在变化和波动环境中的选择和突变
Selection and mutation in a shifting and fluctuating environment
摘要：
我们研究了一个表型结构种群在变化环境中的进化动力学，其中环境条件以线性趋势变化，但以振荡的方式。这种现象可以用具有非局部竞争和不定常增长率的抛物型Lotka-Volterra型方程来描述。我们首先研究了该问题解的长时间行为。接下来，使用基于Hamilton-Jacobi方程的方法，当突变的影响很小时，我们渐近地研究这样的长时间解。我们证明，作为突变的影响消失，人口的表型密度集中在一个单一的性状随时间线性变化，而人口的规模周期性振荡。与没有线性变化的环境相比，这种显性性状在平均环境中不具有最大生长速率，并且由于气候变化而存在生长速率的成本。我们还提供了一个渐近展开的平均规模的人口和临界速度以上的人口灭绝，这是密切相关的推导的渐近展开的Floquet特征值的扩散率。通过一个生物学的例子，这种扩展可以表明，环境的波动可能有助于人口以更好的方式跟随气候变化。
英文摘要：
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic Lotka-Volterra type equations with non-local competition and a time dependent growth rate. We first study the long time behavior of the solution to this problem. Next, using an approach based on Hamilton-Jacobi equations we study asymptotically such long time solutions when the effects of the mutations are small. We prove that, as the effect of the mutations vanishes, the phenotypic density of the population concentrates on a single trait which varies linearly with time, while the size of the population oscillates periodically. In contrast with the case of an environment without linear shift, such dominant trait does not have the maximal growth rate in the averaged environment and there is a cost on the growth rate due to the climate shift. We also provide an asymptotic expansion for the average size of the population and for the critical speed above which the population goes extinct, which is closely related to the derivation of an asymptotic expansion for the Floquet eigenvalue in terms of the diffusion rate. By mean of a biological example, this expansion allows to show that the fluctuations on the environment may help the population to follow the climatic shift in a better way.
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