"Do all mammals exhibit 
heterogeneity in their mutation 

rates? Do all yeasts exhibit 
uniformity?" 



V A R Y I N G PATTERNS OF M U T A T I O N 

Measuring the Universality of Regional Mutation Rates 

A L E A H F O X 

M U T A T I O N S A R E T H E U L T I M A T E S O U R C E O F G E N E T I C V A R I A T I O N I N D N A . T H E 

P A T T E R N S O F M U T A T I O N , H O W E V E R , C A N V A R Y B O T H W I T H I N A N D A C R O S S G E N O M E S . 

I T H A S P R E V I O U S L Y B E E N S H O W N T H A T S E V E R A L M A M M A L S H A V E H E T E R O G E N E O U S 

M U T A T I O N R A T E S , W H I L E F O U R Y E A S T S H A V E B E E N O B S E R V E D T O H A V E U N I F O R M 

R A T E S . T H E G E N E R A L I T Y O F T H E S E O B S E R V A T I O N S H A S N O T B E E N K N O W N . H E R E W E 

E X A M I N E S I L E N T S I T E S U B S T I T U T I O N S I N C O D I N G R E G I O N S O F 20 M A M M A L S , 27 

Y E A S T , A N D 4 I N S E C T S , T O D E T E R M I N E W H I C H G E N O M E S D E M O N S T R A T E T H I S M O S A I C 

R A T E D I S T R I B U T I O N A N D W H I C H A R E U N I F O R M . O U R F I N D I N G S S H O W T H A T 

M U T A T I O N A L H E T E R O G E N E I T Y O C C U R S I N A L L B R A N C H E S O F T H E M A M M A L I A N 

P H Y L O G E N Y , A S W E L L A S I N F L I E S A N D M O S Q U I T O E S . A L L Y E A S T S H A V E A U N I F O R M 

R A T E A C R O S S T H E I R G E N O M E S W I T H T H E E X C E P T I O N O F T H R E E CANDIDA S P E C I E S ! 

C . ALBICANS, C. D U B L I N I E N SIS, A N D C . TROPICALIS. W E H Y P O T H E S I Z E T H A T T H I S I S 

D U E T O T H E L A C K O F S E X U A L R E C O M B I N A T I O N I N T H E S E S P E C I E S , L E A D I N G T O T H E 

R E G I O N A L A C C U M U L A T I O N O F M U T A T I O N S . 



B A C K G R O U N D 

Popular understanding of gene mutations often focuses on 
those that have obvious effects, such as insects that develop 
resistance to pesticides. However, the majority of muta-
tions have neither a positive nor a negative impact because 
they do not affect functional regulatory elements, which 
generally make up a small percentage of the genome. 
These mutations are known as "neutral mutations." The 
presence and rate at which these mutations occur can be 
used to illuminate evolutionary relationships between dif-
ferent species, as well as to distinguish areas of functional 
regulatory elements from non-functional DNA, a process 
called "phylogenetic footprinting." Though neutral muta-
tion rates were once considered to be uniform, it has been 
discovered that they can vary dramatically, not only from 
one species to the next but also within a single genome.1 

Within-genome heterogeneity has been demonstrated in 
several investigations of mammalian species.u"vn I n these 
species, the rate of neutral mutations is different in differ-
ent regions of the genome, such as that of Chromosome i 
compared to that of Chromosome 4. In contrast, uniform 
mutation rates have been observed only in the phylogeny of 
the sensu stricto yeasts S. cerevisiae, S. paradoxus, S. bayanus, 
and S. mikatae.vm I n these species, neutral mutations 
occur at the same rate in the entire genome. The reason for 
this differing mutational behavior is not known, and little 
is known about regional biases in other species. A better 
characterization of regional biases would improve funda-
mental understanding of DNA mutation. It would also aid 
i n the calibration of phylogenetic footprinting methods, 
which are used to detect sequences under purifying selec-
tion. For example, uncertainties in regional mutation bi-
ases have hindered estimates of the amount of functional 
human DNA. i x 

Most previous studies of mutation rate variation have fo-
cused on mammals, including human, chimp, mouse, rat, 
dog, and cow. Such studies have identified regional effects 
by studying the correlation of independent neutral meas-
ures, such as single nucleotide polymorphism (SNP) den-
sity, insertion-deletion (indel) density, substitution rate in 

ancestral repeats, or substitution rates in silent sites.x 

Regional effects have also been characterized via the length 
scales at which nearby neutral sequences are correlated, as 
well as via the strength of correlations within single 
genes.X1 Proposed causes of mutation rate variation have 
included regional variations in base composition, recombi-
nation, gene density, or pattern of gene expression/1 1 

Unfortunately, the causes of variation in these other fea-
tures are not clearly understood either. Regional effects 
must be different in yeast since yeast chromosomes are typ-
ically only one-hundredth as long as human chromosomes. 
The length scales of these various types of mammalian re-
gional variation are often as large as a yeast chromosome. 

A n important step toward understanding the causes of mu-
tational heterogeneity is to measure which species have 
heterogeneous mutation rates and which species have ho-
mogeneous mutation rates. In this work, we analyze re-
gional mutational biases in 20 mammalian, 27 yeast, and 4 
insect genomes, determining which clades (taxonomic 
groups) have uniform and which have heterogeneous mu-
tation rates. We answer the questions: Do all mammals ex-
hibit heterogeneity in their mutation rates? Do all yeasts 
exhibit uniformity? Studying these phylogenies together 
provides a valuable contrast. 

