Girsanov Transformation and the Rate of Adaptation

吉尔萨诺夫变换和适应率

• 批准号: EP/I028498/1
• 负责人: Feng Yu
• 金额: $ 12.73万
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI028498%2F1
• 关键词: Girsanov; Transformation; Rate; Adaptation

The term natural selection was introduced by Darwin in his 1859 book On the Origins of Species. It is central to the understanding of how species evolve and adapt. Evolution is the product of two opposing forces. Mutations give rise to genetic variation, but natural selection and genetic drift cause these variants to be more or less abundant. Mutations that cause its carrier individual to contribute more offspring to the next generation are referred to as being beneficial, which are made more and more abundant (on average) by the process of natural selection, until they are present in every individual in the population. The presence of genetic drift, however, renders the reproduction process random and thus may cause beneficial mutations to become extinct as well as spread to the entire population. Which of these two scenarios actually happens to a beneficial mutation is further complicated by the fact that in a large population, there will be many beneficial mutations that compete with each other, reducing the probability that each beneficial mutation will spread. In the 1930's, the eminent evolutionary biologist R. A. Fisher raised the following question: how quickly can populations adapt to a novel environment by incorporating beneficial mutations? This is what I call the rate of adaptation problem and has fascinated many biologists, and more recently physicists. Up to now, researchers can only calculate the rate of adaptation approximately for large populations. In the project, we hope to use a technique from probability theory, known as Girsanov transformation, to calculate exactly the rate of adaptation for any population size. Girsanov transformation is a powerful technique that has found wide applications in probability theory, but has so far not been applied to the rate of adaptation problem. We discovered that we could transform a selected model to a non-selected one, which is considerably easier to analyse. Quantities in the selected model have a delicate and complex relationship with quantities in the non-selected model, and we hope to reveal how they relate to each other in more detail in this project. We hope this project will be a vivid illustration of the power of Girsanov transformation in the study of selection.An equally fascinating question is the evolution of sex and recombination. Considering the reduction is the overall number of offspring, known as the two-fold cost of sex, sexual reproduction must confer some benefit, being so prevalent among living organisms. As early as 1889, A. Weissman already understood that the purpose of sex was to generate genetic variation, upon which natural selection act. Thus a sexually reproducing population may adapt faster than an asexually one. This understanding, however, has not been quantified exactly up to now. The methods we have developed for the asexual model, i.e. Girsanov transformation, can also be applied to study the advantage of sex. We should be able to develop exact formulae for the rate of adaptation for any recombination rate, and thus help to quantify the effects of recombination on the rate of adaptation. On top of being interesting to evolutionary biologists, the rate of adaptation problem has practical applications in the study of evolution of viruses and bacteria. For example, the HIV virus eventually evolves drug resistance in individuals undergoing antiretroviral therapy. Being able to predict the rate of adaptation of the HIV virus in this context can help to calibrate drug dosage and combination to maximise their effectiveness, and thus prolong and enhance the quality of life of the patient.

自然选择一词是达尔文在其 1859 年的著作《物种起源》中引入的。它对于理解物种如何进化和适应至关重要。进化是两种相反力量的产物。突变会引起遗传变异，但自然选择和遗传漂变会导致这些变异或多或少丰富。导致其携带者个体为下一代贡献更多后代的突变被称为有益突变，通过自然选择过程，这些突变（平均而言）变得越来越丰富，直到它们出现在种群中的每个个体中。然而，遗传漂变的存在使繁殖过程变得随机，因此可能导致有益的突变灭绝并传播到整个种群。这两种情况中的哪一种实际上发生在有益突变上，这一事实进一步复杂化，因为在大量群体中，将会有许多有益突变相互竞争，从而降低了每个有益突变传播的可能性。 20 世纪 30 年代，著名进化生物学家 R. A. Fisher 提出了以下问题：通过引入有益突变，种群能够多快适应新环境？这就是我所说的适应率问题，它让许多生物学家以及最近的物理学家着迷。到目前为止，研究人员只能计算大群体的大致适应率。在该项目中，我们希望使用概率论中的一种技术（称为吉尔萨诺夫变换）来准确计算任何种群规模的适应率。吉尔萨诺夫变换是一种强大的技术，在概率论中得到了广泛的应用，但迄今为止尚未应用于适应率问题。我们发现我们可以将选定的模型转换为非选定的模型，这更容易分析。所选模型中的数量与未选择模型中的数量有着微妙而复杂的关系，我们希望在这个项目中更详细地揭示它们之间的关系。我们希望这个项目能够生动地展示吉尔萨诺夫变换在选择研究中的力量。一个同样令人着迷的问题是性和重组的进化。考虑到后代总数的减少，即性行为的两倍成本，有性生殖一定会带来一些好处，因为在生物体中如此普遍。早在 1889 年，A. Weissman 就已经认识到，性的目的是产生遗传变异，自然选择会据此产生遗传变异。因此，有性繁殖的种群可能比无性繁殖的种群适应得更快。然而，这种理解迄今为止尚未得到准确量化。我们为无性模型开发的方法，即吉尔萨诺夫变换，也可以用于研究有性的优势。我们应该能够为任何重组率制定适应率的精确公式，从而有助于量化重组对适应率的影响。除了进化生物学家感兴趣之外，适应率问题在病毒和细菌进化的研究中也有实际应用。例如，艾滋病毒最终会在接受抗逆转录病毒治疗的个体中产生耐药性。在这种情况下，能够预测艾滋病毒病毒的适应速度有助于校准药物剂量和组合，以最大限度地发挥其有效性，从而延长和提高患者的生活质量。

项目成果

Detecting and Quantifying Natural Selection at Two Linked Loci from Time Series Data of Allele Frequencies with Forward-in-Time Simulations

• DOI: 10.1534/genetics.120.303463
• 发表时间: 2020-10-01
• 期刊: GENETICS
• 影响因子: 3.3
• 作者: He, Zhangyi;Dai, Xiaoyang;Yu, Feng
• 通讯作者: Yu, Feng

Rescaling limits of the spatial Lambda-Fleming-Viot process with selection

通过选择重新调整空间 Lambda-Fleming-Viot 过程的限制

• DOI: 10.1214/20-ejp523
• 发表时间: 2020
• 期刊: Electronic Journal of Probability
• 影响因子: 1.4
• 作者: Etheridge A

Effects of the Ordering of Natural Selection and Population Regulation Mechanisms on Wright-Fisher Models.

• DOI: 10.1534/g3.117.041038
• 发表时间: 2017-07-05
• 期刊: G3 (Bethesda, Md.)
• 作者: He Z;Beaumont M;Yu F
• 通讯作者: Yu F

Maximum likelihood estimation of natural selection and allele age from time series data of allele frequencies

根据等位基因频率的时间序列数据进行自然选择和等位基因年龄的最大似然估计

• DOI: 10.1101/837310
• 发表时间: 2019
• 作者: He Z

Fixation probability for competing selective sweeps

• DOI: 10.1214/ejp.v17-1954
• 发表时间: 2012-04-23
• 期刊: ELECTRONIC JOURNAL OF PROBABILITY
• 影响因子: 1.4
• 作者: Cuthbertson, Charles;Etheridge, Alison;Yu, Feng
• 通讯作者: Yu, Feng