Adaptation and the 'shifting balance'

Wright proposed that there is a ' shifting balance' between selection within demes, random drift, and selection between demes at different 'adaptive peaks'. We investigate the establishment and spread of new adaptive peaks, considering a chromosome rearrangement, and a polygenic character under disruptive selection. When the number of migrants (Nm) is small, demes fluctuate independently, with a bias towards the fitter peak. When Nm is large, the whole population can move to one of two stable equilibria, and so can be trapped near the lower peak. These two regimes are separated by a sharp transition at a critical Nm of order 1. Just below this critical point, adaptation is most efficient, since the shifting balance greatly increases the proportion of demes that reach the global optimum. This is so even if one peak is only slightly fitter than the other (AWx \/N), and for both strong and weak selection (Ns <§ 1 or Ns > 1). Provided that Nm varies sufficiently gradually from place to place, the fitter peak can be established in regions where Nm « 1, and can then spread through the rest of the range. Our analysis confirms Wright's argument that if selection, migration and drift are of the same order, the ' shifting balance' leads to efficient evolution towards the global optimum.