Novel Statistical methods for extracting information from genetic data

这个数学模型项目包括分析从植物中提取的遗传数据，并开发新的数学和统计工具，从数据中提取信息。这个项目涉及将统计物理学和信息论的思想应用于基因型-表型变异的数据。在这两个学科中，熵和微观状态分布的概念在描述宏观量的理论中是有用的。我们考虑从人群中抽取一个样本，然后根据表型（即一个可观察到的特征，如身高或体重）对其进行排名。通过分析基因型（AA，Aa，aa）各自的顺序，我们得到一个有效的字段，量化如何强烈一个特定的单核苷酸多态性（SNP -一个小的遗传突变）影响一个特定的表型。这为分析基因型-表型互作提供了一种新的方法，它比经典的全基因组关联研究（GWAS）更强大，并且不依赖于Fisher在1901年提出的统计假设。在本博士项目中，这种新的方法将应用于拟南芥，以了解个体的遗传状态如何影响观察到的表型，例如拟南芥中的离子吸收如何影响植物生长。数据来自Sian Bray进行的离子学研究，他研究了植物中一系列离子的运输。我们将典型地关注三个双等位基因状态和这些状态对连续范围的表型值的影响。然后，我们将考虑多个基因对单个表型的影响，该方法量化了基因型-表型依赖性的强度;虽然许多SNP对表型没有显著影响，但有些SNP会对表型产生不同程度的影响。我们将研究连锁不平衡，即当一个人沿着染色体移动到附近的SNP时，相互作用的强度如何变化。通常，在存在具有强表型效应的SNP的情况下，也可以看到染色体上邻近的其他SNP对表型具有显著影响。我们将研究这种相互作用的范围，并构建模型来解释这种相互作用随着与最重要的SNP的距离而衰减的速度。虽然最终目标是解释工厂数据和其他真实的数据集，但新方法将在合成数据上进行测试，以测试其演绎能力。我们将研究模型的一般化，例如，表型可能仅作为“分组”数据可用，即在一系列范围（例如10-20，20-30，30-40等）中的每种基因型（AA，Aa，aa）的数量。在这种情况下，数据的“功效”和信息较少，因此可能不太可能被标记为显著，但由于它更平滑，它可能给出更简单的场强形式。我们还将考虑多等位基因系统-即存在三个以上等位基因的系统。这种高维系统的数学分析明显更加复杂，因为排序列表的可能排列的数量变得越来越大。

This mathematical modelling project involves a combination of analysis of genetic data taken from plants and the development of novel mathematical and statistical tools to extract information from the data.This project involves applying of ideas from statistical physics and information theory to data on genotype-phenotype variations. In both disciplines, the concepts of entropy and the distribution of microstates is useful in theories which describe macroscopic quantities. We consider a sample from the population, which is then ranked by phenotype (that is, an observable characteristic, such as height or weight). By analysing the respective order of genotypes (AA,Aa,aa), we derive an effective field which quantifies how strongly one particular single nucleotide polymorphism (SNP - a minor genetic mutation) influences a particular phenotype. This provides an alternative method for analysing genotype-phenotype interactions, which is more powerful than the classic genome wide association studies (GWAS), and does not rely on the statistical assumptions made by Fisher in 1901.In this PhD project this new method will be applied to Arabidopsis to understand how the genetic states of individuals influence observed phenotypes such as how ions uptake in Arabidopsis influence plant growth. Data comes from ionomic studies performed by Sian Bray, who studies the transport of a range of ions in plants. We will typically be concerned with three bi-allelic states and the impact of these states on a continuous range of phenotype values. We will then consider the effects of multiple genes on a single phenotype.The method quantifies the strength of the genotype-phenotype dependency; whilst many SNPs will have no significant effect on phenotype, some will, and to varying extents. We will investigate linkage disequilibrium, that is, how the strength of interaction varies as one moves along the chromosomes to nearby SNPs. Typically, where there is a SNP with a strong phenotype effect, other SNPs which are close by on the chromosome are also seen to have significant impact on phenotype. We will investigate the range of this interaction, and construct models to explain how rapidly this decays with distance from the most significant SNP. Whilst the ultimate goal is to interpret the plant-data, and other real data sets, new methods will be tested on synthetic data, in order to test their deductive power. We will investigate generalisations of the model, for example, the phenotypes may only available as `binned' data, that is numbers of each genotype (AA,Aa,aa) in a sequence of ranges (eg 10-20, 20-30, 30-40 etc). In this case the data has less 'power' and information, so might be less likely to be flagged as significant, but since it is smoother, it may give a simpler form for the field-strength.We will also consider multi-allelic systems - that is, where more than three alleles are present. The mathematical analysis of such higher-dimensional systems is significantly more complicated, as the number of possible arrangements of the ranked list becomes increasingly large.