Population Dynamics in Space and Time

The current ideas on evolution, usually referred to as the Modern Synthesis, assert that the basic
ingredients of evolution are genetic variation (which arises from random mutation and recombination)
and natural selection. When combined with a large average number of offspring per individual, these
ingredients lead inevitably to the survival of the fittest. Diversification comes about by speciation, which
normally entails the gradual evolution of reproductive isolation among populations. In sexually reproducing
organisms, however, the genetic changes produced by natural evolution spread quickly through
the population, hindering the possibility of a single species branching into two or more new ones. Speciation
is commonly attributed to geographic isolation, which prevents gene flow between groups and allows
each group to follow a different evolutionary path.

This may not, however, be the only possible mechanism of diversification. In a recent work of the
research group at NECSI, we have argued that even in a totally homogeneous environment, spatially
distributed systems can develop inhomogeneity through symmetry breaking and spontaneous pattern
formation.  Typically, the existence of local but spatially overlapping mating neighborhoods in
two-dimensional space may result in a dynamic pattern of polymorphism. The significance of
such spatial patterns for the studies of population distributions in ecological processes has been
realized for some time. But analogous evolutionary studies of the genetics of dynamic spatial
variation are just beginning.

Similar ideas can be applied to the study of predator-prey systems, where individuals in spatially distributed
populations interact mostly with nearby individuals. In the particular case of a system with three species,
a mean field version of the dinamics (without taking space into account) shows the appearance of chaos,
whereas the spatial version shows that chaos may or may not occur, depending on the size of the interacting
neighborhoods. The figure on the left shows an example of the population distribution for a prey (red - like a plant),
a predator (green - like an herbivore) and a super-predator (blue - like a carnivore). The predators, green
and blue, predate only inside their interaction neighborhoods, their home range. Depending on the size of
these neighborhoods the population distribution may be homogeneous, distributed in stripes or in clusters,
like in the figure below. Patterns occur also for systems with only two species, like the striped pattern shown
for the case where the superpredator was eliminated.

           
 

NECSI - New England Complex Systems Institute

Recent Papers (click here for the full list)
 

Chaos and pattern formation in a spatial tritrophic food chain
Daniela O. Maionchi, S. F. dos Reis and M. A. M. de Aguiar, Journal of Ecological Modelling 191 (2006) 219.

Invasion and Extinction in the Mean Field Approximation for a Spatial Host-Pathogen Model
M.A.M. de Aguiar, E. Rauch and Y. Bar-Yam
Journal of Statistical Physics 114, 1417 (2004)

Mean Field Approximation To a Spatial Host-Pathogen Model
M.A.M. de Aguiar, E. Rauch and Y. Bar-Yam
Physical Review E67, 047102  (2003).

Spontaneous pattern formation and genetic invasion in locally mating and competing populations
H. Sayama, M. A.M. de Aguiar, Y. Bar-Yam, and M. Baranger
Phys. Rev. E65 (2002) 051919

Stability and Instability of Polymorphic Populations and the Role of Multiple Breeding Seasons in Phase III of Wright's Shifting Balance Theory
 M. A.M. de Aguiar, H. Sayama, E. Rauch, Y. Bar-Yam, and M. Baranger
 Phys. Rev. E65 (2002) 31909.
 

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