School of Biological Sciences and Department of Mathematics, Washington State University, Pullman, Washington 99164, USA.
Am Nat. 2009 Dec;174(6):E218-29. doi: 10.1086/645086.
Populations unable to evolve to selectively favored states are constrained. Genetic constraints occur when additive genetic variance in selectively favored directions is absent (absolute constraints) or present but small (quantitative constraints). Quantitative--unlike absolute--constraints are presumed surmountable given time. This ignores that a population might become extinct before reaching the favored state, in which case demography effectively converts a quantitative into an absolute constraint. Here, we derive criteria for predicting when such conversions occur. We model the demography and evolution of populations subject to optimizing selection that experience either a single shift or a constant change in the optimum. In the single-shift case, we consider whether a population can evolve significantly without declining or else declines temporarily while avoiding low sizes consistent with high extinction risk. We analyze when populations in constantly changing environments evolve sufficiently to ensure long-term growth. From these, we derive formulas for critical levels of genetic variability that define demography-caused absolute constraints. The formulas depend on estimable properties of fitness, population size, or environmental change rates. Each extends to selection on multivariate traits. Our criteria define the nearly null space of a population's G matrix, the set of multivariate directions effectively inaccessible to it via adaptive evolution.
无法进化到被选择性偏好状态的种群受到限制。当选择性有利方向的加性遗传方差不存在（绝对限制）或存在但很小（数量限制）时，就会出现遗传限制。与绝对限制不同，数量限制被认为是可以随着时间克服的。这忽略了一个种群可能在达到有利状态之前就已经灭绝，在这种情况下，种群动态实际上将数量限制转化为绝对限制。在这里，我们推导出了预测这种转换何时发生的标准。我们对受到最优选择的种群的人口统计学和进化进行建模，这些种群经历了单一的转变或最优的持续变化。在单次转变的情况下，我们考虑种群是否可以在不减少的情况下显著进化，或者在避免与高灭绝风险一致的低大小的情况下暂时减少。我们分析了在不断变化的环境中种群进化到足以确保长期增长的情况。由此，我们推导出了定义由种群动态引起的绝对限制的遗传变异性临界水平的公式。这些公式取决于可估计的适应性、种群大小或环境变化率的特性。每个公式都扩展到多变量特征的选择。我们的标准定义了种群 G 矩阵的近零空间，即通过适应性进化对其有效的多变量方向的集合。
