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Measuring Selection Coefficients Below 10−3 INVESTIGATION Measuring Selection Coefficients Below 1023: Method, Questions, and Prospects Romain Gallet,* Tim F. Cooper,† Santiago F. Elena,‡,§ and Thomas Lenormand*,1 *CEFE–UMR 5175 1919 route de Mende, F-34293 Montpellier, CEDEX 5, France, †Evolution and Ecology Group, Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204, ‡Instituto de Biología Molecular y Celular de Plantas (CSIC-UPV), 46022 València, Spain, and §Santa Fe Institute, Santa Fe, New Mexico 87501 ABSTRACT Measuring fitness with precision is a key issue in evolutionary biology, particularly in studying mutations of small effects. It is usually thought that sampling error and drift prevent precise measurement of very small fitness effects. We circumvented these limits by using a new combined approach to measuring and analyzing fitness. We estimated the mutational fitness effect (MFE) of three independent mini-Tn10 transposon insertion mutations by conducting competition experiments in large populations of Escherichia coli under controlled laboratory conditions. Using flow cytometry to assess genotype frequencies from very large samples alleviated the problem of sampling error, while the effect of drift was controlled by using large populations and massive replication of fitness measures. Furthermore, with a set of four competition experiments between ancestral and mutant genotypes, we were able to decompose fitness measures into four estimated parameters that account for fitness effects of our fluorescent marker (a), the mutation (b), epistasis between the mutation and the marker (g), and departure from transitivity (t). Our method allowed us to estimate mean selection coefficients to a precision of 2 · 1024. We also found small, but significant, epistatic interactions between the allelic effects of mutations and markers and confirmed that fitness effects were transitive in most cases. Unexpectedly, we also detected variation in measures of s that were significantly bigger than expected due to drift alone, indicating the existence of cryptic variation, even in fully controlled experiments. Overall our results indicate that selection coefficients are best understood as being distributed, representing a limit on the precision with which selection can be measured, even under controlled laboratory conditions. UTATIONS of small effect can play an important role 1996). Finally, a low precision in fitness measures limits the Min evolution, but they are difficult to measure exper- ability to determine whether the fitness effect of a mutation imentally because the precision with which fitness effects can varies across different environmental or genetic contexts and be measured is relatively low. For this reason, it remains adds to other sources of stochasticity (Lenormand et al. 2009) unclear to what extent mutations with small beneficial ef- to make it difficult to reliably predict evolutionary trajectories. fi fects contribute to tness improvements (Orr 2005). It is Precisely measuring fitness poses technical, conceptual, also unclear how much deleterious mutations of small effect and statistical challenges. The technical challenge is to set contribute to the genetic load and inbreeding depres- up a technique that allows experiments to be carried out sion (Charlesworth and Charlesworth 1998; Bataillon and efficiently. The first major advance was to use “population Kirkpatrick 2000). More generally, the existence and influence cages” with Drosophila or other small animals (starting in of mutations of small effect is at the heart of the neutralist– the 1930s with the work of L’Heritier and Teissier 1937a,b). selectionist controversy (e.g., Nei 2005). This debate can be With such devices, environmental conditions are relatively addressed experimentally only if the precision of fitness mea- controlled and gene flow can be eliminated. However, drift surements is lower than the inverse of effective population size, and indirect selection caused by loci under selection in link- which seems beyond reach for large populations (Kreitman age disequilibrium with the focal locus are difficult to account for. The same approach was applied to microorgan- Copyright © 2012 by the Genetics Society of America isms (Dykhuizen and Hartl 1980), which can be made iso- doi: 10.1534/genetics.111.133454 Manuscript received July 29, 2011; accepted for publication September 19, 2011 genic save for a focal gene, thereby reducing indirect Supporting information is available online at http://www.genetics.org/content/ selection due to initial linkage disequilibrium (e.g., Carrasco suppl/2011/10/31/genetics.111.133454.DC1. 