Christiansen F B
Department of Ecology and Genetics, University of Aarhus, Denmark.
J Math Biol. 1988;26(6):595-618. doi: 10.1007/BF00276143.
The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2n gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.
n位点双等位基因对称生存力模型是根据衡量适合度中加性上位性的参数来考虑的。通过对配子频率进行简单的线性变换来分析其动态，然后递归方程仅取决于上位性参数和盖林格重组分布。该模型呈现出一个平衡点，即中心平衡点，此时2n种配子的频率相等。这种变换简化了中心点的稳定性分析，并根据其他平衡点的存在条件给出了稳定性条件。对于完全负上位性（所有上位性参数均为负），对于所有重组分布，中心点都是稳定的。对于自由重组，要么中心点（分离一个、两个……或n个位点），要么n位点固定状态是稳定的。对于无重组且一些上位性参数为正的情况，中心点是不稳定的，并且几个边界平衡点可能是局部稳定的。因此，加性上位性的符号结构是n位点对称生存力模型动态的一个重要决定因素。先前分析的非对称多位点模型在动态上是相关的，并且它们都具有类似于乘性生存力模型的上位性符号结构。提出了一个具有完全负上位性且与类似对称模型具有相同动态性质的非对称模型。