RESULTS 

There are many sequences in the genome that can be used 
to determine the neutral mutation rate, such as pseudo-
genes, ancestral repeats, intergenic regions and synony-
mous sites. In this work, we focus on synonymous sites, 
and in particular, four-fold degenerate sites, from coding 
regions in 51 species. These sites can be altered without af-
fecting the encoded amino acid sequence. While recent 
studies indicate that some synonymous sites are under se-
lection, the majority are still likely to be neutral. x i l i To iso-
late lineage-specific effects, species were analyzed in pairs 
with species close to them in the phylogenetic tree. Yeast 
species pairs were determined from the tree of 42 fungal 
species of Fitzpatrick et a l . x i v For the mammals, species 
pairs were chosen based on recent ENCODE (the 

E L E M E N T S S P R I N G 08 



Encyclopedia of DNA Elements Project) and whole-
genome-based phytogenies X V X V 1 Raw substitution rates 
were calculated for each orthologous gene pair (pairs of 
similar genes in different species) by counting the fraction 
of observed substitutions at four-fold sites and then nor-
malizing to z-score values (see Methods). x v n This z-score 
normalization corrects for the stochastic finite-size effects 
that result from genes having different numbers of four-
fold sites. 

Y E A S T 

The distribution of normalized substitution rates provides 
a test of whether substitution rates are uniform throughout 
a genome. Our yeast phylogeny is comprised of 27 
species, and we have calculated substitution rates between 
26 species pairs, based on choosing those which are closely 
related in the phylogeny. In genomes with uniform 
rates, such as S. cerevisiae, the distribution of z-scores is 
very close to a normal distribution with a standard 
deviation of one . x v m However, in heterogeneous genomes 
such as mouse and human, the width of the z-score 
distribution is considerably larger, due to the tendency of 

sites in the same gene to be subject to similar mutational 
pressures (Figure ia). We find that the distributions of 
normalized rates for 22 of the 27 yeast species (23 species 
pairs) fit the normal distribution with unit standard 
deviation (Average s = 1.32, range = [1.02 - 1.40]). This 
indicates that there are generally not regions of high or low 
neutral mutation rates within these genomes (Figure ib). 
As in the sensu stricto yeasts, these 22 yeast species tend to 
have a slight excess of genes with low silent substitution 
rates. This can be explained by codon usage selection. 
The tail at negative z-scores is mainly comprised of riboso-
mal and carbohydrate catabolism genes that are under 
selection for codon usage bias. x l x Of the 432 genes with 
z-scores < -2 in the S. cerevisiae - S. bayanus comparison, 201 
(46.5%) have a ribosomal or metabolism GO annotation. 
Similarly, in the distinct lineage D. hansenii - C. guillier-
mondii, 138 of 253 genes (54.5%) with z-score < -2 map to r i -
bosomal or metabolism GO categories. One caveat is that 
this z-score approach is less applicable for comparisons of 
species with saturated divergence. Of the full set of 26 
species pairs, we observe 8 with less than 90% of the diver-
gence that would be expected at saturation, given the base 

THIS IS THE DISTRIBUTION OF NORMALIZED 4-FOLD SUBSTI-

TUTION RATES FOR MAMMALS AND YEASTS. THE NORMAL 

GAUSSIAN DISTRIBUTION (SMOOTH CRAY LINE) IS WHAT 

WOULD BE EXPECTED IF ALL 4-FOLD SITES IN EACH CENE 

HAVE AN EQUAL AND INDEPENDENT PROBABILITY OF BEING 

SUBSTITUTED. 

TOP: ALL MAMMALIAN DISTRIBUTIONS HAVE A BIAS TOWARD 

HIGH AND LOW SUBSTITUTION RATES, CONSISTENT WITH RE-

GIONAL MUTATION BIASES IN MAMMALIAN GENOMES. 

MIDDLE: MOST YEAST DISTRIBUTIONS FIT MORE CLOSELY TO 

THE GAUSSIAN, EXCEPT FOR A TAIL OF GENES WITH LOW SUB-

STITUTION RATES STEMMING FOR CODON USAGE SELECTION. 

BOTTOM: THIS I S THE DISTRIBUTION OF C. ALBICANS, C. 

DUBLIENSIS, C. TROPICALIS, N. CRASSA, A N D C. CLOBOSUM. 

THESE SPECIES HAVE A WIDER DISTRIBUTION SIMILAR TO THE 

MAMMALIAN DISTRIBUTION. 

