A Probabilistic Analysis of Fire‐Induced Tree‐Grass Coexistence in Savannas

Emergent structure and dynamics of tropical forest-grassland landscapes

Previous work indicates that tropical forest can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid forest dieback that is not easily reversed. A hypothesized mechanism for such bistability is feedback between fire and vegetation, where fire spreads as a contagion process on grass patches. Theoretical models have largely implemented this mechanism implicitly, by assuming a threshold dependence of fire spread on flammable vegetation. Here, we show how the nonlinear dynamics and bistability emerge spontaneously, without assuming equations or thresholds for fire spread. We find that the forest geometry causes the nonlinearity that induces bistability. We demonstrate this in three steps. First, we model forest and fire as interacting contagion processes on grass patches, showing that spatial structure emerges due to two counteracting effects on the forest perimeter: forest expansion by dispersal and forest erosion by fires originating in adjacent grassland. Then, we derive a landscape-scale balance equation in which these two effects link forest geometry and dynamics: Forest expands proportionally to its perimeter, while it shrinks proportionally to its perimeter weighted by adjacent grassland area. Finally, we show that these perimeter quantities introduce nonlinearity in our balance equation and lead to bistability. Relying on the link between structure and dynamics, we propose a forest resilience indicator that could be used for targeted conservation or restoration.

Fire Responses Shape Plant Communities in a Minimal Model for Fire Ecosystems across the World

AbstractAcross plant communities worldwide, fire regimes reflect a combination of climatic factors and plant characteristics. To shed new light on the complex relationships between plant characteristics and fire regimes, we developed a new conceptual mechanistic model that includes plant competition, stochastic fires, and fire-vegetation feedback. Considering a single standing plant functional type, we observed that highly flammable and slowly colonizing plants can persist only when they have a strong fire response, while fast colonizing and less flammable plants can display a larger range of fire responses. At the community level, the fire response of the strongest competitor determines the existence of alternative ecological states (i.e., different plant communities) under the same environmental conditions. Specifically, when the strongest competitor had a very strong fire response, such as in Mediterranean forests, only one ecological state could be achieved. Conversely, when the strongest competitor was poorly fire adapted, alternative ecological states emerged-for example, between tropical humid savannas and forests or between different types of boreal forests. These findings underline the importance of including the plant fire response when modeling fire ecosystems, for example, to predict the vegetation response to invasive species or to climate change.

African savanna grasses outperform trees across the full spectrum of soil moisture availability

Models of tree-grass coexistence in savannas make different assumptions about the relative performance of trees and grasses under wet vs dry conditions. We quantified transpiration and drought tolerance traits in 26 tree and 19 grass species from the African savanna biome across a gradient of soil water potentials to test for a trade-off between water use under wet conditions and drought tolerance. We measured whole-plant hourly transpiration in a growth chamber and quantified drought tolerance using leaf osmotic potential (Ψ_osm ). We also quantified whole-plant water-use efficiency (WUE) and relative growth rate (RGR) under well-watered conditions. Grasses transpired twice as much as trees on a leaf-mass basis across all soil water potentials. Grasses also had a lower Ψ_osm than trees, indicating higher drought tolerance in the former. Higher grass transpiration and WUE combined to largely explain the threefold RGR advantage in grasses. Our results suggest that grasses outperform trees under a wide range of conditions, and that there is no evidence for a trade-off in water-use patterns in wet vs dry soils. This work will help inform mechanistic models of water use in savanna ecosystems, providing much-needed whole-plant parameter estimates for African species.

