Meiosis at three loci in autotetraploids: Probabilities of gamete modes and genotypes without and with preferential cross-over formation

A long-standing goal in the field of polyploid biology has been the derivation of mathematical models of gamete mode formation. These models form the basis of statistical inference and evolutionary theory. Here, we present 3-locus models of gamete mode formation in autotetraploids without and with preferential cross-over formation. The three loci are assumed to occur on one arm of the same chromosome. For preferential cross-over formation, one of the three loci affects the tendency for sets of sister chromatids to pair and therefore affects rates of recombination. The models are derived such that the process of double reduction is a function of rates of synaptic partner switches and recombination, as opposed to being independent of these processes. We assume potentially one synaptic partner switch per meiosis. We also assume the coefficient of coincidence is one, such that cross-over events are independent, given a set of cross-over rates. Illustrative cases are examined demonstrating d..., ,

多倍体生物学领域长期以来的核心目标之一，是推导配子形成模式的数学模型。此类模型是统计推断与进化理论的重要基础。本文中，我们构建了同源四倍体（autotetraploids）中配子形成模式的三座位（3-locus）模型，分别涵盖无优先交叉形成与存在优先交叉形成两种情形。我们假定三个座位位于同一条染色体的同一臂上。针对存在优先交叉形成的情形，三个座位中的其中一个会影响姐妹染色单体组的配对倾向，进而改变重组速率。本模型的推导将双减数（double reduction）过程定义为突触伴侣切换（synaptic partner switches）与重组速率的函数，而非与这两个过程相互独立。我们假定每次减数分裂最多发生一次突触伴侣切换，同时设定并发系数（coefficient of coincidence）为1，即给定一组交叉速率时，交叉事件相互独立。我们还对若干示例场景进行了分析，以展示其……