M E A S U R I N G T H E U N I V E R S A L I T Y O F R E G I O N A L M U T A T I O N R A T E S 



T A B L E 1 : P E A R S O N C O R R E L A T I O N F O R T H E S U B S T I T U T I O N R A T E O F N E I G H B O R I N G G E N E S 

A V E R A G E N U M B E R O F P E A R S O N 

S P E C I E S 1 S P E C I E S 2 D I V E R G E N C E O R T H O L O G S C O R R E L A T I O N P - V A L 

S_CEREVISIAE S_PARADOXUS 0 . 2 5 9 2 4 4 3 4 0 . 0 2 3 4 0 . 1 1 8 8 THE DATA COLLECTED WAS FROM 

S_CEREVISIAE S_BAYAN YUS 0 . 4 7 0 9 3781 0 .0305 0 . 0 6 0 6 2 6 SPECIES PAIRS A M O N G 2 7 

S_CASTELLII S_M 1 KATAE 0 . 6 5 8 5 3 2 4 7 0 . 0 0 2 9 0 . 8 6 4 9 YEASTS, AVERAGE DIVERGENCE 

K_LACTIS C_GLABRATA 0 . 6 5 4 5 4 0 7 7 -0 .0135 0 . 3 8 8 7 IS THE FRACTION OF ALL 

D_HAN S EN 1t C_LUSITANIAE 0 . 6 9 2 6 3 4 2 5 0 .041 7 0 . 0 1 4 4 AL IGNED 4-FOLD SITES W H I C H 

D_HANSENII C_GUILLIERMONDII 0 . 6 8 4 2 3 5 3 8 0 .0221 0 . 1 8 8 3 DIFFER BETWEEN THE TWO 

D_HAN S E N 11 L_ELONGISPORUS 0 . 6 6 2 8 3 3 4 5 0 .0083 0 . 6 2 7 5 SPECIES. PEARSON 

D_HANSENII C_PARAPSILOSiS 0 .6561 3 3 2 4 0 . 0 2 5 7 0 . 1 3 7 8 CORRELATIONS FORTHE NOR-

D_HAN S EN 11 C_TROPICALIS 0 . 6 1 0 4 3 3 5 8 0 .0073 0 .6685 MALIZED SUBSTITUTION RATES 

E_GOSSYPII S_POMBE 0 . 7 6 1 6 1 5 3 6 0 . 0 8 3 7 0 . 0 0 1 0 OF NEIGHBORING GENES ARE 

E_COSSYPII Y_LIPOLYTICA 0 . 7 1 1 4 2 4 4 1 0 . 0 2 9 7 0 . 1 4 1 4 SHOWN IN COLUMN 5. THE 

Y_LIPOLYTICA M_GRISEA 0 .6751 2 4 6 4 0 . 0 4 1 0 0 . 0 4 1 8 ONLY SPECIES WITH PEARSON 

Y_LIPOLYTICA A_N1DU LANS 0 . 7 0 7 2 2 5 1 5 0 . 0 1 6 2 0 . 4 1 5 6 
CORRELATION WITH 

Y_LIPOLYTICA C_IMMITIS 0 . 7 1 0 9 2 5 8 4 0 .0021 0 . 9 1 1 7 SIGNIFICANCE < 0 .001 ARE 

Y_LIPOLYTICA S_POMBE 0 .7271 1 2 7 0 0 . 0 4 0 4 0 .1495 
THOSE AMONG C. 

0 .6551 1461 0 . 0 5 4 9 0 . 0 3 5 8 
DUBLINIENSIS, C. ALBICAN, AND 

S_POMBE SJAPONICUS 0 .6551 1461 0 . 0 5 4 9 0 . 0 3 5 8 
DUBLINIENSIS, C. ALBICAN, AND 

SJAPONICUS 

0 .2893 3 7 9 6 0 . 2 1 7 6 6.3 E -42 
C. TROPICALIS. 

C_DUBLINIENSIS C_ALBICANS 0 .2893 3 7 9 6 0 . 2 1 7 6 6.3 E -42 
C. TROPICALIS. 

C_DUBLINIENSIS C_TROPICALIS 0 .5522 3 5 1 4 0 . 1 0 2 9 9.8 E - 1 0 

C_TROPICALIS C_PARAPSILOSIS 0 . 6 0 5 9 3 3 9 0 0 . 0 4 2 6 0 . 0 1 3 0 

CTROPICALIS L_ELONGISPORUS 0 . 6 2 5 7 3 4 4 2 - 0 . 0 2 2 7 0 . 1 8 1 8 

N_CRASSA C_GLOBOSUM 0 . 5 8 4 2 2 3 6 9 -0 .0085 0 . 6 7 5 7 

U_REESII C_IMMITIS 0 .5293 9 1 7 - 0 . 0 5 1 3 0 .1201 

A_N1DU LANS A_TERREUS 0 . 6 3 6 4 1121 0 . 0 3 7 0 0 . 2 1 4 7 

H_CAPSU LATUM C_IMMITIS 0 . 6 8 3 9 8 4 7 0 . 0 3 5 6 0 . 2 9 9 9 

H_CAPSU LATUM U_REESII 0 . 6 6 5 5 393 0 . 0 0 3 4 0 . 9 4 5 9 

L_ELONGISPORUS C_PARAPSILOSIS 0 .6363 3 1 5 2 0 .0265 0 . 1 3 6 6 

T A B L E 2: M A M M A L I A N P A I R W I S E C O M P A R I S O N S 

P A I R A V E R A G E N U M B E R P E A R S O N 

N U M B E R S P E C I E S 1 S P E C I E S 2 D I V E R G E N C E O R T H O L O G S C O R R E L A T I O N P - V A L 
1 H U M A N MOUSE 0 . 3 3 1 7 1 7 1 1 2 0 . 2 3 0 6 2.0E -205 MAMMALIAN PAIRWISE COMPAR-

