Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in “geno-phenotype” space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where “total genotypic selection” vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

自然选择作用于发育过程中构建的表型，这就提出了发育如何影响进化的问题。经典进化理论表明，发育通过调节选择所依据的遗传共变来影响进化，从而影响遗传约束。然而，遗传约束是否是相对的，从而使适应偏离最陡峭的适应度上升的方向，还是绝对的，从而阻碍某些方向的适应，仍然不确定。这限制了对发育构建表型的长期进化的理解。在这里，我们制定了一个通用的、易于处理的数学框架，整合了年龄进展、显性发展（即受发​​展约束的整个生命表型的构建）和进化动力学，从而描述了进化和发展（evo-devo）动力学。该框架产生可以排列在分层结构中的简单方程，我们称之为 evo-devo 过程，其中五个核心基本组件生成所有方程，包括那些机械地描述遗传协变和 evo-devo 动力学的方程。该框架以梯度形式恢复进化动态方程，并从基因型、表型、环境和突变共变的进化来描述遗传共变的进化。这表明基因型和表型进化必须同时进行，才能以梯度形式对长期表型进化进行动态充分的描述，使得被描述为适应性景观攀爬的进化发生在“基因-表型”空间中。基因-表型空间中的遗传限制必然是绝对的，因为表型通过发育与基因型相关。 因此，发育表型的长期进化动力学是非常不标准的：（1）进化平衡要么不存在，要么数量无限，并且取决于遗传共变，从而取决于发育； (2) 发展约束决定了可接受的进化路径，从而决定了哪些进化平衡是可接受的； （3）进化结果发生在可接受的进化平衡处，这种平衡通常不会发生在基因表型空间的适应景观峰值处，而是发生在可接受的进化路径的峰值处，如果外源可塑性反应消失和突变变异，“总基因型选择”就会消失存在于基因型空间的各个方向。因此，如果不存在绝对突变约束和外源可塑性反应，选择和发展共同定义进化结果，而不是仅由选择定义结果。此外，我们的框架提供了递归敏感性的公式和动态优化的替代方法（即动态规划或最优控制），以识别具有发育动态特征的模型中的进化结果。这些结果表明，发展具有重大的进化效应。