Hexaploids, a group of organisms containing three complete sets of chromosomes in a single nucleus, are of utmost importance to evolutionary studies and breeding programs. Many studies have focused on hexaploid linkage analysis and QTL mapping in controlled crosses, but little methodology has been developed to reveal how hexaploids diversify and evolve in natural populations. We formulate a general framework for studying the pattern of genetic variation in autohexaploid populations through testing deviation from Hardy–Weinberg equilibrium (HWE) at individual molecular markers. We confirm that hexaploids cannot reach exact HWE, but can approach asymptotic HWE at 8–9 generations of random mating. We derive a statistical algorithm for testing HWE and the occurrence of double reduction for autopolyploids, a phenomenon that affects population variation during long evolutionary processes. We perform computer simulation to validate the statistical behavior of our test procedure and demonstrate its usefulness by analyzing a real data set for autohexaploid chrysanthemum. By extending it to allothexaploids, our test procedure will provide a generic tool for illustrating the genome structure of hexaploids in the quest to infer their evolutionary status and design association studies of complex traits.

中文翻译：

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六倍体中 Hardy-Weinberg 平衡的渐近检验

六倍体是一组在单个细胞核中包含三组完整染色体的生物，对于进化研究和育种计划至关重要。许多研究都集中在受控杂交中的六倍体连锁分析和 QTL 定位，但几乎没有开发出揭示六倍体如何在自然种群中多样化和进化的方法。我们通过在单个分子标记处测试哈迪-温伯格平衡 (HWE) 的偏差来制定研究同源六倍体种群遗传变异模式的一般框架。我们确认六倍体不能达到精确的 HWE，但可以在 8-9 代随机交配时接近渐近 HWE。我们推导出一个统计算法来测试 HWE 和同源多倍体的双重减少的发生，在漫长的进化过程中影响种群变异的现象。我们执行计算机模拟来验证我们测试程序的统计行为，并通过分析自六倍体菊花的真实数据集来证明其有用性。通过将其扩展到异源六倍体，我们的测试程序将提供一个通用工具来说明六倍体的基因组结构，以推断它们的进化状态并设计复杂性状的关联研究。