On measuring selection in experimental evolution.

Abstract

Distributions of mutation fitness effects from evolution experiments are available in an increasing number of species, opening the way for a vast array of applications in evolutionary biology. However, comparison of estimated distributions among studies is hampered by inconsistencies in the definitions of fitness effects and selection coefficients. In particular, the use of ratios of Malthusian growth rates as 'relative fitnesses' leads to wrong inference of the strength of selection. Scaling Malthusian fitness by the generation time may help overcome this shortcoming, and allow accurate comparison of selection coefficients across species. For species reproducing by binary fission (neglecting cellular death), ln2 can be used as a correction factor, but in general, the growth rate and generation time of the wild-type should be provided in studies reporting distribution of mutation fitness effects. I also discuss how density and frequency dependence of population growth affect selection and its measurement in evolution experiments.

Full text

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Evolutionary biology
Opinion piece
On measuring selection in
experimental evolution
Distributions of mutation fitness effects from
evolution experiments
increasing number of species, opening the way
for a vast array of applications in evolutionary
biology. However, comparison of estimated dis-
tributionsamong studies
inconsistencies in the definitions of fitness effects
and selection coefficients. In particular, the use
of ratios of Malthusian growth rates as ‘relative
fitnesses’ leads to wrong inference of the strength
of selection. Scaling Malthusian fitness by the
generation time may help overcome this short-
coming,andallowaccurate
selection coefficients across species. For species
reproducing by binary fission (neglecting cellular
death), ln2 can be used as a correction factor, but
in general, the growth rate and generation time of
the wild-type should be provided in studies
reporting distribution of mutation fitness effects.
Ialso discusshowdensity
dependence of population growth affect selection
and its measurement in evolution experiments.
areavailable inan
is hamperedby
comparisonof
andfrequency
Keywords: mutation fitness effects; experimental
evolution; population growth; density dependence;
frequency dependence
1. INTRODUCTION
The aim of this opinion piece is to clarify the definition
and measurement of selection coefficients in evolution
experiments investigating fitness effects of mutations.
Such studies, from the accumulation of deleterious
mutations under relaxed selection over many gener-
ations [1–3] to the identification of spontaneous or
induced mutations as they arise [4–7], have generated
considerable interest recently (reviewed in [8,9]), nota-
bly because of their important bearings on many
questions across evolutionary genetics. First, they
allow testing theoretical predictions about the genetics
of adaptation, such as the size of beneficial mutations
that get fixed in a population, or the cost of complexity
for adaptation (reviewed in [10]). Second, they
uncover the intensity of deleterious mutation effects,
enabling quantitative predictions to be made about,
e.g. the evolution of recombination [11], of selfing
[12], or the extinction of small populations [13].
Third, they allow us to address fitness interactions
between genes (epistasis) and the ruggedness of fitness
landscapes [14–16], which determines the very nature
of the evolutionary process from a genetic standpoint.
Here I argue that one of the most popular measure-
ments of fitness in evolution experiments (the ratio of
Malthusian parameters)doesnothaveaclear
evolutionary meaning, and should be replaced by a
measurement relating more directly to the dynamics
of frequency change of mutations.
2. FITNESS AND SELECTION
The primary goal of measuring fitness effects of
mutations is to relate them to the evolutionary
dynamics of alleles under selection. This is quantified
by the selection coefficient s. Consider an asexual
(haploid) population consisting of two genotypes, a
mutant and a wild-type, with population sizes (or
density) M and N, and frequencies p and (1 2 p).
With continuous growth and no age structure, the
selection coefficient can be defined as
?
[17], which has units of time21. The frequency of the
mutant increases if s . 0 and decreases if s , 0, at a
speed determined by s. Since the ratio of allelic fre-
quencies is also the ratio of numbers (or densities) of
each genotype, we may also write
s ¼d
dtln
p
1 ? p
?
ð2:1Þ
s ¼dlnM
dt
?dlnN
dt
:
ð2:2Þ
In particular, if selection is density independent and
there are no interactions between genotypes, then
s ¼ rm? rw;
where r is the Malthusian parameter [17] or intrinsic
rate of increase of each genotype (m, mutant; w,
wild-type).
In practice, r is estimated as the regression slope of
log-population size against time in the exponential
phase, that is, at low population density (assuming
no Allee effects). Note that selection can be density
independent even if population growth is density
dependent, but this implies that the genotype which
initially grows faster also has a higher carrying capacity
(figure1a,firstrow;
material, appendix; see also [18,19]). When this is
valid, s is constant and from equation (2.1), the ratio
of genotypic frequencies increases exponentially in
time (figure 1a, second row), resulting in a logistic tra-
jectory of the mutant frequency in time. Moreover, in
this case, equation (2.3) holds whether each r is
measured from cultures of each genotype in isolation,
or in a competition experiment mixing both genotypes.
However, when in competition, more statistical signifi-
cance can be obtained by estimating s directly from
equation (2.1) [20].
If selection is density dependent, the selection coef-
ficient changes with population size (figure 1b), so that
measuring the growth rate in the exponential phase is
not sufficient to estimate s. Similarly, with genotype-
by-genotype interactions in fitness, s changes with the
relative frequencies of each genotype (figure 1c).
Disentangling these two possible causes of changes in
s (density dependence and frequency dependence)
requires combining a competition experiment with
cultures of each genotype in isolation (electronic
supplementary material, appendix).
Most population genetic models are formulated in
discrete non-overlapping
ð2:3Þ
electronicsupplementary
generationsratherthan
Electronic supplementary material is available at http://dx.doi.org/
10.1098/rsbl.2010.0580 or via http://rsbl.royalsocietypublishing.org.
Biol. Lett. (2011) 7, 210–213
doi:10.1098/rsbl.2010.0580
Published online 1 September 2010
Received 26 June 2010
Accepted 11 August 2010
210
This journal is q 2010 The Royal Society