Linking resource- and disturbance-based models to explain tree-grass coexistence in savannas

Savannas cover a significant fraction of the Earth's land surface. In these ecosystems, C₃ trees and C₄ grasses coexist persistently, but the mechanisms explaining coexistence remain subject to debate. Different quantitative models have been proposed to explain coexistence, but these models make widely contrasting assumptions about which mechanisms are responsible for savanna persistence. Here, we show that no single existing model fully captures all key elements required to explain tree-grass coexistence across savanna rainfall gradients, but many models make important contributions. We show that recent empirical work allows us to combine many existing elements with new ideas to arrive at a synthesis that combines elements of two dominant frameworks: Walter's two-layer model and demographic bottlenecks. We propose that functional rooting separation is necessary for coexistence and is the crux of the coexistence problem. It is both well-supported empirically and necessary for tree persistence, given the comprehensive grass superiority for soil moisture acquisition. We argue that eventual tree dominance through shading is precluded by ecohydrological constraints in dry savannas and by fire and herbivores in wet savannas. Strong asymmetric grass-tree competition for soil moisture limits tree growth, exposing trees to persistent demographic bottlenecks.

The two faces of Janus: Processes can be both exogenous forcings and endogenous feedbacks with wind as a case study

Janus is the Roman god of transitions. In many environments, state transitions are an important part of our understanding of ecological change. These transitions are controlled by the interactions between exogenous forcing factors and stabilizing endogenous feedbacks. Forcing factors and feedbacks are typically considered to consist of different processes. We argue that during extreme events, a process that usually forms part of a stabilizing feedback can behave as a forcing factor. And thus, like Janus, a single process can have two faces. The case explored here pertains to state change in drylands where interactions between wind erosion and vegetation form an important feedback that encourages grass-to-shrub state transitions. Wind concentrates soil resources in shrub-centered fertile islands, removes resources through loss of fines to favor deep-rooted shrubs, and abrades grasses' photosynthetic tissue, thus further favoring the shrub state that, in turn, experiences greater aeolian transport. This feedback is well documented but the potential of wind to act also as a forcing has yet to be examined. Extreme wind events have the potential to act like other drivers of state change, such as drought and grazing, to directly reduce grass cover. This study examines the responses of a grass-shrub community after two extreme wind events in 2019 caused severe deflation. We measured grass cover and root exposure due to deflation, in addition to shrub height, grass patch size, and grass greenness along 50-m transects across a wide range of grass cover. Root exposure was concentrated in the direction of erosive winds during the storms and sites with low grass cover were associated with increased root exposure and reduced greenness. We argue that differences between extreme, rare wind events and frequent, small wind events are significant enough to be differences in kind rather than differences in degree allowing extreme winds to behave as endogenous forcings and common winds to participate in an endogenous stabilizing feedback. Several types of state change in other ecological systems in are contextualized within this framework.

The generation mechanism of Turing-pattern in a Tree-grass competition model with cross diffusion and time delay

In this paper, we study the general mechanism of Turing-pattern in a tree-grass competition model with cross diffusion and time delay. The properties of four equilibrium points, the existence of Hopf bifurcation and the sufficient conditions for Turing instability caused by cross-diffusion are analyzed, respectively. The amplitude equation of tree-grass competition model is derived by using multi-scale analysis method, and its nonlinear stability is studied. The sensitivity analysis also verified that fire frequency plays a key role in tree-grass coexistence equilibrium. Finally, the Turing pattern of tree-grass model obtained by numerical simulation is consistent with the spatial structure of tree-grass density distribution observed in Hulunbuir grassland, China.

Opportunities and challenges in using remote sensing for invasive tree species management, and in the identification of restoration sites in tropical montane grasslands

