what molecular clock might be useful to examine the evolutionary relationship between several phyla

Proc Natl Acad Sci U S A. 2007 Sep 25; 104(39): 15388–15393.

Evolution

Metabolic rate does not calibrate the molecular clock

Robert Lanfear

*Heart for the Written report of Evolution, Schoolhouse of Life Sciences, Academy of Sussex, E Sussex BN1 2LE, United Kingdom;

^†Centre for Macroevolution and Macroecology, School of Phytology and Zoology, Edifice 116 Daley Road, Australian National Academy, Human action 0200, Australia;

Jessica A. Thomas

*Eye for the Written report of Evolution, School of Life Sciences, University of Sussex, Eastward Sussex BN1 2LE, United kingdom;

^†Middle for Macroevolution and Macroecology, School of Botany and Zoology, Edifice 116 Daley Road, Australian National Academy, ACT 0200, Australia;

John J. Welch

*Center for the Written report of Development, School of Life Sciences, University of Sussex, East Sussex BN1 2LE, United Kingdom;

^‡Found for Evolutionary Biology, University of Edinburgh, Kings Buildings, Ashworth Laboratories, Westward Mains Road, Edinburgh EH9 3JT, U.k.; and

Thomas Brey

^§Alfred Wegener Found for Polar and Marine Inquiry, P.O. Box 120161, 27515 Bremerhaven, Germany

Lindell Bromham

*Centre for the Study of Development, School of Life Sciences, University of Sussex, Due east Sussex BN1 2LE, U.k.;

^†Center for Macroevolution and Macroecology, School of Phytology and Zoology, Building 116 Daley Road, Australian National University, ACT 0200, Commonwealth of australia;

Supplementary Materials: Supporting Appendices

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Abstract

Rates of molecular evolution vary widely among lineages, but the causes of this variation remain poorly understood. It has been suggested that mass-specific metabolic rate may be one of the primal factors determining the rate of molecular evolution, and that it can exist used to derive "corrected" molecular clocks. Yet, previous studies have been hampered by a paucity of mass-specific metabolic charge per unit data and have been largely express to vertebrate taxa. Using mass-specific metabolic rate measurements and Deoxyribonucleic acid sequence information for >300 metazoan species for 12 different genes, nosotros find no evidence that mass-specific metabolic charge per unit drives substitution rates. The mechanistic footing of the metabolic rate hypothesis is discussed in light of these findings.

Keywords: molecular development, phylogeny, molecular dating, metazoa, comparative method

Molecular dating (the employ of Dna sequences to estimate evolutionary deviation times) can provide extremely useful historical information on the timing of evolutionary events. Molecular dating analyses were initially premised on the supposition that the rate of molecular evolution is constant; however, in that location is increasing testify that the rate of molecular evolution varies widely among lineages (1–4). For example, previous studies accept indicated that smaller-bodied vertebrates tend to have higher rates of molecular development than larger-bodied vertebrates (two, 5, 6). One caption for this outcome is the metabolic rate hypothesis. This hypothesis suggests that smaller-bodied vertebrates generate higher levels of mutagenic oxygen radicals than larger vertebrates (v) as a consequence of their higher mass-specific metabolic rates (7). Oxygen radicals, which are byproducts of normal metabolism (8), can crusade damage to Dna in a variety of means, and this damage has been shown to induce mutations (9).

Although some studies have reported a correlation between mass-specific metabolic rate and molecular evolutionary rate (5, x), other studies using larger data sets found no evidence for the metabolic rate hypothesis, even when the covariation of metabolic rate with other life history variables (such as generation time) was taken into business relationship (ii, half-dozen). Despite this, a number of studies have invoked the metabolic rate hypothesis to explicate patterns of variation in the charge per unit of molecular evolution (5, 11, 12).

In a recent study, Gillooly et al. (13) used measurements of body size and temperature to derive predictions of metabolic charge per unit in a range of creature species and compared these predicted mass-specific basal metabolic charge per unit (BMR) values to substitution rates gathered from the literature. They concluded that "there is indeed a unmarried molecular clock… but that information technology 'ticks' at a constant exchange rate per unit of measurement of mass-specific metabolic energy rather than per unit of time" (13). Still, at that place are a number of reasons why this claim requires further empirical validation.