Page 2

continuous ones as above, and in this case, an equivalent
to equation (2.1) is
?
with primes denoting values in the next generation, and
the subscript T indicating that the evolutionary change
is taken over a generation. In this case, if selection is den-
sity independent and there are no genotype-by-genotype
interactions, then
?
with lmand lwthe density-independent components of
the per-generation multiplicative growth rate of each
genotype (electronic supplementary material, appen-
dix). With overlapping (but discrete) generations, such
that the population is structured by ages, or if life
stages can be identified (such as larva, juvenile, adult),
equation (2.5) is also valid for asexuals (and can be
used as a weak-selection approximation for sexuals) if
l is the leading eigenvalue of the projection matrix of
transition rates (juvenile/adult survival and fecundity)
[21,22, p. 61].
Hence, with discrete generations, the ratio lm/ lwof
the fitness of the mutant to that of the wild-type
sT¼ ln
p0=ð1 ? p0Þ
p=ð1 ? pÞ
?
¼ ln
M0=N0
M=N
??
;
ð2:4Þ
sT¼ ln
lm
lw
?
?lm
lw? 1;
ð2:5Þ
(or ‘relative fitness’, unitless) determines the evolution-
ary dynamics. Note that l is necessarily positive (and
the population size decreases if l , 1), while r can be
negative for a decreasing population. Because a
negative r cannot be measured starting from a small
population, some authors have pooled all mutants
with (unmeasured) negative growth rates into the
class r ¼ 0 (sometimes labelled as ‘lethals’), thus
artificially inflating this class [6,7,23].
Although equations (2.3) and (2.5) are classical
results in population genetics [22,24], a persistent tra-
dition in experimental evolution has been to measure
relative fitness in continuously growing populations
as rm/rw, that is, as a ratio of Malthusian parameters
[6,7,23,25–28]. Accordingly, the selection coefficient
of a mutation is often inferred from demographic
parameters as sr¼ rm/rw2 1, mirroring the definition
in discrete-time models
[7,9,29,30]. However this measure does not directly
relate to the evolutionary dynamics of mutations,
even for density-independent selection with no inter-
actions between genotypes. Notably, since sr¼ s/rw, it
would predict faster evolution per unit time in a popu-
lation with the smaller growth rate rwof the wild-type,
while the actual evolutionary dynamics is the same
if s is equal. This has important consequences for
any application of these measures to questions in
fromequation (2.5)
50 100150 200
20 000
60 000
100 000
20 000
60 000
100 000
20 000
60 000
100 000
20 000
60 000
100 000
20 000
60 000
100 000
20 000
60 000
100 000
100200
time (generations)
300400500600
2
10
50
200
50100150200
1.0
1.5
1.1
1.3
50100150200
2004006008001000
0.001
0.010
0.100
1.000
p/(1–p)
population size
(competition)
population size
(isolation)
(a)(b)(c)
time (generations)time (generations)
Figure 1. Selection and demography in isolation versus competition. The population sizes of two genotypes grown in isolation
(first row: dark grey, wild-type; light grey, mutant) or in competition (second row: dark grey area, wild-type; light grey area,
mutant) are shown together with the ratio of genotypic frequencies in competition (third row: note the logarithmic scale on
the y-axis) for three demographic scenarios. Scenario (a) leads to frequency- and density-independent selection. Scenario
(b) illustrates frequency-independent but density-dependent selection, in the particular case where both genotypes have
the same carrying capacity K. In this case, s tends to 0 as the population approaches the carrying capacity. In scenario (c),
selection is density-independent but frequency-dependent. Recursions were made from the discrete-generation model in
equation (A2) from the electronic supplementary material, appendix, with logistic population growth, using lw¼ 1.08,
lm¼ 1.09, Kw¼ 100 000 in all scenarios, and Km¼ Kwln(lm)/ln(lw) and iw¼ im¼ 1 in (a); Km¼ Kwand iw¼ im¼ 1 in
(b); Km¼ Kwln(lm/lw), iw¼ 1 and im¼ 0.98 in (c).
Opinion piece. Fitness in experimental evolution
L.-M. Chevin211
Biol. Lett. (2011)

