Integrating theoretical climate and fire effects on savanna and forest systems

Reassessing the alternative ecosystem states proposition in the African savanna-forest domain

Ecologists are being challenged to predict how ecosystems will respond to climate changes. According to the Multi-Colored World (MCW) hypothesis, climate impacts may not manifest because consumers such as fire and herbivory can override the influence of climate on ecosystem state. One MCW interpretation is that climate determinism fails because alternative ecosystem states (AES) are possible at some locations in climate space. We evaluated theoretical and empirical evidence for the proposition that forest and savanna are AES in Africa. We found that maps which infer where AES zones are located were contradictory. Moreover, data from longitudinal and experimental studies provide inconclusive evidence for AES. That is, although the forest-savanna AES proposition is theoretically sound, the existing evidence is not yet convincing. We conclude by making the case that the AES proposition has such fundamental consequences for designing management actions to mitigate and adapt to climate change in the savanna-forest domain that it needs a more robust evidence base before it is used to prescribe management actions.

Pattern Formation in Mesic Savannas

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.

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.

Limited climatic space for alternative ecosystem states in Africa

One of the foundational premises of ecology is that climate determines ecosystems. This has been challenged by alternative ecosystem state models, which illustrate that internal ecosystem dynamics acting on the initial ecosystem state can overwhelm the influence of climate, and by observations suggesting that climate cannot reliably discriminate forest and savanna ecosystem types. Using a novel phytoclimatic transform, which estimates the ability of climate to support different types of plants, we show that climatic suitability for evergreen trees and C4 grasses are sufficient to discriminate between forest and savanna in Africa. Our findings reassert the dominant influence of climate on ecosystems and suggest that the role of feedbacks causing alternative ecosystem states is less prevalent than has been suggested.

A cyclical wildfire pattern as the outcome of a coupled human natural system

Over the past decades, wildfire has imposed a considerable cost on natural resources and human lives. In many regions, annual wildfire trends show puzzling oscillatory patterns with increasing amplitudes for burned areas over time. This paper aims to examine the potential causes of such patterns by developing and examining a dynamic simulation model that represents interconnected social and natural dynamics in a coupled system. We develop a generic dynamic model and, based on simulation results, postulate that the interconnection between human and natural subsystems is a source of the observed cyclical patterns in wildfires in which risk perception regulates activities that can result in more fire and development of vulnerable properties. Our simulation-based policy analysis points to a non-linear characteristic of the system, which rises due to the interconnections between the human side and the natural side of the system. This has a major policy implication: in contrast to studies that look for the most effective policy to contain wildfires, we show that a long-term solution is not a single action but is a combination of multiple actions that simultaneously target both human and natural sides of the system.

Climate-driven, but dynamic and complex? A reconciliation of competing hypotheses for species' distributions

Estimates of the percentage of species "committed to extinction" by climate change range from 15% to 37%. The question is whether factors other than climate need to be included in models predicting species' range change. We created demographic range models that include climate vs. climate-plus-competition, evaluating their influence on the geographic distribution of Pinus edulis, a pine endemic to the semiarid southwestern U.S. Analyses of data on 23,426 trees in 1941 forest inventory plots support the inclusion of competition in range models. However, climate and competition together only partially explain this species' distribution. Instead, the evidence suggests that climate affects other range-limiting processes, including landscape-scale, spatial processes such as disturbances and antagonistic biotic interactions. Complex effects of climate on species distributions-through indirect effects, interactions, and feedbacks-are likely to cause sudden changes in abundance and distribution that are not predictable from a climate-only perspective.

Evasion of tipping in complex systems through spatial pattern formation

[Figure: see text].

Stationary distributions of persistent ecological systems

We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary distribution). Since it is usually impossible to characterize this invariant probability measure analytically, we develop a powerful method for numerically approximating invariant probability measures. This allows us to shed light upon how the various parameters of the ecosystem impact the stationary distribution. We analyze different types of environmental fluctuations. At first we study ecosystems modeled by stochastic differential equations. In the second setting we look at piecewise deterministic Markov processes. These are processes where one follows a system of differential equations for a random time, after which the environmental state changes, and one follows a different set of differential equations-this procedure then gets repeated indefinitely. Finally, we look at stochastic differential equations with switching, which take into account both the white noise fluctuations and the random environmental switches. As applications of our theoretical and numerical analysis, we look at competitive Lotka-Volterra, Beddington-DeAngelis predator-prey, and rock-paper-scissors dynamics. We highlight new biological insights by analyzing the stationary distributions of the ecosystems and by seeing how various types of environmental fluctuations influence the long term fate of populations.

