Spatial self-organisation enables species coexistence in a model for savanna ecosystems

Delayed loss of stability of periodic travelling waves: Insights from the analysis of essential spectra

Periodic travelling waves (PTW) are a common solution type of partial differential equations. Such models exhibit multistability of PTWs, typically visualised through the Busse balloon, and parameter changes typically lead to a cascade of wavelength changes through the Busse balloon. In the past, the stability boundaries of the Busse balloon have been used to predict such wavelength changes. Here, motivated by anecdotal evidence from previous work, we provide compelling evidence that the Busse balloon provides insufficient information to predict wavelength changes due to a delayed loss of stability phenomenon. Using two different reaction-advection-diffusion systems, we relate the delay that occurs between the crossing of a stability boundary in the Busse balloon and the occurrence of a wavelength change to features of the essential spectrum of the destabilised PTW. This leads to a predictive framework that can estimate the order of magnitude of such a time delay, which provides a novel "early warning sign" for pattern destabilisation. We illustrate the implementation of the predictive framework to predict under what conditions a wavelength change of a PTW occurs.

Precipitation governing vegetation patterns in an arid or semi-arid environment

In an arid or semi-arid environment, precipitation plays a vital role in vegetation growth. Recent researches reveal that the response of vegetation growth to precipitation has a lag effect. To explore the mechanism behind the lag phenomenon, we propose and investigate a water-vegetation model with spatiotemporal nonlocal effects. It is shown that the temporal kernel function does not affect Turing bifurcation. For better understanding the influences of lag effect and nonlocal competition on the vegetation pattern formation, we choose some special kernel functions and obtain some insightful results: (i) Time delay does not trigger the vegetation pattern formation, but can postpone the evolution of vegetation. In addition, in the absence of diffusion, time delay can induce the occurrence of stability switches, while in the presence of diffusion, spatially nonhomogeneous time-periodic solutions may emerge, but there are no stability switches; (ii) The spatial nonlocal interaction may trigger the pattern onset for small diffusion ratio of water and vegetation, and can change the number and size of isolated vegetation patches for large diffusion ratio. (iii) The interaction between time delay and spatial nonlocal competition may induce the emergence of traveling wave patterns, so that the vegetation remains periodic in space, but is oscillating in time. These results demonstrate that precipitation can significantly affect the growth and spatial distribution of vegetation.

Enhanced species coexistence in Lotka-Volterra competition models due to nonlocal interactions

We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the nonlocal interactions. In both cases, nonlocal interactions can create spatial patterns of population densities in which highly populated clumps alternate with unpopulated regions. These non-populated regions provide spatial niches for a weaker competitor to establish in the community and persist in conditions in which local models predict competitive exclusion. Moreover, depending on the balance between local and nonlocal competition intensity, the clumps of the weaker competitor vary from M-like structures with higher densities of individuals accumulating at the edges of each clump to triangular structures with most individuals occupying their centers. These results suggest that long-range competition, through the creation of spatial patterns in population densities, might be a key driving force behind the rich diversity of species observed in natural ecological communities.

Evasion of tipping in complex systems through spatial pattern formation

[Figure: see text].

Self-organised pattern formation increases local diversity in metacommunities

Self-organised formation of spatial patterns is known from a variety of different ecosystems, yet little is known about how these patterns affect the diversity of communities. Here, we use a food chain model in which autotroph diversity is described by a continuous distribution of a trait that affects both growth and defence against heterotrophs. On isolated patches, diversity is always lost over time due to stabilising selection, and the local communities settle on one of two alternative stable community states that are characterised by a dominance of either defended or undefended species. In a metacommunity context, dispersal can destabilise these states and complex spatio-temporal patterns in the species' abundances emerge. The resulting biomass-trait feedback increases local diversity by an order of magnitude compared to scenarios without self-organised pattern formation, thereby maintaining the ability of communities to adapt to potential future changes in biotic or abiotic environmental conditions.

Belowground feedbacks as drivers of spatial self-organization and community assembly

Vegetation patterning in water-limited and other resource-limited ecosystems highlights spatial self-organization processes as potentially key drivers of community assembly. These processes provide insight into predictable landscape-level relationships between organisms and their abiotic environment in the form of regular and irregular patterns of biota and resources. However, two aspects have largely been overlooked; the roles played by plant - soil-biota feedbacks and allelopathy in spatial self-organization, and their potential contribution, along with plant-resource feedbacks, to community assembly through spatial self-organization. Here, we expand the drivers of spatial self-organization from a focus on plant-resource feedbacks to include plant - soil-biota feedbacks and allelopathy, and integrate concepts of nonlinear physics and community ecology to generate a new hypothesis. According to this hypothesis, below-ground processes can affect community assemblages through two types of spatial self-organization, global and local. The former occurs simultaneously across whole ecosystems, leading to self-organized patterns of biota, allelochemicals and resources, and niche partitioning. The latter occurs locally in ecotones, and determines ecotone structure and motion, invasion dynamics, and species coexistence. Studies of the two forms of spatial self-organization are important for understanding the organization of plant communities in drier climates which are likely to involve spatial patterning or re-patterning. Such studies are also important for developing new practices of ecosystem management, based on local manipulations at ecotones, to slow invasion dynamics or induce transitions from transitive to intransitive networks of interspecific interactions which increase species diversity.