Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach.

The frequency distributions can characterize the population-potential landscape related to the stability of ecological states. We illustrate the practical utility of this approach by analyzing a forest-savanna model. Savanna and forest states coexist under certain conditions, consistent with past theoretical work and empirical observations. However, a grassland state, unseen in the corresponding deterministic model, emerges as an alternative quasi-stable state under fluctuations, providing a theoretical basis for the appearance of widespread grasslands in some empirical analyses. The ecological dynamics are determined by both the population-potential landscape gradient and the steady-state probability flux. The flux quantifies the net input/output to the ecological system and therefore the degree of nonequilibriumness. Landscape and flux together determine the transitions between stable states characterized by dominant paths and switching rates. The intrinsic potential landscape admits a Lyapunov function, which provides a quantitative measure of global stability. We find that the average flux, entropy production rate, and free energy have significant changes near bifurcations under both finite and zero fluctuation. These may provide both dynamical and thermodynamic origins of the bifurcations. We identified the variances in observed frequency time traces, fluctuations, and time irreversibility as kinematic measures for bifurcations. This framework opens the way to characterize ecological systems globally, to uncover how they change among states, and to quantify the emergence of quasi-stable states under stochastic fluctuations.

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.

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.

Thinner bark increases sensitivity of wetter Amazonian tropical forests to fire.

Understory fires represent an accelerating threat to Amazonian tropical forests and can, during drought, affect larger areas than deforestation itself. These fires kill trees at rates varying from < 10 to c. 90% depending on fire intensity, forest disturbance history and tree functional traits. Here, we examine variation in bark thickness across the Amazon. Bark can protect trees from fires, but it is often assumed to be consistently thin across tropical forests. Here, we show that investment in bark varies, with thicker bark in dry forests and thinner in wetter forests. We also show that thinner bark translated into higher fire-driven tree mortality in wetter forests, with between 0.67 and 5.86 gigatonnes CO2 lost in Amazon understory fires between 2001 and 2010. Trait-enabled global vegetation models that explicitly include variation in bark thickness are likely to improve the predictions of fire effects on carbon cycling in tropical forests.

En los bosques tropicales de la Amazonia, los incendios de sotobosque representan una amenaza que se está acelerando. Durante la sequía, pueden afectar un área mayor que la deforestación misma. Estos incendios pueden matan árboles a tasas que varían desde <10 hasta cerca de 90% dependiendo de la intensidad del fuego, la historia de perturbaciones forestales y los rasgos funcionales de los árboles. En este estudio, examinamos la variación en el grosor de la corteza en la Amazonía. La corteza puede proteger los árboles de los incendios, pero normalmente se supone que es uniformemente delgada en los bosques tropicales. Aquí, mostramos que el grosor de la corteza varía bastante, con una corteza más gruesa en los bosques secos y más delgada en los bosques húmedos. También, mostramos que cortezas más delgadas resultan en tasas de mortalidad más altas en bosques más húmedos. En total, estimamos que los incendios en el sotobosque de la Amazonía han añadido entre 0,67 y 5,86 gigatoneladas de CO2 atmosférico entre 2001-2010. Los modelos globales de vegetación que predicen los efectos de los incendios sobre el reciclaje de carbono en los bosques tropicales deberían incluir explícitamente la variación en el grosor de la corteza.

Os incêndios rasteiros de sub-bosque representam uma ameaça cada vez maior às florestas tropicais da Amazônia. Durante secas, eles podem afetar áreas maiores do que àquelas desmatadas. Esses incêndios matam árvores a taxas que variam de <10 a c. 90%, dependendo da intensidade do fogo, da história de distúrbios florestais e das características funcionais das árvores. Neste estudo, examinamos a variação na espessura da casca na Amazônia. A casca pode proteger árvores do fogo, mas geralmente é considerada uniformemente fina para diversas florestas tropicais. Aqui, mostramos que a espessura da casca varia, com cascas mais espessas ocorrendo em florestas secas e mais finas ocorrendo em florestas mais úmidas. Mostramos também que a casca mais fina resulta em taxas de mortalidade mais altas em florestas úmidas. No total, estimamos que os incêndios de sub-bosque adicionaram entre 0,67 e 5,86 gigatoneladas de CO2 atmosférico entre 2001-2010. Os modelos globais de vegetação devem incluir explicitamente a variação na espessura da casca ao prever os efeitos do fogo no ciclo do carbono de florestas tropicais.

Rooting depth as a key woody functional trait in savannas.

Dimensions of tree root systems in savannas are poorly understood, despite being essential in resource acquisition and post-disturbance recovery. We studied tree rooting patterns in Southern African savannas to ask: how tree rooting strategies affected species responses to severe drought; and how potential rooting depths varied across gradients in soil texture and rainfall. First, detailed excavations of eight species in Kruger National Park suggest that the ratio of deep to shallow taproot diameters provides a reasonable proxy for potential rooting depth, facilitating extensive interspecific comparison. Detailed excavations also suggest that allocation to deep roots traded off with shallow lateral root investment, and that drought-sensitive species rooted more shallowly than drought-resistant ones. More broadly across 57 species in Southern Africa, potential rooting depths were phylogenetically constrained, with investment to deep roots evident among miombo Detarioids, consistent with results suggesting they green up before onset of seasonal rains. Soil substrate explained variation, with deeper roots on sandy, nutrient-poor soils relative to clayey, nutrient-rich ones. Although potential rooting depth decreased with increasing wet season length, mean annual rainfall had no systematic effect on rooting depth. Overall, our results suggest that rooting depth systematically structures the ecology of savanna trees. Further work examining other anatomical and physiological root traits should be a priority for understanding savanna responses to changing climate and disturbances.

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.