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.

Spatial structure in protected forest-grassland mosaics: Exploring futures under climate change

In mosaic ecosystems, multiple land types coexist as alternative stable states exhibiting distinct spatial patterns. Forest-grassland mosaics are ecologically valuable, due to their high species richness. However, anthropogenic disturbances threaten these ecosystems. Designating protected areas is one approach to preserving natural mosaics. Such work must account for climate change, yet there are few spatially explicit models of mosaics under climate change that can predict its effects. We construct a spatially explicit simulation model for a natural forest-grassland mosaic, parameterized for Southern Brazil. Using this model, we investigate how the spatial structure of these systems is altered under climate change and other disturbance regimes. By including local spatial interactions and fire-mediated forest recruitment, our model reproduces important spatial features of protected real-world mosaics, including the number of forest patches and overall forest cover. Multiple concurrent changes in environmental conditions have greater impacts on tree cover and spatial structure in simulated mosaics than single changes. This sensitivity reflects the narrow range of conditions under which simulated mosaics persist and emphasizes their vulnerability. Our model predicts that, in protected mosaics, climate change impacts on the fire-mediated threshold to recruitment will likely result in substantial increases in forest cover under Representative Concentration Pathway (RCP) 8.5, with potential for mosaic loss over a broad range of initial forest cover levels. Forest cover trajectories are similar until 2150, when cover increases under RCP 8.5 outpace those under RCP 2.6. Mosaics that persist under RCP 8.5 may experience structural alterations at the patch and landscape level. Our simple model predicts several realistic aspects of spatial structure as well as plausible responses to likely regional climate shifts. Hence, further model development could provide a useful tool when building strategies for protecting these ecosystems, by informing site selection for conservation areas that will be favourable to forest-grassland mosaics under future climates.

Mathematical model for the dynamics of Savanna ecosystem considering fire disturbances

In this article, the stability of equilibrium solutions of a recently formulated mathematical model of Savanna ecosystem is analytically and numerically analyzed. The mathematical model is formulated by generalizing all plant life into three components; trees, tree saplings, and grass under ecologically valid effects of fire, rainfall and competition for space. Fire has a considerable effect on trees by delaying the recruitment of saplings to trees and the recruitment rate is a piecewise linear decreasing function of grass with a sigmoidal shape. This leads to there existing different equilibria in the plant community of a Savanna ecosystem. It is rigorously demonstrated that the local stability of equilibria depends on the slope and value of the recruitment function. Moreover, it is found that the composition of high grass cover and low tree cover or low grass cover and high tree cover are the stable equilibria, while intermediate cover results in unstable equilibria. In analyzing the global stability of solutions, it is found that the limit set is an equilibrium solution. Several numerical simulations are provided to validate the analytical studies of the behavior of the equilibrium solutions. The numerical solutions are generated using a Python ordinary differential equation(ODE) solver. The analytical and numerical solutions presented in this work are very important for further developments in the area of mathematical ecology.

Dispersal limitation and fire feedbacks maintain mesic savannas in Madagascar

Madagascar is regarded by some as one of the most degraded landscapes on Earth, with estimates suggesting that 90% of forests have been lost to indigenous Tavy farming. However, the extent of this degradation has been challenged: paleoecological data, phylogeographic analysis, and species richness indicate that pyrogenic savannas in central Madagascar predate human arrival, even though rainfall is sufficient to allow forest expansion into central Madagascar. These observations raise a question-if savannas in Madagascar are not anthropogenic, how then are they maintained in regions where the climate can support forest? Observation reveals that the savanna-forest boundary coincides with a dispersal barrier-the escarpment of the Central Plateau. Using a stepping-stone model, we show that in a limited dispersal landscape, a stable savanna-forest boundary can form because of fire-vegetation feedbacks. This phenomenon, referred to as range pinning, could explain why eastern lowland forests have not expanded into the mesic savannas of the Central Highlands. This work challenges the view that highland savannas in Madagascar are derived by human-lit fires and, more importantly, suggests that partial dispersal barriers and strong nonlinear feedbacks can pin biogeographical boundaries over a wide range of environmental conditions, providing a temporary buffer against climate change.