Get-go, as the authors acknowledge, their model did non distinguish between the metabolic rate and generation time hypotheses (the hypothesis that organisms with faster generation times tend to accumulate more copy errors and hence substitutions, per unit fourth dimension; e.g., ref. xiv). 2nd, only 10 of 60 data points in the study were invertebrates, which makes it difficult to assess the generality of the conclusions beyond vertebrate animals. Third, estimates of exchange rate were collected from the literature from studies by using widely differing methods and are thus non directly comparable (a point acknowledged by the authors). Fourth, independent contrasts were not used, which led to some data being counted multiple times in a unmarried analysis, violating the assumption of statistical independence inherent in the analyses.

To overcome limitations in previous studies, we undertook a taxonomically broad exam of the metabolic rate hypothesis among the Metazoa using measured values of mass-specific metabolic rate. Nosotros collected mass-specific BMR information from the literature and genetic data from GenBank (www.ncbi.nlm.nih.gov) for a range of >300 metazoan species from 11 different phyla, including representatives from all three major bilaterian clades (Ecdysozoa, Lophotrochozoa, and Deuterostomia). We and so used phylogenetic comparative methods (due east.g., ref. fifteen) to test for an association between mass-specific BMR and rates of molecular evolution. We found significant show of variation in the charge per unit of molecular evolution. However, we establish no evidence that the variation in the rate of molecular development is correlated with differences in mass-specific metabolic charge per unit.

Results

Evidence for Rate Variation.

Significant rate variation was observed in 9 of 12 genes and more than one-third of the comparisons used in this study [see Table 1 and supporting information (SI) Appendix one], despite the depression ability of Likelihood Ratio Tests to detect differences in the rate of molecular evolution (sixteen).

Table ane.

Summary of sequence data used in this analysis

Abridgement	Full proper noun	Genome	Coding	Comparisons
12S	12S RNA	Mitochondrial	RNA	36
16S	16S RNA	Mitochondrial	RNA	32
COX1	Cytochrome oxidase one	Mitochondrial	Protein	49
COX2	Cytochrome oxidase 2	Mitochondrial	Protein	2
CYTB	Cytochrome B	Mitochondrial	Protein	54
ND2	NADH dehydrogenase 2	Mitochondrial	Protein	11
ND5	NADH dehydrogenase 5	Mitochondrial	Protein	5
18S	18S ribosomal RNA	Nuclear	RNA	33
28S	28S ribosomal RNA	Nuclear	RNA	eighteen
H3A	Histone three blastoff	Nuclear	Protein	4
VWF	von Willebrand cistron	Nuclear	Protein	xiv
ATP7A	ATPase seven alpha	Nuclear	Poly peptide	3

No Bear witness for a Metabolic Charge per unit Effect.

Nosotros constitute no evidence for a human relationship betwixt mass-specific BMR and rate of molecular development. No pregnant clan betwixt substitution rate and mass-specific BMR was seen in any of the nonparametric sign tests, including those in which all comparison pairs were included and those in which dissimilar taxonomic or genomic (i.eastward., mitochondrial or nuclear) subsets of the data were analyzed independently (Table ii). Results were qualitatively identical if sign tests used only those comparisons with both significant variation in substitution rate and at to the lowest degree two-fold differences in mass-specific BMR (see SI Appendix 1). Tortoise/Hare sign tests, which included only those comparisons with the largest differences in mass-specific BMR, showed no significant association between mass-specific BMR and substitution rate, despite comparisons having an boilerplate 17-fold difference in mass-specific BMR (run into SI Appendix two).

Table 2.

