Jones Adam G, Arnold Stevan J, Bürger Reinhard
Department of Biology, 3258 TAMU, Texas A&M University, College Station, Texas 77843, USA.
Evolution. 2007 Apr;61(4):727-45. doi: 10.1111/j.1558-5646.2007.00071.x.
Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, r(mu), the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at -1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.
可进化性是任何进化系统的关键特征，可进化性的概念是与进化理论相关的广泛学科中的一个统一主题。数量遗传学领域提供了一个探索可进化性的框架，有望产生具有全球重要性的见解。就生物系统的数量遗传学而言，与可进化性最相关的参数是G矩阵，它描述了一组性状的现有加性遗传方差和协方差，以及M矩阵，它描述了新突变对遗传方差和协方差的影响。种群对选择的即时反应由G矩阵控制。然而，可进化性还涉及突变过程产生适应性变异的能力，因此M矩阵是一个关键的数量遗传参数。在这里，我们通过使用分析理论和基于模拟的模型来研究突变相关性r(mu)的进化，以探索可进化性的进化，r(mu)是决定M施加的遗传约束性质的关键参数。该模型使用一个有限大小的二倍体有性繁殖种群，在一个双性状表型上经历稳定选择。我们假设突变相关性是一个由多个加性基因座决定的第三数量性状。个体的突变相关性性状值决定了新等位基因在该个体中出现时其多效性效应之间的相关性。我们的结果表明，突变相关性尽管不直接参与个体适合度的指定，但确实会因对双变量表型的选择而进化。突变方差表现出一种微弱的进化趋势，以使M矩阵与适应性景观对齐，但由于遗传漂变而容易出现不稳定的波动。对这一结果的解释是，种群的可进化性能够对选择做出反应，而这种反应导致可进化性增加还是减少取决于双变量表型最优值预期移动的方式。有趣的是，分析和模拟结果都表明，突变相关性经历了间断选择，在-1和+1处有局部适合度最大值。然而，遗传漂变抵消了突变相关性在这些极值处持续存在的趋势。我们的结果还表明，在大多数情况下，不断进化的M矩阵倾向于增加G矩阵的稳定性。因此，以前关于G矩阵稳定性的研究假设M矩阵不进化，可能高估了G相对于自然系统中预期的不稳定程度。总体而言，我们的结果表明，可进化性可以在自然系统中以一种倾向于使G矩阵、M矩阵和适应性景观对齐的方式进化，并且这种进化倾向于在进化时间内稳定G矩阵。
