We propose a class of evolution models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and after that a genome is removed according to the selection scheme that involves fitness. Thus, the population size remains constant. The process evolves according to a Markov chain, and, unlike in many other existing models, the stationary distribution – so called mutation-selection equilibrium – can easily found and studied. As a special case our model contains a (sub) class of Moran models. The behaviour of the stationary distribution when the population size increases is our main object of interest. Several phase-transition theorems are proved.

我们提出了一类进化模型，其中涉及作为育种过程和不同选择方案的任意可交换过程。在那些模型中，根据育种过程出生了一个新的基因组，然后根据涉及适应性的选择方案删除了​​一个基因组。因此，人口规模保持不变。该过程根据马尔可夫链演化，并且与许多其他现有模型不同，可以容易地发现和研究平稳分布（即所谓的突变选择平衡）。作为特殊情况，我们的模型包含Moran模型的（子）类。当人口规模增加时，平稳分布的行为是我们关注的主要对象。证明了几个相变定理。