2 H U M A N DOG 0 .2451 1 6 5 3 2 0 . 3 0 1 7 9.8E -247 ISONS. 4-FOLD SITE 

3 H U M A N CAT 0 . 2 4 1 7 7 5 2 9 0 .3263 2 . 5 E - 1 8 6 DIVERGENCE BETWEEN THE TWO 

4 H U M A N COW 0 .5761 6 9 7 2 0 . 0 5 4 0 6 . 2 E - 0 6 SPECIES IS SHOWN IN COLUMN 

5 DOG CAT 0 .1831 12931 0 . 2 4 3 8 1 . 9 E - 1 7 4 
3. PEARSON CORRELATIONS FOR 

6 CAT MOUSE 0 .3581 6 7 2 6 0 . 2 2 9 2 6 . 0 E - 8 1 
THE NORMALIZED 

0 . 1 5 8 6 
SUBSTITUTION RATES OF NEIGH-

7 RAT MOUSE 0 . 1 5 8 6 2 0 0 5 4 0 . 1 5 7 6 I . O E - 1 1 1 
BORING GENES ARE SHOWN IN 

8 MOUSE RABBIT 0 . 3 6 0 6 1 2 4 4 2 0 .1851 2 . 2 E - 9 6 
COLUMN 5. EVERY MAMMALIAN 

0 .1851 2 . 2 E - 9 6 
COLUMN 5. EVERY MAMMALIAN 

9 EURO. HEDGEHOG TENREC 0 . 3 6 7 9 2 3 6 0 0 . 1 9 6 8 4 . 6 E - 2 2 
COMPARISON SHOWS A SIGNIFI-

1 0 EURO. HEDGEHOG TREE SHREW 0 . 3 3 2 2 1 6 5 0 0 . 3 1 3 2 6 . 7 E - 3 9 CANT CORRELATION BETWEEN 

1 1 BUSHBABY OPOSSUM 0 . 4 5 9 9 1 2 9 2 2 0 . 2 0 9 7 2 . 0 E - 1 2 8 RATES OF NEIGHBORING GENES 

1 2 COW DOG 0 . 2 5 3 2 16941 0 . 2 6 0 6 4.4E -261 (COLUMN 6). 

1 3 COW CAT 0 . 2 5 3 0 13355 0 . 2 6 2 6 1 .5E -209 

1 4 DOG MOUSE 0 . 3 5 5 0 1 6 5 2 2 0 . 2 1 5 2 2 . 4 E - 1 7 2 

1 5 COW MOUSE 0 . 3 6 4 6 1 7 3 4 0 0 . 2 1 5 2 6 . 5 E - 1 8 1 

1 6 H U M A N MACAQUE 0 .0673 1 6 0 0 0 0 . 2 7 5 4 2 . 0 E - 2 7 6 

1 7 BAT RAT 0 . 3 6 2 7 5 9 3 8 0 . 1 9 9 5 2 . 2 E - 5 4 

1 8 MACAQUE C H I M P 0 . 0 7 1 0 1 7 6 2 1 0 . 2 2 3 1 1.1 E - 1 9 7 

1 9 ARMADILLO ELEPHANT 0 . 2 5 2 7 2 0 4 5 0 . 1 9 4 8 5 . 9 E - 1 9 

2 0 MOUSE SQUIRREL 0 . 3 3 0 4 1 2 7 9 4 0 . 1 7 8 9 1 .4E-92 

21 TENREC ELEPHANT 0 .2741 2 2 4 4 0 . 1 6 6 7 1 . 8 E - 1 5 

22 C O M M O N SHREW TREE SHREW 0 . 3 4 4 2 2 1 2 4 0 .2503 I .OE-31 

23 DOC BAT 0 . 2 4 5 9 1 3 6 6 9 0 . 3 5 2 7 < E - 2 7 6 

24 COW BAT 0 . 2 5 7 9 1 4 1 7 4 0 . 3 3 9 8 < E - 2 7 6 

25 OPOSSUM PLATYPUS 0 . 4 9 9 2 9 7 8 6 0 .2701 3 . 3 E - 1 6 3 



F I G U R E 2: A U T O C O R R E L A T I O N O F N O R M A L I Z E D S U B S T I T U T I O N 

R A T E S F O R P A I R W I S E A N A L Y S E S 

F I G U R E 3: C A I V S . N O R M A L I Z E D S U B S T I T U T I O N R A T E S F O R 

SENSU STRICTO Y E A S T S A N D N. CRASSA 

ALBICANS A N D C. DUBLIENSIS 

5 0 0 0 0 1 E + 0 5 0 5 0 0 0 0 1 E + 0 5 

D I S T A N C E B E T W E E N G E N E S ( B P ) 

RATES ARE NOT CORRELATED ALONG THE GENOMES IN FIGURE 2A. ANALAGOUS GRAPHS WERE PRODUCED FOR ALL YEAST 

SPECIES PAIRS, EACH INDICATING NO AUTOCORRELATION ALONG THE GENOME, EXCEPT FOR THE C. DUBLI ENSIS/C. AL-

BICANS A N D C. TROPICALIS/C. DUBLIENSIS COMPARISONS. THOSE PAIRS SHOW THAT RATES OF NEIGHBORING GENES 

ARE CORRELATED UP TO 50 KB APART. 