Dispersal Increases the Resilience of Tropical Savanna and Forest Distributions

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. We examine the contributions of dispersal to determining biome distributions using a 2D reaction-diffusion model, comparing results qualitatively to empirical savanna and forest distributions in sub-Saharan Africa. We find that the diffusion model resolves both the aforementioned limitations 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.

Forecasting semi-arid biome shifts in the Anthropocene

Shrub encroachment, forest decline and wildfires have caused large-scale changes in semi-arid vegetation over the past 50 years. Climate is a primary determinant of plant growth in semi-arid ecosystems, yet it remains difficult to forecast large-scale vegetation shifts (i.e. biome shifts) in response to climate change. We highlight recent advances from four conceptual perspectives that are improving forecasts of semi-arid biome shifts. Moving from small to large scales, first, tree-level models that simulate the carbon costs of drought-induced plant hydraulic failure are improving predictions of delayed-mortality responses to drought. Second, tracer-informed water flow models are improving predictions of species coexistence as a function of climate. Third, new applications of ecohydrological models are beginning to simulate small-scale water movement processes at large scales. Fourth, remotely-sensed measurements of plant traits such as relative canopy moisture are providing early-warning signals that predict forest mortality more than a year in advance. We suggest that a community of researchers using modeling approaches (e.g. machine learning) that can integrate these perspectives will rapidly improve forecasts of semi-arid biome shifts. Better forecasts can be expected to help prevent catastrophic changes in vegetation states by identifying improved monitoring approaches and by prioritizing high-risk areas for management.

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.

The potential role of intrinsic processes in generating abrupt and quasi-synchronous tree declines during the Holocene

Multiple abrupt and sometimes near-synchronous declines in tree populations have been detected in the temperate forests of eastern North America and Europe during the Holocene. Traditional approaches to understanding these declines focus on searching for climatic or other broad-scale extrinsic drivers. These approaches include multi-proxy studies that match reconstructed changes in tree abundance to reconstructed changes in precipitation or temperature. Although these correlative approaches are informative, they neglect the potential role of intrinsic processes, such as competition and dispersal, in shaping tree community dynamics. We developed a simple process-based community model that includes competition among tree species, density-dependent survival, and dispersal to investigate how these processes might generate abrupt changes in tree abundances even when extrinsic climatic factors do not themselves change abruptly. Specifically, a self-reinforcing (i.e., positive) feedback between abundance and survival can produce abrupt changes in tree abundance in the absence of long-term climatic changes. Furthermore, spatially correlated, short-term environmental variation and seed dispersal can increase the synchrony of abrupt changes. Using the well-studied, late-Holocene crash of Tsuga canadensis (eastern hemlock) populations as an empirical case study, we find that our model generates abrupt and quasi-synchronized crashes qualitatively similar to the observed hemlock patterns. Other tree taxa vary in the frequency and clustering of abrupt change and the proportion of increases and decreases. This complexity argues for caution in interpreting abrupt changes in species abundances as indicative of abrupt climatic changes. Nonetheless, some taxa show patterns that the model cannot produce: observed abrupt declines in hemlock abundance are more synchronized than abrupt increases, whereas the degree of synchronization is the same for abrupt decreases and increases in the model. Our results show that intrinsic processes can be significant contributing factors in abrupt tree population changes and highlight the diagnostic value of analyzing entire time series rather than single events when testing hypotheses about abrupt changes. Thus, intrinsic processes should be considered along with extrinsic drivers when seeking to explain rapid changes in community composition.

