  Although many phenotypic traits are determined by a large number of genetic
variants, how a polygenic trait adapts in response to the changes in the
environment is still poorly understood. Here we study the adaptation dynamics
of a polygenic trait that is determined by a finite number of genetic loci in
an infinitely large population which is evolving under stabilising selection
and recurrent mutations. We find that in a changing environment, modeled here
by a linearly moving phenotypic optimum, the mean trait also moves linearly
with time. But its speed is smaller than that of the phenotypic optimum when
the effect sizes of the genetic variants are small and approaches that of the
environmental change for larger effect sizes. Our study thus highlights the
influence of the genetic architecture of a polygenic trait on its adaptability.
