Vivo vitrothingamajig

Simulating “evolve & resequence” experiments

Kevin Thornton

Asexual

Sexual

http://en.wikipedia.org/wiki/File:Drosophila_speciation_experiment.svg


Supplementary Figure 1. Phylogeny of the populations used in this study. Long periods of independent evolution separate the founding of each experimental population. The ACO treatment imposes a 9/10-day generation cycle and selection for accelerated development. The CO treatment imposes a 28-day generation cycle, with no pressure on development time and moderate selection for postponed reproduction. ACO populations were derived from their same-numbered CO (control) populations in 1991. At the time of resequencing, the CO populations had experienced 252 generations, and the ACO treatments had experienced 605 generations.

www.nature.com / nature 1

Burke et al. (2010) 10.1038/nature09352

Big phenotype changes

LETTERdoi:10.1038/nature09352

Genome-wide analysis of a long-term evolutionexperiment with DrosophilaMolly K. Burke1, Joseph P. Dunham2, Parvin Shahrestani1, Kevin R. Thornton1, Michael R. Rose1 & Anthony D. Long1

Experimental evolution systems allow the genomic study ofadaptation, and so far this has been done primarily in asexualsystems with small genomes, such as bacteria and yeast1–3. Herewe present whole-genome resequencing data from Drosophilamelanogaster populations that have experienced over 600 genera-tions of laboratory selection for accelerated development. Flies inthese selected populations develop from egg to adult ,20% fasterthan flies of ancestral control populations, and have evolved anumber of other correlated phenotypes. On the basis of 688,520intermediate-frequency, high-quality single nucleotide poly-morphisms, we identify several dozen genomic regions that showstrong allele frequency differentiation between a pooled sample offive replicate populations selected for accelerated development andpooled controls. On the basis of resequencing data from a singlereplicate population with accelerated development, as well as singlenucleotide polymorphism data from individual flies from eachreplicate population, we infer little allele frequency differentiationbetween replicate populations within a selection treatment.Signatures of selection are qualitatively different than what hasbeen observed in asexual species; in our sexual populations,adaptation is not associated with ‘classic’ sweeps whereby newlyarising, unconditionally advantageous mutations become fixed.More parsimonious explanations include ‘incomplete’ sweep models,in which mutations have not had enough time to fix, and ‘soft’ sweepmodels, in which selection acts on pre-existing, common geneticvariants. We conclude that, at least for life history characters suchas development time, unconditionally advantageous alleles rarelyarise, are associated with small net fitness gains or cannot fix becauseselection coefficients change over time.

Experimental evolution uses well-defined selection protocols to forcephenotypic divergence4,5. Studies of experimentally evolved popula-tions have identified mutations responsible for particular adaptations6

and provided some general insights into the nature of adaptation inasexually reproducing populations7. Adaptation in these populations isdriven by so-called classic selective sweeps, or the fixation of newlyarising beneficial mutations and the genome-wide haplotypes asso-ciated with them. By contrast, an obligate sexually reproducing systemcan harbour a great deal of standing genetic variation on which selectioncan act. Standing variation is theoretically predicted to lead to rapidevolution in novel environments8, and case studies of ecologically rel-evant genes bear out this prediction9–11. The idea that short-term evolu-tion may act primarily on pre-existing intermediate-frequency geneticvariants that are swept the remainder of the way to fixation has beentermed a soft sweep8,12 model.

We collected genome-wide resequence data for outbred, sexuallyreproducing, replicated populations of D. melanogaster selected foraccelerated development and their matched control populations.Using the Illumina platform, we obtained short-read sequences fromthree genomic DNA libraries: a pooled sample of five replicate popula-tions that have undergone sustained selection for accelerated develop-ment and early fertility for over 600 generations (ACO); a pooled

sample of five replicate ancestral control populations, which experi-ence no direct selection on development time (CO); and a single ACOreplicate population (ACO1). The ACO treatment has evolved stronglydifferentiated life history phenotypes relative to those of the CO treat-ment13 (summarized in Fig. 1; see also Supplementary Fig. 1 for thehistory of the populations).