Tropical montane grasslands (TMG) support biodiverse and endemic taxa and provide vital ecosystem services to downstream communities. Nevertheless, invasive alien tree species across the world have threatened tropical grasslands and grassland endemic species. In India, TMG in the Shola Sky Islands of the Western Ghats have been reduced due to exotic tree invasions (Acacias, Pines, and Eucalyptus species). The loss of grassland habitat has, in turn, reduced the range sizes of species endemic to grasslands (plants, birds, amphibians, and mammals), driving some populations to local extinction. Grassland conversion to exotic trees has also impacted ecosystem services in the Western Ghats. Conserving existing grassland and restoring invaded habitat is critical to reverse these losses. This research focused on identifying grassland restoration sites using satellite images with a high spatial resolution (RapidEye). We used an object-oriented Random Forest classification to map the area for grassland restoration. We identified an area of 254 sq. km. as suitable for grassland restoration and an area of 362 sq. km. for grassland conservation and preventing invasion by exotic tree species. For restoration, we recommend careful removal of young and isolated exotic trees at the invasion front and restoring grasslands, instead of removing dense stands of mature exotic trees. Although our limited data indicate that areas with low fire frequency tend to be invaded, and areas invaded by exotic trees tend to burn at higher intensities, we recommend a broader investigation of these patterns to critically examine a potential role for the use of fire in invasive species management. We assume that removing exotic tree species in the identified restoration sites and restoring the grassland will help recover lost habitat and ensure the viability of indigenous and endemic species and increase streamflow.

Flammability thresholds or flammability gradients? Determinants of fire across savanna-forest transitions

Vegetation-fire feedbacks are important for determining the distribution of forest and savanna. To understand how vegetation structure controls these feedbacks, we quantified flammability across gradients of tree density from grassland to forest in the Brazilian Cerrado. We experimentally burned 102 plots, for which we measured vegetation structure, fuels, microclimate, ignition success and fire behavior. Tree density had strong negative effects on ignition success, rate of spread, fire-line intensity and flame height. Declining grass biomass was the principal cause of this decline in flammability as tree density increased, but increasing fuel moisture contributed. Although the response of flammability to tree cover often is portrayed as an abrupt, largely invariant threshold, we found the response to be gradual, with considerable variability driven largely by temporal changes in atmospheric humidity. Even when accounting for humidity, flammability at intermediate tree densities cannot be predicted reliably. Fire spread in savanna-forest mosaics is not as deterministic as often assumed, but may appear so where vegetation boundaries are already sharp. Where transitions are diffuse, fire spread is difficult to predict, but should become increasingly predictable over multiple fire cycles, as boundaries are progressively sharpened until flammability appears to respond in a threshold-like manner.

Increased aridity drives post-fire recovery of Mediterranean forests towards open shrublands

Recent observations suggest that repeated fires could drive Mediterranean forests to shrublands, hosting flammable vegetation that regrows quickly after fire. This feedback supposedly favours shrubland persistence and may be strengthened in the future by predicted increased aridity. An assessment was made of how fires and aridity in combination modulated the dynamics of Mediterranean ecosystems and whether the feedback could be strong enough to maintain shrubland as an alternative stable state to forest. A model was developed for vegetation dynamics, including stochastic fires and different plant fire-responses. Parameters were calibrated using observational data from a period up to 100 yr ago, from 77 sites with and without fires in Southeast Spain and Southern France. The forest state was resilient to the separate impact of fires and increased aridity. However, water stress could convert forests into open shrublands by hampering post-fire recovery, with a possible tipping point at intermediate aridity. Projected increases in aridity may reduce the resilience of Mediterranean forests against fires and drive post-fire ecosystem dynamics toward open shrubland. The main effect of increased aridity is the limitation of post-fire recovery. Including plant fire-responses is thus fundamental when modelling the fate of Mediterranean-type vegetation under climate-change scenarios.

