An individual-based, stochastic and spatial model to simulate the ramification of grass tillers and their distribution in swards

Abstract

Understanding the vegetation dynamics of a grass sward at fine-scale requires breaking the interplay between density-dependent processes and environmental variability. Simulation of one of these interacting processes may be a powerful tool. SISTAL is a spatially explicit, object-oriented model of the spatial distribution and spatio-temporal dynamics of individual grass tillers in cut swards. It focuses both on the spatial movement of existing tillers and on the birth and death of tillers. The time management is based on discrete events, and the system dynamics is computed with thermal time. The space management uses both a spatial grid and real coordinates.

The paper exposes implementation choices that have been carefully selected: inputs and outputs; edge effects; implementation of the memory management and the handling of pseudo-parallelism. The simulation diary is described since it was found a very useful tool for verification. Essential results and comparisons with real observations allowing the validation of the model are presented.

Introduction

The vegetation dynamics of a grassland depends on plant competition [19] and on gap colonisation [6]. In a pasture, ingressions and competition are involved at spatial scales between a few square centimetres and a few square decimetres [43]. At such scales in perennial grass swards, the horizontal structure of the stand is very heterogeneous, with empty spaces adjoining very densely populated ones at changing places [26]. Grass patches are composed of grass sprigs, called tillers that are continually renewed by ramification, as the old ones die. In most species, these tillers live from a few months to one or a few years, but “plants” (that is sets of connected tillers) are perennial.

The density of all natural populations varies in space and time, according to density-dependent processes and environmental variability, which always interact [30]. Understanding the vegetation dynamics requires to break this interplay. Simulation of one of both interacting processes may be a powerful tool. The aim of our work is to generate fine-scale stand structures of pure grass swards from a spatial simulation of the demographic processes of a perennial grass species in given environmental conditions, in order to know the relative weights of the species-specific patterns and of the local environmental conditions in observed heterogeneities of local tiller densities. In a grass patch, demographic processes are the birth of new tillers, the death of the existing tillers and, when a spatial pattern is taken into account, the positioning of the tillers.

The few existing tiller-density simulators are sub-models in dry-mass growth models [38]. They simulate a mean density at a too coarse scale. Existing spatial demographic models for grasses focus on tussocks (for examples [45], [16]). We chose a model generating individual tillers from mother tillers and distributing them on the ground. In this way, we focused on clonal multiplication rather than on seedling recruitment, which is always possible but minor [41]. The biological side of this model was described and discussed in a companion paper [27]. In this study, we want to explain and discuss our modelling choices and to describe the computer model, its implementation and verification. At the end, we will show results and compare them with fine-scale observations in established swards.