Facilitation in drylands: Modeling a neglected driver of savanna dynamics

Metastability as a Coexistence Mechanism in a Model for Dryland Vegetation Patterns

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species' average fitness, measured by the ratio of a species' capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding [Formula: see text] years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.

A dominance shift in arid savanna: An herbaceous legume outcompetes local C4 grasses

The characteristic vegetation structure of arid savannas with a dominant layer of perennial grass is maintained by the putative competitive superiority of the C4 grasses. When this competitive balance is disturbed by weakening the grasses or favoring the recruitment of other species, trees, shrubs, single grass, or forb species can increase and initiate sudden dominance shifts. Such shifts involving woody species, often termed "shrub encroachment", or the mass spreading of so-called increaser species have been extensively researched, but studies on similar processes without obvious preceding disturbance are rare. In Namibia, the native herbaceous legume Crotalaria podocarpa has recently encroached parts of the escarpment region, seriously affecting the productivity of local fodder grasses. Here, we studied the interaction between seedlings of the legume and the dominant local fodder grass (Stipagrostis ciliata). We used a pot experiment to test seedling survival and to investigate the growth of Crotalaria in competition with Stipagrostis. Additional field observations were conducted to quantify the interactive effect. We found germination and growth of the legume seedlings to be facilitated by inactive (dead or dormant) grass tussocks and unhindered by active ones. Seedling survival was three times higher in inactive tussocks and Crotalaria grew taller. In the field, high densities of the legume had a clear negative effect on productivity of the grass. The C4 grass was unable to limit the recruitment and spread of the legume, and Crotalaria did outcompete the putative more competitive grass. Hence, the legume is able to spread and establish itself in large numbers and initiate a dominance shift in savannas, similar to shrub encroachment.

The impact of inter-annual rainfall variability on African savannas changes with mean rainfall

Savannas are mixed tree-grass ecosystems whose dynamics are predominantly regulated by resource competition and the temporal variability in climatic and environmental factors such as rainfall and fire. Hence, increasing inter-annual rainfall variability due to climate change could have a significant impact on savannas. To investigate this, we used an ecohydrological model of stochastic differential equations and simulated African savanna dynamics along a gradient of mean annual rainfall (520-780 mm/year) for a range of inter-annual rainfall variabilities. Our simulations produced alternative states of grassland and savanna across the mean rainfall gradient. Increasing inter-annual variability had a negative effect on the savanna state under dry conditions (520 mm/year), and a positive effect under moister conditions (580-780 mm/year). The former resulted from the net negative effect of dry and wet extremes on trees. In semi-arid conditions (520 mm/year), dry extremes caused a loss of tree cover, which could not be recovered during wet extremes because of strong resource competition and the increased frequency of fires. At high mean rainfall (780 mm/year), increased variability enhanced savanna resilience. Here, resources were no longer limiting and the slow tree dynamics buffered against variability by maintaining a stable population during 'dry' extremes, providing the basis for growth during wet extremes. Simultaneously, high rainfall years had a weak marginal benefit on grass cover due to density-regulation and grazing. Our results suggest that the effects of the slow tree and fast grass dynamics on tree-grass interactions will become a major determinant of the savanna vegetation composition with increasing rainfall variability.

An impulsive modelling framework of fire occurrence in a size-structured model of tree-grass interactions for savanna ecosystems

Fires and mean annual rainfall are major factors that regulate woody and grassy biomasses in savanna ecosystems. Within the savanna biome, conditions of long-lasting coexistence of trees and grasses have been often studied using continuous-time modelling of tree-grass competition. In these studies, fire is a time-continuous forcing while the relationship between woody plant size and fire-sensitivity is not systematically considered. In this paper, we propose a new mathematical framework to model tree-grass interactions that takes into account both the impulsive nature of fire occurrence and size-dependent fire sensitivity (via two classes of woody plants). We carry out a qualitative analysis that highlights ecological thresholds and bifurcation parameters that shape the dynamics of the savanna-like systems within the main ecological zones. Through a qualitative analysis, we show that the impulsive modelling of fire occurrences leads to more diverse behaviors including cases of grassland, savanna and forest tristability and a more realistic array of solutions than the analogous time-continuous fire models. Numerical simulations are carried out with respect to the three main ecological contexts (moist, mesic, semi-arid) to illustrate the theoretical results and to support a discussion about the bifurcation parameters and the advantages of the model.