To identify single nucleotide polymorphisms (SNPs) significantlydifferentiated between the ACO and CO populations, we aligned readsto the reference genome of Drosophila and considered only thosegenomic positions at which there were two observed allelic states.After quality-filtering, we were left with 688,520 SNPs: approximatelyone SNP for every 175 base pairs (bp) on the 120-megabase (Mb)euchromatic genome (Methods). The average alignment depth atidentified SNPs was ,203 in both the ACO and CO libraries(Supplementary Fig. 2), and ,103 in the ACO1 library. For everySNP, we calculated 2log10(P) from a Fisher’s exact test (L10FET) fora difference in allele frequency between the ACO and CO libraries, aswell as the ACO and ACO1 libraries.

We examined each SNP to determine whether it encodes an amino-acid polymorphism, a segregating stop codon or a segregating inter-ruption to a consensus splice junction (Supplementary Fig. 3). We

1Ecology and Evolutionary Biology, University of California, Irvine, 321 Steinhaus Hall, Irvine, California 92697-2525, USA. 2Molecular and Computational Biology, University of Southern California; LosAngeles, California 90098, USA.

220

100

90

80

70

60

50

40

30

4.5

4.0

3.5

3.0

2.5

2.0

60

50

40

30

20

Tim

e to

ecl

osio

n (h

)Ti

me

to d

eath

(h)

Tim

e of

dea

th (d

)W

eigh

t (m

g)

200

180

ACO CO

Mean development time

B ACO CO

Dry weight at eclosion

B

ACO CO

Mean starvation time

B ACO CO

Mean longevity

B

160

Figure 1 | Summary of phenotypic divergence in the selection treatmentsdescribed in this study. Grey bars represent values measured in each of the fivereplicate populations in the ACO and CO treatments. Measures from the fivebaseline (B) replicate populations represent phenotypes typical of populationskept on two-week generation maintenance schedules. Only data for females areshown. Longevity and starvation resistance data were collected after at least 619generations of ACO treatment, and both development time and dry weight data(dry weight values are mean masses of groups of ten females) were collectedafter 640 generations of ACO treatment. Error bars, s.e.m. for each replicatepopulation.

0 0 M O N T H 2 0 1 0 | V O L 0 0 0 | N A T U R E | 1

Macmillan Publishers Limited. All rights reserved©2010


What are the genetic changes?


identified 37,185 non-synonymous SNPs, 190 segregating stop codonsand 118 segregating splice variants. Of the ,37,000 putative non-synonymous SNPs, 662 SNPs in 506 genes are associated with anL10FET score .4 (only 3.7 SNPs are expected to exceed this thresholdby chance alone). These 662 SNPs are potential candidates for encod-ing the causative differences between the ACO and CO populations, tothe extent that those differences are due to structural as opposed toregulatory variants (compare with ref. 14). We carried out a functionalanalysis of the 475 of these genes that have DAVID IDs (http://david.abcc.ncifcrf.gov/; ref. 15) and present the results for the functionalcategories that have a false-discovery rate of less than 10% for Swiss-Protprotein keywords, InterPro domains and all Gene Ontology biologicalprocesses (Supplementary Table 1). For the biological processes, thereis an apparent excess of genes important in development; for example,the top ten categories are imaginal disc development, smoothenedsignalling pathway, larval development, wing disc development, larvaldevelopment (sensu Amphibia), metamorphosis, organ morpho-genesis, imaginal disc morphogenesis, organ development and regio-nalization. This is not an unexpected result, given the ACO selectiontreatment for short development time, but it indicates an importantrole for amino-acid polymorphisms in short-term phenotypic evolu-tion. We have created custom tracks representing our data for theUCSC Genome Browser that allow a user to browse a region of interestand examine allele frequency divergence in that region along withfunctional annotations of segregating SNPs (see, for example, Sup-plementary Fig. 4).