Integrating anthropogenic factors into regional-scale species distribution models-A novel application in the imperiled sagebrush biome

Species distribution models (SDMs) that rely on regional-scale environmental variables will play a key role in forecasting species occurrence in the face of climate change. However, in the Anthropocene, a number of local-scale anthropogenic variables, including wildfire history, land-use change, invasive species, and ecological restoration practices can override regional-scale variables to drive patterns of species distribution. Incorporating these human-induced factors into SDMs remains a major research challenge, in part because spatial variability in these factors occurs at fine scales, rendering prediction over regional extents problematic. Here, we used big sagebrush (Artemisia tridentata Nutt.) as a model species to explore whether including human-induced factors improves the fit of the SDM. We applied a Bayesian hurdle spatial approach using 21,753 data points of field-sampled vegetation obtained from the LANDFIRE program to model sagebrush occurrence and cover by incorporating fire history metrics and restoration treatments from 1980 to 2015 throughout the Great Basin of North America. Models including fire attributes and restoration treatments performed better than those including only climate and topographic variables. Number of fires and fire occurrence had the strongest relative effects on big sagebrush occurrence and cover, respectively. The models predicted that the probability of big sagebrush occurrence decreases by 1.2% (95% CI: -6.9%, 0.6%) when one fire occurs and cover decreases by 44.7% (95% CI: -47.9%, -41.3%) if at least one fire occurred over the 36 year period of record. Restoration practices increased the probability of big sagebrush occurrence but had minimal effect on cover. Our results demonstrate the potential value of including disturbance and land management along with climate in models to predict species distributions. As an increasing number of datasets representing land-use history become available, we anticipate that our modeling framework will have broad relevance across a range of biomes and species.

An Assessment of Multiple Drivers Determining Woody Species Composition and Structure: A Case Study from the Kalahari, Botswana

Savannas are extremely important socio-economic landscapes, with pastoralist societies relying on these ecosystems to sustain their livelihoods and economy. Globally, there is an increase of woody vegetation in these ecosystems, degrading the potential of these multi-functional landscapes to sustain societies and wildlife. Several mechanisms have been invoked to explain the processes responsible for woody vegetation composition; however, these are often investigated separately at scales not best suited to land-managers, thereby impeding the evaluation of their relative importance. We ran six transects at 15 sites along the Kalahari transect, collecting data on species identity, diversity, and abundance. We used Poisson and Tobit regression models to investigate the relationship among woody vegetation, precipitation, grazing, borehole density, and fire. We identified 44 species across 78 transects, with the highest species richness and abundance occurring at Kuke (middle of the rainfall gradient). Precipitation was the most important environmental variable across all species and various morphological groups, while increased borehole density and livestock resulted in lower bipinnate species abundance, contradicting the consensus that these managed features increase the presence of such species. Rotating cattle between boreholes subsequently reduces the impact of trampling and grazing on the soil and maintains and/or reduces woody vegetation abundance.

Resilience of tropical tree cover: The roles of climate, fire, and herbivory

Fires and herbivores shape tropical vegetation structure, but their effects on the stability of tree cover in different climates remain elusive. Here, we integrate empirical and theoretical approaches to determine the effects of climate on fire- and herbivore-driven forest-savanna shifts. We analyzed time series of remotely sensed tree cover and fire observations with estimates of herbivore pressure across the tropics to quantify the fire-tree cover and herbivore-tree cover feedbacks along climatic gradients. From these empirical results, we developed a spatially explicit, stochastic fire-vegetation model that accounts for herbivore pressure. We find emergent alternative stable states in tree cover with hysteresis across rainfall conditions. Whereas the herbivore-tree cover feedback can maintain low tree cover below 1,100 mm mean annual rainfall, the fire-tree cover feedback can maintain low tree cover at higher rainfall levels. Interestingly, the rainfall range where fire-driven alternative vegetation states can be found depends strongly on rainfall variability. Both higher seasonal and interannual variability in rainfall increase fire frequency, but only seasonality expands the distribution of fire-maintained savannas into wetter climates. The strength of the fire-tree cover feedback depends on the spatial configuration of tree cover: Landscapes with clustered low tree-cover areas are more susceptible to cross a tipping point of fire-driven forest loss than landscapes with scattered deforested patches. Our study shows how feedbacks involving fire, herbivores, and the spatial structure of tree cover explain the resilience of tree cover across climates.

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.

