Shaw, A. K. and Levin, S. A. To breed or not to breed: a model of partial migration. – Oikos 120: 1871–1879.
Equation 4 should read
This is the correct equilibrium condition, given that we have not specified a form of density-dependence at this point in the paper. Once we assume a specific form of density-dependence (e.g. Ricker type as given by Eq. 6), then we can solve for the values of and explicitly. Equation 4 as shown in the original paper is the equilibrium assuming Ricker density-dependence.
Note that this correction does not affect any of our results.