Jordi Bascompte

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.

Fractals and search paths in mammals

The fractal index by Katz and George (1985) for thecharacterization of planar curves is applied to wolf search pathsrecorded by radio-telemetry. All the sets of paths studied showspatial patterns whose complexity is between a straight line anda true random walk. Females‘ fractal dimensions show significantchanges throughout the year, depending on the state of their lifecycle (normal, breeding and wandering). There are alsodifferences between males and females, but not between adults andnon-adults. The results are discussed with regard to wolffood-search strategies.

Are Critical Phenomena Relevant to Large-Scale Evolution?

Recent theoretical studies, based on the theory of self-organized critical systems, seem to suggest that the dynamical patterns of macroevolution could belong to such class of critical phenomena. Two basic approaches have been proposed: the KauffmanJohnsen model (based on the use of coupled fitness landscapes) and the Bak─Sneppen model. Both are reviewed here. These models are oversimplified pictures of biological evolution, but the (possible) validity of them is based on the concept of universality, i. e. that apparently very different systems sharing some few common properties should also behave in a very similar way. In this paper we explore the current evidence from the fossil record, showing that some properties that are suggestive of critical dynamics would also be the result of random phenomema. Some general properties of the large-scale pattern of evolution, which should be reproduced by these models, are 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.

Chaotic Turing structures

Abstract Turing-like structures are obtained in a two-dimensional coupled map lattice model. Such structures have a well-defined stable pattern in space, but highly chaotic local fluctuations can also be observed. Two well-defined regions in phase space are separated, defining the domains of emergence of phase separation. Chaotic behavior is widely present in both situations and the Allen-Cahn theory of phase separation is applied. The transient behavior is also analysed and some implications for species competition in ecology are outlined.