Alternative Mutational Architectures Producing Identical M-Matrices can Lead to Different Patterns of Evolutionary Divergence

Abstract

Explaining macroevolutionary divergence in light of population genetics requires understanding the extent to which the patterns of mutational input contribute to long-term trends. In the context of quantitative traits, mutational input is typically described by the mutational variance-covariance matrix, the M-matrix, which summarizes phenotypic variances and covariances introduced by new mutations per generation. However, as a summary statistic, the M-matrix does not fully capture all the relevant information from the underlying mutational architecture, and there exist a myriad of possible underlying mutational architectures that give rise to the same M-matrix. Using individual-based simulations, we demonstrate mutational architectures that produce the same M-matrix can lead to different levels of constraint on evolution and result in difference in within-population genetic variance, between-population divergence, and rate of adaptation. In particular, the rate of adaptation and that of neutral evolution are both reduced when a greater proportion of loci are pleiotropic. Our results reveal that aspects of mutational input not reflected by the M-matrix can have a profound impact on long-term evolution and suggest it is important to take them into account in order to connect patterns of long-term phenotypic evolution to underlying microevolutionary mechanisms.

Keywords: M-matrix; adaptation; phenotypic evolution; pleiotropy.

Fig. 1.

a) A comparison of pleiotropic and nonpleiotropic mutations with the same phenotypic effect on focal trait(s) but different fitness effects. The origin point denotes the optimal phenotype, and fitness decrease with the distance to the optimum. Grey area in each graph represents a zone of effective neutrality determined by the effective population size; mutations that do not cause the phenotype to move outside this zone are effectively neutral. Left: Both traits under concern are under stabilizing selection. Nonpleiotropic mutations $\overrightarrow{m_1}$ and $\overrightarrow{m_2}$ are within the zone of effective neutrality, where as the pleiotropic mutation $\overrightarrow{m_P}$, which as the same effects on each traits, moves the phenotype outside the zone. Right: Only trait 2 is under stabilizing selection. A nonpleiotropic mutation $\overrightarrow{m_1}$ is neutral, whereas a pleiotropic mutation $\overrightarrow{m_P}$, which has the same effect on trait 1 is deleterious. b–d) Schematic illustration of alternative genotype–phenotype maps that produce the same $\mathbf{M}$-matrix. A locus’s effect on a trait is indicated by a line connecting the trait and the locus. In all three scenarios, each trait is affected by five loci, the distribution of mutations’ per-trait effect is the same for all loci, and pleiotropic mutation’s effect on two traits are uncorrelated. Thus, the two traits have the same mutational variance and zero genetic covariance in all scenarios. b) Each trait affected by five nonpleiotropic loci. c) Each trait is affected by three nonpleiotropic loci and two pleiotropic loci. d) Both traits are affected by the same five loci.

Fig. 2.

Phenotypic variance within and between populations when all traits are under stabilizing selection. Colors correspond to the dimensionality of $\mathbf{M}$-matrices being compared. a) Within-population genetic variance ($V_G$), which is averaged across populations for each trait and then averaged across traits. Error bars reflect standard error, which is first calculated for each trait and then averaged across traits. b) Between-population variance ($V_R$), which is first calculated for each trait and then averaged across traits. Error bars reflect sampling standard deviation of sample variance at sample size of 50. Y-axes are in log10 scale.

Fig. 3.

Variance of a neutral trait ($z_1$) within and between populations when all other traits are under stabilizing selection. Colors correspond to the dimensionality of $\mathbf{M}$-matrices being compared. a) Within-population genetic variance ($V_G$) of $z_1$, which is averaged across populations. Error bars reflect standard error, which is first calculated for each trait and then averaged across traits. b) Between-population variance ($V_R$) of $z_1$. Error bars reflect sampling standard deviation of sample variance at sample size of 50. Y-axes are in log10 scale.

Fig. 4.

Adaptive evolution when one trait is under directional selection and others are under stabilizing selection. Colors correspond to the dimensionality of $\mathbf{M}$-matrices being compared. a) Mean value of trait under directional selection ($z_1$) at the end of simulation in Wright–Fisher (WF) populations. b) Mean $z_1$ at the end of simulation in non-WF populations. Mean $z_1$ was first calculated for each population, then the population means were averaged to obtain a cross-population mean. c) Mean population size ($\overline{N}$) at the end of simulation in non-WF populations (no population went extinct during the simulations). Dashed lines in (a) and (b) represent the optimal phenotype. The dark red dashed line in (c) represents the carrying capacity (K). Error bars in both panels reflect standard error.