I try several rates of \( \mu \), including Clark (\( 3x10^-8 \)) and Gaut (\( 6,5x10^-9 \)) estimates.

mu = c(1, 6.5, 10, 30, 100, 1000)
mu = 10^-9 * mu

Assume P(no change)\( =(1-\mu)^\tau \) where \( \tau \) is divergence time to Tripsacum/Sorghum. Try Sorghum at 10MYA and 15MYA and one assuming both branches or \( 2*10MYA=20MYA \). Also try Tripsacum at 1MYA and 5MYA. Ignore depth of coalescent. Mutation to same bp \( =\mu/3 \), and thus P(change) \( =(1-mu/3)^\tau \).

tripsacum_1 <- (1 - mu/3)^(1 * 10^6)
tripsacum_5 <- (1 - mu/3)^(5 * 10^6)
sorghum_same_15 <- (1 - mu/3)^(15 * 10^6)
sorghum_same_10 <- (1 - mu/3)^(10 * 10^6)
sorghum_same_20 <- (1 - mu/3)^(20 * 10^6)

Horizontal lines at 5% and 10%.

plot((1 - sorghum_same_10) ~ mu, log = "x", ylab = "Probability homoplasy", 
    ylim = c(10^-3, 1), xaxt = "n", type = "b", lwd = 2, col = "red", lty = 2)
axis(side = 1, at = mu)
lines((1 - sorghum_same_15) ~ mu, type = "b", lwd = 2, col = "blue", lty = 2)
lines((1 - sorghum_same_20) ~ mu, type = "b", lwd = 2, col = "green", lty = 2)
lines((1 - tripsacum_1) ~ mu, type = "b", lwd = 2, col = "black", lty = 2)
lines((1 - tripsacum_5) ~ mu, type = "b", lwd = 2, col = "grey", lty = 2)
legend("topleft", lty = 2, lwd = 2, col = c("green", "blue", "red", "grey", 
    "black"), legend = c("Sorghum 2*10MYA", "Sorghum 15MYA", "Sorghum 10MYA", 
    "Trip 5MYA", "Trip 1MYA"))
abline(h = c(0.05, 0.1), col = "grey", lwd = 0.5)