发散适应度最优值的自适应动力学
Adaptive Dynamics of Diverging Fitness Optima
AI总结：
本研究针对含两个不同偏移速度局部最优性状的表型结构种群进化模型，通过特征值问题确定种群存续条件，分析小突变极限下的解的集中特性，揭示了环境变化中性状竞争主导的影响因素。
摘要：
我们分析了一个非局部抛物型积分-微分方程，该方程用于建模变化环境中表型结构种群的进化动力学。这类模型出现在从气候变化、化学治疗到机体衰老的多种场景中。本研究的主要创新点在于存在两个局部最优性状，每个性状都可能以不同的线性速度发生偏移。我们通过相关的特征值问题确定了保证种群灭绝或持续存在的充分条件。当种群未灭绝时，我们在长时间、小突变的极限下分析了解的性质。如果两个最优值的偏移速度相等，解会集中在一组“滞后最优值”的点集上，这些点严格滞后于真实的偏移最优值。如果偏移速度不同，我们确定解实际上会以狄拉克δ函数的形式集中在具有最大滞后适应度的正滞后最优值上，该值取决于真实最优值和偏移速率。我们的结果表明，对于在时间变化环境中经历竞争的种群而言，真实最优适应度以及每个发散最优性状所需的适应速率，都会导致某一性状最终占据主导地位。
英文摘要：
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models arise in a variety of contexts from climate change to chemotherapy to the ageing body. The main novelty is that there are two locally optimal traits, each of which shifts at a possibly different linear velocity. We determine sufficient conditions to guarantee extinction or persistence of the population in terms of associated eigenvalue problems. When it does not go extinct, we analyse the solution in the long time, small mutation limits. If the optimas have equal shift velocities, the solution concentrates on a point set of "lagged optima" which are strictly behind the true shifting optima. If the shift velocities are different, we determine that the solution in fact concentrates as a Dirac delta function on the positive lagged optimum with maximum lagged fitness, which depends on the true optimum and the rate of shift. Our results imply that for populations undergoing competition in temporally changing environments, both the true optimal fitness and the required rate of adaptation for each of the diverging optimal traits contribute to the eventual dominance of one trait.
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