Plant biomass and soil moisture dynamics: analytical results

In semi-arid ecosystems, successful use of the limited water resources is of central importance in determining the evolutionary trends of the vegetation. The competition between different species and individuals for this resource is driven by variations in physiology and metabolic regulation strategies, expressed by such parameters as rooting depth, wilting point or stomatal opening, among others. It is typically not practical to simulate the full evolutionary dynamics of every plant individual in the landscape because of the difficulties introduced by the spatial heterogeneity, as well as the many timescales involved, ranging from hourly up to intergenerational. Instead, the amount of biomass of a given species assimilated per unit area of the landscape may serve as a proxy for its competitiveness and evolutionary success. It is the behaviour of the biomass, which must be described probabilistically due to the stochasticity of the rainfall, which is the subject here. This paper develops a new analytical description of the stationary and transient joint behaviour of plant biomass and soil moisture. Additionally, the effects of climatic fluctuations are considered, including the important case of a bi-seasonal climate regime consisting of alternating wet and dry seasons, which is characteristic of many ecosystems of interest.

Hydraulic lift as a determinant of tree-grass coexistence on savannas

The coexistence of woody plants and grasses in savannas is determined by a complex set of interacting factors that determine access to resources and demographic dynamics, under the control of external drivers and vegetation feedbacks with the physical environment. Existing theories explain coexistence mainly as an effect of competitive relations and/or disturbances. However, theoretical studies on the way facilitative interactions resulting from hydraulic lift affect tree-grass coexistence and the range of environmental conditions in which savannas are stable are still lacking. We investigated the role of hydraulic lift in the stability of tree-grass coexistence in savannas. To that end, we developed a new mechanistic model that accounts for both competition for soil water in the shallow soil and fire-induced disturbance. We found that hydraulic lift favors grasses, which scavenge the water lifted by woody plants. Thus, hydraulic lift expands (at the expenses of woodlands) the range of environmental conditions in which savannas are stable. These results indicate that hydraulic lift can be an important mechanism responsible for the coexistence of woody plants and grasses in savannas. Grass facilitation by trees through the process of hydraulic lift could allow savannas to persist stably in mesic regions that would otherwise exhibit a forest cover.

The role of vegetation-microclimate feedback in promoting shrub encroachment in the northern Chihuahuan desert

Many arid and semi-arid landscapes around the world are affected by a shift from grassland to shrubland vegetation, presumably induced by climate warming, increasing atmospheric CO2 concentrations, and/or changing land use. This major change in vegetation cover is likely sustained by positive feedbacks with the physical environment. Recent research has focused on a feedback with microclimate, whereby cold intolerant shrubs increase the minimum nocturnal temperatures in their surroundings. Despite the rich literature on the impact of land cover change on local climate conditions, changes in microclimate resulting from shrub expansion into desert grasslands have remained poorly investigated. It is unclear to what extent such a feedback can affect the maximum extent of shrub expansion and the configuration of a stable encroachment front. Here, we focus on the case of the northern Chihuahuan desert, where creosotebush (Larrea tridentata) has been replacing grasslands over the past 100-150 years. We use a process-based coupled atmosphere-vegetation model to investigate the role of this feedback in sustaining shrub encroachment in the region. Simulations indicate that the feedback allows juvenile shrubs to establish in the grassland during average years and, once established, reduce their vulnerability to freeze-induced mortality by creating a warmer microclimate. Such a feedback is crucial in extreme cold winters as it may reduce shrub mortality. We identify the existence of a critical zone in the surroundings of the encroachment front, in which vegetation dynamics are bistable: in this zone, vegetation can be stable both as grassland and as shrubland. The existence of these alternative stable states explains why in most cases the shift from grass to shrub cover is found to be abrupt and often difficult to revert.

