Impact of the strength of selection on the persistence of cyclic phenotype frequency dynamics (A1–A4): Persistence of phenotype oscillations (black regions) for increased selection coefficients based on analytical predictions. When selection is weak (A1) cycles will continue indefinitely only for minimal or maximal levels of induced switching in both species. As selection becomes stronger (A2–A3), cyclic dynamics become more difficult to destroy and persist at higher levels of induced switching. For exceptionally high values of selection coefficients (A4), allele frequency oscillations will become unaffected by induced switching, including their speed and amplitude. As explained in the main text, the nature of cycles for minimal and maximal values of induced switching is different because of being driven by different evolutionary forces. (B1–B4): Numerical calculation of the amplitude of cycles from computer simulations confirms the analytical calculations in panels A1-A4. It also reveals that the amplitude of cycles decreases as the cycles reemerge at high values of induced switching in both species X and Y . The following parameter values were used: (A1,B1) sX = sY = 0.30, (A2,B2) sX = sY = 0.57, (A3,B3) sX = sY = 0.60, (A4,B4) sX = sY = 0.90; panels A1-A4 were made in resolution 101×101; in panels B1-B4 were made in resolution 51×51, and cycles of amplitude 0.5×10−2 where considered non-existent.
Mostowy et al. BMC Evolutionary Biology 2012 12:93 doi:10.1186/1471-2148-12-93