Evolution of discrete populations and the canonical diffusion of adaptive dynamics
Evolution of discrete populations and the canonical diffusion of adaptive dynamics
复制标题
DOI：
10.1214/105051606000000628
复制
发表时间：
2007-02-01
影响因子：
1.8
通讯作者：
Lambert, Amaury
中科院分区：
文献类型：
--
作者：
Champagnat, Nicolas;Lambert, Amaury
适应动力学的生物学理论提出了一种对结构化无性种群的长期进化的描述。它是基于大种群、罕见突变和小突变步骤的假设，导致了一首描述主导类型进化的确定性颂歌，称为“适应动力学的正则方程”。在这里，为了包括随机性(遗传漂移)的影响，我们考虑了自我调节的随机波动的种群受到突变的影响，因此共存类型的数量可能会波动。我们对这些种群应用了有限的罕见突变，同时保持种群规模有限。这导致了一个跳跃过程，即所谓的“特征替换序列”，在这个过程中，进化通过对突变类型的连续入侵和固定来进行。然后，我们对这个跳跃过程应用有限的小突变步骤(弱选择)，这导致了一个我们称为“自适应动力学的规范扩散”的扩散过程，在这个过程中，遗传漂移与由固定概率的梯度驱动的定向选择相结合，也被解释为入侵适应度。最后，我们详细地研究了多类型Logistic分支种群的具体情况，并寻求了略偏离居民型的突变体的入侵适应度的显式公式。具体地说，固定概率的二阶项是初始突变频率的函数与初始总种群规模的函数的乘积，称为居民因生育、防御、攻击性、隔离或生存而增加的入侵系数。
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a deterministic ODE describing the evolution of the dominant type, called the "canonical equation of adaptive dynamics." Here, in order to include the effect of stochasticity (genetic drift), we consider self-regulated randomly fluctuating populations subject to mutation, so that the number of coexisting types may fluctuate. We apply a limit of rare mutations to these populations, while keeping the population size finite. This leads to a jump process, the so-called "trait substitution sequence," where evolution proceeds by successive invasions and fixations of mutant types. Then we apply a limit of small mutation steps (weak selection) to this jump process, that leads to a diffusion process that we call the "canonical diffusion of adaptive dynamics," in which genetic drift is combined with directional selection driven by the gradient of the fixation probability, also interpreted as an invasion fitness. Finally, we study in detail the particular case of multitype logistic branching populations and seek explicit formulae for the invasion fitness of a mutant deviating slightly from the resident type. In particular, second-order terms of the fixation probability are products of functions of the initial mutant frequency, times functions of the initial total population size, called the invasibility coefficients of the resident by increased fertility, defence, aggressiveness, isolation or survival.