Woody plant encroachment of grasslands: a comparison of terrestrial and wetland settings

A global trend of woody plant encroachment of terrestrial grasslands is co-incident with woody plant encroachment of wetland in freshwater and saline intertidal settings. There are several arguments for considering tree encroachment of wetlands in the context of woody shrub encroachment of grassland biomes. In both cases, delimitation of woody shrubs at regional scales is set by temperature thresholds for poleward extent, and by aridity within temperature limits. Latitudinal expansion has been observed for terrestrial woody shrubs and mangroves, following recent warming, but most expansion and thickening has been due to the occupation of previously water-limited grassland/saltmarsh environments. Increases in atmospheric CO₂, may facilitate the recruitment of trees in terrestrial and wetland settings. Improved water relations, a mechanism that would predict higher soil moisture in grasslands and saltmarshes, and also an enhanced capacity to survive arid conditions, reinforces local mechanisms of change. The expansion of woody shrubs and mangroves provides a negative feedback on elevated atmospheric CO₂ by increasing carbon sequestration in grassland and saltmarsh, and is a significant carbon sink globally. These broad-scale vegetation shifts may represent a new stable state, reinforced by positive feedbacks between global change drivers and endogenic mechanisms of persistence in the landscape.

Modeling shrub encroachment in subalpine grasslands under different environmental and management scenarios

Woody plants are spreading in many alpine and subalpine ecosystems and are expected to continue increasing in response to land abandonment and global warming. This encroachment threatens species diversity, and considerable efforts have been deployed to control it. In this study, we combined a lattice model and field data to investigate the efficiency of different management strategies in controlling shrub encroachment in alpine grasslands. The model parameter values were estimated in the field based on the thorny shrub Echinospartum horridum (erizón) which is currently encroaching in central Spanish Pyrenees. Our study shows that encroachment could accelerate if climate warming continues. Different management scenarios consisting of a gradient of livestock pressures, fire events and mechanical removal were simulated to identify scenarios able to control the expansion of shrubs into grasslands. Our study shows that grazing alone cannot stop encroachment. Rather, a combination of grazing and shrub removal (either by fire or mechanical removal) is needed, and our model can help estimate the frequency and intensities of the shrub removal. This model can be used to investigate the consequences of different management scenarios and environmental variability which could be of practical value in the preservation of alpine grasslands.

Competition between trees and grasses for both soil water and mineral nitrogen in dry savannas

The co-existence of trees and grasses in savannas in general can be the result of processes involving competition for resources (e.g. water and nutrients) or differential response to disturbances such as fire, animals and human activities; or a combination of both broad mechanisms. In moist savannas, the tree-grass coexistence is mainly attributed to of disturbances, while in dry savannas, limiting resources are considered the principal mechanism of co-existence. Virtually all theoretical explorations of tree-grass dynamics in dry savannas consider only competition for soil water. Here we investigate whether coexistence could result from a balanced competition for two resources, namely soil water and mineral nitrogen. We introduce a simple dynamical resource-competition model for trees and grasses. We consider two alternative hypotheses: (1) trees are the superior competitors for nitrogen while grasses are superior competitors for water, and (2) vice-versa. We study the model properties under the two hypotheses and test each hypothesis against data from 132 dry savannas in Africa using Kendall's test of independence. We find that Hypothesis 1 gets much more support than Hypothesis 2, and more support than the null hypothesis that neither is operative. We further consider gradients of rainfall and nitrogen availability and find that the Hypothesis 1 model reproduces the observed patterns in nature. We do not consider our results to definitively show that tree-grass coexistence in dry savannas is due to balanced competition for water and nitrogen, but show that this mechanism is a possibility, which cannot be a priori excluded and should thus be considered along with the more traditional explanations.

