A Mathematical Formulation of Evolution and Innovation II. From Unicellular Monoploid Eukaryotes to Multicellular Diploid Eukaryotes

Among the evolutionary lines of eukaryotes after the acquirement of the mitochondria, the present study focuses on the evolution and innovation from unicellular monoploids to multicellular diploids. It is first investigated mathematically how the conjugation of monoploid eukaryotes to exchange homologous chromosomes and the hybridization of diploid eukaryotes are effective on the accumulation of new genes generated from gene duplication. In the monoploid eukaryote containing multiple kinds of chromosomes, the exchange of homologous chromosomes enhances the chance to yield new style monoploids receiving many kinds of new genes sufficient for causing multicellularity and cell differentiation. Although the multicellular diploid eukaryote is the next in the line of fixing a full set of new genes homologously, various variants carrying partial sets of new genes are generated on the way to establish the new style diploids homologously and these variants successively hybridize with other latent variants to yield the next stage of new style diploids. This explains the punctuated mode of explosive divergence of body plans suggested from paleontology. Second, this innovation from the monoploids to diploids is theoretically investigated from the physiological aspect of cell differentiation. Although the cooperative action of differentiated cells is an excellent strategy to acquire the energy and material sources from the outside, the material and energy are also required for the development of cell differentiation and their amount becomes larger in the diploid state than in the monoploid state. On the other hand, the diploid state is suitable for elongating the duration time of differentiated cells against nucleotide base changes. To attain this purpose overcoming the first physiological problem, the eukaryotes have advanced their organization to multicellular diploids through the intermediate stages of alternating the monoploid generation differentiated into female and male types with the diploid one. This innovation process is illustrated in green plants and animals.