Parentage exclusion probability is usually calculated to evaluate the informativeness of a set of markers for, and the statistical power of, a parentage analysis. Equations for parentage exclusion probability have been derived in various scenarios such as paternity exclusion when maternity is known or unknown or when candidate males are unrelated or loosely related (being from the same subpopulation) to the father. All previous work assumes a diploid species. Although marker-based parentage analyses have been conducted in haploidiploid species (such as ants, bees and wasps) for diploid offspring at the individual level or haploid offspring at the class level, rigorously derived formulations of parentage exclusion probability for haploid offspring at the individual level are lacking, which prevents the precise evaluation of the informativeness for and the statistical power of a parentage analysis. In this study we derive equations for the exclusion probability of maternity of a haploid male when multiple mother candidates (workers or queens) are unrelated or fullsibs to the mother. The usefulness of the equations is exemplified by numerical examples, and the results are discussed in the context of the study of worker reproductivity in eusocial haplodiploid species. The results are especially valuable for an optimal experimental design in determining sampling intensities (e.g. number of markers and number of individuals) to achieve satisfactory statistical power of a parentage analysis in investigating workers’ reproductivity in eusocial haplodiploid species.

通常计算亲子排除概率来评估亲子分析的一组标记的信息量和统计功效。亲子排除概率的方程已经在各种情况下推导出来，例如当母性已知或未知时或当候选男性与父亲无关或松散相关（来自同一亚群）时的亲子排除。之前的所有工作都假设是二倍体物种。尽管基于标记的亲子关系分析已经在单倍二倍体物种（例如蚂蚁、蜜蜂和黄蜂）中进行了个体水平的二倍体后代或类水平的单倍体后代，但严格推导了个体水平的单倍体后代的亲子排除概率缺乏，这阻碍了对亲子分析的信息量和统计功效的精确评估。在这项研究中，我们推导出当多个母亲候选者（工蜂或蜂王）与母亲无关或完全同胞时，单倍体雄性生育的排除概率的方程。这些方程的有用性通过数值例子进行了例证，并且在研究真社会性单倍二倍体物种的工蚁繁殖的背景下讨论了结果。这些结果对于确定采样强度（例如标记数量和个体数量）的最佳实验设计特别有价值，以在调查真社会性单倍二倍体物种中工蚁的繁殖力时获得令人满意的亲子分析统计功效。