Geroldinger Ludwig, Bürger Reinhard
Department of Mathematics, University of Vienna, Austria; Vienna Graduate School of Population Genetics, Austria.
Department of Mathematics, University of Vienna, Austria.
Theor Popul Biol. 2015 Feb;99:43-66. doi: 10.1016/j.tpb.2014.10.006. Epub 2014 Nov 11.
The existence, uniqueness, and shape of clines in a quantitative trait under selection toward a spatially varying optimum is studied. The focus is on deterministic diploid two-locus n-deme models subject to various migration patterns and selection scenarios. Migration patterns may exhibit isolation by distance, as in the stepping-stone model, or random dispersal, as in the island model. The phenotypic optimum may change abruptly in a single environmental step, more gradually, or not at all. Symmetry assumptions are imposed on phenotypic optima and migration rates. We study clines in the mean, variance, and linkage disequilibrium (LD). Clines result from polymorphic equilibria. The possible equilibrium configurations are determined as functions of the migration rate. Whereas for weak migration, many polymorphic equilibria may be simultaneously stable, their number decreases with increasing migration rate. Also for intermediate migration rates polymorphic equilibria are in general not unique, however, for loci of equal effects the corresponding clines in the mean, variance, and LD are unique. For sufficiently strong migration, no polymorphism is maintained. Both migration pattern and selection scenario exert strong influence on the existence and shape of clines. The results for discrete demes are compared with those from models in which space varies continuously and dispersal is modeled by diffusion. Comparisons with previous studies, which investigated clines under neutrality or under linkage equilibrium, are performed. If there is no long-distance migration, the environment does not change abruptly, and linkage is not very tight, populations are almost everywhere close to linkage equilibrium.
研究了在朝着空间变化的最优值进行选择时，数量性状中渐变群的存在性、唯一性和形状。重点是受各种迁移模式和选择场景影响的确定性二倍体双位点n-群体模型。迁移模式可能表现出距离隔离，如在踏脚石模型中，或随机扩散，如在岛屿模型中。表型最优值可能在单一环境步骤中突然变化、更逐渐地变化或根本不变。对表型最优值和迁移率施加对称假设。我们研究均值、方差和连锁不平衡（LD）中的渐变群。渐变群由多态平衡产生。可能的平衡构型被确定为迁移率的函数。对于弱迁移，许多多态平衡可能同时稳定，但其数量随着迁移率的增加而减少。同样，对于中等迁移率，多态平衡通常不是唯一的，然而，对于具有相等效应的位点，均值、方差和LD中的相应渐变群是唯一的。对于足够强的迁移，不会维持多态性。迁移模式和选择场景都对渐变群的存在和形状产生强烈影响。将离散群体的结果与空间连续变化且扩散由扩散建模的模型结果进行比较。与之前在中性或连锁平衡下研究渐变群的研究进行比较。如果没有长距离迁移，环境不会突然变化，且连锁不太紧密，那么种群几乎在所有地方都接近连锁平衡。