Previous work suggests that linkage disequilibrium in individualACO and CO replicate populations may extend anywhere from 20to 100 kilobases5 (kb). Strong linkage disequilibrium suggests thatalthough the individual Fisher’s exact tests on the SNPs of this studydo not have a great deal of power to detect changes in allele frequency,a sliding-window analysis may have considerable power. We carriedout a 100-kb genome-wide sliding-window analysis to identify regionsdiverged in allele frequency between the ACO and CO libraries andbetween the ACO and ACO1 libraries (Fig. 2; see Methods for detailsincluding the definition of L10FET5%Q). The sliding-window analysisidentifies a large number of genomic regions showing significantdivergence between the accelerated development populations andtheir matched controls (Fig. 2, black line), and very little evidencefor divergence between a single replicate evolved population (ACO1)and the pooled sample consisting of all five ACO populations (Fig. 2,grey line). We observe an apparent excess of diverged regions on the Xchromosome relative to on the autosomes, an observation that mightbe expected if adaptation were driven by selection on initially rarerecessive or partially recessive alleles. The sharpness of the peaks inFig. 2 suggests that regions of the genome that have responded toexperimental evolution are precisely identified, but in fact even thesharpest peaks tend to delineate ,50–100-kb regions (compare withSupplementary Fig. 5). We are unable to determine the extent to whichadditional sequencing coverage would offer increased resolution, orwhether the levels and patterns of linkage disequilibrium in thesepopulations are limiting. Regardless, it is apparent that allele frequenciesin a large portion of the genome have been affected following selectionon development time, suggesting a highly multigenic adaptive response.

Recent research on evolutionary genetics has focused on classicselective sweeps, which are evolutionary processes involving the fixa-tion of newly arising beneficial mutations16. In a recombining region, aselected sweep is expected to reduce heterozygosity at SNPs flankingthe selected site. Sliding-window plots (100 kb) of heterozygosity inACO and CO lines suggest that there are indeed local losses of hetero-zygosity (Fig. 3, red and blue lines, respectively). This is the caseparticularly for the ACO populations, which have experienced moregenerations of stronger selection in their recent evolutionary historythan the CO populations. Regions of reduced heterozygosity arestrongly associated with regions of differentiated allele frequency(compare Figs 2 and 3; Supplementary Fig. 6). Notably, we observe

no location in the genome where heterozygosity is reduced to any-where near zero, and this lack of evidence for a classic sweep is a featureof the data regardless of window size.

The ACO1 sample and the ACO pool show very little evidence forallele frequency differentiation (Fig. 2, grey line). Similarly, the sliding-window analysis of heterozygosity in ACO1 (Fig. 3, grey line) showsremarkable concordance with the reductions in heterozygosity in theACO pool (Fig. 3, red line). To better assess allele frequency differencesbetween replicate populations, we individually genotyped 35 femalesfrom the five replicate populations of each selection treatment at 30loci at which the resequence data predicted significantly different allelefrequencies. Replicate populations within a selection treatment havevery similar allele frequencies (Fig. 4a), and individual genotypes areconsistent with allele frequency estimates from the resequenced pooledlibraries (Fig. 4b). We therefore conclude that the congruence in allelefrequencies and patterns of heterozygosity between the ACO1 andACO libraries is unlikely to be some sort of artefact of sample prepara-tion or data analysis.

