论文标题
部分可观测时空混沌系统的无模型预测
An evolution model with uncountably many alleles
论文作者
论文摘要
我们研究了一类进化模型，其中繁殖过程涉及任意可交换过程，从而允许突变出现。人口尺寸$ n $是固定的，因此在繁殖后进行选择。个人的特征是他们的基因组，在集合$ x $（可能是无数的）中挑选，并且每个基因组都有适合性。不太合适意味着在选择过程中被丢弃的机会更高。可以描述和研究该过程的固定分布。我们对这种固定分布的渐近行为感兴趣，因为$ n $转到了无限。选择一个参数$λ> 0 $来调整$ n $生长时的健身缩放，我们证明限制定理既不取决于$ n $，又要限制繁殖过程的情况，而对于dirichlet进程给出的情况。在这两种情况下，极限均取决于参数$λ
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are characterized by their genome, picked inside a set $X$ (which may be uncountable), and there is a fitness associated to each genome. Being less fit implies a higher chance of being discarded in the selection process. The stationary distribution of the process can be described and studied. We are interested in the asymptotic behavior of this stationary distribution as $n$ goes to infinity. Choosing a parameter $λ>0$ to tune the scaling of the fitness when $n$ grows, we prove limiting theorems both for the case when the breeding process does not depend on $n$, and for the case when it is given by a Dirichlet process prior. In both cases, the limit exhibits phase transitions depending on the parameter $λ
