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1 Testing the accuracy of ancestral state reconstruction The accuracy of the ancestral state reconstruction with maximum likelihood methods can depend on the underlying model used in the reconstruction. Thus, we performed several tests to confirm the robustness of our results with regard to the accuracy of the ancestral state reconstruction. First, we compared the TIR values obtained using 8 different models implemented in the PAML package 1 to verify that the high TIR ratio is not a factor of our model of choice. The TIR values we used for our main analyses obtained using the HKY model give the most conservative estimate of the deviation from the neutral expectation (Supplementary Table 1). Second, for the data from the HKY model we selected ancestral states that have been reconstructed with a high (> 0.9) posterior probability and obtained a TIR of 14.7 : 1 (235 : 16). Third, we measured TIR using only branches with a Ks < 1 obtaining a value of 3.3 : 1 (158 : 48) Finally, to eliminate the possibility of unspecified factors of the maximum likelihood methods affecting our results we reconstructed all ancestral states using parsimony as implemented in Mesquite 2 obtaining a TIR value of 11 : 1 and a Bayesian approach as implemented in SIMMAP 3 (Version 1.0 Beta 2.4) obtaining a TIR value of 4.3 : 1 (Supplementary Table 1). The ancestral states obtained using the Bayesian inference with a high posterior probability (>0.9) also showed a skewed TIR of 6.8 : 1 (390 : 57). Thus, the reported TIR values and the estimate of a 7-fold increase of clustering of compensatory substitutions obtained by maximum likelihood ancestral state reconstructions are conservative estimates. Taken together, these safeguards demonstrate that the difference of TIR from the neutral expectation cannot be caused by poorly reconstructed ancestral states, or the choice of model or method of ancestral state reconstruction. 1

2 Fluctuating negative selection In theory, fluctuating negative selection can lead to a deviation of TIR values from the 1:1 ratio in the same direction as that reported here for compensatory switches. To test this possibility we utilized a model of the effect of fluctuating selection on TIR from Bazykin et al.[4]. Briefly, the model assumes that negative selection in a lineage can switch on and off at random moments, with the expected waiting times for this to occur is T and bt, respectively. Thus, negative selection is present in a lineage with a probability of b/(1 + b) [4] and the skew of TIR from the 1 : 1 expectation increases with b. Since the rate of compensatory evolution is ~35 times slower than synonymous evolution, under the fluctuating selection model negative selection must have operated 97% of the time, implying a b of ~ The corresponding skew of the TIR value is less than 5% from the 1 : 1 expectation (see Supplementary Material in [4]), while the observed skew in complementary switches we observe in mt-trnas is ~700%. Thus, fluctuating selection in mt-trnas cannot account for our results. 2

3 Supplementary Table 1 Ancestral state reconstructions and their TIR value for AU-GC type of compensatory switches using different maximum likelihood models as implemented in the PAML package 19. The HKY85 model used for our analyses in the main text is shown in bold. GU-rich mt-trnas AC-rich mt-trnas Method Model Ancestral state AU or GC Ancestral state AC or GU TIR value Ancestral state AU or GC Ancestral state AC or GU TIR value Maximum Likelihood JC : : 1 K : : 1 F : : 1 F : : 1 HKY : : 1 T : : 1 TN : : 1 REV : : 1 Parsimony : : 1 Bayesian GTR : : 1 3

4 Supplementary Table 2 P-values of one-tailed Mann-Whitney U-test of the human mitochondrial minor allele frequency distributions. P-values of pairwise comparisons of the distribution of highly mutable alleles (G->A and T -> C on the AC-rich and A -> G and C -> T on the GT-rich strand) are above the diagonal and alleles with a low rate of mutation (A -> G and C -> T on the GT-rich strand and G->A and T -> C on the AC-rich strand) below the diagonal. AC alleles GU alleles Nonsynonymous alleles 4-fold synonymous alleles AC alleles < 1x10-6 GU alleles < 1x10-6 Nonsynonymous alleles < 2.8x fold synonymous alleles < 1x10-6 < 1x10-6 < 4.1x

5 Supplementary Table 3 Rates of mutation and polymorphic frequencies of GU and AC Watson-Crick pairs in mammalian mt-trna stems. P μ S GU in GU-rich trnas 1.7x x x10-3 GU in AC-rich trnas 3.9x x x10-3 AC in GU-rich trnas 2.0x x x10-2 AC in AC-rich trnas 1.4x x x10-2 *See Methods for estimate of the mutation rate. 5

