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Table 4 Alphabet size and performance.

From: Detecting coevolution without phylogenetic trees? Tree-ignorant metrics of coevolution perform as well as tree-aware metrics

(A) Tetrapod Myoglobin
Method A1 A2 A3 A4 A5
  τ p-value τ p-value τ p-value τ p-value τ p-value
MI -0.20 4.8 × 10-1 0.42 1.1 × 10-1 0.16 6.0 × 10-1 -0.33 2.2 × 10-1 0.24 3.8 × 10-1
NMI -0.29 2.9 × 10-1 0.24 3.8 × 10-1 0.24 3.8 × 10-1 0.16 6.0 × 10-1 0.56 2.9 × 10-3
RMI 0.11 7.3 × 10-1 0.33 2.2 × 10-1 -0.51 4.7 × 10-3 -0.02 1.0 0.64 9.1 × 10-3
SCA8 -0.24 3.8 × 10-1 0.78 9.5 × 10-34* 0.56 2.9 × 10-3 -0.02 1.0 0.87 1.2 × 10-34*
MIp 0.16 6.0 × 10-1 0.47 7.3 × 10-2 0.29 2.9 × 10-1 -0.11 7.3 × 10-1 0.78 9.5 × 10-34 *
AS -0.02 1.0 0.64 9.1 × 10-3 0.29 2.9 × 10-1 -0.47 7.3 × 10-2 0.07 8.6 × 10-1
G7 0.16 6.0 × 10-1 0.64 9.1 × 10-3 0.33 2.2 × 10-1 0.42 1.1 × 10-1 0.47 7.3 × 10-2
(B) Randomized Tetrapod Myoglobin
Method A1 A2 A3 A4 A5
  τ p-value τ p-value τ p-value τ p-value τ p-value
MI -0.38 1.6 × 10-1 -0.29 2.9 × 10-1 -0.07 8.6 × 10-1 0.16 6.0 × 10-1 0.60 1.7 × 10-3
NMI -0.29 2.9 × 10-1 -0.16 6.0 × 10-1 -0.47 7.3 × 10-2 -0.07 8.6 × 10-1 0.16 6.0 × 10-1
RMI -0.38 1.6 × 10-1 -0.29 2.9 × 10-1 -0.11 7.3 × 10-1 -0.16 6.0 × 10-1 0.56 2.9 × 10-3
SCA8 -0.73 2 2 × 10-3 -0.69 4.7 × 10-3 -0.60 1.7 × 10-3 -0.64 9.1 × 10-3 0.07 8.6 × 10-1
MIp -0.38 1.6 × 10-1 -0.69 4.7 × 10-3 -0.42 1.1 × 10-1 -0.11 7.3 × 10-1 0.29 2.9 × 10-1
AS -0.56 2.9 × 10-3 -0.42 1.1 × 10-1 -0.38 1.6 × 10-1 -0.38 1.6 × 10-1 -0.24 3.8 × 10-1
G7 0.60 1.7 × 10-3 0.29 2.9 × 10-1 -0.29 2.9 × 10-1 0.56 2.9 × 10-3 0.20 4.8 × 10-1
(C) Chordate Myosin
Method A1 A2 A3 A4 A5
  τ p-value τ p-value τ p-value τ p-value τ p-value
MI 0.78 9.5 × 10-34* 0.78 9.5 × 10-34* 0.64 9.1 × 10-3 0.60 1.7 × 10-3 0.82 3.6 × 10-34*
NMI 0.69 4.7 × 10-3 0.78 9.5 × 10-34* 0.56 2.9 × 10-3 0.29 2.9 × 10-1 0.82 3.6 × 10-34*
RMI 0.29 2.9 × 10-1 0.29 2.9 × 10-1 -0.07 8.6 × 10-1 -0.51 4.7 × 10-3 0.60 1.7 × 10-3
SCA6 0.56 2.9 × 10-3 0.20 4.8 × 10-1 0.16 6.0 × 10-1 -0.07 8.6 × 10-1 0.16 6.0 × 10-1
MIp 0.78 9.5 × 10-34* 0.78 9.5 × 10-34* 0.69 4:7 × 10-3 0.60 1.7 × 10-3 0.73 2.2 × 10-3
AS -0.16 6.0 × 10-1 0.29 2.9 × 10-1 0.73 2:2 × 10-3 0.42 1.1 × 10-1 0.29 2.9 × 10-1
(D) Randomized Chordate Myosin
Method A1 A2 A3 A4 A5
  τ p-value τ p-value τ p-value τ p-value τ p-value
MI -0.51 4.7 × 10-3 -0.33 2.2 × 10-1 -0.07 8.6 × 10-1 0.16 6.0 × 10-1 -0.16 6.0 × 10-1
NMI -0.20 4.8 × 10-1 -0.78 9.5 × 10-34* -0.29 2.9 × 10-1 0.51 4.7 × 10-3 0.20 4.8 × 10-1
RMI -0.33 2.2 × 10-1 -0.60 1.7 × 10-3 -0.24 3.8 × 10-1 0.16 6.0 × 10-1 -0.11 7.3 × 10-1
SCA6 -0.16 6.0 × 10-1 -0.56 2.9 × 10-3 -0.60 1.7 × 10-3 0.20 4.8 × 10-1 -0.24 3.8 × 10-1
MIp -0.29 2.9 × 10-1 -0.47 7.3 × 10-2 -0.64 9.1 × 10-3 0.38 1.6 × 10-1 -0.51 4.7 × 10-3
AS 0.20 4.8 × 10-1 0.20 4.8 × 10-1 -0.11 7.3 × 10-1 0.02 1.0 -0.11 7.3 × 10-1
  1. For each of the five heuristically defined alphabets, Kendall correlation coefficients (τ) and corresponding p-values are provided to illustrate the relationship between performance rank and alphabet size. Bolded values highlight p-values = 0.05, and starred values indicated p-values significant after adjustment for multiple comparisons (A-B Bonferroni-adjusted α = 0.0014, C-D Bonferroni-adjusted α = 0.0017). Tau range: [-1., 1.]. A positive τ value indicates a positive correlation (i.e., increased alphabet size is associated with increased performance), and a negative τ value indicates a negative correlation (i.e., decreased alphabet size is associated with increased performance).