Skip to main content

Table 1 Description of model parameters and variables

From: Vector control with driving Y chromosomes: modelling the evolution of resistance

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, \({\upgamma }\left( t \right)\)
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)