Palaeo-trajectories of forest savannization in the southern Congo

Tropical savannah and forest are thought to represent alternative stable states in ecosystem structure in some climates. The implication is that biomes are maintained by positive feedbacks, e.g. with fire, and that historical distributions could play a role in determining modern ones. In this context, climate alone does not govern transitions between biomes, and understanding the causes and pathways of such transitions becomes crucial. Here, we use a multi-proxy analysis of a 2000-year core to evaluate modes of transition in vegetation structure and fire regimes. We demonstrate a first transition ca 1540 BP, when a cyclic fire regime entered a forested landscape, eventually resulting, by ca 1060 BP, in a transition to a more open savannah-like or mosaicked structure. This pattern may parallel currently accelerating fire regimes in tropical forests suggesting that fires can savannize forests, but perhaps more slowly than feared. Finally, ca 540 BP, a drought combined with anthropogenic influences resulted in a conclusive transition to savannah, probably resembling the modern landscape in the region. We show here that fire interacted with drought to transition forest to savannah, suggesting that disturbance by fire can be a major driver of biome change.

Tropical tree cover in a heterogeneous environment: A reaction-diffusion model

Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna. However, when including spatial interaction in nonspatial differential equation models of a bistable quantity, only the state with the lowest potential energy remains stable. Our recent reaction-diffusion model of Amazonian tree cover confirmed this and was able to reproduce the observed spatial distribution of forest versus savanna satisfactorily when forced by heterogeneous environmental and anthropogenic variables, even though bistability was underestimated. These conclusions were solely based on simulation results for one set of parameters. Here, we perform an analytical and numerical analysis of the model. We derive the Maxwell point (MP) of the homogeneous reaction-diffusion equation without savanna trees as a function of rainfall and human impact and show that the front between forest and nonforest settles at this point as long as savanna tree cover near the front remains sufficiently low. For parameters resulting in higher savanna tree cover near the front, we also find irregular forest-savanna cycles and woodland-savanna bistability, which can both explain the remaining observed bimodality.

Persistence and extinction for stochastic ecological models with internal and external variables

The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. To understand this interplay, we prove theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for internal and external variables. Specifically, we use a stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for (i) all population densities spending little time at low densities i.e. stochastic persistence, and (ii) population trajectories asymptotically approaching the extinction set with positive probability. For (i) and (ii), respectively, we provide quantitative estimates on the fraction of time that the system is near the extinction set, and the probability of asymptotic extinction as a function of the initial state of the system. Furthermore, in the case of persistence, we provide lower bounds for the expected time to escape neighborhoods of the extinction set. To illustrate the applicability of our results, we analyze stochastic models of evolutionary games, Lotka-Volterra dynamics, trait evolution, and spatially structured disease dynamics. Our analysis of these models demonstrates environmental stochasticity facilitates coexistence of strategies in the hawk-dove game, but inhibits coexistence in the rock-paper-scissors game and a Lotka-Volterra predator-prey model. Furthermore, environmental fluctuations with positive auto-correlations can promote persistence of evolving populations and persistence of diseases in patchy landscapes. While our results help close the gap between the persistence theories for deterministic and stochastic systems, we highlight several challenges for future research.

Grass and tree cover responses to intra-seasonal rainfall variability vary along a rainfall gradient in African tropical grassy biomes

Although it is well known that mean annual rainfall (MAR) and rainfall seasonality have a key role in influencing the distribution of tree and grass cover in African tropical grassy biomes (TGBs), the impact of intra-seasonal rainfall variability on these distributions is less agreed upon. Since the prevalent mechanisms determining biome occurrence and distribution change with MAR, this research investigates the role of intra-seasonal rainfall variability for three different MAR ranges, assessing satellite data on grass and tree cover, rainfall and fire intervals at a sub-continental scale in sub-Saharan Africa. For MAR below 630 mm y⁻¹, rainfall frequency had a positive relationship with grass cover; this relationship however became mostly negative at intermediate MAR (630–1200 mm y⁻¹), where tree cover correspondingly mostly increased with rainfall frequency. In humid TGBs, tree cover decreased with rainfall intensity. Overall, intra-seasonal rainfall variability plays a role in determining vegetation cover, especially in mesic TGBs, where the relative dominance of trees and grasses has previously been largely unexplained. Importantly, the direction of the effect of intra-seasonal variability changes with MAR. Given the predicted increases in rainfall intensity in Africa as a consequence of climate change, the effects on TGBs are thus likely to vary depending on the MAR levels.

