Kopp Michael, Gavrilets Sergey
Department of Ecology and Evolutionary Biology, University of Tennessee, 1416 Circle Drive, Knoxville, Tennessee 37996, USA.
Evolution. 2006 Jul;60(7):1321-36.
We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci.
我们开发并分析了一个明确的多基因座协同进化遗传模型。我们假设两个物种（互利共生者、竞争者或受害者与剥削者）之间的相互作用由一对加性数量性状介导，这些性状也受到朝向中间最优值的直接稳定选择。使用弱选择近似，我们推导出了具有相等基因座效应且无突变的对称情况的分析结果，并通过更一般情况的数值模拟对这些结果进行补充。我们表明，互利共生和竞争相互作用总是导致协同进化至一个稳定平衡，每个物种不超过一个多态基因座。受害者 - 剥削者相互作用可导致不同的动态模式，包括向稳定平衡、周期和混沌的进化。在平衡状态下，受害者通常具有非常大的遗传方差，而剥削者在不超过一个基因座上是多态的。与相关的单基因座或数量遗传模型相比，多基因座模型展现出两个主要的新特性。首先，平衡结构要复杂得多。我们推导了各类平衡存在和稳定的详细条件，并证明了多个同时稳定状态的可能性。其次，遗传方差动态变化，这反过来又显著影响平均性状值的动态。特别是，动态往往会因基因座数量的增加而变得不稳定。