F I G U R E 4: A U T O C O R R E L A T I O N O F N O R M A L I Z E D S U B S T I T U T I O N 

R A T E S A T 4 - F O L D D E G E N E R A T E S I T E S 

CAI VS. Z-SCORE FOR N. CRASSA 

C O W A N D D O G A U T O C O R R E L A T I O N H U M A N A N D M A C A Q U E A U T O C O R R E L A T I O N 
1.2 

5E+06 I E + 0 7 1.5E+07 0 5E+06 1E+07 

D I S T A N C E B E T W E E N G E N E S ( B P ) 

AUTOCORRELATION FOR NORMALIZED SUBSTITUTION RATES AT 4-FOLD DEGENERATE SITES 

BETWEEN COW AND DOC (LEFT) AND HUMAN AND MACAQUE (RIGHT). BOTH GRAPHS 

SHOW CORRELATION OF RATES FOR GENES WITHIN WMB OF EACH OTHER. 

Z-SCORE 

THESE ARE GRAPHS OF CAI VS. NORMALIZED SUBSTITUTION RATES FOR SENSU 

S T R I C T O Y E A S T S (S. CEREVISIAE, S. BAYANUS, S. MIKATAE, S. PARADOXUS) (BOT-

TOM) AND N. CRASSA (TOP). IN EACH GRAPH, THERE IS A LARGE CLUSTER OF 

GENES WITH LOWER CAI VALUES AND SUBSTITUTION RATES DISTRIBUTED 

AROUND ZERO. EACH GRAPH ALSO CONTAINS A SECOND GROUP OF GENES WITH 

HIGHER CAI VALUES AND LOWER SUBSTITUTION RATES, AND SUCH GENES ARE 

L I K E L Y TO B E UNDER CODON USAGE SELECTION. THE SENSU STRICTO Y E A S T S 

HAVE 727 GENES THAT HAVE CAI VALUES GREATER THAN 0.40 WHILE N. CRASSA 

HAS 949 WITH CAI VALUES GREATER THAN 0.70, SUGGESTING THAT MORE GENES 

A R E UNDER CODON USAGE SELECTION IN N. CRASSA. THE N. CRASSA CODON 

USAGE TABLE WAS USED TO CALCULATE CAI VALUES IN THE TOP GRAPH AND THE 

S. CEREVISIAE CODON USAGE TABLE WAS USED TO COMPUTE THE CAI VALUES IN 

THE BOTTOM GRAPH. 

CAI VS. Z-SCORE FOR SENSU STRICTO YEAST 

Z-SCORE 



F I G U R E 5: C O M P A R I S O N O F T H E W I D T H S O F T H E R A T E D I S T R I B U T I O N S 

M A M M A L S U N I F O R M N O N - U N I F O R M 

Y E A S T Y E A S T 

THE BLUE LINE AT S = 1 SHOWS THE EXPECTED STANDARD DE-

VIATION FOR A NORMAL DISTRIBUTION. 

THE MAMMALS HAVE AN AVERAGE STANDARD DEVIATION OF 

2.056, INDICATING THEIR BIAS TOWARD BOTH HIGH AND 

LOW RATES. 

THERE ARE THREE YEAST PAIRWISE COMPARISONS (C. 

DUBLINIENSIS/C. ALBICANS, C. TROPICALIS/C. DUBLI N I E N SIS, 

AND N. CRASSA/C GLOBOSUM) WHICH HAVE UNUSUALLY 

WIDE RATE DISTRIBUTIONS (SEE FIGURE lc). FOR THESE 

COMPARISONS, THE AVERAGE S IS 1.825. THE REMAINING 22 

YEASTS HAVE A NOTICEABLY LOWER VALUE OF S (AVERAGE 

S=7.32, RANCE = [1.02- 1.40], CONSISTENT WITH THEIR HAV-

ING M 

compositions of these species (see Methods). 

The inference that there is no neutral mutational variation 
within these 22 yeast genomes is further supported by a 
neighboring gene analysis. For each pair of species, the 
Pearson correlation was calculated for the rates of substitu-
tion of neighboring genes (see Methods). These results are 
shown in Table 1, with the 22 homogeneous genomes 
shown in black. There was no significant correlation for 
any of the species pairs made up of two members from 
these 22 genomes. The same results were obtained irre-
spective of which species in the pair was used to specify 
gene locations. 

More generally, an autocorrelation function <r x ^r(o)> was 
computed, where r(o) is the normalized substitution rate of 
a gene and r 1 ^ is the normalized substitution rate of a gene 
that is x base pairs downstream of the first gene.x x The rates 
are normalized around r = 0 so we would expect < r ( o ) r l 6 > 
~ o i f there are no regional rate biases (see Methods). The 
autocorrelation reveals no significant correlation between 
neighboring genes at any finite separation (Figure 2a). 
This shows that these yeast species do not demonstrate the 
heterogeneous mutation rates that have been observed in 
mammals. 

