Evolution process of Periodical cicada

两种假说竞相解释周期蝉的质数繁殖间隔（生命周期）的进化：反掠食性假说和杂交假说。反掠食性假说认为，质数间隔有助于保护蝉不被捕食者打败。杂交假说认为，质数大大降低了蝉窝之间杂交的机会。为了验证杂交假设，我们建立了一个仿真模型。建立了一个具有三个参数的确定性离散种群模型：每年幼虫存活率；出现的成功。在模拟中，10年到20年的繁殖间隔为生存而竞争。该模型有两个关键假设：孟德尔遗传系统和随机交配。此外，长间隔表型有更大的窝，但比短间隔的窝有更高的总死亡率。我们对所有纯间隔期和杂交种的种群大小进行跟踪，非素数间隔期迅速消失，19年表型逐渐被13年和17年表型所淘汰。13年和17年的表型可能共存。13年或17年的间隔选择只发生在种群濒临灭绝的时候。基于周期蝉进化动力学的发展机制，建立了性别比进化、酵母种群动态、浮游生物多样性、物种形成动力学等离散模型。

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.