Maternal selection and overlapping generations can facilitate the stable coexistence of alleles under temporally fluctuating environment. Using mathematical models, we considered the complex effect of both factors on the maintenance of genetic polymorphism in cyclically changing environments. We concentrated on asymmetric cyclic selection, which allows describing fluctuations of environments by analogy of food resources cycles with rare peaks and prolonged decline of prey abundance.

The complex effect of maternal selection and overlapping generations turned out to work as follows: although overlapping generations always tend to dilate the polymorphism region, odd and even external cycles produce different types of polymorphism regions. Maternal selection under external odd cycles extends the coexistence region comparing with classic selection. Even cycles produce a part of parameter region, where the picture changes radically, and classic selection becomes more effective in maintaining polymorphism.

Our models have clear biological interpretation, because we tried to model a situation demonstrated by natural populations of arctic foxes. The litter size being a major life history trait is a sex-limited female trait. It is influenced by maternal selection with cyclical fluctuations because of oscillations in food abundance. Arctic fox is a long-lived species having an age structure. The obtained results showed that compared with the simple Mendelian inheritance in the classic model, this trait inheritance allows polymorphism to be maintained in a wider range of the parameter that characterizes the advantage of survival in a small litter. Besides, adding overlapping generations to the model further broadens the parameter space for the protected polymorphism. Thus, this study shows that maternal selection and overlapping generations increases the chances of maintaining polymorphism in populations of arctic foxes.

母系选择和重叠世代可以促进等位基因在时间波动环境下的稳定共存。使用数学模型，我们考虑了这两个因素对周期性变化环境中遗传多态性维持的复杂影响。我们专注于不对称循环选择，它允许通过类比具有罕见峰值和猎物丰度长期下降的食物资源循环来描述环境的波动。

母体选择和重叠世代的复杂效应结果如下：虽然重叠世代总是倾向于扩大多态性区域，但奇数和偶数外部循环会产生不同类型的多态性区域。与经典选择相比，外部奇循环下的母系选择扩展了共存区域。偶数循环产生参数区域的一部分，其中图片发生根本变化，经典选择在保持多态性方面变得更有效。

我们的模型具有明确的生物学解释，因为我们试图模拟北极狐自然种群所展示的情况。产仔数是一个主要的生活史特征，是一种性别有限的雌性特征。由于食物丰度的波动，它受到具有周期性波动的母体选择的影响。北极狐是具有年龄结构的长寿物种。所得结果表明，与经典模型中简单的孟德尔遗传相比，这种性状遗传使得多态性在表征小窝存活优势的参数范围内得以保持。此外，在模型中添加重叠代进一步拓宽了受保护多态性的参数空间。因此，