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Extending the previous 2-gender dioecious diploid gene-mating evolution model[arXiv:1410.3456], we attempt to answer "whether the Hardy-Weinberg globalstability and the exact analytic dynamical solutions can be found in thegeneralized N-gender N-polyploid gene-mating system with an arbitrary number ofalleles?" For a 2-gender gene-mating evolution model, a pair of male and femaledetermines the trait of their offspring. Each of the pair contributes oneinherited character, the allele, to combine into the genotype of theiroffspring. Hence, for an N-gender N-polypoid gene-mating model, each of Ndifferent genders contributes one allele to combine into the genotype of theiroffspring. We exactly solve the analytic solution of N-gender-mating$(n+1)$-alleles governing highly-nonlinear coupled differential equations inthe genotype frequency parameter space for any positive integer N and $n$. Foran analogy, the 2-gender to N-gender gene-mating equation generalization isanalogs to the 2-body collision to the N-body collision Boltzmann equationswith continuous distribution functions of "discretized" variables instead of"continuous" variables. We find their globally stable solution as a continuousmanifold and find no chaos. Our solution implies that the Laws of Nature, underour assumptions, provide no obstruction and no chaos to support an N-gendergene-mating stable system.

Gene-Mating Dynamic Evolution Theory II: Global stability of N-gender-mating polyploid systems