. 2018 Jun 25;16(6):e2005609. doi: 10.1371/journal.pbio.2005609

Table 2. Parameters determining invasion of mutant neo-Y and neo-W alleles into an ancestrally XY system.

m is a neo-Y (k = 0)

Λ_{Y^{'} A}^{(X Y)} = {(2 ζ)}^{- 1} [{\hat{p}}_{X}^{♀} w_{A}^{♀} w_{A}^{♂} w_{A A}^{♂} + (1 - {\hat{p}}_{X}^{♀}) w_{a}^{♀} w_{A}^{♂} w_{A a}^{♂} (1 + α_{△}^{♂})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♂})

Λ_{Y^{'} a}^{(X Y)} = {(2 ζ)}^{- 1} [(1 - {\hat{p}}_{X}^{♀}) w_{a}^{♀} w_{a}^{♂} w_{a a}^{♂} + {\hat{p}}_{X}^{♀} w_{A}^{♀} w_{a}^{♂} w_{A a}^{♂} (1 - α_{△}^{♂})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♂})

χ_{Y^{'} A}^{(X Y)} = R {(2 ζ)}^{- 1} [(1 - {\hat{p}}_{X}^{♀}) w_{a}^{♀} w_{A}^{♂} w_{A a}^{♂} (1 + α_{△}^{♂})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♂})

χ_{Y^{'} a}^{(X Y)} = R {(2 ζ)}^{- 1} [{\hat{p}}_{X}^{♀} w_{A}^{♀} w_{a}^{♂} w_{A a}^{♂} (1 - α_{△}^{♂})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♂})

m is a neo-W (k = 1)

Λ_{W^{'} A}^{(X Y)} = {[2 (1 - ζ)]}^{- 1} [{\bar{p}}^{♂} w_{A}^{♂} w_{A}^{♀} w_{A A}^{♀} + (1 - {\bar{p}}^{♂}) w_{A}^{♂} w_{A}^{♀} w_{A a}^{♀} (1 + α_{Δ}^{♀})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♀})

Λ_{W^{'} a}^{(X Y)} = {[2 (1 - ζ)]}^{- 1} [(1 - {\bar{p}}^{♂}) w_{a}^{♂} w_{a}^{♀} w_{a a}^{♀} + {\bar{p}}^{♂} w_{A}^{♂} w_{a}^{♀} w_{A a}^{♀} (1 - α_{Δ}^{♀})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♀})

χ_{W^{'} A}^{(X Y)} = R {[2 (1 - ζ)]}^{- 1} [(1 - {\bar{p}}^{♂}) w_{a}^{♂} w_{A}^{♀} w_{A a}^{♀} (1 + α_{Δ}^{♀})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♀})

χ_{W^{'} a}^{(X Y)} = R {[2 (1 - ζ)]}^{- 1} [{\bar{p}}^{♂} w_{A}^{♂} w_{a}^{♀} w_{A a}^{♀} (1 - α_{Δ}^{♀})] / ({\bar{w}}_{H}^{♀} {\bar{w}}_{H}^{♂} {\bar{w}}_{D}^{♀})

${\bar{p}}^{♂} = (1 - {\hat{q}}_{Y}) {\hat{p}}_{X}^{♂} + {\hat{q}}_{Y} {\hat{p}}_{Y}^{♂}$ is the average frequency of the A allele among X- and Y-bearing male gametes. ${\hat{q}}_{Y}$ is the frequency of Y-bearing male gametes. ξ is the zygotic sex ratio (fraction male). Inline graphic is the mean fitness of diploids of sex . is the mean fitness of haploids from sex (see S2 Table). R is the rate of recombination between the neo-sex determiner and the selected locus. Selection terms (, ) are described in Table 1.