Multiple male mating (MMM) causes sperm competition, which may play an important role in the evolution of reproductive traits. The frequency of multiple paternity (MP), where multiple males sire offspring within a single litter, has been used as an index of MMM frequency. However, MP frequency is necessarily lower than MMM frequency. The magnitude of the difference between MMM and MP frequency depends on litter size (LS) and fertilization probability skew (FPS), and this difference may be meaningfully large in animals with small LSs. In this study, we propose a method to estimate MMM frequency using an individual-based model with three variables (MP frequency, LS and FPS). We incorporated observed paternity skew data to infer a possible range of FPS that cannot be measured in free-living populations and tested the validity of our method using a data set from a grey-sided vole (Myodes rufocanus) population and from hypothetical populations. MP was found in 50 out of 215 litters (23.3%) in the grey-sided vole population, while MMM frequency was estimated in 67 of 215 litters (31.2%), with a certainty range of 59-88 (27.4%-40.9%). The point estimation of MMM frequency was realized, and the certainty range was limited within the practical range. The use of observed paternity skew was very effective at narrowing the certainty range of the estimate. Our method could contribute to a deeper understanding of the ecology of MMM in free-living populations.

中文翻译：

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使用父系偏斜估计多个雄性交配频率：以灰边田鼠（Myodes rufocanus）种群为例。

多次交配会引起精子竞争，这可能在生殖性状的进化中起重要作用。多胎父系（MP）的频率已被用作MMM频率的指标，在​​该频率下，多头雄性在一个窝里生下后代。但是，MP频率必须低于MMM频率。MMM和MP频率之间差异的大小取决于产仔数（LS）和受精概率偏斜（FPS），并且该差异在具有较小LS的动物中可能会有意义地大。在这项研究中，我们提出了一种使用具有三个变量（MP频率，LS和FPS）的基于个人的模型来估计MMM频率的方法。我们并入了观察到的亲子偏斜数据，以推断在自由生活群体中无法测量的FPS可能范围，并使用灰边田鼠（Myodes rufocanus）群体和假想群体的数据集测试了我们方法的有效性。在灰边田鼠种群中，有215窝中有50例发现了MP（23.3％），而215窝中有67例（31.2％）估计有MMM频率，确定范围为59-88（27.4％-40.9％） ）。实现了MMM频率的点估计，将确定范围限制在实际范围内。使用观察到的亲子偏斜在缩小估计的确定范围方面非常有效。我们的方法可能有助于更深入地了解自由生活人群中MMM的生态。