The infinitesimal model: Definition, derivation, and implications
The infinitesimal model: Definition, derivation, and implications
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DOI：
10.1016/j.tpb.2017.06.001
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发表时间：
2017-12-01
影响因子：
1.4
通讯作者：
Veber, A.
中科院分区：
文献类型：
--
作者：
Barton, N. H.;Etheridge, A. M.;Veber, A.
我们这里关注的是无穷小模型。在这个模型中，一个或几个数量性状被描述为遗传成分和非遗传成分的总和，第一个数量性状作为一个正态随机变量分布在家庭中，以亲本遗传成分的平均值为中心，其方差与亲本性状无关。因此，家庭内部分离的方差不受选择的干扰，可以从方差成分中预测。这并不一定意味着整个种群的性状分布应该是高斯分布，事实上，选择或种群结构可能对总体性状分布有实质性影响。我们的主要目的之一是确定一些关于等位效应的一般条件，使无穷小模型是准确的。我们首先回顾了数量遗传学中无穷小模型的悠久历史。然后，我们从个体特征值和个体之间的关系出发，在表型水平上构建模型，但包括不同的进化过程：遗传漂变、重组、选择、突变、群体结构、....我们给出了一系列的例子，将其应用于与稳定选择、分类交配、有效种群规模和对选择的反应、栖息地偏好和物种形成有关的进化问题。当具有孟德尔遗传、突变和环境噪声的模型中，当性状的遗传成分纯粹是可加性时，我们提供了该模型的数学证明，即当潜在位点的数量M趋于无穷时，该模型的极限。我们还展示了该模型如何推广到包括上位效应。我们特别证明，在每个家族中，当前一代个体性状值的遗传成分确实是正态分布，其方差与祖先性状无关，误差可达1/根号M阶。模拟表明，在某些情况下，收敛速度可能快至1/M。(C) 2017年作者。Elsevier Inc.出版。
Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure,....We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1/root M. Simulations suggest that in some cases the convergence may be as fast as 1/M. (C) 2017 The Authors. Published by Elsevier Inc.