Results of sign tests

Taxa	Genes	Poly peptide coding				RNA coding
Taxa	Genes	BL_dN (+/−)	P	BL_dS (+/−)	P	BL_T (+/−)	P
All	All	(53/54)	0.500	(56/58)	0.537	(52/39)	0.104
	Mitochondrial	(49/51)	0.540	(49/56)	0.721	(22/21)	0.500
Mammalia	Mitochondrial	(xviii/11)	0.133	(11/eighteen)	0.868	(19/11)	0.100
	Nuclear	(ix/5)	0.212	(9/5)	0.212	n/a	n/a
Aves	Mitochondrial	(8/15)	0.895	(12/12)	0.500	due north/a	n/a
Mollusca	Mitochondrial	(eleven/five)	0.105	(8/9)	0.500	(6/4)	0.377
	Nuclear	n/a	n/a	north/a	n/a	(v/v)	0.500
Arthropoda	Mitochondrial	(8/12)	0.748	(10/12)	0.584	(eleven/10)	0.500
	Nuclear	due north/a	north/a	north/a	n/a	(12/8)	0.252

Parametric regression revealed no significant association betwixt mass-specific BMR and substitution rate in any of the genes analyzed in any of the taxa. These included tests of both nuclear and mitochondrial genes in the Arthropoda (18S, COX1, and 16S), Mollusca (18S, COX1, and 16S) and Mammalia (VWF, CYTB, and 12S), and mitochondrial genes in the Aves (CYTB and ND2). Removal of outliers (see Methods) had no qualitative upshot on this result (Table 3). Z tests indicate there is no bear witness for an clan between BMR and commutation rate when the results of unlike regressions are combined across all taxa or combined separately within the Arthropoda, Mollusca, Mammalia, or Aves (Tabular array four).

Table 3.

Regressions of phylogenetically independent comparisons of molecular branch lengths on mass-specific BMR

Taxon	Gene	y axis	All data points				Outliers removed
Taxon	Gene	y axis	n	r ²	β	P	north	r ²	β	P
Arthropoda	18S	BL_T	13	0.027	0.123	0.573	10	0.120	0.262	0.297
Arthropoda	COX1	BL_dN	18	0.041	−0.192	0.408	14	0.028	0.124	0.551
Arthropoda	16S	BL_T	16	0.063	−0.148	0.327	14	0.026	−0.105	0.565
Mollusca	18S	BL_T	seven	0.059	0.209	0.564	6	0.064	−0.134	0.583
Mollusca	COX1	BL_dN	16	0.032	0.128	0.489	13	0.180	0.226	0.130
Mollusca	16S	BL_T	x	0.002	0.031	0.886	viii	0.002	−0.022	0.901
Mammalia	VWF	BL_dN	fourteen	0.136	0.153	0.176	11	0.006	0.018	0.813
Mammalia	VWF	BL_dS	13	0.001	0.012	0.929	11	0.114	0.176	0.282
Mammalia	CytB	BL_dN	28	0.002	−0.005	0.964	24	0.033	0.001	0.857
Mammalia	CytB	BL_dS	12	0.052	0.840	0.455	11	0.145	−0.462	0.222
Mammalia	12S	BL_T	29	0.008	−0.060	0.641	26	0.017	0.067	0.520
Aves	CytB	BL_dN	21	0.011	0.168	0.645	17	0.004	0.109	0.807
Aves	CytB	BL_dS	8	0.032	−0.395	0.644	7	0.003	0.155	0.893
Aves	ND2	BL_dN	10	0.051	−0.587	0.503	nine	0.247	−0.617	0.143
Aves	ND2	BL_dS	7	0.011	−0.259	0.804	6	0.099	−0.422	0.492

Table 4.

Results of Z tests on P values from regressions of substitution rates on life history traits

Trait	Taxon	n	P (all data points)	P (outliers removed)
BMR	All	fifteen	0.405	0.394
BMR	Arthropoda	3	0.764	0.270
BMR	Mollusca	three	0.207	0.314
BMR	Mammalia	v	0.227	0.341
BMR	Aves	iv	0.677	0.812
M	All	15	0.479	0.042^*
M	Arthropoda	iii	0.823	0.733
M	Mollusca	three	0.095	0.053
M	Mammalia	5	0.423	0.005^**
G	Aves	four	0.673	0.644
G	All	15	0.302	0.050
G	Arthropoda	iii	0.726	0.635
G	Mollusca	iii	0.071	0.062
G	Mammalia	v	0.462	0.065
G	Aves	north/a	n/a	n/a

Some Evidence for an Consequence Using Proxies of Metabolic Rate.