Species pairs from two subclades [(C. albicans, C. dublinien-

sis, C. tropicalis) and (N. crassa, C. globosum)] were found to 
have distributions that did not fit the normal curve. These 
species have substitution rate distributions biased toward 
high and low rates (2.07 < s < 2.20) (Figure ic). This phe-
nomenon mirrors that which has been observed for 
human-mouse substitution rates (see also Figure i a ) . x x l 

For the three Candida species, the autocorrelation analysis 
shows that substitution rates are significantly correlated for 
genes within 50,000 base pairs of each other (Figure 2b). 
This result implies that regional biases extend over scales 
encompassing over 20 genes, since in C. albicans the spac-
ing between genes is 2300 b p . ™ 1 The neighboring gene 
Pearson correlations were also significant (C. 
dubliniensis/C. albicans Pearson correlation = 0.218, p = 6.4 
x io"4 2 ; C. tropicalis/C. dubliniensis Pearson correlation = 
0.103, P = 9-8 x 10-10). SNPs within the C. albicans genome 
have been shown to be unevenly distributed along 
contigs, x x m in agreement with regional mutational biases. 
These regional effects are not due to a CpG dinucleotide ef-
fect. When we excluded CpG sites from the analysis, neigh-
boring genes were still observed to have correlated substi-
tution rates (Pearson-correlation = 0.1096, p < 10"^). 
These Candida species translate CUG as serine instead of 
the usual leucine, and it might be hypothesized that this is 
relevant to the rate inferences.XX1V However, ignoring these 
codons does not significantly diminish the correlation (C. 

E L E M E N T S : : S P R I N G 08 



dubliniensis/C. albicans Pearson correlation = 0.208, p = 10" 
*7). 

Like the Candida species, the species N. crassa and C. globo-
sum have a rate distribution that is wider than the normal 
Gaussian. However, there is no significant rate correlation 
(Pearson correlation = -0.0085, P = 0-6757) between neigh-
boring genes, and the autocorrelation plot appears nearly 
identical to those of the yeast with uniform rates. These 
seemingly contradictory results suggest that the wide dis-
tribution of rates (s = 2.07) is due to pressures on individual 
genes, rather than regional effects. 

We hypothesized that the large s without apparent regional 
correlation could be related to increased selection on the 
silent sites of N. crassa and C. globosum genes. Such selec-
tion could cause some genes to have more extreme conser-
vation, broadening the rate distribution. To test this, we 
considered the codon usage bias in these species, which is 
the best understood type of silent site selection in yeasts. 
Our results indicate that codon usage selection is a stronger 
effect in N. crassa and C. globosum genomes than in sensu 
stricto yeasts. CAI values were calculated for each of N. 
crassa and S. cerevisiae based on their respective codon bi-
ases (Figure 3). N. crassa genes generally have higher CAI 
values (median 0.63) than S. cerevisiae genes (median 0.14). 

In each of the genomes, there is one main cluster of genes 
having z-scores distributed around zero and low CAI val-
ues. Then there is another group having negative z-scores 
and high CAI, and this group is presumably under codon 
usage selection. N. crassa appears to have more genes i n 
the group under codon usage selection (949 genes above 
CAI = 0.7) than S. cerevisiae (121 genes above CAI = 0.4). 
This suggests that codon usage selection affects more 
genes in N. crassa/ C. globosum, and could be responsible for 
the large s in these genomes. 

M A M M A L S 

Al l 20 mammalian species appear to have heterogeneous 
mutation patterns, as evidenced by their wide rate distribu-
tions (1.80 < s < 2.23) (Figures ia and 5). The Pearson cor-
relations (Table 2) and autocorrelations of nearby genes 
(Figure 4) for each pair-wise mammalian comparison are 
all significant. For example, in the cow/human compari-
son, the autocorrelation graph suggests mutational blocks 
along each chromosome as large as 10Mb, similar to the 
length scale that has previously been observed in mouse 
and human. 

The regional variations are also apparent from correlation 
analysis of ancestral repeats, another largely neutral scat-
tered throughout the genome. x x v We analyzed the 18-way 
vertebrate multi-species alignments from UCSC to obtain 

TABLE 3: C O R R E L A T I O N O F S U B S T I T U T I O N A L R A T E S IN N E I G H B O R I N G A N C I E N T R E P E A T S 

N U M B E R P E A R S O N 

S P E C I E S 1 S P E C I E S 2 O F R E P E A T S C O R R E L A T I O N P - V A L 

5 0 8 1 4 2 6 0 . 3 2 1 9 2 < E - 2 7 6 

1 3 7 8 6 9 9 0 . 1 8 8 2 9 < E - 2 7 6 

ELEPHANT 2 4 8 5 7 7 0 . 1 2 1 5 8 < E - 2 7 6 

2 3 1 2 8 3 0 . 1 2 9 2 < E - 2 7 6 

M E A S U R I N G T H E U N I V E R S A L I T Y O F R E G I O N A L M U T A T I O N R A T E S 

IN ALL FOUR MAMMALIAN PAIRS 

CONSIDERED (HUMAN-MACAQUE), 

(DOC-COW), (ELEPHANT-TENREC), AND 

(RAT-MOUSE), THE CORRELATIONS WERE 

E X T R E M E L Y SIGNIFICANT (<1(T^^). 

THIS SUPPORTS THE WIDESPREAD 

HETEROGENEITY OF MUTATION RATES 

IN MAMMALIAN GENOMES. 



