Download A NEUTRAL THEORY OF SPECIATION AND DIVERSITY

A NEUTRAL THEORY OF SPECIATION AND DIVERSITY
M.A.M. de Aguiar1,2, M. Baranger1,3, E.M. Baptestini2, L. Kaufman1,4 and Y. Bar-Yam1
1 New England Complex Systems Institute, Cambridge, MA 02138,USA
2 Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, SP, Brasil
3 University of Arizona, Tucson, AZ 85719, USA
4 Boston University, Boston, MA 02215, USA
keywords: evolution, ecology, speciation
1 - INTRODUCTION
The number of living species on Earth has been estimated to be between 10 and 100 million.
Understanding the processes that have generated such remarkable diversity is one of the greatest
challenges in evolutionary biology. Among the many types of speciation processes studied, the allopatric
has been considered to be the most common and thus largely responsible for biodiversity. It occurs either
by adaptation to new environments of two or more geographically isolated sub-populations, or simply by
random genetic drift and bottlenecks independently affecting these sub-populations [1]. The opposite case
of sympatric speciation, occurring without physical barriers, is more controversial, although a growing set
of experimental data seems to corroborate its validity. Several theoretical models of sympatric speciation,
mostly based on numerical simulations, have been motivated by this observational evidence [2].
In this paper we examine another mechanism of speciation, that we term topopatric, based on symmetrybreaking and spontaneous pattern formation in genetic and physical space [3]. It is an example of a very
general phenomenon, frequently observed in physics, in chemistry, in developmental biology, and in
ecology, in which an initially symmetric (or uniform) distribution happens to be intrinsically unstable and
breaks down asymmetrically, leading to the self-organization of its members into clusters.
2 - THE MODEL
We simulated the evolution of a population whose members, at the beginning, are uniformly distributed in
a homogeneous environment and have identical genomes. The key ingredient of the model is the
introduction of assortative mating based on two critical mating distances: one in physical space and one
in genetic space. In physical space, an individual can mate only with others living in a certain
neighborhood of its location, as opposed to random panmictic mating within the entire population; the
size of this neighborhood is determined by the critical mating space distance S. In genetic space on the
other hand, an individual can mate only with others whose genome is not too different from its own; the
size of the allowed difference is determined by the critical mating genetic distance G. Neither one of
these restrictions, when imposed alone, leads to speciation. However, when they are both present,
speciation may happen depending on the values of parameters such as the spatial density of individuals,
the mutation rate, etc. Although this mating dynamics allows for gene flow only between a restricted set
of individuals in each single mating season, gene flow between any two individuals is possible in a few
generations since the mating neighborhoods always overlap. In the language of physics the system is, on
the average, invariant under space translations and speciation occurs by breaking this symmetry. It
occurs because the `homogeneous solution', i.e. the single uniform population, turns out to be unstable
and statistical fluctuations get amplified to produce patterns of population types in genetic space. This
instability is generated by the interaction between the physical and the genetic spaces.
3 - RESULTS
Figure 1 illustrates the time evolution of a population through 800 generations. Different species are
shown in different colors. After a transient period the population reaches a dynamical equilibrium, where
the rate of extinctions and new speciation events are equal, leading to a fixed average number of species
over long periods of time. The distribution of abundances, measuring the number of individuals per
species, can be calculated from the evolved populations. Typical results are shown in figure 2, compared
with empirical data. The qualitative agreement is remarkable. The observed empirical fits and recent data
on speciation suggest that the combined actions of selection and topopatry, rather that alopatry, may be
the dominant mechanism of speciation.
Figure 1 - Time evolution of a population with 2000 individuals on a 128 x 128 lattice
with G=20, S=6 and mutation rate 0.001.
Figure 2 - Abundance distribution. Black circles show the results of the simulation (left and bottom axis)
and red circles results for Panamanian trees (top and right axis). The blue curve is a lognormal fit.
ACKNOWLEDGEMENTS
We thank Fapesp and CNPq for financial support.
References
[1] Jerry A. Coyne and H. Allen Orr, Speciation, Sinauer Associates Inc., Sunderland, MA, USA (2004).
[2] U. Dieckmann and M. Doebeli, On the origin of species by sympatric speciation Nature (London) 400
354 (1999).
[3] M. A. M. de Aguiar, M. Baranger, E. M. Baptestini, L. Kaufman and Y. Bar-Yam, Global patterns of
speciation and diversity, Nature 460 (2009) 384.