Multiple merger coalescent models in population genetics.

提出的研究是在数学和群体遗传学之间丰富的接口。理论群体遗传学的主要目的是了解突变、自然选择、随机遗传漂变和群体结构相互作用产生和维持物种内观察到的复杂遗传变异模式的方式。第一步是将我们对这些力如何运作的理解提炼成一个可行的数学模型，然后将其预测与数据进行比较。这种方法的一个突出的成功之处在于，金曼的“聚结”提供了一个简单而优雅的描述，描述了一个大型“泛病”群体样本中个体的谱系树。金曼聚结的变化允许引入更现实的种群假设，如空间或遗传结构、选择和重组。在由此产生的“祖先影响图”中，谱系然后分支、迁移和合并。然而，与数据比较表明，这些模型仍然不足。第一个关键观察是，遗传多样性比人口普查人口规模和金曼的“标准”遗传漂变所预测的要低几个数量级。对此的解释是，尽管金曼的联合效应假设单个个体产生的后代总数相对于总体规模而言非常小，但实际上后代的分布可能是非常倾斜的。这可能是由许多因素驱动的，例如大规模的灭绝-重新定居事件或快速席卷整个种群的高度有益的突变的反复出现。因此，当一个人在人群样本中检查与个体相关的家谱树时，它们最好是由多个（我们指的是至少三个）祖先谱系可以在一个单一事件中合并的模型来近似。这与只允许成对聚结的Kingman的聚结形成对比。在Eldon和Wakeley最近发表在《遗传学》杂志上的研究中，他们提出，某些海洋生物（包括大西洋鳕鱼和太平洋牡蛎）的生殖生物学决定了我们应该在考虑人口统计学和自然选择之前就使用这种多重合并。这些生物的特点是广播产卵、体外受精、极高的繁殖力和高的初始死亡率。例如，类似的考虑也适用于一些植物种群（它们传播花粉）和一些昆虫种群（其中一种性别的个体数量远远超过另一种性别的个体数量）。Eldon和Wakeley还指出，他们的繁殖模式也可以解释在这些生物体的序列数据中观察到的过多的单一变异，这一特征通常被归因于其他原因，如自然选择。因此，至少有三种不同的机制引导我们形成多个合并合并模型。但令人惊讶的是，到目前为止，几乎没有人分析最合适的模型应该是什么。在大量所谓的λ和xi-聚结中，是否存在最适合建模生物种群的自然亚类？我们如何区分它们呢？几乎可以肯定的是，仅仅研究单个基因座是不够的，我们必须了解基因座之间的相关性。这个项目的出发点是，通过仔细考虑驱动人口的生物机制，以确定合适的类聚结模型。然后，我们必须理解与给定聚结相一致的（多）祖先选择和祖先重组图。总体目标是，通过分析和模拟的结合，找到从基因数据中分离出各种人口统计和遗传力量的信号的方法，这些信号塑造了人口。

The proposed research lies at the rich interface between mathematics and population genetics. The main purpose of theoretical population genetics is to understand the ways in which the forces of mutation, natural selection, random genetic drift and population structure interact to produce and maintain the complex patterns of genetic variation observed within species. The first step is to distill our understanding of how these forces operate into a workable mathematical model whose predictions can then be compared with data. One of the outstanding successes of this approach is Kingman's coalescent which provides a simple and elegant description of the genealogical trees relating individuals in a sample from a large `panmictic' population. Variations of Kingman's coalescent allow for the introduction of more realistic assumptions about the population such as spatial or genetic structure, selection and recombination. In the resulting `ancestral influence graph', lineages then branch, migrate and coalesce. However, comparison with data shows that these models are still inadequate. The first key observation is that genetic diversity is orders of magnitude lower than predicted by census population size and the `standard' genetic drift captured by Kingman's coalescent. The explanation is that whereas Kingman's coalescent assumes that the total number of offspring produced by a single individual is very small relative to the total population size, in reality offspring distributions can be very skewed. This can be driven by many things, for example large scale extinction-recolonization events or repeated appearances of highly beneficial mutations that rapidly sweep through the population. As a result, when one examines the genealogical trees relating individuals in a sample from the population, they are best approximated by models in which multiple (by which we mean at least three) ancestral lineages can coalesce in a single event. This contrasts with Kingman's coalescent in which only pairwise coalescences are allowed. In recent work of Eldon and Wakeley in the journal Genetics, it is proposed that the reproductive biology of certain marine organisms (including Atlantic cod and Pacific oyster) dictates that we should use such multiple merger coalescents even before we consider demography and natural selection. These organisms are characterized by broadcast spawning, external fertilization, extremely high fecundity and high initial mortality. Similar considerations apply, for example, to some plant populations (which distribute pollen) and some insect populations (where individuals of one gender far outnumber those of the other). Eldon and Wakeley also point out that their mode of reproduction can also account for the excess of single variants observed in sequence data for these organisms, a feature more usually attributed to other causes such as natural selection. There are, then, at least three different mechanisms through which we are led to multiple merger coalescent models. But so far there has been surprisingly little analysis of what the most appropriate models should be. Within the vast collection of so-called lambda and xi-coalescents, are there natural subclasses most suitable for modelling biological populations? And how can we distinguish between them? Almost certainly it will not suffice to look at just a single genetic locus, but rather we must understand correlations across loci. The starting point of this project is, through careful consideration of the biological mechanisms driving the population, to identify suitable classes of coalescent model. We must then understand the (multiple) ancestral selection and ancestral recombination graphs consistent with a given coalescent. The overarching aim is, through a mixture of analysis and simulation, to find ways to disentangle from genetic data the signals of the various demographic and genetic forces that have shaped the population.