48 

a stringent set of ancestral repeats aligned orthologously 
across the species pairs (human, macaque), (mouse, rat), 
(elephant, tenrec), and (dog, cow). We observed that an an-
cestral repeat's substitution rate is significantly correlated 
with that of the neighboring ancestral repeat along the 
genome, for each of the species pairs (Table 3). In each case 
the significance of the correlation was at the l imi t of com-
putational precision (p < 10 

• 2 76). 
The wide distribution of 

ancestral repeat normalized rates mimics those in Figures 
ia and ic, with standard deviations ranging from 1.41 (ele-
phant-tenrec) to 1.96 (human-macaque). 
1N s E C T S 

The yeast species we have studied are at phylogenetic dis-
tances that are generally larger than those for the mam-
malian species. In principle, it is more difficult to measure 
regional variations when inferring rates from more dis-
tantly related species. This is because as species approach 
saturated divergence, all mutation rate inferences become 
increasingly uncertain. Therefore one might be concerned 
that the greater divergence among the yeast species ob-
scures regional effects. 

This hypothesis can be tested by using insect genomes, sev-
eral of which are at phylogenetic divergences as large as 
that of the yeasts. In particular, D. melanogaster and D. 
pseudoobscura are at a separation generally larger than that 
of the mammalian species (four-fold divergence = 0.514) 
and comparable to that of most of the yeast pairs, as are the 
two mosquitoes A. aegypti and A. gambiae (4-fold diver-
gence = 0.632). 

In contrast to the yeasts, flies and mosquitoes both show 
clear evidence of regional effects. D. melanogaster and D. 
pseudoobscura have neighboring genes with significant rate 
correlations at distances up to ~iMb apart (Pearson correla-
tion = 0.1642, p = 9.06-59) and a wide rate distribution (s = 
2.152). This effect is also observed in A. aegypti and A. gam-
biae (Pearson correlation = 0.2099, P = 2.16-89). The width 
of the distribution of normalized rates is s = 1.804. Each of 
these insect lineages demonstrate correlations which are 

more statistically significant than the most significant yeast 
comparison, C. albicans and C. dubliniensis, despite the fact 
that the two Candida species have a lower divergence 
(0.289) than the insects. Therefore, we can conclude that 
the predominant lack of correlations for the yeasts is not an 
artifact of their larger phylogenetic separations. 

C O N C L U S I O N S A N D D I S C U S S I O N 
Based on our examination of 20 mammalian species, we 
conclude that all mammals have regional biases of neutral 
mutation rates. While the factors controlling these re-
gional biases are still not well understood (e.g. base compo-
sition, local recombination rate, pattern of gene expression, 
gene density and DNA repair domain) , X X V 1 our findings in-
dicate that any valid explanations must occur throughout 
the mammalian phylogeny. In contrast, we find that almost 
all yeasts have a uniform neutral mutation rate. This con-
clusion is supported by a recent report that S. cerevisiae 
polymorphism rates are not correlated along the 
genome. x x v n 

The monophyletic group of the three Candida species (C. 
albicans, C. dubliniensis, and C. tropicalis) is an exception to 
the other yeasts. Both the distribution of rates and gene-to-
gene correlations indicate that these species have heteroge-
neous mutation rates, a trait which had not previously been 
observed outside the mammals. Previous studies of SNP 
data also indicate hotspots of polymorphism, supporting 
the concept of regional biases. x x v m 

What characteristic sets these three yeasts apart from the 
others? One intriguing trait is meiosis. Unlike other yeasts, 
sexual reproduction appears to be rare in C. albicans, C. 
dubliniensis, and C. tropicalis. Sexual reproduction in C. al-
bicans and C. dubliniensis was recentiy discovered under 
specialized laboratory conditions; however, no evidence for 
meiosis has been found. x x l x The sexual cycle of C. tropicalis 
has not been extensively explored, but meiosis has not been 
observed for it either. On the other hand, comparative ge-
nomic studies of the uniformly mutating C. glabrata sup-
port a complete sexual cycle, x x x and so-called "defects" in 

E L E M E N T S S P R I N G 08 



the mating type locus of C. parapsiolosis suggest that it is un-
likely to have mating similar to C. albicans and C. dublinien-
s is . 5 ™ Thus, the Candida species without evidence for 
meiosis are the ones with heterogeneous neutral mutation 
rates. How could a lack of meiosis influence regional mu-
tation rates? One possible explanation is that the lack of 
meiosis prevents recombination between homologous 
chromosomes. I f recombination were to cause random 
fluctuations in chromosome length, this could have the ef-
fect of smoothing out regional mutational biases. 

A comparison of N. crassa and C. globosum also fails to give 
a normal distribution of substitution rate z-scores, but this 
is due to stronger codon usage selection, rather than re-
gional mutation effects. This stronger codon usage selec-
tion is more apparent in the context of a mutational defense 
mechanism that N. crassa employs against selfish DNA. 
The mechanism, known as repeat-induced point mutation 
(RIP), protects against selfish DNA by inducing G:C to A:T 
mutations during sexual reproduction and by methylating 
cytosine residues in duplicated sequences/™ 1 This 
process affects all duplicated regions except for ribosomal 
RNA genes, even though these occur i n large copy num-
b e r . ™ 1 This observation is consistent with ribosomal 
genes being under strong codon usage selection and hence 
being more conserved at synonymous sites. RIP drives 
other duplicated genes in N. crassa to unusually high sub-
stitution rates, which would explain the genes with high 
scores i n the rate distribution. The wide substitution rate 
distribution is likely due to RIP in just N. crassa, as the phe-
nomenon has not been observed in C. globosum. 

