Mathematical Foundations of Evolutionary Theory

进化论是生物学中数学上最复杂的领域。然而，形式进化理论是不同模型的集合，建立在不同的假设下，使用不同类型的数学。这个项目将通过展示如何从一些基本的数学原理中推导出所有的机械进化理论来统一这个不同的领域。通过使用一种不需要对遗传学或种群规模进行简化假设的数学方法，研究人员还将研究新发现的经典理论所看不到的进化机制。结果将是一个统一的进化数学理论，适用于任何地方的任何进化系统-包括地球上的所有生命，宇宙中其他地方可能存在的任何生命，以及可以进化的非生命系统，如计算机病毒。除了为生物学家提供重要的工具外，这项工作还将阐明进化科学的统一性和普遍性;这是关于进化论在学校课程中地位的辩论的一个重要观点。在纯粹的实践层面上，初步工作表明，这项工作产生的新的进化过程在规模正在减少的小种群中最为明显;换句话说，那些濒临灭绝的种群。因此，这项研究也将为我们了解濒危和受威胁物种的遗传学做出重要贡献。

Evolutionary theory is the most mathematically sophisticated area of biology. However, formal evolutionary theory is a collection of different models, built under different assumptions and using different kinds of mathematics. This project will unify this diverse field by showing how all mechanistic evolutionary theory can be derived from a few fundamental mathematical principles. By using a mathematical approach that does not require simplifying assumptions about genetics or population size, the researchers will also investigate newly discovered evolutionary mechanisms that are invisible to classical theory.The result will be a unified mathematical theory of evolution that is applicable to any evolving system, anywhere - including all life on earth, any life that may exist elsewhere in the universe, and nonliving systems that can evolve, such as computer viruses. In addition to providing important tools for biologists, this work will clarify the unity and universality of evolutionary science; an important point given debates about the status of evolution in school curricula. On a purely practical level, preliminary work has shown that the new evolutionary processes that emerge from this work are most pronounced in small populations that are decreasing in size; in other words, those that are on the verge of extinction. This study will thus also make important contributions to our understanding of the genetics of endangered and threatened species.