N-gender Population In The Evolution

The process of evolution is long and mysterious, changing from the origin of life to the present diverse population. Nowadays, people want to explore the evolution history from the level of gene and find connections between all the organisms, both living and extinct, according to the genetic relationship. And people inclined to find a simple method to describe the process of evolution. The networks in graph theory can help a lot.In graph theory, the graphs contain two factors-dots and edges, in which the dots represent the objects to study while the edges represent the relation-ships between objects. If we consider all the organisms as dots and use direct edges to represent the genetic relationship between organisms, we can obtain a graph illustrating the process of evolution.Darwin was convinced that all the organisms have the same ancestor. And heredity is not reversible. So in systematic biology, we inclined to describe the evolution graph as a tree. In fact, the gene transfer happens between different organisms, like lateral gene transfer(LGT) or hybridization, which make the evolution graph look like a network. Thinking about all above, we should describe the process of evolution with a’tree-like’graph.In2012, Samuel A. Alexander proposed a conception of n-gender pop-ulation, a’tree-like’graph which could accurately illustrate the genetic rela- tionships between organisms in a certain population. If a infinite sequence s=(s1, s2,...)∈{1,..., n}N can be represent in any infinite n-gender pop-ulation,then it is biologically unavoidable, or else it is biologically avoidable. Both the two kinds of sequence exist in a infinite n-gender population.Since n-gender population is a simple and practical model to describe the genetic relationships, we want to apply it to the process of evolution. Based on the Knight-Darwin Law, no organnic being self-fertilises itself for a perpetuity of generations. Therefore, the number of genders of species may alter in the process of evolution. So we should make a little change on n-gender population in order to apply it to illustrate the process of evolution.This paper will describe the concept of n-gender population, prove that the eventually periodic sequences are biologically unavoidable and prove the existence of biologically avoidable sequence. Then we will construct a new n-gender population, in which ’n’ varies in a particular timing. And we will explore the characters of the new n-gender population.