Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes.

We report for the first time on the formation of spirals like vegetation patterns in isotropic and uniform environmental conditions. The vegetation spirals are not waves and they do not rotate. They belong to the class of dissipative structures found out of equilibrium. Isolated or interacting spirals and arcs observed in South America (Bolivia) and North Africa (Morocco) are interpreted as a result of curvature instability that affects the circular shape of localized patches. The biomass exhibits a dynamical behaviour with arcs that transform into spirals. Interpretation of observations and of the predictions provided by the theory is illustrated by recent measurements of peculiar plant morphology (the alfa plant, or Stipa tenacissima L.) originated from northwestern Africa and the southern part of the Iberian Peninsula.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

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.

Seeing Central African forests through their largest trees.

Large tropical trees and a few dominant species were recently identified as the main structuring elements of tropical forests. However, such result did not translate yet into quantitative approaches which are essential to understand, predict and monitor forest functions and composition over large, often poorly accessible territories. Here we show that the above-ground biomass (AGB) of the whole forest can be predicted from a few large trees and that the relationship is proved strikingly stable in 175 1-ha plots investigated across 8 sites spanning Central Africa. We designed a generic model predicting AGB with an error of 14% when based on only 5% of the stems, which points to universality in forest structural properties. For the first time in Africa, we identified some dominant species that disproportionally contribute to forest AGB with 1.5% of recorded species accounting for over 50% of the stock of AGB. Consequently, focusing on large trees and dominant species provides precise information on the whole forest stand. This offers new perspectives for understanding the functioning of tropical forests and opens new doors for the development of innovative monitoring strategies.

Plant clonal morphologies and spatial patterns as self-organized responses to resource-limited environments.

We propose here to interpret and model peculiar plant morphologies (cushions and tussocks) observed in the Andean Altiplano as localized structures. Such structures resulting in a patchy, aperiodic aspect of the vegetation cover are hypothesized to self-organize thanks to the interplay between facilitation and competition processes occurring at the scale of basic plant components biologically referred to as 'ramets'. (Ramets are often of clonal origin.) To verify this interpretation, we applied a simple, fairly generic model (one integro-differential equation) emphasizing via Gaussian kernels non-local facilitative and competitive feedbacks of the vegetation biomass density on its own dynamics. We show that under realistic assumptions and parameter values relating to ramet scale, the model can reproduce some macroscopic features of the observed systems of patches and predict values for the inter-patch distance that match the distances encountered in the reference area (Sajama National Park in Bolivia). Prediction of the model can be confronted in the future with data on vegetation patterns along environmental gradients so as to anticipate the possible effect of global change on those vegetation systems experiencing constraining environmental conditions.

Orthonormal transform to decompose the variance of a life-history trait across a phylogenetic tree.

In recent years, there has been an increased interest in studying the variability of a quantitative life-history trait across a set of species sharing a common phylogeny. However, such studies have suffered from an insufficient development of statistical methods aimed at decomposing the trait variance with respect to the topological structure of the tree. Here we propose a new and generic approach that expresses the topological properties of the phylogenetic tree via an orthonormal basis, which is further used to decompose the trait variance. Such a decomposition provides a structure function, referred to as an "orthogram," which is relevant to characterize in both graphical and statistical aspects the dependence of trait values on the topology of the tree ("phylogenetic dependence"). We also propose four complementary test statistics to be computed from orthogram values that help to diagnose both the intensity and the nature of phylogenetic dependence. The relevance of the method is illustrated by the analysis of three phylogenetic data sets, drawn from the literature and typifying contrasted levels and aspects of phylogenetic dependence. Freely available routines which have been programmed in the R framework are also proposed.

Localized vegetation patches: a self-organized response to resource scarcity.

We show that spatial self-organization allows vegetation to survive greater resource limitation. Isolated vegetation patches observed in nutrient-poor territories of South America and West Africa are interpreted as localized structures arising from the bistability between the bare state and the patchy vegetation state.