HYPOTHETICAL MECHANISM OF SPECIATION
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In recent years it has been widely disputed whether sympatric speciation can and does actually occur. On one hand, acceptance of the hypothesis of sympatric speciation lends support to a natural interpretation of a number of phenomena pertaining to the realm of ecology, biogeography, and systematics. In favor of the possible existence of such a mechanism are data on the emergence of isolation under the effect of disruptive selection in laboratory populations. On the other hand, the prerequisite for sympatric speciation is that forms representing newly emerging species should not be ecologically identical at the very onset of the process. In other words, they have to occupy slightly different niches. This suggestion seems rather artificial, however, for otherwise one of the forms would be excluded by the other competing form, in accordance with Gause's theorem. The natural question to ask is whether sympatric and allopatric speciation are mutually exclusive, or, could there exist a third mechanism, in some respects intermediate, but essentially different? The present work is an attempt to solve the problem by methods of mathematical population genetics. The main factor in sympatric speciation should, apparently, always be disruptive selection. In the case of divergence of the initial species and the emergence of a hiatus between the arising species, individuals intermediate in some respect should be less fit than the "terminal" ones. Let us examine a simple case of disruptive selection. It is assumed that a pair of alleles of one gene is responsible for the character studied and that the heterozygote is less fit than both homozygotes. If homozygote fitness is equal and all genotypes are ecologically identical (the assumption is always implied in further reasoning), then, at first glance, the situation appears trivial. One of the alleles is inevitably forced out by the other. Formally this means that q = 0 and q = 1 correspond to a stable balance of the system, while q = 1/2 to an unstable one, where q is the allelic frequency. It is as simple as that, provided that it is assumed that allelic frequency is constant throughout all their distribution area and that the frequency is only time dependent. This is what is usually assumed in mathematical genetics. The problem turns out to be more complex when one considers that allelic frequency may differ in various parts of their geographic distribution and that it can change not only under selective pressure but also under the effect of migration (diffusion). A problem of this type, including some types of selection in a onedimensional area of distribution, has been considered earlier (Kolmogorov et al., 1937; Fisher, 1937). It has been shown, in particular, that in the framework of rather general and acceptable hypotheses, the dynamics of allelic frequency must be expressed by diffusion equations with the right-hand of the equations determined by the type of selection. It should be indicated that under "a one-dimensional area of geographic distribution" the actual "narrowness," the "strip" of distribution area is not necessarily implied. What is actually introduced on hypothetical grounds is the dependency of allelic frequency on only one of the two spatial coordinates. In the analyzed case of selection against heterozygotes the dynamics of allelic frequency in time and throughout the area will be given by:
[1] R. Fisher. THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .