Genealogy of branching populations, new descriptions of large random trees, and a mathematical framework for the evolution of senescence

分支种群的谱系、大型随机树的新描述​​以及衰老进化的数学框架

• 批准号: 0907630
• 负责人: Steven Evans
• 金额: $ 57.11万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0907630&HistoricalAwards=false
• 关键词: Genealogy; branching; populations; new; descriptions

Not only do most complex organisms age, in the sense that they degenerateas time passes, but they often do so according to similar patterns. Biologistshave proposed qualitative explanations of this fact based on the concept ofmutation-selection balance: that natural selection does not oppose mutationswith deleterious effects if those effects are felt primarily after the bearer has been able to reproduce. However, it has been a challenge to provide a rigorous quantitative version of this notion because it involves large numbers of genes with complex interactions, and yet the resulting patterns of aging should be fairly insensitive to the underlying specifics. One part of the project aims to improve understanding of this important problem in evolutionary biology and biodemography using ideas from infinite-dimensional, non-linear dynamical systems.Another common question in evolutionary biology is whether evolutionaryprocesses leave some sort of signature in the shape of the phylogenetic tree ofa collection of present day species. Similarly, with the increasing availability of large amounts of data, computer scientists wonder if the current structure of a large network that has grown over time reveals something about the dynamics of that growth. Motivated by such questions, one seeks "statistics" that somehow summarize the shape of trees and more general graphs, and to determine the behavior of these quantities when the graphs are generated by specific mechanisms. Mathematically natural candidates for such descriptors are the so-calledeigenvalues of the graph. Two further goals of the project are, firstly, to userelatively simple techniques from linear algebra and probability to understandthe eigenvalues of broad classes of large random graphs, and, secondly, to useideas from the theory of Martin boundaries to delineate fully all the possibleways that certain models for growing trees can behave when the tree becomes large.The last objective of the proposal is to study how the age of the most-recent-common ancestor (MRCA) of a population changes over time. Any asexually reproducing population has a unique MRCA, from whom the entire population is descended. In sexually reproducing species, the same is true for each non-recombining piece of DNA. For instance, our "mitochondrial Eve" from whom all modern-day humans inherited their mitochondrial DNA is estimated to have lived around 180,000 years ago. As time progresses into the future, eventually the mitochondrial lineages of all but one of the daughters of the current mitochondrial Eve will die out, at which point the new mitochondrial Eve will have lived somewhat later in time. The proposed research will investigate the dynamics by which the age of the MRCA varies.

大多数复杂的生物体不仅会随着时间的流逝而衰老，而且它们的衰老模式也很相似。生物学家对这一事实提出了基于突变选择平衡概念的定性解释：自然选择不会反对具有有害影响的突变，如果这些影响主要是在携带者能够繁殖之后才感受到的话。然而，为这一概念提供一个严格的定量版本一直是一个挑战，因为它涉及大量具有复杂相互作用的基因，而由此产生的衰老模式应该对潜在的细节相当不敏感。该项目的一部分目的是利用无限维非线性动力系统的思想，提高对进化生物学和生物人口学中这一重要问题的理解。进化生物学中另一个常见的问题是，进化过程是否会在现代物种的系统发育树上留下某种印记。同样，随着大量数据的可用性越来越高，计算机科学家想知道，随着时间的推移，一个大型网络的当前结构是否揭示了这种增长的动态。在这些问题的激励下，人们寻求“统计”，以某种方式总结树的形状和更一般的图形，并确定当图形由特定机制生成时这些数量的行为。这种描述符在数学上的自然候选者是图的所谓特征值。该项目的两个进一步目标是，首先，使用线性代数和概率论的相对简单的技术来理解大型随机图的大类的特征值，其次，使用马丁边界理论的思想来描述当树变大时，某些生长树的模型可以表现的所有可能的方式。该提案的最后一个目标是研究一个种群的最近共同祖先（MRCA）的年龄如何随时间变化。任何无性繁殖的种群都有一个独特的MRCA，整个种群都是它的后裔。在有性繁殖的物种中，每个非重组的DNA片段也是如此。例如，据估计，我们的“线粒体夏娃”生活在大约18万年前，所有现代人类都从她那里继承了线粒体DNA。随着时间的推移，最终除了当前线粒体夏娃的一个女儿外，所有的线粒体血统都将消亡，到那时，新的线粒体夏娃将在时间上稍微晚一些。拟议的研究将调查MRCA年龄变化的动态。