Mara Baudena

Multiple equilibria on planet Dune: Climate-vegetation dynamics on a sandy planet

ABSTRACT We study the interaction between climate and vegetation on an ideal water-limited planet, focussing on the influence of vegetation on the global water cycle. We introduce a simple mechanistic box model consisting in a two-layer representation of the atmosphere and a two-layer soil scheme. The model includes the dynamics of vegetation cover, and the main physical processes of energy and water exchange among the different components. With a realistic choice of parameters, this model displays three stable equilibria, depending on the initial conditions of soil water and vegetation cover. The system reaches a hot and dry state for low values of initial water content and/or vegetation cover, while we observe a wet, vegetated state with mild surface temperature when the system starts from larger initial values of both variables. The third state is a cold desert, where plants transfer enough water to the atmosphere to start a weaker, evaporation-dominated water cycle before they wilt. These results indicate that in this system vegetation plays a central role in transferring water from the soil to the atmosphere and trigger a hydrologic cycle. The model adopted here can also be used to conceptually illustrate processes and feedbacks affecting the water cycle in water-limited continental areas on Earth. †Now at: International Max Planck Research School on Earth System Modelling, Hamburg, Germany

Complexity and coexistence in a simple spatial model for arid savanna ecosystems

Tree–grass coexistence is broadly observed in tropical savannas. Recent studies indicate that, in arid savannas, such coexistence is stable and related to water availability. The role of different factors (from niche separation to demographic structure) has been explored. Nevertheless, spatial mechanisms of water–vegetation interactions have been rarely taken into account, despite their well-known importance for vegetation distribution. Here, we introduce a spatial model including tree and grass biomass dynamics, together with soil and surface water dynamics. We consider two water–vegetation feedbacks. Grasses increase water infiltration into the soil, while tree shadow limits evaporation, and both mechanisms increase soil water availability, leading to positive feedbacks. The infiltration feedback can also lead to spatial pattern formation. Despite the fact that trees and grasses compete for the same resource, namely water, we observe stable coexistence as a possible model outcome. The system displays a complex behavior, with multiple stable states and possible catastrophic shifts between states, e.g., patterned grassland, bare soil and forest. In our model, coexistence is always linked with multi-stability and spatial pattern formation, driven by grass infiltration feedback. Given such complex model solutions, we expect that, under real conditions, heterogeneities and disturbances, acting on the multi-stable states, may further foster coexistence.

Tree‐grass competition for soil water in arid and semiarid savannas: The role of rainfall intermittency

Arid and semiarid savannas are characterized by the coexistence of trees and grasses in water limited conditions. As in all dry lands, also in these savannas rainfall is highly intermittent. In this work, we develop and use a simple implicit-space model to conceptually explore how precipitation intermittency influences tree-grass competition and savanna occurrence. The model explicitly includes soil moisture dynamics, and life-stage structure of the trees. Assuming that water availability affects the ability of both plant functional types to colonize new space and that grasses outcompete tree seedlings, the model is able to predict the expected sequence of grassland, savanna, and forest along a range of mean annual rainfall. In addition, rainfall intermittency allows for tree-grass coexistence at lower mean annual rainfall values than for constant precipitation. Comparison with observations indicates that the model, albeit very simple, is able to capture some of the essential dynamical processes of natural savannas. The results suggest that precipitation intermittency affects savanna occurrence and structure, indicating a new point of view for reanalyzing observational data from the literature.

How will increases in rainfall intensity affect semiarid ecosystems

Model studies suggest that semiarid ecosystems with patterned vegetation can respond in a nonlinear way to climate change. This means that gradual changes can result in a rapid transition to a desertified state. Previous model studies focused on the response of patterned semiarid ecosystems to changes in mean annual rainfall. The intensity of rain events, however, is projected to change as well in the coming decades. In this paper, we study the effect of changes in rainfall intensity on the functioning of patterned semiarid ecosystems with a spatially explicit model that captures rainwater partitioning and runoff-runon processes with simple event-based process descriptions. Analytical and numerical analyses of the model revealed that rainfall intensity is a key parameter in explaining patterning of vegetation in semiarid ecosystems as low mean rainfall intensities do not allow for vegetation patterning to occur. Surprisingly, we found that, for a constant annual rainfall rate, both an increase and a decrease in mean rainfall intensity can trigger desertification. An increase negatively affects productivity as a greater fraction of the rainwater is lost as runoff. This can result in a shift to a bare desert state only if the mean rainfall intensity exceeds the infiltration capacity of bare soil. On the other hand, a decrease in mean rainfall intensity leads to an increased fraction of rainwater infiltrating in bare soils, remaining unavailable to plants. Our findings suggest that considering rainfall intensity as a variable may help in assessing the proximity to regime shifts in patterned semiarid ecosystems and that monitoring losses of resource through runoff and bare soil infiltration could be used to determine ecosystem resilience. Key Points Rainfall intensity controls patterning and the resilience of arid ecosystems Both an increase and decrease in rainfall intensity can trigger desertification In line with observations, three types of rain events were identified in our model