To facilitate comparing of our results with those of previous studies, we consider whether a previously reported predictor of mass-specific BMR [a function of body size and environmental temperature (17) that we term G] or body size (G) might explain some of the variation in substitution rates observed here. Both of these quantities have been reported to correlate with substitution rates, although these studies have been limited nigh exclusively to vertebrate taxa (2, 5, 6, xi, 18).

Afterward removing outliers (meet Methods), regression revealed significant positive correlations between 1000 and substitution charge per unit in 1 factor for mammals (VWF synonymous substitutions, P = 0.048) and one gene for molluscs (COX1 nonsynonymous substitutions, P = 0.012). A meaning negative correlation between body size (Thousand) and substitution rate was observed in i cistron for mammals (12S, P = 0.002).

Z tests betoken in that location is a highly pregnant negative association between body size and exchange rate across all taxa, (P = 0.042; Table 4), simply analyzing taxa separately suggests that this entirely stems from a strong result in the mammals (P = 0.005, with P > 0.05 in all other taxa; Table 4). Z tests bespeak that at that place are no pregnant associations between Thou and substitution rate in whatever taxa when treated individually (P > 0.05 in all cases; Table 4) or when results from all taxa are combined (P = 0.05; Table iv). These results are in accordance with previous studies, which show a significant torso-size result in mammalian species (ii) but find no evidence of a torso size effect in invertebrate species (3). Despite the lack of significant associations betwixt G and substitution rate in the Z tests, it is of note that P values obtained for G closely mirror those obtained for torso size (Table four). It therefore seems possible that Gillooly et al.'s (xiii) result primarily reflects a torso size issue on the rate of molecular evolution in mammals rather than a universal metabolic charge per unit event.

Discussion

The results of this study show no evidence that measured mass-specific BMR drives commutation rate in whatsoever of the genes or taxa studied. This result is in accord with previous studies, which find no show for the metabolic rate hypothesis in either mammals (2) or birds (vi). The parameter G (predicted metabolic rate based on temperature and body mass) explains a significant proportion of the variance in substitution rates in only 2 of xi data sets examined, and these correlations are not significant after correction for multiple tests (Table four). These results bandage doubt on the claim that there exists a single molecular clock that can be calibrated with measurements of body size and temperature. Because we analyze data sets from each of the three major groupings of the modern tree of bilaterians (Deuterostoma, Ecdysozoa, and Lophotrochozoa) and notice no show for the metabolic charge per unit effect, nosotros conclude that the metabolic rate effect is not a universal feature of metazoan molecular development.

We are confident there is sufficient power in our analysis to detect an effect of mass-specific metabolic charge per unit on commutation rate. First, we utilize the largest data set so far compiled to test the metabolic rate hypothesis. Second, nosotros clarify a broad range of taxa and genes, both together and separately, to reduce the possibility that a significant metabolic charge per unit effect in some taxa or genes was obscured by the lack of an outcome in other taxa or genes. Third, in the parametric regression we exclude very small or saturated branches and reanalyze the data after removal of outliers. Nosotros are therefore confident that the failure to detect an event was not considering of the influence of a small number of highly influential data points. Finally, the Tortoise/Hare sign tests, which use only those comparisons with the largest differences in mass-specific BMR, are unlikely to suffer a lack of power because of measurement error in mass-specific BMR, withal none of these tests show any bear witness of a relationship between metabolic charge per unit and rate of molecular evolution.

The Metabolic Charge per unit Hypothesis: A Reevaluation.

