Interplay between geometry and randomness in fitness landscapes for expanding populations

人口增长的健身景观中几何与随机性之间的相互作用

• 批准号: EP/X040089/1
• 负责人: Marcel Ortgiese
• 金额: $ 55.47万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX040089%2F1
• 关键词: Interplay; between; geometry; randomness; fitness

The course of evolution is a constant conflict shaped by the interplay between the deterministic forces of selective advantage, characterised by the geometry of a fitness landscape, and the randomness of mutation and reproduction. A central question in this context is predictability: given the geometry of the fitness landscape, can we predict the trajectory of evolution? Two regimes are very well understood, from both biological and mathematical perspectives, but both these regimes are essentially deterministic in the limit; once we fix the parameters and the fitness landscape, evolution is pre-determined. The focus of our proposal is on cases where mutations are sufficiently frequent and the number of local optima in the fitness landscape is sufficiently large, so that the population does not necessarily move as one and several species or quasispecies may exist concurrently. There is a significant lack of rigorous mathematical work in this situation, although simulations have shown intriguing results. The aim of this proposal is to develop new rigorous mathematical tools to gain insight into the possible random pathways taken by evolutionary processes.

进化的过程是一个持续的冲突，由选择优势的决定性力量之间的相互作用形成，其特征是适应性景观的几何形状，以及突变和繁殖的随机性。在这种背景下，一个中心问题是可预测性：给定适应度景观的几何形状，我们能否预测进化的轨迹？从生物学和数学的角度来看，两种机制都很好理解，但这两种机制在极限上基本上都是确定性的;一旦我们确定了参数和适应度景观，进化就是预先确定的。我们的建议的重点是在突变是足够频繁的情况下，在健身景观的局部最优的数量是足够大的，使人口不一定移动作为一个和几个物种或准物种可能同时存在。在这种情况下，尽管模拟显示了有趣的结果，但严重缺乏严格的数学工作。该提案的目的是开发新的严格的数学工具，以深入了解进化过程中可能采取的随机路径。