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evolutionary biology where the magnitude of fitness
effects of mutations is critical [11–13,31].
3. COMPARING SELECTION COEFFICIENTS
The motivation for presenting results in terms of ‘rela-
tive Malthusian fitness’ in experimental evolution has
been to obtain a dimensionless parameter [20], allow-
ing for comparison between genotypes and species
with different generation times. For instance, a selec-
tion coefficient measured in h21(say, for Escherichia
coli) is not comparable to one measured in days21
(say, for Caenorhabditis elegans). The important ques-
tion for comparative purposes is how fast evolution
occurs per generation. A dimensionless measurement
of selection that allows comparison between studies
carried out over different time scales is then
sT¼ ðrm? rwÞT;
where T is the generation time [22, p. 178]. Electronic
supplementary material, table S1, shows an overview
of some of the relevant literature where fitness is
measured in continuous time (that is, not from survival
and fecundity per generation). In six out of nine
articles, the selection coefficient per unit time s, or
per generation sT, is not provided and cannot be esti-
mated, because only ratios of Malthusian fitness are
given, not the fitness of the wild-type rw. In only one
article is rwgiven, so sTcan be estimated using the gen-
eration time reported in another study for the same
organism (yeast). In two cases, the selection coefficient
that is provided is directly sT, since it is a difference of
Malthusian fitnesses measured as growth rates per gen-
eration, not per unit time. Overall, the available data
make it difficult to compare selection coefficients
across species and studies.
Generation times can also vary among mutants.
This may even be the main cause of genetic variation
in growth rates (per unit time) for some organisms
and life cycles [32]. In this case, T should be replaced
by Tw, thus measuring how fast evolution occurs rela-
tive to the generation time of the wild-type (or
‘resident’) genotype [30]. In particular, selection coef-
ficients are often measured for unicellular organisms
that reproduce by binary fission. In this case, neglect-
ingcellulardeaths,the
(division events) of the wild-type per unit time is
simply rw/ln2, and the generation time of the wild-
type is ln2/rw. A correct measure of the dynamics of
selection per generation for species reproducing by
binary fission (neglecting cellular death) is then
ð3:1Þ
numberofgenerations
sT;bin¼rm? rw
rw
ln2:
ð3:2Þ
Note that if the focus of the study is fixation prob-
abilities rather than the (deterministic) evolutionary
dynamics, then Tmshould be used as a scaling factor
instead of Tw, thus measuring the expected lifetime
reproductive output of the mutant. This should affect
the shape of the distribution of s, since a different scal-
ing factor would be used for each mutant. None of the
studies reported in electronic supplementary material,
table S1, provided information about variation in gen-
eration times among mutants. Besides, comparison of
expected fixation probabilities across species based
solely on measures of selection coefficients from fre-
quency changes is not to be recommended anyway,
since for a given s, fixation probabilities can differ
widely depending on how stochasticity affects offspring
numbers [33].
4. CONCLUSION
Although distributions of mutation fitness effects are
being measured in a growing number of organisms,
lack of consistency between estimates still prevents
proper comparison of selection coefficients for differ-
ent species, even when selection is density and
frequency independent. In particular, the use of rela-
tive Malthusian fitness results in overestimating the
per-generation strength of selection (in terms of evol-
utionary dynamics) by a factor (ln2)21? 1.44 for
species that reproduce by binary fission (neglecting
cellular deaths), and by an undetermined factor in
other cases. It is worthwhile noting that this bias has
no effect on the shape of the distribution and on the
coefficient of variation of selection coefficients of
mutations originating from a given genotype, an
important parameter relating to the effective number
of phenotypic traits under selection and to the ‘cost
of complexity’ for adaptation [9,34]. Apart from this,
the fitness effects of mutations across species should
be re-examined in the light of the present argument,
with particular attention to comparisons between
species that reproduce by binary fission and others.
I thank Thomas Lenormand, Guillaume Martin, Arpat
Ozgul, Lilia Perfeito, Gabriel Perron, Olivier Tenaillon and
an anonymousreviewerfor
comments on an earlier draft. This work was supported by
a Newton International Fellowship by the Royal Society.
helpfuldiscussionsand
Luis-Miguel Chevin*
Division of Biology, Imperial College London, Silwood
Park, Buckhurst Road, Ascot SL5 7PY, UK
*l.chevin@imperial.ac.uk
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