Although the mechanistic basis of the metabolic rate hypothesis is reasonable (v), a number of assumptions are made to link mass-specific BMR and commutation charge per unit (Fig. 1). The first assumption is that species with higher mass-specific BMR values take higher levels of oxygen radical product (Fig. 1, link i). Withal, in that location are at least two mechanisms by which this link between BMR and oxygen radical product may have been decoupled during metazoan evolution. First, the efficiency with which mitochondria generate ATP varies betwixt species. This tin lead to very different rates of mitochondrial oxygen radical generation in taxa with like mass-specific BMRs (8, 19–21). Second, mitochondrial oxygen radical production can be decoupled from oxygen intake (which is often used equally a proxy of BMR) by various mitochondrial proteins, which permit protons to leak across the mitochondrial membrane without the generation of ATP (22). In this way, it is possible for college rates of oxygen intake (and by inference, college mass-specific BMR) to be associated with lower rates of oxygen radical product.

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For mass-specific BMR to influence substitution rates every bit predicted by the metabolic charge per unit hypothesis, a number of assumptions must exist fabricated. In particular, each numbered link (discussed individually to a higher place) shown above indicates an assumption of a monotonic positive relationship between the two linked quantities.

The second supposition of the metabolic rate hypothesis is that the species with higher organism-broad rates of oxygen radical production will suffer higher rates of germ-line DNA harm (Fig. 1, link two). There are a number of reasons why this may not exist the case. Both the loftier reactivity of oxygen radicals and the presence of an assortment of antioxidant defenses (23) in eukaryotic cells mean that oxygen radicals practice not travel far. Indeed, although oxidative impairment to both mitochondrial and nuclear DNA is extensive in mammalian cells (24), oxygen radicals generated in the mitochondria are not responsible for the damage to nuclear DNA (25). It is therefore unlikely that the organism-wide rate of oxygen radical production provides a reliable guess of the concentration of oxygen radicals (and thus the oxygen radical induced Dna damage) in the germ-line tissue, particularly if the germ-line mitochondria are under pick to remain largely inactive (see, e.g., refs. 26 and 27).

The third supposition of the metabolic rate hypothesis is that species with higher levels of Deoxyribonucleic acid impairment should take higher mutation rates (Fig. 1, link iii). Although data on DNA repair in nonmodel organisms are scarce, at that place is prove that DNA repair efficiency varies in natural populations (28, 29) and may thus be influenced past natural selection. It is therefore possible that differences in Deoxyribonucleic acid repair efficiency may arise in response to changes in rates of Deoxyribonucleic acid impairment, which could confound any unproblematic relationship betwixt the charge per unit of DNA harm and the charge per unit of mutation. Finally, it is not certain that an increase in mutation rate will atomic number 82 to a proportionate increase in the rate of substitution (Fig. 1, link iv). Indeed, there are plausible models of adaptive exchange in which the two rates are largely independent (xxx).

In determination, there are a number of ways in which the relationship betwixt mass-specific BMR and commutation rate proposed by the metabolic rate hypothesis may be obscured. Many of the assumptions required for such a relationship practise not always hold, even among closely related species, and others are predicted to be direct counteracted by the furnishings of natural choice. Although there may exist a function for metabolically induced mutation in molecular development, particularly for the mitochondrial genome, the results presented in this study reject the hypothesis that mass-specific BMR is a universal commuter of rates of substitution.

Conclusions

This written report provides an empirical test of the hypothesis that metabolic rate is a primary determinant in variation in charge per unit of molecular evolution between species. We discover no evidence of whatever kind of association betwixt metabolic charge per unit and exchange rate for a wide range of fauna taxa and many dissimilar genes. Withal, we do notice some evidence of a body size effect on rates of molecular evolution in mammals. Our detection of the mammalian body size effect, which has been reported in several previous studies, suggests that our data set has sufficient ability to observe life history correlates of rates of molecular evolution. It seems possible that the torso size result explains why the proxy for metabolic rate used in a previous report has some explanatory ability for rate variation in several genes in mammals and molluscs; nonetheless, this requires further investigation. Even if the proxy, Grand, is shown to explain a significant proportion of variation in charge per unit of molecular evolution for some taxa, our results suggest two of import qualifications. First, the correlation betwixt G and substitution rate is not universal, but specific to particular genes and taxonomic groups. 2nd, we do non know the mechanism underlying the human relationship between G and substitution rate, only we are confident it is not explained by BMR. If information technology were, then nosotros would expect to come across a human relationship between substitution rate and metabolic rate. We find no hint of such a relationship in our database of 300 metazoan species, even when nosotros consider simply those comparisons with dramatic differences in metabolic charge per unit.