The Impact of Spatial and Temporal Dimensions of Disturbances on Ecosystem Stability

Ecosystems constantly face disturbances which vary in their spatial and temporal features, yet little is known on how these features affect ecosystem recovery and persistence, i.e., ecosystem stability. We address this issue by considering three ecosystem models with different local dynamics, and ask how their stability properties depend on the spatial and temporal properties of disturbances. We measure the spatial dimension of disturbances by their spatial extent while controlling for their overall strength, and their temporal dimension by the average frequency of random disturbance events. Our models show that the return to equilibrium following a disturbance depends strongly on the disturbance's extent, due to rescue effects mediated by dispersal. We then reveal a direct relation between the temporal variability caused by repeated disturbances and the recovery from an isolated disturbance event. Although this could suggest a trivial dependency of ecosystem response on disturbance frequency, we find that this is true only up to a frequency threshold, which depends on both the disturbance spatial features and the ecosystem dynamics. Beyond this threshold the response changes qualitatively, displaying spatial clusters of disturbed regions, causing an increase in variability, and even a system-wide collapse for ecosystems with alternative stable states. Thus, spanning the spatial dimension of disturbances is a way to probe the underlying dynamics of an ecosystem. Furthermore, considering spatial and temporal dimensions of disturbances in conjunction is necessary to predict ecosystem responses with dramatic ecological consequences, such as regime shifts or population extinction.

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.

Soil texture mediates tree responses to rainfall intensity in African savannas

Rainfall variability is a major determinant of soil moisture, but its influence on vegetation structure has been challenging to generalize. This presents a major source of uncertainty in predicting vegetation responses to potentially widespread shifts in rainfall frequency and intensity. In savannas, where trees and grasses coexist, conflicting lines of evidence have suggested, variously, that tree cover can either increase or decrease in response to less frequent, more intense rainfall. Here, we use remote sensing products and continent-wide soil maps for sub-Saharan Africa to analyze how soil texture and fire mediate the response of savanna tree cover to rainfall climatology. Tree cover increased with mean wet-season rainfall and decreased with fire frequency, consistent with previous analyses. However, responses to rainfall intensity varied: tree cover dramatically decreased with rainfall intensity on clayey soils, at high rainfall, and with rainfall spread over longer wet seasons; conversely, on sandy soils, at low rainfall, and with shorter wet seasons, tree cover instead increased with rainfall intensity. Tree cover responses to rainfall climatology depend on soil texture, accounting for substantial variation in tree cover across African savannas. Differences in underlying soils may lead to divergent responses of savannas to global change.

Abrupt Climate Change in an Oscillating World

The notion that small changes can have large consequences in the climate or ecosystems has become popular as the concept of tipping points. Typically, tipping points are thought to arise from a loss of stability of an equilibrium when external conditions are slowly varied. However, this appealingly simple view puts us on the wrong foot for understanding a range of abrupt transitions in the climate or ecosystems because complex environmental systems are never in equilibrium. In particular, they are forced by diurnal variations, the seasons, Milankovitch cycles and internal climate oscillations. Here we show how abrupt and sometimes even irreversible change may be evoked by even small shifts in the amplitude or time scale of such environmental oscillations. By using model simulations and reconciling evidence from previous studies we illustrate how these phenomena can be relevant for ecosystems and elements of the climate system including terrestrial ecosystems, Arctic sea ice and monsoons. Although the systems we address are very different and span a broad range of time scales, the phenomena can be understood in a common framework that can help clarify and unify the interpretation of abrupt shifts in the Earth system.

On the complex dynamics of savanna landscapes

Simple mathematical models can exhibit rich and complex behaviors. Prototypical examples of these drawn from biology and other disciplines have provided insights that extend well beyond the situations that inspired them. Here, we explore a set of simple, yet realistic, models for savanna-forest vegetation dynamics based on minimal ecological assumptions. These models are aimed at understanding how vegetation interacts with both climate (a primary global determinant of vegetation structure) and feedbacks with chronic disturbances from fire. The model includes three plant functional types-grasses, savanna trees, and forest trees. Grass and (when they allow grass to persist in their subcanopy) savanna trees promote the spread of fires, which in turn, demographically limit trees. The model exhibits a spectacular range of behaviors. In addition to bistability, analysis reveals (i) that diverse cyclic behaviors (including limit and homo- and heteroclinic cycles) occur for broad ranges of parameter space, (ii) that large shifts in landscape structure can result from endogenous dynamics and not just from external drivers or from noise, and (iii) that introducing noise into this system induces resonant and inverse resonant phenomena, some of which have never been previously observed in ecological models. Ecologically, these results raise questions about how to evaluate complicated dynamics with data. Mathematically, they lead to classes of behaviors that are likely to occur in other models with similar structure.

