Pattern formation in prey-taxis systems

Lee, J. M.; Hillen, Thomas; Lewis, Mark A.

doi:10.1080/17513750802716112

Cited by 178 publications

(126 citation statements)

References 36 publications

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“…Deviations from uniformity get damped with time, and no instability (and hence no pattern formation) can arise. In the words of Lee et al (17), "prey-taxis tends to transform heterogeneous environments into homogeneous environments, which gives an opposite result to the chemotaxis case," implying that simple prey-taxis does not lead to complex patch dynamics.…”

Section: Taxis Modelsmentioning

confidence: 99%

“…This simple expectation is actually false, as argued in a comprehensive work in ref. 17. Intuitively, there is an important difference in the sign patterns of h KS and h PT : In KS, the individuals reinforce the chemical by secreting it (positive feedback), whereas in the prey-taxis, the consumption of prey depletes local patches (negative feedback).…”

Section: Taxis Modelsmentioning

confidence: 99%

“…Some models track single individuals, positing rules of interaction (1,9) and others formulate equations to describe densities of populations. Most such models are PDEs (17) or (if nonlocal) integro-PDEs (20).…”

Section: Taxis Modelsmentioning

confidence: 99%

“…There is great interest in extending analytical and empirical studies to understanding the spatiotemporal dynamics of social aggregation, although tools for doing so are as yet emerging. Both individual-based models tracking single organisms (14) and density-based theories using partial differential equations (PDEs) (8,17) contribute to such technology. The Keller-Segel (KS) model (18) provides a great avenue for exploration that already has a history to build on.…”

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confidence: 99%

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Role of social interactions in dynamic patterns of resource patches and forager aggregation

Tania

Vanderlei

Heath

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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The dynamics of resource patches and species that exploit such patches are of interest to ecologists, conservation biologists, modelers, and mathematicians. Here we consider how social interactions can create unique, evolving patterns in space and time. Whereas simple prey taxis (with consumable prey) promotes spatial uniform distributions, here we show that taxis in producer-scrounger groups can lead to pattern formation. We consider two types of foragers: those that search directly ("producers") and those that exploit other foragers to find food ("scroungers" or exploiters). We show that such groups can sustain fluctuating spatiotemporal patterns, akin to "waves of pursuit." Investigating the relative benefits to the individuals, we observed conditions under which either strategy leads to enhanced success, defined as net food consumption. Foragers that search for food directly have an advantage when food patches are localized. Those that seek aggregations of group mates do better when their ability to track group mates exceeds the foragers' food-sensing acuity. When behavioral switching or reproductive success of the strategies is included, the relative abundance of foragers and exploiters is dynamic over time, in contrast with classic models that predict stable frequencies. Our work shows the importance of considering two-way interactioni.e., how food distribution both influences and is influenced by social foraging and aggregation of predators.pattern formation | foraging strategies | ecological patchiness | chemotaxis | spatial ecology I n this paper, we study the dynamics of social interactions to explore the consequences for spatiotemporal population structure and dynamics. We show that interactions among individuals are key for pattern formation and self-organization when foragers either follow gradients of food or socialize with those that do. Our aim is to demonstrate that social interactions among foragers could have particularly important implications for spatial models of forager-resource dynamics. A comprehensive understanding of the spatial dynamics of social foraging needs to consider the two-way dynamic interaction between forager aggregation and resource patchiness, a problem that remains poorly understood (1, 2).A secondary theme is the discovery of another pattern-forming mechanism. Nature abounds with patterns that the human eye is adept at picking out. Patterns occur in chemical, physical, and biological systems on many scales, from distribution of proteins in a cell, and tissue morphogenesis, to patchy distribution of species in ecology (3-5, 6). There is great interest in finding both universal mechanisms for such patterns (e.g., the balance of repulsion-attraction forces, local activation and long-range inhibition, or motion in an external field; ref. 7), as well as specific examples that have rich pattern-forming features (8).Patterns formed by organisms, and the way they shape their environment, is a rich area with physical (phase transitions), engineering (robotics), sociological (e.g...

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Section: Taxis Modelsmentioning

confidence: 99%

Section: Taxis Modelsmentioning

confidence: 99%

Section: Taxis Modelsmentioning

confidence: 99%

mentioning

confidence: 99%

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Role of social interactions in dynamic patterns of resource patches and forager aggregation

Tania

Vanderlei

Heath

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…It is worthwhile to mention that besides the competition model, the advection, which is referred to as the prey-taxis, has been studied in predator-prey models by various authors. See [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%