Counter-invasion of resident alleles in migratory populations and conditions for partial migration in relation to competition (y-axis) and relative site quality (x-axis). (a,b) The shared-breeding case and (c,d) the shared-non-breeding case with different values of x for each panel. For all panels, the partial migration (grey) region represent the conditions in which the growth rate of the resident allele is greater than 1 in a population otherwise fixed for the migratory allele (i.e. a stable polymorphism will occur). The dark region represents conditions in which the growth rate of the resident allele is less than or equal to 1 (counter-invasion is not successful and population remains migratory). For the shared-non-breeding case, x = 1 is not shown because the resident allele never invades (population always completely migratory) and x = 0.5 is not shown because the resident allele always invades (population always partially migratory). All panels represent the case for HF–LS species and all parameters, except x, correspond to figure 2a,b. (a) x = 1; (b) x = 0.5; (c) x = 0.85; (d) x = 0.7.