**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 *Δ*_{JC} is shown (dashed green line) in the interval [*t*_{0},*t*_{1}], where *t*_{0} and *t*_{1} are the smallest and largest of the six pairwise distances (resp.). The dashed blue line shows the linear interpolation *Δ*_{int}=*At* + *B* of *Δ*_{JC} in the interval [*t*_{0},*t*_{1}]. 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, *t*_{0}=*t*_{12} and *t*_{1}=*t*_{34}, and so *Δ*_{int}(1,2) + *Δ*_{int}(3,4)=*Δ*_{JC}(1,2) + *Δ*_{JC}(3,4). However, for *i* ∈{1,2} and *j* ∈{3,4}, *Δ*_{int}(*i*,*j* )<*Δ*_{JC}(*i*,*j* ). Therefore, the deviation from additivity of *Δ*_{JC}* increases* its FPM separation, denoted _{SEPJC}, compared to the FPM separation _{SEPint} of *Δ*_{int}. **(b)** In quartets of type B, *t*_{0}=*t*_{13} and *t*_{1}=*t*_{24}, and so *Δ*_{int}(1,3) + *Δ*_{int}(2,4)=*Δ*_{JC}(1,3) + *Δ*_{JC}(2,4). However, *Δ*_{int}(1,2)=*Δ*_{int}(3,4)<*Δ*_{JC}(1,2)=*Δ*_{JC}(3,4), and so *Δ*_{int}(1,2) + *Δ*_{int}(3,4)<*Δ*_{JC}(1,2) + *Δ*_{JC}(3,4). Therefore, the deviation from additivity of *Δ*_{JC}* decreases* its FPM separation, denoted _{SEPJC}, compared to the FPM separation _{SEPint} of *Δ*_{int}. 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.

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