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Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development. 

Subtitle: Grassy biomes are >20 million years old but are undervalued and under threat today. Abstract: Grassy biomes—from the steppes of Mongolia to the savannas of Tanzania—are predicted to be the ecosystems hardest hit by the ongoing climate and land use crises. The history of humans has been profoundly intertwined with grassy biomes. Homo evolved in the savannas 2 million years ago (Ma), and agricultural societies arose through the domestication of grasses, such as wheat and barley, 10,000 years ago. These grass crops, as well as corn and rice, remain dominant staple foods globally (1). Livestock production also centers in areas that were once (and sometimes still are) native grasslands. Grassy biomes harbor distinct and diverse sets of plants and animals that have adapted to these environments through millions of years of evolution (2). As the biodiversity and economic prominence of grassy biomes are increasingly being recognized, there is a demand for better understanding of their past and present function to inform policy and management. 

Tropical savannas have been increasingly targeted for carbon sequestration by afforestation, assuming large gains in soil organic carbon (SOC) with increasing tree cover. Because savanna SOC is also derived from grasses, this assumption may not reflect real changes in SOC under afforestation. However, the exact contribution of grasses to SOC and the changes in SOC with increasing tree cover remain poorly understood. Here we combine a case study from Kruger National Park, South Africa, with data synthesized from tropical savannas globally to show that grass-derived carbon constitutes more than half of total SOC to a soil depth of 1 m, even in soils directly under trees. The largest SOC concentrations were associated with the largest grass contributions (>70% of total SOC). Across the tropics, SOC concentration was not explained by tree cover. Both SOC gain and loss were observed following increasing tree cover, and on average SOC storage within a 1-m profile only increased by 6% (s.e. = 4%, n = 44). These results underscore the substantial contribution of grasses to SOC and the considerable uncertainty in SOC responses to increasing tree cover across tropical savannas. 

Fire is an important climate-driven disturbance in terrestrial ecosystems, also modulated by human ignitions or fire suppression. Changes in fire emissions can feed back on the global carbon cycle, but whether the trajectories of changing fire activity will exacerbate or attenuate climate change is poorly understood. Here, we quantify fire dynamics under historical and future climate and human demography using a coupled global climate–fire–carbon cycle model that emulates 34 individual Earth system models (ESMs). Results are compared with counterfactual worlds, one with a constant preindustrial fire regime and another without fire. Although uncertainty in projected fire effects is large and depends on ESM, socioeconomic trajectory, and emissions scenario, we find that changes in human demography tend to suppress global fire activity, keeping more carbon within terrestrial ecosystems and attenuating warming. Globally, changes in fire have acted to warm climate throughout most of the 20th century. However, recent and predicted future reductions in fire activity may reverse this, enhancing land carbon uptake and corresponding to offsetting ∼5 to 10 y of global CO 2 emissions at today’s levels. This potentially reduces warming by up to 0.11 °C by 2100. We show that climate–carbon cycle feedbacks, as caused by changing fire regimes, are most effective at slowing global warming under lower emission scenarios. Our study highlights that ignitions and active and passive fire suppression can be as important in driving future fire regimes as changes in climate, although with some risk of more extreme fires regionally and with implications for other ecosystem functions in fire-dependent ecosystems. 

Fire activity varies substantially at global scales because of the influence of climate, but at broad spatiotemporal scales, the possible effects of herbivory on fire activity are unknown. Here, we used late Quaternary large-bodied herbivore extinctions as a global exclusion experiment to examine the responses of grassy ecosystem paleofire activity (through charcoal proxies) to continental differences in extinction severity. Grassy ecosystem fire activity increased in response to herbivore extinction, with larger increases on continents that suffered the largest losses of grazers; browser declines had no such effect. These shifts suggest that herbivory can have Earth system–scale effects on fire and that herbivore impacts should be explicitly considered when predicting changes in past and future global fire activity. 

Abstract Fire–vegetation feedbacks potentially maintain global savanna and forest distributions. Accordingly, vegetation in savanna and forest ecosystems should have differential responses to fire, but fire response data for herbaceous vegetation have yet to be synthesized across biomes. Here, we examined herbaceous vegetation responses to experimental fire at 30 sites spanning four continents. Across a variety of metrics, herbaceous vegetation increased in abundance where fire was applied, with larger responses to fire in wetter and in cooler and/or less seasonal systems. Compared to forests, savannas were associated with a 4.8 (±0.4) times larger difference in herbaceous vegetation abundance for burned versus unburned plots. In particular, grass cover decreased with fire exclusion in savannas, largely via decreases in C₄grass cover, whereas changes in fire frequency had a relatively weak effect on grass cover in forests. These differential responses underscore the importance of fire for maintaining the vegetation structure of savannas and forests. 

Modeling fire spread as an infection process is intuitive: An ignition lights a patch of fuel, which infects its neighbor, and so on. Infection models produce nonlinear thresholds, whereby fire spreads only when fuel connectivity and infection probability are sufficiently high. These thresholds are fundamental both to managing fire and to theoretical models of fire spread, whereas applied fire models more often apply quasi-empirical approaches. Here, we resolve this tension by quantifying thresholds in fire spread locally, using field data from individual fires ( n = 1,131) in grassy ecosystems across a precipitation gradient (496 to 1,442 mm mean annual precipitation) and evaluating how these scaled regionally (across 533 sites) and across time (1989 to 2012 and 2016 to 2018) using data from Kruger National Park in South Africa. An infection model captured observed patterns in individual fire spread better than competing models. The proportion of the landscape that burned was well described by measurements of grass biomass, fuel moisture, and vapor pressure deficit. Regionally, averaging across variability resulted in quasi-linear patterns. Altogether, results suggest that models aiming to capture fire responses to global change should incorporate nonlinear fire spread thresholds but that linear approximations may sufficiently capture medium-term trends under a stationary climate.