基于复制子-增变子方程的进化分支
Evolutionary branching via replicator-mutator equations
摘要：
考虑一类非局部反应-扩散问题，在进化遗传学中称为复制-增变方程。对于一个限制适应度函数，我们证明了适定性，并明确地写的解决方案，通过一些基本的薛定谔谱元素（我们提供新的和非标准的估计）。因此，长时间行为由主本征函数或基态决定。在此基础上，我们讨论（严格和通过数值探索）的适应度函数和突变率的条件，进化分支发生。
英文摘要：
We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some underlying Schrödinger spectral elements (for which we provide new and non-standard estimates). As a consequence, the long time behaviour is determined by the principal eigenfunction or ground state. Based on this, we discuss (rigorously and via numerical explorations) the conditions on the fitness function and the mutation rate for evolutionary branching to occur.
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