Besides reviewing the unusual case of sex-ratio in the lemming and presenting alternative analyses of general models in which the shift in the usual sex-ratio 1:1 is determined by autosomal or sex-linked mutant alleles, three novel models are presented, in which the shift on the progeny sex-ratio depends on the number of copies of a mutant allele present in the parental pair. The analysis of these models with additive effects shows that: 1) autosomal mutations that alter the usual sex-ratio are eliminated from the population; 2) mutations occurring on the X chromosome lead to an evolutionary stable 1:1 sex-ratio only if the mutation favors the production of males; when the mutant allele favors the production of females, however, females will prevail in the population, with a frequency dependent impact on δ (the deviation from the usual 0.5 proportion) ; for most of the range of possible values of δ the stable but extraordinary sex-ratio will vary from 1 male : 1 female to 1 male : 3 females or 1 male : 2 females approximately depending whether the mutant allele is randomly inactivated or not.

中文翻译：

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性别比的演变：对一些简单新颖模型的数学研究的简要回顾。


除了回顾旅鼠性别比例的异常情况并提出一般模型的替代分析（其中通常性别比例 1:1 的变化是由常染色体或性别连锁突变等位基因决定）之外，还提出了三个新模型，其中后代性别比例的变化取决于亲本对中存在的突变等位基因的拷贝数。对这些具有加性效应的模型的分析表明：1）改变通常性别比例的常染色体突变从人群中被消除； 2）只有当X染色体上发生的突变有利于产生雄性时，才会导致进化稳定的1:1性别比；然而，当突变等位基因有利于生育雌性时，雌性将在种群中占主导地位，并对 δ 产生频率依赖性影响（偏离通常的 0.5 比例）；对于 δ 的大部分可能值范围，稳定但异常的性别比例将从 1 男 : 1 女到 1 男 : 3 女或 1 男 : 2 女，大约取决于突变等位基因是否随机失活。