Hydrologic variability in dryland regions: impacts on ecosystem dynamics and food security

Research on ecosystem and societal response to global environmental change typically considers the effects of shifts in mean climate conditions. There is, however, some evidence of ongoing changes also in the variance of hydrologic and climate fluctuations. A relatively high interannual variability is a distinctive feature of the hydrologic regime of dryland regions, particularly at the desert margins. Hydrologic variability has an important impact on ecosystem dynamics, food security and societal reliance on ecosystem services in water-limited environments. Here, we investigate some of the current patterns of hydrologic variability in drylands around the world and review the major effects of hydrologic fluctuations on ecosystem resilience, maintenance of biodiversity and food security. We show that random hydrologic fluctuations may enhance the resilience of dryland ecosystems by obliterating bistable deterministic behaviours and threshold-like responses to external drivers. Moreover, by increasing biodiversity and the associated ecosystem redundancy, hydrologic variability can indirectly enhance post-disturbance recovery, i.e. ecosystem resilience.

Stochastic dynamics of snow avalanche occurrence by superposition of Poisson processes

We study the dynamics of systems with deterministic trajectories randomly forced by instantaneous discontinuous jumps occurring according to two different compound Poisson processes. One process, with constant frequency, causes instantaneous positive random increments, whereas the second process has a state-dependent frequency and describes negative jumps that force the system to restart from zero (renewal jumps). We obtain the probability distributions of the state variable and the magnitude and intertimes of the jumps to zero. This modelling framework is used to describe snow-depth dynamics on mountain hillsides, where the positive jumps represent snowfall events, whereas the jumps to zero describe avalanches. The probability distributions of snow depth, together with the statistics of avalanche magnitude and occurrence, are used to explain the correlation between avalanche occurrence and snowfall as a function of hydrologic, terrain slope and aspect parameters. This information is synthesized into a ‘prediction entropy’ function that gives the level of confidence of avalanche occurrence prediction in relation to terrain properties.

Integrating theoretical climate and fire effects on savanna and forest systems

The role of fire and climate in determining savanna and forest distributions requires comprehensive theoretical reevaluation. Empirical studies show that climate constrains maximum tree cover and that fire feedbacks can reduce tree cover substantially, but neither the stability nor the dynamics of these systems are well understood. A theoretical integration of rainfall effects with fire processes in particular is lacking. We use simple, well-supported assumptions about the percolation dynamics of fire spread and the demographic effects of climate and fire on trees to build a dynamic model examining the stability of tree cover in savannas and forests. Fire results in the potential for one or possibly two stable equilibria, while the effects of increasing rainfall on tree demography result in (discontinuous) increases in tree cover and in forest tree dominance. As rainfall increases, the system moves from (1) stable low tree cover to (2) bistability of low and high tree cover to (3) stable high tree cover. Thus, theory suggests that tree cover uniquely determined by climate at low and high rainfall but determined by fire feedbacks at intermediate rainfall-as empirical studies suggest-may be a universal feature of systems where fire has strong effects on tree demography.

Evaluating ecohydrological theories of woody root distribution in the Kalahari

The contribution of savannas to global carbon storage is poorly understood, in part due to lack of knowledge of the amount of belowground biomass. In these ecosystems, the coexistence of woody and herbaceous life forms is often explained on the basis of belowground interactions among roots. However, the distribution of root biomass in savannas has seldom been investigated, and the dependence of root biomass on rainfall regime remains unclear, particularly for woody plants. Here we investigate patterns of belowground woody biomass along a rainfall gradient in the Kalahari of southern Africa, a region with consistent sandy soils. We test the hypotheses that (1) the root depth increases with mean annual precipitation (root optimality and plant hydrotropism hypothesis), and (2) the root-to-shoot ratio increases with decreasing mean annual rainfall (functional equilibrium hypothesis). Both hypotheses have been previously assessed for herbaceous vegetation using global root data sets. Our data do not support these hypotheses for the case of woody plants in savannas. We find that in the Kalahari, the root profiles of woody plants do not become deeper with increasing mean annual precipitation, whereas the root-to-shoot ratios decrease along a gradient of increasing aridity.