We consider two possible explanations for the convergence of allelefrequencies and heterozygosity levels between replicate populations.First, selection is acting on the same intermediate-frequency variants ineach population. Under this scenario, convergence in allele frequencies isdue to parallel evolution. Second, unwanted migration between replicatepopulations, even at very low levels, could explain observed similarities.Despite preventative measures in place to isolate replicate populationsduring routine maintenance, some degree of migration between the rep-licate populations within a selection treatment is probable (successfulmigration between treatments is not as likely, owing to the selection

7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210

0 5 10 15Location along chromosome (Mb)

20 25

Figure 2 | Differentiation throughout the genome. Sliding-window analysis(100 kb) of differentiation in allele frequency between the ACO and COpopulations: the solid black line depicts L10FET5%Q scores at 2-kb steps(Methods). The dotted line is the threshold that any given window has a 0.1%chance of exceeding relative to the genome-wide level of noise. The grey linedepicts L10FET5%Q scores for a difference in allele frequency between ACO1

and the ACO pooled sample. The five panels show the five major D.melanogaster chromosome arms (as indicated).

RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0


What are the genetic changes?







7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210


20 25



RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0








7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210


20 25



RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0



Heterozygosity

regimes effectively precluding the survival and reproduction of migrants).If migration is occurring, its rate must be low, as we have observedsubstantial and sustained phenotypic differences between replicate popu-lations within selection treatments (compare with Fig. 1). A small amount

of cross-contamination between replicate populations does not rule outour inference that classic selective sweeps have not occurred during theevolution of these populations. If classic sweeps are occurring in thepresence of migration, the ACO pool should show regions of zero hetero-zygosity, because unconditionally beneficial alleles can move betweenpopulations, whereas in the absence of migration we expect to see regionsof zero heterozygosity in a single replicate population. In fact, we see noevidence for sweeps in ACO1 nor in the pool of all the populations withaccelerated development.

There are several possible explanations for our failure to observe thesignature of a classic sweep in these populations, despite strong selec-tion. Classic sweeps may be occurring, but have had insufficient time toreach fixation. This explanation is consistent with observed data, butrequires that newly arising beneficial alleles have small associatedselection coefficients (Supplementary Fig. 7). Alternatively, selectionin these lines may generally act on standing variation, and not newmutations. This soft sweep model predicts partial losses of heterozy-gosity flanking selected sites, provided that selection begins actingwhen mutations are at low frequencies12,17, and this is consistent withour observed data. However, if a large fraction of the total adaptiveresponse is due to loci fixed by means of soft sweeps, there should beinsufficient genetic variation to allow reverse evolution in these popu-lations. But forward experimental evolution can often be completelyreversed with these populations5, which suggests that any soft sweepsin our experiment are incomplete and/or of small effect (Supplemen-tary Fig. 5). A third explanation is that the selection coefficients asso-ciated with newly arising mutations are not static but in fact decreaseover time. This could be the case if initially rare selected alleles increaseto frequencies where additional change is hindered, perhaps by linkeddeleterious alleles or antagonistic pleiotropy. Laboratory evolutionexperiments typically expose populations to novel environments inwhich focal traits respond quickly and then plateau at some new value(compare with refs 13, 18). Chevin and Hospital19 recently modelledthe trajectory of an initially rare beneficial allele that does not reachfixation because its selective advantage is inversely proportional to thedistance to a new phenotypic optimum, and that optimum is reached,because of other loci, before the variant fixes. This model therefore hasappeal in the context of experimental evolution, as it assumes popula-tions generally reach a new phenotypic optimum before newly arisingbeneficial mutations of modest effect have had time to fix.

Our work provides a new perspective on the genetic basis of adapta-tion. Despite decades of sustained selection in relatively small, sexuallyreproducing laboratory populations, selection did not lead to the fixa-tion of newly arising unconditionally advantageous alleles. This isnotable because in wild populations we expect the strength of naturalselection to be less intense and the environment unlikely to remainconstant for ,600 generations. Consequently, the probability of fixa-tion in wild populations should be even lower than its likelihood inthese experiments. This suggests that selection does not readilyexpunge genetic variation in sexual populations, a finding which inturn should motivate efforts to discover why this is seemingly the case.

