Joaquim Valls

Spiral waves, chaos and multiple attractors in lattice models of interacting populations

Abstract Stable spatial patterns are shown to appear in a 2D coupled map lattice (CML) approach. The model is constructed from a two-dimensional nonlinear map based on the dynamics of interacting populations. Such structures are mainly spiral waves. Chaotic and periodic dynamics are present for different parameter combinations, as shown by the largest Lyapunov exponent. Multiple attractors are present for some range of initial conditions and spiral waves are also present at the chaotic domain of parameters. implications for ecosystem dynamics are also discussed.

Stability and Complexity of Spatially Extended Two-species Competition

Lotka & Volterras studies showed the dynamics of two species in competition. Although it is very simple, the model has not been improved until recently. As Margalef (1980) pointed out, space must be taken into account in all fundamental aspects of ecological organization. On the other hand, in the last few years unexpected results on non-linear dynamical systems have changed our view of complexity. In this paper we explore the spatiotemporal behaviour of a two-species competition coupled map lattice. The coexistence of the two competitors is demonstrated although they have high interspecific competition coefficients. This coexistence is closely related with spatial segregation and the formation of a well-defined Turing-like structure. Moreover, the patches observed can have a large influence on the temporal dynamics. Some implications for population extinction and for the competitive exclusion principle are also discussed.

Nonequilibrium dynamics in lattice ecosystems: Chaotic stability and dissipative structures

A generalized coupled map lattice (CML) model of ecosystem dynamics is presented. We consider the spatiotemporal behavior of a prey-predator map, a model of host-parasitoid interactions, and two-species competition. The latter model can show phase separation of domains (Turing-like structures) even when chaos is present. We also use this CML model to explore the time evolution and structural properties of ecological networks built with a set of N competing species. The May-Wigner criterion is applied as a measure of stability, and some regularities in the stable networks observed are discussed.

On structural stability and chaos in biological systems

A spatially extended model of density-dependent discrete maps is presented. This model is based in the so-called coupled map lattice formalism and is applied to two well-known discrete models of population biology. Several new results are obtained, showing the importance of space on the qualitative properties of these models. Chaotic dynamics is more widely present in the spatially extended models than in the uncoupled counterpart but the presence of this behavior can be undistinguishable in real situations from a point attractor with added noise. Some general implications are also discussed.

Order and chaos in a 2D Lotka-Volterra coupled map lattice

Abstract A numerical analysis of a dissipative coupled map lattice is performed in order tocharacterize temporal and spatial behavior. It is shown that spatial ordered structures take place coexisting with chaotic (temporal) attractors.

Simulation modelling of bacterial growth in yoghurt.

INDISIM, an individual-based simulator, was used to specifically study the influence of the shape and size of Streptococcus salivarius subsp. thermophilus and Lactobacillus delbrueckii subsp. bulgaricus in yoghurt processing. To this effect, two different sets of simulations were carried out. In the first set of simulations, it was assumed that the initial acidity of the medium has the same value as the acidity of the cytoplasm of the microorganisms. Hence, the differences in bacterial growth by the two species are only attributable to differences in their geometry. It was found that, in an optimum culture, the growth in biomass of S. salivarius subsp. thermophilus is larger than that of L. delbrueckii subsp. bulgaricus. An important factor for understanding this difference might be the larger mass-to-surface ratio of the former. In the second set of simulations, a simplified model of yoghurt, the parametrisation differs both in the geometry and the metabolism of the two species. The results of these simulations are in very good qualitative agreement with the experimental data of [Lait 69 (1989) 519]. Finally, by inhibiting the uptake of amino acids by S. salivarius subsp. thermophilus, the large relative importance of lactic acid in yoghurt processing was highlighted.

Thermodynamic approach to biomass distribution in ecological systems

In the derivation of the biomass distribution function for an ecological population critical use is made of an energetic constraint on the maximization of biomass diversity. The nature of this constraint is explored in detail using Kleibers relation σ(m) = cmγ between animal metabolic rate σ(m) and body weight m in conjunction with the Prigogine-Wiame thermodynamic paradigm for specific entropy production in biological stationary states. These two inputs fix the energetic constraint on the maximization of biomass diversity to be the constancy of the mean metabolic rate of the ecosystem. The resulting biomass distribution function is tested against observational data.

Individual based simulations of bacterial growth on agar plates

The individual based simulator, INDividual DIScrete SIMulations (INDISIM) has been used to study the behaviour of the growth of bacterial colonies on a finite dish. The simulations reproduce the qualitative trends of pattern formation that appear during the growth of Bacillus subtilis on an agar plate under different initial conditions of nutrient peptone concentration, the amount of agar on the plate, and the temperature.

To achieve an earlier IFN-γ response is not sufficient to control Mycobacterium tuberculosis infection in mice.

The temporo-spatial relationship between the three organs (lung, spleen and lymph node) involved during the initial stages of Mycobacterium tuberculosis infection has been poorly studied. As such, we performed an experimental study to evaluate the bacillary load in each organ after aerosol or intravenous infection and developed a mathematical approach using the data obtained in order to extract conclusions. The results showed that higher bacillary doses result in an earlier IFN-γ response, that a certain bacillary load (BL) needs to be reached to trigger the IFN-γ response, and that control of the BL is not immediate after onset of the IFN-γ response, which might be a consequence of the spatial dimension. This study may have an important impact when it comes to designing new vaccine candidates as it suggests that triggering an earlier IFN-γ response might not guarantee good infection control, and therefore that additional properties should be considered for these candidates.

Self-organized criticality in Monte Carlo simulated ecosystems

Abstract A self-organized critical state is observed in a simple ecosystem model based on a Monte Carlo simulation approach. A 1 ⨍ Fourier spectrum is obtained, related with a dynamical process with fluctuations on a wide range of time scales, showing a well defined power law. The system shows a fractal spatial organization generated from a spatially homogeneous energy flow. Indeed our studies provide evidence for self-organized critically in realistic biological models, showing the reliability of a previous conjecture about the application of this approach to real living systems. Some general implications are also discussed.