Figure 2
From: Stochastic errors vs. modeling errors in distance based phylogenetic reconstructions
Performance of the Four Point Method using Δ JC on K2P quartets with ti-tv ratio R = 2. The concave non affine-additive SR function ΔJC is shown (dashed green line) in the interval [t0,t1], where t0 and t1 are the smallest and largest of the six pairwise distances (resp.). The dashed blue line shows the linear interpolation Δint=At + B of ΔJC in the interval [t0,t1]. Horizontal dotted lines correspond to half of the two competing sums computed by FPM under the two SR functions (see legend). (a) In quartets of type A, t0=t12 and t1=t34, and so Δint(1,2) + Δint(3,4)=ΔJC(1,2) + ΔJC(3,4). However, for i ∈{1,2} and j ∈{3,4}, Δint(i,j )<ΔJC(i,j ). Therefore, the deviation from additivity of ΔJC increases its FPM separation, denoted SEPJC, compared to the FPM separation SEPint of Δint. (b) In quartets of type B, t0=t13 and t1=t24, and so Δint(1,3) + Δint(2,4)=ΔJC(1,3) + ΔJC(2,4). However, Δint(1,2)=Δint(3,4)<ΔJC(1,2)=ΔJC(3,4), and so Δint(1,2) + Δint(3,4)<ΔJC(1,2) + ΔJC(3,4). Therefore, the deviation from additivity of ΔJC decreases its FPM separation, denoted SEPJC, compared to the FPM separation SEPint of Δint. Note that SEPint remains invariant in both types of quartets under fixed t i whereas SEPJC changes, depending on the type of quartet and the t s /t l ratio.