Methods

Data Collection.

Information on the BMR, body mass, and the temperature at which measurements were taken were collected from the literature. Nosotros excluded data that did not represent the BMR of the species under report (e.g., animals that were under stress, were non of representative adult mass, or were not measured within the normal temperature range of that species). When more than one measurement existed for a species, the arithmetic mean of all measurements was taken. If sample sizes were too reported, weighted arithmetic ways were calculated based on sample size. Much of the information for marine invertebrate species were taken from a database collated by T.B. (bachelor from the authors on asking), and the rest was taken from the literature (meet SI Appendices 1 and ii). Data for the Mammalia and the Aves were taken from contempo compendia (31, 32). For the Mammalia, measurements of mass-specific BMR from the Artiodactyla, Macropodidae, Lagomorpha, and Soricidae were excluded because of methodological difficulties in obtaining accurate measurements (32). In the Aves, BMR values were taken exclusively from wild-caught birds, because pregnant differences in BMR values accept been observed betwixt wild-caught and captive specimens (31). Nosotros converted all body mass data into grams of wet mass and all BMR data to mass-specific BMR in Watts per gram past using conversion factors gathered from the literature (see SI Appendices 1 and ii).

Available genetic information for each species were taken from GenBank (world wide web.ncbi.nlm.nih.gov). Where possible, nosotros included at least 1 example of a poly peptide- and RNA-coding cistron from both the mitochondrial and nuclear genomes for all species pairs. The final data gear up comprised seven mitochondrial (cytochrome oxidase 1, COX1; cytochrome oxidase 2, COX2; mitochondrial 12S RNA, 12S; mitochondrial 16S RNA, 16S; cytochrome B, CYTB; NADH dehydrogenase 2, ND2; and NADH dehydrogenase 5, ND5) and five nuclear (18S ribosomal RNA, 18S; 28S ribosomal RNA, 28S; histone 3 blastoff, H3A; von Willebrand factor, VWF; and ATPase alpha, ATP7a) genes, with each gene represented in an average of just over xl species (run across Table 1 and SI Appendix 1).

Comparative Method.

Most commonly used statistical tests presume that all data points are independent of one another. To avoid counting single instances of trait change multiple times, we use contained pairs of species from the last branches of the phylogeny (e.grand., ref. xv). In this method, each data indicate is calculated as the difference in the value of a trait betwixt a pair of lineages, where all pairs of lineages are monophyletic with respect to all other pairs. Considering reliable phylogenies are not available for many taxa included in this analysis, independent pairs were selected by using the taxonomy published on the National Center for Biotechnology Information'southward Taxonomy database (www.ncbi.nlm.nih.gov). To exercise this, we assumed that all families and genera were monophyletic, and we chose a maximum of one independent pair per genus. Where we had data for more than ii species in a particular genus, we chose the two that maximized the difference in mass-specific BMR. This arroyo yielded 156 contained comparisons from eleven phyla: 74 comparisons from the Chordata (comprising 48 pairs from Mammalia, 25 from Aves, and 1 from Ascidiacea); 36 from Arthropoda; 25 from Mollusca; 10 from Echinodermata; 3 from Cnidaria; 3 from Annelida; two from Nematoda; and 1 each from Chaetognatha, Nemertea, Platyhelminthes, and Porifera (run across SI Appendix 1). We avoid very deep comparison pairs (e.grand., between phyla), considering we are less confident that life history trait values of unmarried species are representative of widely divergent groups.

Exchange Rate Estimation.

