Subgroup Contributed Talks

eSMB2020 eSMB2020 Follow Wednesday at 11:15am EDT
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Annalisa Iuorio

University of Vienna
"Modelling competitive interactions and plant-soil feedback in vegetation dynamics"
Plant-soil feedback has been proved to play an important role in the formation of vegetation patterns for a single species. In real-life, however, plants rarely grow in monoculture; hence multi-species scenarios are more realistic. In these cases, additional effects between different species - such as competition and interaction - must be considered. Moreover, plant-soil feedback is recognised as a causal mechanism for plant-species coexistence. Using a mathematical model consisting of four PDEs, we investigate mechanisms of inter- and intra-specific plant-soil feedback on the coexistence of two competing plant species. In particular, the model takes into account both negative and positive feedback influencing the growth of the same and the other plant species. Both the coexistence of the plant species and the dominance of a particular plant species are examined with respect to all model parameters. Analytical and numerical results reveal the emergence of spatio-temporal patterns.

Lukas Eigentler

University of Dundee
"Spatial self-organisation enables species coexistence in a model for dryland vegetation patterns"
Vegetation patterns are a ubiquitous feature of drylands across the globe. Despite the competition for water, species coexistence of herbaceous and woody species is commonly observed. Thus, tree-grass coexistence in drylands provides an apparent contradiction to the principle of competitive exclusion. In this talk, I propose that a pattern-inducing spatial self-organisation principle, caused by a positive feedback between local vegetation growth and water redistribution towards dense biomass patches, can also act as a coexistence mechanism for plant species in water-limited ecosystems. To this end, I present a bifurcation analysis of an ecohydrological PDE model for two plant species interacting with a sole limiting resource, based on the Klausmeier reaction-advection-diffusion system for vegetation patterns. Patterned solutions occur as periodic travelling waves and thus theory on limit cycles in dynamical systems can be utilised in the analysis. Firstly, a stability analysis of the system's single-species patterns, performed through a calculation of their essential spectra, provides an insight into the onset of coexistence states. I show that coexistence solution branches bifurcate off single-species solution branches as the single-species states lose their stability to the introduction of a second species. Secondly, I present a comprehensive existence and stability analysis to establish key conditions, including a balance between the species' local competitive abilities and their colonisation abilities, for species coexistence in the model. Finally, I show that the inclusion of intraspecific competition dynamics has a significant impact on the coexistence mechanism that significantly differs from results on classical, nonspatial competition models. (Joint work with Jonathan A. Sherratt)

Gabriel Maciel

"Spatial self-organization promotes coexistence between two species in nonlocal competition models"
Nonlocal interactions are a remarkable feature of several ecological systems ranging from microorganisms and coral reefs to plants and animals. The potential of spatially extended interactions to generate patterns of space distribution in single populations has been extensively explored in the past few decades. In systems of two competing species, nonlocal interactions and the self-organization of populations can have critical dynamical effects but our understanding in these situations is still very limited. In this talk, I will present a kernel-based model for the dynamics of two species competition with nonlocal interactions. Inspired by different biological examples I will show that we can have two distinct scenarios that differ in how intra and interspecific interaction ranges are determined based on each species competition characteristics. In both scenarios we will see that pattern formation offers a coexistence mechanism where the inferior competitor takes advantage of low density locations in the superior competitor spatial distribution.

Nikunj Goel

University of Texas at Austin
"Dispersal increases the resilience of tropical savanna and forest distribution"
Global change may induce changes in savanna and forest distributions, but the dynamics of these changes remain unclear. Classical biome theory suggests that climate is predictive of biome distributions, such that shifts will be continuous and reversible. This view, however, cannot explain the overlap in the climatic ranges of tropical biomes, which some argue may result from fire-vegetation feedbacks, maintaining savanna and forest as bistable states. Under this view, biome shifts are argued to be discontinuous and irreversible. Mean-field bistable models, however, are also limited, as they cannot reproduce the spatial aggregation of biomes. Here we suggest that both models ignore spatial processes, such as dispersal, which may be important when savanna and forest abut. Using a combination of spatial mathematical models and remote sensing data, we examine the contributions of dispersal to determining biome distributions. We find that including dispersal in biome dynamics resolves both the limitations mentioned above of biome models. First, local dispersive spatial interactions, with an underlying precipitation gradient, can reproduce the spatial aggregation of biomes with a stable savanna-forest boundary. Second, the boundary is determined not only by the amount of precipitation but also by the geometrical shape of the precipitation contours. These geometrical effects arise from continental-scale source-sink dynamics, which reproduce the mismatch between biome and climate. Dynamically, the spatial model predicts that dispersal may increase the resilience of tropical biome in response to global change: the boundary continuously tracks climate, recovering following disturbances, unless the remnant biome patches are too small.

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Virtual conference of the Society for Mathematical Biology, 2020.