Table 1.

Description of model parameters and variables

Symbol	Definition
R m	Intrinsic growth rate of the population, λ/μ
λ	Density-independent birth rate
μ	Density-independent death rate
γ	Density-dependent rate constant per generation time
m	Proportion of progeny of driving Y males that inherit the driving Y
u	The fraction of female progeny of a driving Y male that inherit an X chromosome with a resistant mutation (Model I)
v	The chance of a suppressor mutation arising on an autosome (per individual per autosome, for all births, male or female) (Model II)
w	Fitness parameter for mutations (relative to fitness one for wild-types and driving Y males without the resistant gene). Model I: w for heterozygote females, $w^2$ for homozygous females and hemizygous males; Model II: w for heterozygotes, w 2 for homozygotes
a	Amplitude of seasonal variation in parameter for density-dependence, $\mathrm{\gamma }\left(t\right)$
N 0	Equilibrium wild-type population size (before release of driving Y and in absence of mutation)
h 0	Release amount of driving Y males
$H\left(t\right),M\left(t\right),F(t)$	Driving Y, wild-type male and wild-type female population sizes (non-mutant)
N(t)	Total population size
P 1	Probability that at least one mutation arises and establishes, preventing population elimination
P Mut	Probability that at least one mutation arises (regardless of its fate)
P Con	Conditional probability that if one or more mutations arise, at least one establishes
p est(t a)	Probability that a single mutation arising at time t a after release of the driving Y will establish (in the absence of other mutations)