For heterochronous sequences on a rooted phylogeny with sampling times \(t_i\) and root-to-tip distances \(d_{r,i}\), a strict molecular clock implies \(E[d_{r,i}] = u (t_i - t_r)\) (eq. 1 of the paper). Ordinary least squares of d on t estimates the substitution rate u as the slope and the root time \(t_r\) (time of the most recent common ancestor) as the x-intercept. Correlation and R-squared diagnose temporal signal; residuals flag incongruent sequences.
References
Rambaut, A., Lam, T. T., Max Carvalho, L. and Pybus, O. G. (2016), Exploring the temporal structure of heterochronous sequences using TempEst (formerly Path-O-Gen), Virus Evolution 2(1), vew007. Equation (1) and Section 2, Root-to-tip regression.
Examples
V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Phylog(V, V)
#> $rate
#> [1] 1
#>
#> $intercept
#> [1] 0
#>
#> $tmrca
#> [1] 0
#>
#> $correlation
#> [1] 1
#>
#> $r_squared
#> [1] 1
#>
#> $residuals
#> [1] 0 0 0 0 0 0 0 0
#>
#> $n
#> [1] 8
#>
#> $method
#> [1] "root-to-tip regression dating (Rambaut et al. 2016)"
#>