Coevolutionary motion and swarming in a niche space model of ecological species interactions

Organisms are involved in coevolutionary relationships with their competitors, predators, preys and parasites. In this context, we present a simple model for the co-evolution of species in a common niche space, where the fitness of each species is defined via the network of interactions with all other species. In our model, the sign and type of the pairwise interactions (being either beneficial, harmful or neutral) is given by a pre-determined community matrix, while the interaction strength depends on the niche-overlap, i.e. the pairwise distances between species in niche space. The evolutionary process drives the species toward the places with the higher local fitness along the fitness gradient. This gives rise to a dynamic fitness landscape, since the evolutionary motion of a single species can change the landscape of the others (known as the Red Queen Principle). In the simplest case of only two-species we observe either a convergence/divergence equilibrium or a coevolutionary arms race. For a larger number of species our analysis concentrates on an antisymmetric interaction matrix, where we observe a large range of dynamic behaviour, from oscillations, quasiperiodic to chaotic dynamics. In dependence of the value of a first integral of motion we observe either quasiperiodic motion around a central region in niche space or unbounded movement, characterised by chaotic scattering of species pairs. Finally, in a linear food-chain we observe complex swarming behaviour in which the swarm moves as a whole only if the chain consists of an even number of species. Our results could be an important contribution to evolutionary niche theory.