modeling the chemical reaction. We present a derivation of this system using the chemical mas-ter equation and the mean-field approximation, and prove the existence, uniqueness, and linear stability of equilibrium solution of the ODE system. Next, we consider a single, nonlinear diffusion equation for one species that results from the slow diffusion of the others. Using variational techniques, we prove the existence and uniqueness of solution to a boundary-value problem of this nonlinear diffusion equation. Finally, we consider the full system of reaction-diffusion equations, both steady-state and time-dependent. We use the monotone method to construct iteratively upper and lower solutions and show that their respective limits are solutions to the reaction-diffusion system. For the time-dependent system of reaction-diffusion equations, we obtain the existence and uniqueness of global solutions. We also obtain some asymptotic properties of such solutions