Evolution process of Periodical cicada

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Two hypotheses compete to, explain the evolution of prime number reproductive intervals (life cycles) among periodical cicadas: the anti-predatory hypothesis and hybridization one. The anti-predatory hypothesis claims that prime number intervals help to protect cicadas from being overwhelmed by their predators. The hybridization hypothesis claims that prime numbers greatly reduce the chance of hybridization among cicada broods. To test the hybridization hypothesis we build a simulation model. A deterministic, discrete population model is build with three parameters: larval survival per year clutch size; emergence success. Reproductive intervals from ten years to twenty years compete far survival in the simulations. The model makes two key assumptions: a Mendelian genetic system and random mating. In addition, longer-interval phenotypes have larger broods but suffer higher total mortality than shorterinterval broods. We keep track all population sizes of all pure intervals and hybrids with birth year Non-prime number reproductive intervals rapidly disappear Then the 19-year phenotype is gradually eliminated by the 13- and 17-year phenotypes. The 13- and 17-year phenotypes may coexist. The selection of 13- or 17-year intervals happens only when populations are at the verge of extinction.We also build several discrete models of evolutionary and population dynamics: sex ratio evolution, yeast population dynamics, biodiversity of planktons, speciation dynamics, etc. based on the mechanisms developed in the evolutionary dynamics of periodical cicadas.