A two-dimensional traveling wave model makes predictions about G-matrices and the scope of mutation bias in shaping adaptation
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Short-term evolution is determined by the G matrix, whose covariance terms represent a combination of pleiotropy and linkage disequilibrium, shaped by the population's history. Observed genetic covariance is most often interpreted in pleiotropic terms. In particular, functional constraints restricting which phenotypes are physically possible can lead to a stable G matrix with high genetic variance in fitness-associated traits and high pleiotropic negative covariance along the phenotypic curve of constraint. We describe the evolution of G when pleiotropy is excluded by design, such that all covariance comes from linkage disequilibrium, which reaches high levels in rapidly adapting microbial populations. To do this, we extended the influential one-dimensional travelling wave model of rapid adaptation of an asexual population into two dimensions, representing two distinct fitness-associated traits in an asexual population. We find that the associated G-matrix maintains a stable orientation, but is far less stable in magnitude than predicted by previous models. Different mechanisms drive the instabilities along different principal components of G. Their origin is not drift, but rather small amounts of linkage disequilibria generated by mutations on the fittest backgrounds, which are subsequently amplified during competing selective sweeps. By competing one trait with a higher beneficial mutation rate with another with larger mutational effect sizes, we illustrate the range of parameters for which mutation-driven adaptation is possible.