METHODS SUMMARYExperimental evolution system. The ACO1–ACO5 selection treatments aremaintained on a 9–10-d cycle and the control treatments, CO1–CO5, are main-tained on a 28-d cycle. The flies used for sequencing were collected after 605generations (ACO) and 252 generations (CO) of selection.Genome sequencing. DNA was extracted from 25 female flies collected from eachof the ACO1–ACO5 and CO1–CO5 populations and pooled within selection treat-ments to make two Illumina paired-end libraries. We also created a library for theACO1 replicate population only. The pooled libraries were each run on four(unpaired 54-bp) lanes of an Illumina Genome Analyser II, and the ACO1 librarywas run on a single (paired-end 36-bp) lane.SNP identification and sliding-window analysis. We used MOSAIKALIGNERto align all of our sequences to the reference genome of Drosophila. We then usedcustom PERL scripts to count the number of single nucleotide mismatches at everyposition in the genome, as a function of selection treatment. Fisher’s exact tests

1.0

0.0 0.2 0.4 0.6Allele frequency measured by resequencing

SNP location

0.8 1.0

Alle

le fr

eque

ncy 0.8

0.6

0.4

0.2

0.0

1.0

Alle

le fr

eque

ncy

mea

sure

d by

CA

PS

0.8

0.6

0.4

0.2

0.0

a

b

Figure 4 | Analysis of individual genotypes, measured by cleaved amplifiedpolymorphic sequence (CAPS) techniques. a, Allele frequency estimates ofthe most common allele at 30 SNPs genotyped in 35 females per replicatepopulation. Red circles represent ACO estimates and grey squares representCO estimates. Open symbols are allele frequencies for ACO1–ACO5 and CO1–CO5, and filled symbols represent treatment means. Alternating black and greybars designate the X, 2L, 2R, 3L, and 3R arms, respectively, with grey linesindicating SNP location. b, Scatter plot comparing allele frequency estimates atthe same 30 SNPs obtained from the Illumina resequencing versus individualgenotyping. Red circles represent ACO, black squares represent CO and thestraight line represents a slope of unity.

0.5X

2L

2R

3L

3R

0.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.0


Het

eroz

ygos

ity

20 25

Figure 3 | Heterozygosity throughout the genome. Sliding-window analysis(100 kb) of heterozygosity in the CO pool (blue), the ACO pool (red) and ACO1

(grey), with a 2-kb step size. The panels show the five major chromosome armsof D. melanogaster.