Sequences were first aligned past eye into global alignments for each factor by using Se-Al (33). Regions of genes that could not be confidently aligned (e.g., hypervariable regions of rRNAs) were excluded. Triplet alignments of the two species in each comparison and one outgroup species (see SI Appendix one for accession numbers) were and so extracted from the global alignment and edited by hand. Alignments are available from the authors at world wide web.tempoandmode.com. Triplet alignments were used to estimate maximum likelihood co-operative lengths on unrooted trees with exchange rates free to vary across the tree (see SI Appendices 1 and 2). For each comparison, the National Center for Biotechnology Information'due south Taxonomy database was used to select the most closely related outgroup with appropriate sequence data. The branch length of each of the two ingroup species represents an estimate of the number of changes that have occurred in the Deoxyribonucleic acid sequence of each lineage since the two species diverged. Thus, the species with the longest co-operative length is inferred to have the higher rate of molecular development. For RNA-coding sequences, co-operative lengths were estimated past using baseml (34), with the TN93 (35) model of nucleotide substitution and gamma distributed rates across sites. This model was selected equally the best from the suite of 29 possible commutation models implemented in PAML using the Akaike Information Criterion (36); calculations were performed in MODELTEST version 3.6 (37). For coding sequences synonymous (dS) and nonsynonymous (dN), co-operative lengths were estimated in codeml (34), with codon frequencies estimated from the data and dN/dS ratios complimentary to vary across the tree. Model parameters were estimated independently for each triplet of species.

Statistical Analysis.

Each betoken in our analysis represents the deviation in a trait between ii sister species. The independent variable was calculated as ln(B ₁/B _ii), where B ₁ is the mass-specific BMR of species ane, B ₂ is the mass-specific BMR of species ii, and species 1 and species 2 are randomly assigned to the two species of a comparing pair. The dependent variable was calculated equally ln(λ₁/λ₂), where λ₁ is the branch length of species one, and λ₂ is the branch length of species ii. Comparisons in which one of the branch lengths was zippo were excluded from the assay.

We analyzed the information in two ways. First, nosotros tested for an clan between substitution rate and mass-specific BMR using a nonparametric sign test. For this test, nosotros score each comparison pair as a "+" if the sign of the difference in metabolic charge per unit and substitution rate are identical and every bit a "−" if the sign of the divergence in metabolic rate and commutation charge per unit are unlike. We and then assess whether in that location is a significant excess of either "+" or "−" signs by comparing our observed numbers of each to a binomial distribution. Considering the metabolic rate hypothesis is predicted to operate in a similar manner on all genes, and the sign test considers just the direction, not the magnitude, of the difference in substitution charge per unit, this examination allowed us to include branch length information from unlike genes (e.g., COX1 and ND2) into one analysis (see Tabular array 1). Yet, nosotros never included the same taxon multiple times in a single assay. In cases where one comparison had more than than one gene available within a particular subdivision of the data, we used co-operative lengths from the gene with the nearly meaning difference in substitution rate between the two species (assessed using a likelihood ratio test; see beneath), such that each comparison was represented only once in each sign test. Nosotros tested subdivisions of the data to define whether there was evidence for a metabolic rate effect on a universal scale (all genes in all taxa), a genome-specific scale (either mitochondrial or nuclear genes in all taxa), or a taxon- and genome-specific scale (either mitochondrial or nuclear genes in some taxa). Poly peptide and RNA coding sequences were treated separately in all cases, because previous studies have suggested that some patterns are axiomatic merely for analyses of protein coding sequences (meet, due east.g., ref. 2).

In the sign examination, it is important that the sign of the difference of a trait between a species pair (e.g., the difference in substitution rate or in metabolic rate) be known with confidence, because a small number of incorrect signs may drastically decrease the power of the test to discover an event. We therefore performed an additional sign test on each subdivision of the data prepare, where nosotros included only those comparisons in which the difference in substitution rate was significant, and in which the measured mass-specific BMR of the two species differed by ≥2-fold. Nosotros used a likelihood ratio test to ascertain the significance of the difference in commutation rate between the two ingroup species in each comparing pair. This test compares the likelihood of a tree in which the two ingroup species were forced to have the aforementioned rate of molecular evolution, to one in which their rates of molecular evolution were allowed to differ. Significance is assessed past comparing twice the difference in the likelihood scores of the ii trees to a χ² distribution with degrees of freedom equal to the difference in the number of parameters of the ii models (one in this example). Considering tests of this kind are known to have relatively low power to detect rate variation (16), significance levels of both 5% and 25% were used to assess the significance of rate variation. Although a 5% significance level is likely to exist conservative (i.e., exclude a number of comparisons which bear witness substantial charge per unit variation), a 25% significance level should exist thought of every bit removing those comparison pairs virtually likely to yield faux negatives in the sign tests. The results of analyses using both significance levels are presented.

