Neff B D, Repka J, Gross M R
Department of Zoology, University of Western Ontario, London, Ontario N6A 5B7, Canada.
Theor Popul Biol. 2001 Jun;59(4):315-31. doi: 10.1006/tpbi.2001.1520.
We develop fractional allocation models and confidence statistics for parentage analysis in mating systems. The models can be used, for example, to estimate the paternities of candidate males when the genetic mother is known or to calculate the parentage of candidate parent pairs when neither is known. The models do not require two implicit assumptions made by previous models, assumptions that are potentially erroneous. First, we provide formulas to calculate the expected parentage, as opposed to using a maximum likelihood algorithm to calculate the most likely parentage. The expected parentage is superior as it does not assume a symmetrical probability distribution of parentage and therefore, unlike the most likely parentage, will be unbiased. Second, we provide a mathematical framework for incorporating additional biological data to estimate the prior probability distribution of parentage. This additional biological data might include behavioral observations during mating or morphological measurements known to correlate with parentage. The value of multiple sources of information is increased accuracy of the estimates. We show that when the prior probability of parentage is known, and the expected parentage is calculated, fractional allocation provides unbiased estimates of the variance in reproductive success, thereby correcting a problem that has previously plagued parentage analyses. We also develop formulas to calculate the confidence interval in the parentage estimates, thus enabling the assessment of precision. These confidence statistics have not previously been available for fractional models. We demonstrate our models with several biological examples based on data from two fish species that we study, coho salmon (Oncorhychus kisutch) and bluegill sunfish (Lepomis macrochirus). In coho, multiple males compete to fertilize a single female's eggs. We show how behavioral observations taken during spawning can be combined with genetic data to provide an accurate calculation of each male's paternity. In bluegill, multiple males and multiple females may mate in a single nest. For a nest, we calculate the fertilization success and the 95% confidence interval of each candidate parent pair.
我们开发了用于交配系统中亲权分析的分数分配模型和置信统计量。例如，这些模型可用于在已知遗传母亲的情况下估计候选雄性的父权，或在双亲均未知时计算候选亲本对的亲权。我们的模型不需要先前模型所做的两个隐含假设，而这些假设可能是错误的。首先，我们提供了计算预期亲权的公式，而不是使用最大似然算法来计算最可能的亲权。预期亲权更具优势，因为它不假设亲权的概率分布是对称的，因此与最可能的亲权不同，它不会有偏差。其次，我们提供了一个数学框架，用于纳入额外的生物学数据以估计亲权的先验概率分布。这些额外的生物学数据可能包括交配期间的行为观察或已知与亲权相关的形态测量。多种信息源的价值在于提高估计的准确性。我们表明，当亲权的先验概率已知且计算出预期亲权时，分数分配提供了生殖成功方差的无偏估计，从而纠正了先前困扰亲权分析的一个问题。我们还开发了计算亲权估计置信区间的公式，从而能够评估精度。这些置信统计量以前在分数模型中是不可用的。我们用基于我们研究的两种鱼类——银大麻哈鱼（Oncorhychus kisutch）和蓝鳃太阳鱼（Lepomis macrochirus）的数据的几个生物学例子来展示我们的模型。在银大麻哈鱼中，多个雄性竞争使单个雌性的卵子受精。我们展示了如何将产卵期间的行为观察与遗传数据相结合，以准确计算每个雄性的父权。在蓝鳃太阳鱼中，多个雄性和多个雌性可能在单个巢穴中交配。对于一个巢穴，我们计算每个候选亲本对的受精成功率和95%置信区间。
