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

Table 2 Tree-aware methods compared on myoglobin and myosin.

(A) Tetrapod Myoglobin
	GCTMPCA (ε = 0.70)		LnLCorr99		LnLCorr07		Ancestral States		CoMap
	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	χ ²	p – value
(i,i+3)	0	53	1	5	0	7	2	51	0	9	7.51	1.11 × 10^-1
(i,i+4)	10	43	0	6	0	7	4	49	0	9	6.75	1.50 × 10^-1
(B) Randomized Tetrapod Myoglobin
	GCTMPCA (ε = 0.70)		LnLCorr99		LnLCorr07		Ancestral States		CoMap
	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	χ ²	p – value
(i,i+3)	1	52	0	6	0	7	0	53	0	9	1.43	8.40 × 10^-1
(i,i+4)	0	53	0	6	0	7	0	53	0	9	n/a	n/a
(C) Chordate Myosin
	GCTMPCA (ε = 0.70)		LnLCorr99		LnLCorr07		Ancestral States		CoMap
	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	χ ²	p – value
(i,i+3)	-	-	5	1	-	-	41	12	8	1	0.69	7.09 × 10^-1
(i,i+4)	-	-	2	4	-	-	48	5	8	1	14.18	8.33 × 10 ^-3
(D) Randomized Chordate Myosin
	GCTMPCA (ε = 0.70)		LnLCorr99		LnLCorr07		Ancestral States		CoMap
	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	p ≤ α	p > α	χ ²	p – value
(i,i+3)	-	-	0	6	-	-	7	46	0	9	2.21	3.31 × 10^-1
(i,i+4)	-	-	0	6	-	-	0	53	0	9	n/a	n/a

χ² goodness-of-fit tests comparing the performance of tree-aware methods for detecting alpha helix periodicity at (i, i + 3) and (i, i + 4). Counts are calculated for GCTMPCA with the empirically validated optimal ε = 0.70. In most cases, there is no statistically significant difference in performance between the tree-aware methods with the single exception being (i, i+ 4) in myosin, where AS and CoMap out-perform LnLCorr99. Data is not presented on the myosin alignment for tree-aware methods which proved too computationally intensive to be practical. Counts in Table 2 can be directly compared with counts in Table 3. α = 0.01.