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Mechanisms of Species Diversity Change in Stressed Environments

Ehud Meron

The impacts of environmental changes on species diversity, and thus on ecosystem function and stability, is a central topic of current ecological research. While such changes may independently affect animal and plant species, plants standout in being primary producers; by storing solar energy in chemical compounds they constitute the basal trophic level of the food chain that animal species, including humans, depend on. Plant communities respond to environmental changes at different scales. At the landscape scale, where symmetry breaking vegetation patterns appear (Fig. 1), a transition from one pattern state to another may take place (Animation 1). At smaller, single-patch scales, environmental changes may affect inter- and intra-specific plant interactions. Using a mathematical modeling approach, we developed a theory of plant communities in water limited system, and are currently using it to highlight mechanisms of species diversity change in response to climate changes and disturbances. Special attention is given to mechanisms that involve different levels of organization, e.g. mechanisms by which pattern transitions at the landscape level affect plant interactions and species richness at the single-patch level.

Figure 1: Aerial photograph of vegetation bands on hill slopes in Niger. Reprinted from C. Valentin, J. M. d'Herbes, and J. Poesen, Catena 37, 1 (1999), ©1999.

Animation 1: Model simulation showing a transition from a banded vegetation pattern to a spotted pattern induce by a local clear-cut disturbance. Downhill direction is to the right. Produced by Erez Gilad.
Can't see the movie? here it is in animated GIF.

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Non-equilibrium Localized Structures

Ehud Meron

Localized spatial structures, such as defects in periodic patterns, fronts and vortices, are ubiquitous in non-equilibrium systems. Understanding the mechanisms by which they form, their stability and how to manipulate them, is significant for exploiting them in technological applications.

A localized structure may involve a single mode, e.g. a spiral wave in an oscillating medium (showcasing a Hopf mode), but quite often richer structures appear. This is particularly true when a system is driven far from thermal equilibrium and the number of growing modes increases. The system may still be governed by a single dominant mode that damps all other modes by means of nonlinear mode coupling. However, localized structures of the dominant mode, where its amplitude vanishes or becomes sufficiently small, can host the hidden damped mode, giving rise to multimode structures. We studied structures of this kind in systems that go through dual (Hopf-Turing) instabilities. Among our findings are defect lines acting as self-organized wave-guides for traveling pulses (Fig. 1), breathing defects, and multi-state localized structures, that are potentially significant for data storage applications.

Figure 1: Self-organized waveguide. A pulse of a Hopf mode (amplitude B) propagating along a defect line in a Turing pattern (amplitude A). Time proceeds from top to bottom. Produced by Adam Lampert.

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