M E T H O D S 

O R T H O L O C G E N E R A T I O N 

For the yeast analysis, FASTA files of coding regions and an 
ortholog tree listing predicted gene relationships between 
all 32 yeast species were obtained as described in Tsong 
et a l . x x x l v Mammalian and mosquito genes were obtained 
using the ENSEMBL BioMart (release 45) database. 
Fly CDS and peptide files were downloaded from FlyBase 
(version FB2oo6_oi). For the fly species, the amino acid 

sequences were run through BLAST and tagged as true or-
thologs i f they were each other's mutual best hit when ap-
plying BLASTALL with a worst-case E-value cutoff of 10" 1 0 . 

C A L C U L A T I O N O F S U B S T I T U T I O N R A T E S 

Our substitution rate calculations parallel those in previous 
w o r k s . x x x v x x x v l Nucleotide sequences of orthologous cod-
ing regions were translated into amino acid residues, 
aligned using CLUSTALW, and then back-translated to de-
termine the aligned DNA sequence. The four-fold synony-
mous sites—the third base i n a codon for which the amino 
acid is determined by the first two positions—were ana-
lyzed. I f a sequence contained fewer than 20 four-fold sites 
before occurrence of a stop codon, the entire sequence was 
discarded. To ensure equivalent sequence context, only 
four-fold sites for which both the preceding and succeeding 
base matched for the two species were considered. 

The raw neutral substitution rate was calculated based on 
the fraction of observed differences at silent sites within a 
gene. Individual gene rates were then normalized i n order 
to correct for the finite-size of each gene (Table 1 & 2), and 
this new rate was defined to be 

r=(p-<p>)/s(N), 
where p is the observed four-fold substitution rate for the 
gene i n question and <p> is the average substitution rate 
for all ortholog pairs for the two species in question. s(N) 
was defined to be the expected standard deviation for a gene 
with N independent four-fold sites, i.e. s(N) = (<p>(i-
<p>) /N) 1 / 2 . The distribution of the normalized substitu-
tion rates would be expected to follow a normal Gaussian 
(f(x) = e x " x / 2 / V(2TT)) i f each four-fold site was mutating at 
the same rate and independently of each other. 

C O R R E L A T I O N C A L C U L A T I O N S 

We tested whether or not neighboring genes had similar 
substitution rates by calculating a Pearson correlation be-
tween the rate of gene r(o) and the rate of gene r 1 ® which is 
located x base pairs downstream. Gene pairs in ortholo-
gous blocks up to the 35th gene downstream from the start-
ing gene were considered. Blocks were determined by 

M E A S U R I N G T H E U N I V E R S A L I T Y O F R E G I O N A L M U T A T I O N R A T E S 



genes located on the same chromosome (scaffolds were 

used when chromosomal data was not available). 

Correlations were measured twice, in each case using loca-

tion data from one of the species, except in cases where lo-

cation data was available in only one species. For yeast, the 

data for each pairwise calculation was binned into 50 uni-

formly spaced groups covering x = {o, 300000} and aver-

aged over each bin to determine the autocorrelation func-

tion <r(o)r x ^>. Error bars were assigned based on the 

standard deviation of the values in each bin. For the larger 

genomes of mammals and insects, data was binned into 

200 groups where x ranged from o to 15Mb. 

C A I 

CodonW (Peden 1999) was downloaded and used to calcu-

late the CAI values for the yeast species. The input file for 

each species was a CDS FASTA file of all genes (predicted 

and known) and the background CAI was set to 

Saccharomyces cerevisiae for all sensu stricto. The EMBOSS 

package was also downloaded locally. This includes codon 

usage tables for a number of species including N. 

crassa.xxxvn This table was used to calculate the CAI for the 

genes in N. crassa. 

E N D N O T E S 

i . Baer 2007 
i i . Chuang 2004 
i i i . Lercher 2001 
vi . Liu 2006 
v. Malcom 2003 
vi . Matassi 1999 
v i i . Wolfe 1989 
v i i i . Chin 2005 
ix. Pheasant 2007 
x. Hardison 2003 
xi . Chuang 2004 
xi i . Baer 2007 
xi i i . Chamary 2006 
xiv. Fitzpatrick 2006 
xv. Murphy 2007 
xvi. Nikolaev 2007 
xvii . Chuang 2004 
xvii i . Chin 2005 
xix. Ibid. 
xx. Ibid. 
xxi. Chuang 2004 

xxii. M I 2007 
xxii i . Lott 2005 
xxiv. Yokogawa 1992 
xxv. Lunter 2006 
xxvi. Baer 2007 
xxvh. Ruderfe 2006 
xxviii. Jones 2004 
xxix. Pujol 2004 
xxx. Wong 2003 
xxxi. Logue 2005 
xxxii. Selke 1990 
xxxiii. Vyas 2005 
xxxiv. Tsong 2006 
xxxv. Chuang 2004 
xxxvi. Chin 2005 
xxxvii. Ikemura 1985 

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