Speakers

Abstract:

Vegetation patterns are a ubiquitous feature of semi-arid regions and are a prime example of a self-organisation principle in ecology, caused by positive feedback between local plant growth and water redistribution. The Klausmeier reaction-advection-diffusion model is a deliberately simple system describing the formation of vegetation stripes on sloped terrain. In this talk, I present two model extensions to (i) investigate the effects of nonlocal seed dispersal, and (ii) propose mechanisms that enable species coexistence despite competition for a limiting resource.

In the first part of the talk, I present a model extension in which plant dispersal is modelled by a nonlocal convolution term, motivated by empirical data. Asymptotic analysis of the model is possible due to a scale difference between plant dispersal and water transport. I show that a condition for pattern onset in the model can be derived analytically, which indicates that long-range seed dispersal inhibits the onset of spatial patterns. Results on pattern existence and stability, obtained via a numerical continuation method, further show a change in the type of stability boundaries in the pattern's stability regions as dispersal distance is varied. This suggests increased resilience of patterns to reductions in precipitation due to long dispersal distances. Stability results further propose a resolution of a mismatch between previous mathematical models predicting an uphill movement of vegetation bands and some field studies reporting stationary patterns.

In the second part of the talk, I present two mechanisms that enable species coexistence despite the species' competition for the same limiting resource. Firstly, coexistence occurs as a metastable state if the average fitness difference between both species, a measure of the species' competitiveness in a spatially uniform setting, is small. Secondly, a stability analysis of the system's single-species patterns shows that a solution branch in which both species coexist bifurcates off the single-species solution branch as it loses its stability to the introduction of a second species. 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.

Abstract:

Widespread extension of forest into savannas have been reported in Central Africa over the last decades, but this dynamics is liable to encompass different processes (local thickening-up, nucleation, edge movements) of varying strength and kinetics that have insufficiently been studied in sufficiently diverse conditions. We focused on two nearby landscapes in central Cameroon displaying a variety of soil conditions and two distinct levels of human presence to monitor complex forest-savanna dynamics. Open access satellite imagery and cloud computing facilities (Google Earth Engine) was used to track land cover change. Field inventory data from grass and woody layer as well as soil properties were collected. Landsat image archives recorded a long-term (> 40 years) forest spread into savanna at a rate of ca. 1%.year^-1 (6Km².year^-1). Fire occurrence recorded via Landsat archives, modulated bush encroachment and forest expansion with a five-year fire frequency found to be the threshold below which woody savanna dominates and opens the way to forest transition. While a large share of savannas turned into forest during the last decades, vegetation in the remaining savannas was shaped by a gradient leading from sandy soils with low grass production and low fire frequencies to clayey soils with high grass production and frequent fire situations. These findings highlights the importance of soil modulation of the grass-fire feedback and can serve as a reference to vegetation models that predict forest savanna dynamics in the area.

Abstract:

The savanna biome encompasses variations of vegetation physiognomies that traduce complex dynamical responses of plants to the rainfall gradients leading from tropical forests to hot deserts. Such responses are shaped by interactions between woody and grassy plants that can be either direct, disturbance-mediated (e.g. fire) or both. There has been increasing evidence that several (highly contrasted) vegetation physiognomies may durably coexist in humid savannas, which are fire-prone, suggesting multi-stability (i.e. mosaic of vegetation). Therefore, a major question consists on understanding/characterizing how fires may impact vegetation mosaic dynamics. This question has triggered several modelling efforts relying either on space-implicit or on space-explicit mathematical models. I will present some recent space-explicit models designed to study the impact of fire on the long-term dynamics of a forest-grassland vegetation mosaic in humid savannas by the mean of a bistable travelling wave. Notably, I show that depending on fire-return time as well as difference in diffusion potential of woody and herbaceous vegetation, fires are able to greatly slow down or even stop the progression of forest in humid regions. Finally, in the case of a monostable forest invasion wave, numerical approximation of the spreading is also presented.