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Mathematical physics

Borderless biodiversity

Computer simulation indicates that species may form without geographical isolation

New species of live beings may arise without natural selection favoring the fittest or without geographical barriers isolating people. At least in the virtual world of simulation developed by physicist Marcus de Aguiar, from the State University of Campinas (Unicamp), described in an article in the July 16 issue of Nature.

A chaos theory expert, Aguiar teaches in the Department of Condensed Matter Physics, where subjects such as crystallography, materials properties and optical phenomena are studied. In this setting, it is surprising to find, on a researcher’s desk, the book Why evolution is true, in which Jerry Coyne, an American evolutionist, gives the layman a detailed defense of his field of study. The interest of the Unicamp physicist was born out of a chance meeting at Necsi, the New England Complex Systems Institute, in the United States, when physicist Yaneer Bar-Yam introduced Aguiar to a simple problem of the application of theoretical models to biological systems.

At first, it was like solving a puzzle for relaxation, but back in Campinas, Aguiar continued to study and to think about evolution. He proposed to his American colleagues testing the neutral theory, according to which the diversity of the species results from random processes that act upon similar populations. And this is what he did, as part of a Thematic Project financed by FAPESP: together with Necsi researchers and with the help of PhD candidate Elizabeth Baptestini, he wrote a computer program that simulates the evolution of a virtual population during the course of hundreds of generations.

This approach allows one to conduct virtual experiments in order to test different parameters in the search for the most important variables in the generation of biological diversity. In these experiments, the researchers can vary the maximum distance that an organism can cover in the search of a partner and the degree of genetic divergence that makes two individuals incompatible. They also tested the importance of the migration capacity (i.e., the distance that each individual covers to establish residence), the mutation rate, and  the probability of each individual reproducing. The last parameter was included at the suggestion of Les Kaufman, the only biologist among the article’s authors. “He said that it was unrealistic to assume that all the members of the population would have the same rate of reproduction”, recalls Aguiar. “In our model, it is possible for an organism to never reproduce and for another to have several offspring.”

The simulation starts off with some thousands of genetically identical individuals, whose DNA is a 125-number series, in which each figure represents a gene and has the value of zero or one. Each organism appears as a colored dot that randomly chooses a partner for reproduction within the limits imposed by the distance between them and by their genetic similarity. The program’s parameters also determine the mutation and migration rates, besides the chance of each member of the population reproducing. The outcome is a genetic diversity that, after 300 generations, gives rise to different species. “We showed that it is easy for a species to appear and that this does not depend on the isolation of different populations,” tells us the Unicamp physicist.

The model indicates that new species may arise even when there are no barriers to keep the organisms from moving, contrary to the theory of most of the evolutionists. Aguiar showed that the maximum limits of the distance between partners and of the generation differences between them are essential for speciation. “Just one of these parameters does not generate sufficient diversity,” he says. He identified in the simulations a pattern of distribution and abundance of species similar to what the neutral theory forecasts. This theory was put forth in 2001 by the American ecologist Stephen Hubbell: as in a raffle, chance easily does away with small populations and leads nascent species to extinction. However, as new species arise all the time, after some 700 generations, researchers saw that a dynamic equilibrium emerged, in which extinctions were offset by speciations and in which the number of species remained more or less constant.

For the time being, Aguiar suggests adding another speciation model to the theoretical list that already includes sympatric speciation, when space does not interfere with the process; allopatric, when the populations are isolated; and parapatric, when species arise in adjacent regions. “I invented the expression ‘topopatric speciation’,” says Aguiar, “because the distance between the individuals is essential” (in Greek, topos means place). Curious to find out how this will be received by biologists, the physicist has already overcome the first obstacle: as part of the review process of Nature, the work was analyzed by three biologists, who accepted the article for publication after some adjustments.

From the virtual to the real
The novel aspect of the study, which ensured it was approved, was the fact that it bridged the gap between theory and what happens in nature. “Just a simulation would have been insufficient to be published in Nature,” explains the physicist. He went beyond the simulation and compared the virtual results to the data on real distribution and on species abundance that other researchers had observed in nature – in trees in Panama and birds in the United Kingdom. The graphs showed a very similar relation between the number of species in the space, despite the obvious difference between the migration capabilities of birds and trees. However, the authors explain that birds, despite being migratory animals, return to the site where they were born in order to reproduce. The distribution of the number of members in each species looks similar, when one compares the empirical and the simulated data: species with a population of average size are more common.

Aguiar’s model is surprising because it reproduces speciation patterns found in nature, although with a simplified representation. All members of the population have the same longevity and the environment lacks areas that are more favorable than others. Therefore, the probability of reproducing does not depend on the organism’s genome or on where it is – a different reality relative to that observed by the biologists.

“There is no organism that is not limited by its environmental context,” states the evolutionist João Alexandrino, from Paulista State University (Unesp) at Rio Claro. Even if a certain type of frog is abundant in a forest, it needs water to live and to reproduce and cannot exist in dry areas or on treetops, for example. Furthermore, he argues that although the virtual environment of the simulation was built with no geographical landmarks, such as rivers or mountains, there are barriers built into the organisms: the very low migration capabilities of the colored points form isolated populations.

The points of view of theoretical physics and ecology may diverge, but the meeting of ideas highlights how a computer model can contribute to the study of evolution. The coincidence between the results obtained via the simulation and certain empirical data seems to point to something real and could become a starting point for reflection on what determines the species diversity. “Perhaps the emerging of the species diversity pattern observed by Aguiar is an inherent property of biological systems,” speculates Alexandrino. “The space limitation restricts the number of highly abundant species, but constant speciation produces a large number of very rare species,” he reflects, transferring to the species level a process that is already known in connection with genes. It seems that if physicists, ecologists and evolutionist put their heads together, new understanding about the possible origins of species might arise.

Scientific article
DE AGUIAR, M. A. M. et al. Global patterns of speciation and diversity. Nature, v. 460, n. 7.253, p. 384-387. 16 July 2009.