Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination rate, which are usually based on the idea of integrating over the unobserved possible evolutionary histories of a sample, can therefore be noisy. Here we consider a related question: how would an estimator behave if the evolutionary history actually was observed? This would offer an upper bound on the performance of estimators used in practice. In this paper we derive an expression for the maximum likelihood estimator for the recombination rate based on a continuously observed, multi-locus, Wright--Fisher diffusion of haplotype frequencies, complementing existing work for an estimator of selection. We show that, contrary to selection, the estimator has unusual properties because the observed information matrix can explode in finite time whereupon the recombination parameter is learned without error. We also show that the recombination estimator is robust to the presence of selection in the sense that incorporating selection into the model leaves the estimator unchanged. We study the properties of the estimator by simulation and show that its distribution can be quite sensitive to the underlying mutation rates.

翻译：重组是一种基本的进化力量，但由于重组事件对遗传数据样本中变异模式的影响难以辨别，因此量化重组较为困难。通常基于对样本未观测到的可能进化历史进行积分的思想构建的重组率估计量，往往存在较大的噪声。本文探讨一个相关问题：如果进化历史实际上被观测到，估计量的表现将如何？这将为实际应用的估计量性能提供上限。本文推导了基于连续观察的多位点Wright-Fisher单倍型频率扩散的重组率最大似然估计量的表达式，补充了现有关于选择估计量的研究工作。与选择估计量不同，该估计量具有特殊性质：观测信息矩阵可能在有限时间内爆炸，此时重组参数可被无误地学习。我们还证明，重组估计量对选择的存在具有稳健性，即模型中纳入选择不影响该估计量。通过模拟研究估计量的性质，发现其分布对潜在突变率相当敏感。