10.15 \(f_{4}\)-ratio statistic

The branch length proportionality of the \(f_4\) statistic is useful for deriving yet another statistic, called the \(\mathbf{f_{4}}\)-ratio statistic.

As implied by its name, this simply a ratio of two different \(f_{4}\) statistics. Unlike \(D\) and \(f_{4}\), the \(f_{4}\)-ratio tells us how much Neanderthal ancestry a given individual possesses.

Calculate the \(f_{4}\)-ratio using the code block below:

f4_ratio_result <- f4ratio(data = snps,
                           X = pops, A = "Altai", B = "Vindija", C = "Yoruba", O = "Chimp") %>%
  # convert z score to pvalue
  mutate(p = 2 * pnorm(-abs(Zscore)))

f4_ratio_result

##       A       B           X      C     O     alpha   stderr Zscore            p
## 1 Altai Vindija      French Yoruba Chimp  0.023774 0.006176  3.850 1.181178e-04
## 2 Altai Vindija   Sardinian Yoruba Chimp  0.024468 0.006071  4.031 5.554004e-05
## 3 Altai Vindija         Han Yoruba Chimp  0.022117 0.005892  3.754 1.740349e-04
## 4 Altai Vindija      Papuan Yoruba Chimp  0.037311 0.005812  6.420 1.362743e-10
## 5 Altai Vindija Khomani_San Yoruba Chimp  0.003909 0.005913  0.661 5.086123e-01
## 6 Altai Vindija       Mbuti Yoruba Chimp  0.000319 0.005717  0.056 9.553418e-01
## 7 Altai Vindija       Dinka Yoruba Chimp -0.001500 0.005394 -0.278 7.810124e-01

For this statistic, alpha represents the proportion of the genome whose ancestry traces to Neanderthal introgression.