Change of information by positive frequency-dependent selection in two very different models (laser-like and chirality of shell-coiling in the snail Partula suturalis)

Abstract

Although according to the second law of thermodynamics the world tends toward maximum disorder, over millions of years evolution has given rise to an enormous variety of complex organisms. To explain this, one must assume that natural selection is a process of information acquisition. Since some years an information theory of selection exists that can quantify this change and thus helps to understand the apparent contradiction between the existence of biological complexity and the tendency toward disorder that generally prevails in nature. Here I apply this theory to examples of frequency-dependent selection (this means: in which phenotype frequency determines its fitness). The snail Partula suturalis gave an evolutionary and ecologically unique and hence very valuable example of this type of selection before it became extinct about thirty years ago on its native island. Spatially separated populations with left- and right-coiled shells occurred on Moorea, but also hybridization zones. Since both types of shells were the same except for chirality, the question is whether selection happened at all. The inheritance of this character is monogenic and in this respect simple, but is complicated by the fact that it is the maternal genotype, not the own, that determines the phenotype. This causes that for the calculation of the information change by selection not the genotype or phenotype frequencies are sufficient, but one must consider their combination. The simulation shows that frequency-dependent selection in P. suturalis indeed increased information. It has already been shown that selection can also be important outside animate nature, for example in the generation of laser light, which has extraordinary properties: it is monochromatic, monoaxial and monophasic. Phase selection is frequency(=density)-dependent and therefore of interest here. In selection theory the mean fitness {omega} is of special significance. In a laser-like model, in modeling phase selection, we find that {omega}=1+A2, where A2 is the the light intensity or the square of the amplitude, respectively. During selection, {omega} increases and, in parallel, since selection is a process of information acquisition, so does the information. Because of the connection between {omega} and A2 this also means for the laser-like model that - assuming a constant number of photons - a larger amplitude always means more information (less entropy).