1Corresponding author: CEFE–UMR 5175 1919 route de Mende, F-34293 Montpellier, et al. 2007; Domingo-Calap et al. 2009 for distribution of CEDEX 5, France. E-mail: [email protected] mutation fitness effects; Elena et al. 1998; Sanjuan et al. 2004; Genetics, Vol. 190, 175–186 January 2012 175 Peris et al. 2010) and can be propagated as large popu- Manly 1985; Arnason and Lewontin 1991; Lenormand and lations, minimizing the effect of drift relative to selection. Raymond 2000; Saccheri et al. 2008; Labbe et al. 2009), They can also be followed over many generations (Dykhuizen which can include drift if longitudinal data are available and Hartl 1983; Thatcher et al. 1998; Lunzer et al. 2002). (Manly 1985; O’hara 2005; Bollback et al. 2008). When Long-term monitoring increases the ability to detect small selection can be approximated by a continuous process differences in fitness between competing genotypes, but through time in an isolated population, a simple approach adds the complication that newly arising mutations may is to regress Log(p/q) (where p and q represent the frequen- perturb the assay (Dykhuizen and Hartl 1983). An impor- cies of the two competitors) over time expressed in units of tant technical issue in all competition experiments is to de- generations (Fisher 1930). The connection with logistic re- termine the frequency of competing genotypes reliably and gression and general linear models is then straightforward quickly. In many cases the idea is to link an easily recognized (Arnason and Barker 1999) and more appropriate than the marker with the gene under scrutiny. It is, however, impor- use of least squares. However, complications arise in the tant to recognize that a marker can confer a selective differ- analysis of time series and correlated error in repeated mea- ence (a marker “cost”), which might vary with the genetic surement through time (Arnason and Barker 1999; O’hara background (epistasis) or external environment (G · E inter- 2005), especially when both drift and fluctuating selection actions). Finally, inferring allelic selection coefficients cause frequency variation. The latter problems can be im- against a common reference strain requires that genotypic portant, particularly when analyzing multiple time point se- fitness is transitive. These potential complications require ries (e.g., arising in long-term population cage or chemostat adding proper controls to competition experiments. experiments), although they are rarely taken into account. Often, replicated experiments are simply pooled, even if Akeyconceptualdifficulty in measuring the fitness effects fi of mutations is to distinguish selection from drift (Beatty 1984; signi cantly different, and not analyzed to consider variance Millstein 2008), which is at the heart of several population in the estimates of selection. The development of mixed cage experiments with Drosophila (Dobzhansky and Pavlovsky models offers an attractive alternative to circumvent this 1957). To account for the effect of drift, a selection coefficient problem and to measure selection and its variation. can be defined from the expected change in allele frequency We present an approach combining several features to over one generation (e.g., Rousset 2004), which can be es- improve and quantify the precision of fitness measures. First, timated from the mean frequency change in independent we use techniques that have proved to be among the most competition experiments. Because of drift, replication is fun- efficient to measure fitness: competition assay between large damentally necessary to estimate fitness, and the precision populations of Escherichia coli strains to minimize drift and of a given fitness measure must account for the interrepli- engineered mutations to avoid the problem of indirect selec- cate variance. Indeed, it is possible to count all organisms in tion. Specifically, we used three genotypes, each carrying an experimental population, so that the genotype frequen- a single mutation introduced by the integration of a mini- cies are known without sampling error. Such an experiment Tn10 transposon. These mutations were considered neutral, would allow frequency variation to be determined “exactly,” relative to a common progenitor genotype, in a previous ex- but would clearly not account for the possibility that drift periment (Elena et al. 1998). We use two fluorescent markers will cause different outcomes in different replicates. A fur- (Rosenfeld et al. 2005) combined with flow cytometry ther complication is that fitness may vary because of chang- (Lunzer et al. 2002) to measure frequency variation with ing environmental conditions. Fluctuating selection during great precision, and thus minimize sampling error. Other the course of a competition experiment or varying selection studies have shown the utility of these approaches in mea- across replicates of a competition assay can mimic drift suring genotype fitness
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