Nosotros performed three additional sign tests to ensure that potential measurement error in mass-specific BMR was not influencing our ability to discover an consequence. These tests, which nosotros term Tortoise/Hare tests, included simply the 20 comparisons with the largest ratios in mass-specific BMR. The kickoff of these tests placed no restrictions on the significance of the deviation in branch lengths, the second considered only those comparisons with substitution rate variation meaning at the 5% level, and the third considered simply those comparisons with substitution rate variation significant at the 25% level.

In the 2nd set of analyses, we used blazon I (least squares) regression to test for an association between commutation rate and three possible independent variables: mass-specific BMR, body size, and the proxy of metabolic rate derived by Gillooly et al. (13). All regressions were forced through the origin. Contrasts in mass-specific BMR were calculated as above. Contrasts in trunk size were calculated as ln(M ₁/Grand ₂), where M ₁ is the average mass (in grams) of species ane, and G ₂ is the average mass of species ii. Contrasts in Gillooly et al.'s (13) proxy of mass-specific metabolic rate (here termed G) were calculated as ln(K ₁/One thousand ₂), where M ₁ is the average Grand for species one, and G ₂ is the average G for species 2. G values were calculated for each measurement for which both torso size and temperature information were bachelor, using the post-obit formula (17):

equation image

where b is a abiding that cancels out when ratios of G values are taken between comparison pairs (and whose value is thus unimportant), M is the mass (in grams) of the individual, T is the temperature (in Kelvins) at which the measurement was made, k is Boltzmann's constant, and E is the boilerplate activation energy, which is taken to exist 0.65 eV (13). Contrasts for G were not calculated for avian taxa, because measurements of temperature were non available, and assumption of a constant temperature for all avian taxa would simply reduce contrasts in G to exist equivalent to contrasts in G. Contrasts using M and G were calculated for iv boosted pairs of mammalian taxa, for which measured mass-specific BMR measurements were excluded because of methodological issues (encounter above). In full, 154 contrasts were calculated for M, and 116 contrasts were calculated for Chiliad.

In type I regression analyses, multiple genes cannot be combined in the same analysis, and so separate tests were carried out for each factor for which sufficient information were available (Table 2). These comprised two nuclear (18S and VWF) and five mitochondrial genes (COX1, 16S, 12S, CYTB, and ND2) from iv unlike taxonomic groups (Arthopoda, Mollusca, Mammalia, and Aves). Comparisons in which either ane of the co-operative lengths was very small (<0.0001 substitutions per site) were excluded, because the error variance in such short branches is likely to be high. Comparisons in which either one of the branches was saturated (branch length >1) were also excluded. Visual inspection of the data indicated that outliers may exist having undue influence on some results; nosotros therefore repeated each analysis afterward excluding outliers. Outliers were identified by beginning calculating the leverage, h_i , of each point every bit follows (38):

equation image

where n is the number of points in the analysis, x_i is the data bespeak of interest, and $\bar{x}$ is the arithmetics mean of x variable. We then excluded all points for which h_i >(4 p/due north), where p is the number of parameters of the model. This cutoff for h_i is twice that which indicates a highly influential point (38). This procedure was carried out on both the ten and y variables for each regression. Tests for homogeneity of variance were carried out equally described by Garland et al. (39), and contrasts were normalized with the foursquare root of the sum of the branch lengths when appropriate.

To combine tests performed on different taxa and different genes, the P values from the various regressions were analyzed by using the Z test (40). The Z test requires P values to be one-tailed. In this example, nosotros converted P values from regressions (which are 2-tailed) to one-tailed values by assuming that substitution charge per unit would be positively associated with BMR and K (every bit predicted by the metabolic rate hypothesis) and negatively associated with M (as observed by other investigators; encounter, east.g., ref. 2).

Supplementary Material

Abbreviation

Footnotes

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