6 Supplementary Table 4 Average frequencies of minor highly mutable (G->A and T -> C on the AC-rich strand and A -> G and C -> T on the GT-rich strand) alleles and alleles with low mutation rate (A -> G and C -> T on the ACrich strand and G->A and T -> C on the GT-rich strand) for 8 mammalian species. P-values of the Mann-Whitney U-tests between GC or AT WC pair disrupting alleles and nonsynonymous or synonymous alleles are shown in parentheses with significant differences in bold. Species (number of individuals) Canis familiaris Mutability of alleles Polymorphisms disrupting GC or AT WC pairs in mt-trnas Polymorphisms in nonsynonymous sites of mitochondrial genes Polymorphisms in 4-fold synonymous sites of mitochondrial genes High 4.8x x10-4 (p=0.28) 9.1x10-3 (p=3.7x10-5 ) (256) Low 1.9x x10-4 (p=0.45) 3.5x10-3 (p=0.035) Bos taurus High 2.7x x10-4 (p=0.47) 4.5x10-3 (p=5.7x10-6 ) (145) Low 1.7x x10-4 (p=0.45) 8.4x10-4 (p=0.01) Sus scrofa High 1.1x x10-4 (p=0.45) 3.0x10-2 (p< 4.0x10-6) (90) Low 6.1x x10-3 (p=0.48) 4.9x10-3 (p=0.046) Mus musculus High 9.9x x10-4 (p=0.41) 1.9x10-2 (p< 3.1x10-6 ) (73) Low 7.0x x10-4 (p=0.45) 3.3x10-3 (p=0.11) Ursus spelaeus High 2.8x x10-3 (p=0.0001) 3.1x10-2 (p< 2.6x10-6 ) (33) Low 1.0x x10-3 (p=0.008) 1.1x10-2 (p=0.0005) Mammuthus High 6.3x x10-4 (p=0.43) 9.3x10-3 (p=0.045) primigenius (20) Low x10-4 (p=0.43) 3.2x10-3 (p=0.21) Rattus norvegicus High 2.9x x10-3 (p=0.41) 2.0x10-2 (p=0.012) (16) Low 5.7x x10-4 (p=0.49) 4.0x10-3 (p=0.28) Ursus thibetanus High 4.7x x10-3 (p=0.44) 2.2x10-2 (p=0.0046) (12) Low 4.0x x10-3 (p=0.33) 1.2x10-2 (p=0.075) 6

7 Supplementary Figure 1 Reconstructed phylogenies of taxa not displayed in the main text. Cetartiodactyla (A), Primate (B) and Rodentia (C). Bos taurus Bos indicus Bubalus bubalis Capra hircus Ovis aries Pantholops hodgsonii Cervus nippon yesoensis Cervus nippon centralis Cervus nippon yakushimae Muntiacus crinifrons Muntiacus muntjak a Muntiacus reevesi 7

8 b Pan paniscus Pan troglodytes Homo sapiens Gorilla gorilla Pongo pygmaeus abelii Pongo pygmaeus Hylobates lar Macaca mulatta Macaca sylvanus Papio hamadryas Cercopithecus aethiops Trachypithecus obscurus Colobus guereza Cebus albifrons Lemur catta Nycticebus coucang Tarsius bancanus 8

9 Mus musculus molossinus Mus musculus Rattus norvegicus Nannospalax ehrenbergi Jaculus jaculus Cavia porcellus Thryonomys swinderianus Myoxus glis c Sciurus vulgaris 9

10 1. Yang, Z. PAML: A program package for phylogenetic analysis by maximum likelihood. Comput. Appl. Biosci. 13, (1997). 2. Maddison, W. P., & Maddison, D. R. Mesquite: a modular system for evolutionary analysis. Version (2009). 3. Bollback, J. P. SIMMAP: Stochastic character mapping of discrete traits on phylogenies. BMC Bioinformatics. 7, 88 (2006). 4. Bazykin, G. A., Kondrashov, F. A., Ogurtsov, A. Y., Sunyaev, S. & Kondrashov, A. S. Positive selection at sites of multiple amino acid replacements since rat-mouse divergence. Nature. 429, (2004). 10