A new family of standardized and symmetric indices for measuring the intensity and importance of plant neighbour effects

1. Measurements of competition and facilitation between plants often rely upon intensity and importance indices that quantify the net effect of neighbours on the performance of a target plant. A systematic analysis of the mathematical behaviour of the indices is lacking and leads to structural pitfalls, e.g. statistical problems detected in importance indices. 2. We summarize and analyse themathematical properties that the indices should display. We reviewthe properties of the commonly used indices focusing on standardization and symmetry, which are necessary to avoid compromising data interpretation.We introduce a new family of indices ‘Neighbour-effect Indices’ that meet all the proposed properties. 3. Considering the commonly used indices, none of the importance indices are standardized, and onlyRII (Relative Interaction Index) displays all the required mathematical properties. The existing indices show two types of symmetries, namely, additive or commutative, which are currently confounded, potentially resulting in misleading interpretations. Our Neighbour-effect Indices encompass two intensity and two importance indices that are standardized and have different and defined symmetries. 4. Our new additive intensity index, NIntA, is the first of its kind, and it is generally more suitable for assessing competition and facilitation intensity than the widely used RII, which may underestimate facilitation. Our new standardized importance indices solve the main statistical problems that are known to affectCimp and Iimp. Intensity and importance with the same symmetry should be used within the same study. The Neighbour-effect Indices, sharing the same formulation, will allow for unbiased comparisons between intensity and importance, and between types of symmetry.

Demographic noise and resilience in a semi-arid ecosystem model

The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies. Some of these generate water–vegetation feedback mechanisms that can lead to spatial self-organisation of vegetation, as it has been shown with models representing plants by a density of biomass, varying continuously in time and space. However, although plants are usually quite plastic they also display discrete qualities and stochastic behaviour. These features may give rise to demographic noise, which in certain cases can influence the qualitative dynamics of ecosystem models. In the present work we explore the effects of demographic noise on the resilience of a model semi-arid ecosystem. We introduce a spatial stochastic eco-hydrological hybrid model in which plants are modelled as discrete entities subject to stochastic dynamical rules, while the dynamics of surface and soil water are described by continuous variables. The model has a deterministic approximation very similar to previous continuous models of arid and semi-arid ecosystems. By means of numerical simulations we show that demographic noise can have important effects on the extinction and recovery dynamics of the system. In particular we find that the stochastic model escapes extinction under a wide range of conditions for which the corresponding deterministic approximation predicts absorption into desert states.

Revealing patterns of local species richness along environmental gradients with a novel network tool

How species richness relates to environmental gradients at large extents is commonly investigated aggregating local site data to coarser grains. However, such relationships often change with the grain of analysis, potentially hiding the local signal. Here we show that a novel network technique, the “method of reflections”, could unveil the relationships between species richness and climate without such drawbacks. We introduced a new index related to potential species richness, which revealed large scale patterns by including at the local community level information about species distribution throughout the dataset (i.e., the network). The method effectively removed noise, identifying how far site richness was from potential. When applying it to study woody species richness patterns in Spain, we observed that annual precipitation and mean annual temperature explained large parts of the variance of the newly defined species richness, highlighting that, at the local scale, communities in drier and warmer areas were potentially the species richest. Our method went far beyond what geographical upscaling of the data could unfold, and the insights obtained strongly suggested that it is a powerful instrument to detect key factors underlying species richness patterns, and that it could have numerous applications in ecology and other fields.

Frequency-dependent feedback constrains plant community coexistence

Ecological theory suggests that coexistence of many species within communities requires negative frequency-dependent feedbacks to prevent exclusion of the least fit species. For plant communities, empirical evidence of negative frequency dependence driving species coexistence and diversity patterns is rapidly accumulating, but connecting these findings to theory has been difficult as corresponding theoretical frameworks only consider small numbers of species. Here, we show how frequency-dependent feedback constrains community coexistence, regardless of the number of species and inherent fitness inequalities between them. Any interaction network can be characterized by a single community interaction coefficient, IC, which determines whether community-level feedback is positive or negative. Negative feedback is a necessary (but not sufficient) condition for persistence of the entire community. Even in cases where the coexistence equilibrium state cannot recover from perturbations, IC < 0 can enable species persistence via cyclic succession. The number of coexisting species is predicted to increase with the average strength of negative feedback. This prediction is supported by patterns of tree species diversity in more than 200,000 deciduous forest plots in the eastern United States, which can be reproduced in simulations that span the observed range of community feedback. By providing a quantitative metric for the strength of negative feedback needed for coexistence, we can now integrate theory and empirical data to test whether observed feedback–diversity correlations are strong enough to infer causality.Outlining a framework based on a generalized plant–soil feedback model, the authors show that negative frequency-dependent feedback is necessary for the persistence of whole plant communities, and establish a quantitative metric for the strength of feedback needed for coexistence.