Fire forbids fifty-fifty forest

Recent studies have interpreted patterns of remotely sensed tree cover as evidence that forest with intermediate tree cover might be unstable in the tropics, as it will tip into either a closed forest or a more open savanna state. Here we show that across all continents the frequency of wildfires rises sharply as tree cover falls below ~40%. Using a simple empirical model, we hypothesize that the steepness of this pattern causes intermediate tree cover (30‒60%) to be unstable for a broad range of assumptions on tree growth and fire-driven mortality. We show that across all continents, observed frequency distributions of tropical tree cover are consistent with this hypothesis. We argue that percolation of fire through an open landscape may explain the remarkably universal rise of fire frequency around a critical tree cover, but we show that simple percolation models cannot predict the actual threshold quantitatively. The fire-driven instability of intermediate states implies that tree cover will not change smoothly with climate or other stressors and shifts between closed forest and a state of low tree cover will likely tend to be relatively sharp and difficult to reverse.

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.

Effects of fire frequency on litter decomposition as mediated by changes to litter chemistry and soil environmental conditions

Litter quality and soil environmental conditions are well-studied drivers influencing decomposition rates, but the role played by disturbance legacy, such as fire history, in mediating these drivers is not well understood. Fire history may impact decomposition directly, through changes in soil conditions that impact microbial function, or indirectly, through shifts in plant community composition and litter chemistry. Here, we compared early-stage decomposition rates across longleaf pine forest blocks managed with varying fire frequencies (annual burns, triennial burns, fire-suppression). Using a reciprocal transplant design, we examined how litter chemistry and soil characteristics independently and jointly influenced litter decomposition. We found that both litter chemistry and soil environmental conditions influenced decomposition rates, but only the former was affected by historical fire frequency. Litter from annually burned sites had higher nitrogen content than litter from triennially burned and fire suppression sites, but this was correlated with only a modest increase in decomposition rates. Soil environmental conditions had a larger impact on decomposition than litter chemistry. Across the landscape, decomposition differed more along soil moisture gradients than across fire management regimes. These findings suggest that fire frequency has a limited effect on litter decomposition in this ecosystem, and encourage extending current decomposition frameworks into disturbed systems. However, litter from different species lost different masses due to fire, suggesting that fire may impact decomposition through the preferential combustion of some litter types. Overall, our findings also emphasize the important role of spatial variability in soil environmental conditions, which may be tied to fire frequency across large spatial scales, in driving decomposition rates in this system.

Amazonian forest-savanna bistability and human impact

A bimodal distribution of tropical tree cover at intermediate precipitation levels has been presented as evidence of fire-induced bistability. Here we subdivide satellite vegetation data into those from human-unaffected areas and those from regions close to human-cultivated zones. Bimodality is found to be almost absent in the unaffected regions, whereas it is significantly enhanced close to cultivated zones. Assuming higher logging rates closer to cultivated zones and spatial diffusion of fire, our spatiotemporal mathematical model reproduces these patterns. Given a gradient of climatic and edaphic factors, rather than bistability there is a predictable spatial boundary, a Maxwell point, that separates regions where forest and savanna states are naturally selected. While bimodality can hence be explained by anthropogenic edge effects and natural spatial heterogeneity, a narrow range of bimodality remaining in the human-unaffected data indicates that there is still bistability, although on smaller scales than claimed previously.

Deforestation and edge effects around cleared areas impact forest stability. Here, the authors examine human impacts on Amazonian forest-savanna bistability and show that tree cover bimodality is enhanced in regions close to human activities and is nearly absent in regions unaffected by human activities.

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.