**Principal Investigator**
Ian Noble **Project **p55

Research School of Biological Sciences **Machine
**VP

**Co-Investigators **Sandra
Lavorel and Peter Chesson,

C.N.R.S., Montpellier, France, and Research School of Biological Sciences

**A Spatial Model of Community dynamics in Patchy
Landscapes**

This study focuses on how the interaction between biological characteristics, habitat pattern, and disturbance regime can promote diversity in plant communities. The main goals are to improve the theoretical understanding of the mechanisms of maintenance of species diversity in spatio-temporally variable environments, and to provide measurable criteria that will allow diagnosis and prediction of patterns of species coexistence.

A simulation model of dynamics of two species assemblages in habitats with various spatial patterns and local disturbance frequencies is used to examine specific relationships between species dispersal and germination strategies and their coexistence in those environments. The first step was to identify robust variables to describe various components of the interaction independently. The second step has been to obtain simulated values for these variables under a factorial design of values for the biological and environmental parameters, and to analyze their relative contributions to species coexistence. The third step, presently in progress, is to obtain simulated estimates for variables derived from an analytical resolution of the model.

**What are the basic questions addressed?**

The aim of this project is to propose mechanisms for the theory of the regeneration niche which proposes that species coexistence can be maintained through interspecific differences in regeneration characteristics. Simulations have been used to investigate the relationships between population growth rate and the biological and environmental characteristics. Specific questions are: Do species need to be different and how much to coexist in variable environments? What are the relative role of spatial pattern and disturbance regimes in promoting species diversity? What sort of demographic mechanisms determine species coexistence?

**What are the results to date and future of the
work?**

The invasion of a resident population with short dispersal distance by a species with longer-range dispersal was simulated for combinations of habitat pattern, disturbance frequency and germination strategies. Coexistence depended on both habitat suitability and disturbance frequency.

The analysis of invader's low density growth rate showed that two different mechanisms are involved in the coexistence of species with different niches. Differences in regeneration niches permit coexistence through competitive equivalency with trade-offs between dispersal and germination traits, but for a limited range of habitat pattern and disturbance conditions. On the other hand, coexistence through density fluctuations of a disturbance-broken species can be achieved for a broad range of environmental conditions and species germination strategies. Our results also demonstrate the importance of detailed attention to spatial patterns and dispersal because of the complexity of spatial effects. Further, spatial pattern and disturbance frequencies need to be considered jointly to understand the dynamics of species diversity.

An analytical resolution of the model dynamics was calculated. We obtain a decomposition of the population low-density growth rate according to environmental and competition variables and their covariances. Simulations were run to estimate the components of the analytical equation. Results to date indicate that the covariance between local density in germinable seeds and competition for germination has the strongest contribution to species coexistence, while terms related to the spatial heterogeneity of seed dispersal have little importance. Then, local disturbances which stimulate germination are the major driver of the dynamics in our model. These analyses need further refinement to fully validate the generalised theory of competitive lottery.

**What computational techniques are used and why
is a supercomputer required?**

The model simulates the demography of a two-species community. The dynamics is modelled at the individual level, for a landscape consisting in a patterned lattice of habitat sites. First, a landscape pattern is generated using a hierarchical dichotomy for suitable vs unsuitable spatial units. At each time step, the algorithm sweeps across the landscape to calculate the destinations of all seeds produced by established individuals, updates the composition of the seed bank at each site, and draws the adults for the next generation. Calculations are mainly convolutions of basic operations and functions on large arrays; the algorithm also involves numerous random draws. Population maps after a fixed number of generation are stored and analyzed using algorithms of point pattern analysis. The investigation of stochastic processes requires replicated experiments. Hence, a run for a given parameter set consists in a set of 5 simulations for a given set of parameters. Inter-simulation mean and variance for a number of synthetic descriptors are calculated to analyze the dynamics of species coexistence.

The program is written in FORTRAN 77. Since the algorithm relies on convolution of operations on large arrays (100 x 100), vectorizing appears as particularly well suited to reduce calculation time. Investigating stochastic processes requires that seeds are dispersed individually and independently. Such a procedure, when in scalar form, is extremely time-expensive (several thousands calculations per time step!), and in fact takes over 2/3 of total simulation time. After reprogramming for maximum vectorization and flexibility to further sophistications, vectorization is still only partial (about 45% at present), due to unavoidable recursivity in the seed bank dynamics. The version of the program for the estimation of the analytical terms, on the other hand, achieves 60% vectorisation.

**Publications**

*How species with different regeneration niches
coexist in patterned landscapes: a simulation study,*
S. Lavorel and P. Chesson, 1995, Oikos** 74:** 103-114.

*An analysis of coexistence of annual plants in
spatio-temporally variable landscapes,*
P. Chesson and S. Lavorel, in preparation.