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) |