Fig. 4

a Time evolution of wild-type female mosquito population F(t) before driving Y release (dotted line), and for introduction of the driving Y at time T (blue line), 1.25T (green line), 1.5T (red line), and 1.75T (orange line). For R _m  = 6, m = 0.95, T = 18.25, h ₀ = 0.05, w = 1, a = 0.9825 (amplitude selected for peak to trough ratio of 100:1). Note h ₀ is the proportion of the time-averaged pre-release population size \(\bar{N}\left( a \right) ( = N_{0} )\), so the absolute numbers released at different time points are assumed to be the same. b \(P_{Mut}\), P ₁, and \(P_{Con}\) as a function of \(t_{release} ,\) the time when the driving Y is released during the period T of the seasonally-varying wild-type population, for a = 0.9825 (solid lines) and a = 0 (dotted lines; no seasonality). For parameters R _m  = 6, m = 0.95, h ₀ = 0.05, uN ₀ = 1, w = 1, T = 18.25, and with \({\upgamma}_{0} \left[ a \right]\) adjusted as described as above, such that average wild-type populations over a period \(\bar{N}\left( a \right) = N_{0}\)