This theory seeks to define species and to explore evolutionary forces and genetic elements in speciation and species maintenance. The theory explains how speciation and species maintenance are caused by natural selection acting on non-Mendelian and Mendelian variation, respectively. The emergence and maintenance of species as groups of populations are balanced by evolutionary forces including complementary mechanisms of gene flow within and between populations at population-specific rates: sexual and asexual reproduction, recombining and nonrecombining genome regions, vertical and horizontal DNA transfer, and transposon proliferation and control. While recombining genome regions carry conserved genes and are subjected to meiotic recombination, nonrecombining genome regions carry accessory genes and are not subjected to such structural restrain. Sexual reproduction, vertical DNA transfer, recombining genome regions and transposon control keep species in existence by maintaining recombining chromosome number and structure, while asexual reproduction, horizontal DNA transfer, nonrecombining genome regions and transposon proliferation help species emerge by promoting reproductive isolation and changes in chromosome number and structure. The theory is based on the analysis of the genome sequences of isolates in the Fusarium oxysporum complex. The rate of horizontal supernumerary chromosome transfer in this complex was estimated to be 0.1 per genome per year.