LETTER RESEARCH

0 0 M O N T H 2 0 1 0 | V O L 0 0 0 | N A T U R E | 3







1.0


SNP location

0.8 1.0

Alle

le fr

eque

ncy 0.8

0.6

0.4

0.2

0.0

1.0

Alle

le fr

eque

ncy

mea

sure

d by

CA

PS

0.8

0.6

0.4

0.2

0.0

a

b


0.5X

2L

2R

3L

3R

0.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.0


Het

eroz

ygos

ity

20 25



LETTER RESEARCH

0 0 M O N T H 2 0 1 0 | V O L 0 0 0 | N A T U R E | 3



Questions






1.0


SNP location

0.8 1.0

Alle

le fr

eque

ncy 0.8

0.6

0.4

0.2

0.0

1.0

Alle

le fr

eque

ncy

mea

sure

d by

CA

PS

0.8

0.6

0.4

0.2

0.0

a

b


0.5X

2L

2R

3L

3R

0.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.0


Het

eroz

ygos

ity

20 25



LETTER RESEARCH

0 0 M O N T H 2 0 1 0 | V O L 0 0 0 | N A T U R E | 3








7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210


20 25



RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0



Simulation

Supplementary Figure 7: Models of selection. The distribution of allele frequencies after 600 generations of selection were obtained by simulating a Wright-Fisher population of N = 1000 diploids, under a model of genic selection (fitnesses 1, 1+s, and 1+2s for the wild-type homozygote, heterozygous mutant, and homozygous mutant genotypes, respectively, with the strength of selection remaining constant each generation). All results are conditioned on the beneficial allele not being lost from the population. For both panels, the neutral expectation shown is for a sample of n = 100 chromosomes sampled from a diploid population at equilibrium for mutation and drift. Top panel: The distribution of allele frequencies for a newly-arisen beneficial mutation with an initial frequency of 1/(2N) based on 5000 replicate simulations. These simulations show that newly arising mutations having selection coefficients >1% are likely to show the signature of a classic sweep, whereas those having selection coefficients of <0.1% are unlikely to display sufficient allele frequency divergence from control populations to be detected in our experiment. Therefore, given the length of the experiment to date, it is possible that classic sweeps may be occurring, but alleles have small associated selection coefficients and have not had time to fix. Bottom panel: The distribution of allele frequencies for a beneficial mutation at an initial frequency of 10% in the population. These simulated predictions of selection from standing variation. Under this soft-sweep model, we see that mutations with selection coefficients >0.5% are likely to fix.

www.nature.com / nature 7


Questions






1.0


SNP location

0.8 1.0

Alle

le fr

eque

ncy 0.8

0.6

0.4

0.2

0.0

1.0

Alle

le fr

eque

ncy

mea

sure

d by

CA

PS

0.8

0.6

0.4

0.2

0.0

a

b


0.5X

2L

2R

3L

3R

0.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.0


Het

eroz

ygos

ity

20 25



LETTER RESEARCH

0 0 M O N T H 2 0 1 0 | V O L 0 0 0 | N A T U R E | 3








7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210


20 25



RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0



Time and strength of selection

??

Let’s do this in silico



Open tools

http://arxiv.org/abs/1401.3786

github.com/molpopgen

http://github.com/molpopgen

//!segsites: 32!positions: 0.0184 0.0366 0.0412 0.0760 0.1158 0.1611 0.1667 0.1739 0.3435 0.3494 0.3676 0.5053 0.5669 0.5807 0.5911 0.5942 0.6100 0.6290 0.6736 0.6767 0.7173 0.7529 0.8120 0.8545 0.9333 0.9430 0.9585 0.9769 0.9774 0.9799 0.9846 0.9928 !00100001010000001100010010010000!00000100000010000000010000000000!01110011010001100000000000000110!00000100101010000000010000000000!00100001100010000001000100100000!00100011000000001100010000010000!00000100101010000000010000000000!00000100101010000000010000000000!00100001100010000001001100100000!00100001100010000001000100100000!00101001010001100010010001010000!00000100101010000000010000000000!00000100100010000000010000000001!01110011010101100000000000000110!00100001010001110010100000001110!10000100100010000001001100100000



parameters to be at their ideal values (1,000 individuals perpopulation, 500 founder haplotypes, and 25 replicate popu-lations) for the case of a selection coefficient of 0.1, but rea-sonable levels of power can also be achieved with less costlyexperimental designs or higher selection coefficients. Our sim-ulations suggest that the experimental designs that could bemost effectively utilized for detecting CRs and localizing CSsunder the E&R paradigm are not currently widely employedand likely require considerable experimental effort. Still, theparameter space that provides reasonable power levels is notoutside the realm of possibility for E&R studies using macro-scopic organisms.

Results

The False-Positive RateFrom the perspective of a naı̈ve observer, any given simulated1 Mb genomic region might or might not contain a CS. Todetermine the fraction of times that we falsely identified a CR,we calculated for every parameter combination (!) wheres = 0 the fraction of cases in which at least one SNP was foundto have a P value of less than 10!1, 10!2, 10!3, and so on,through 10!14. We referred to this as the false-positive CRdetection rate (fig. 1); that is, the fraction of neutrally evolving

regions that are nonetheless flagged as “significantly di-verged.” It is apparent from the figure that the false-positiverate is quite high for certain parameter combinations regard-less of the statistical threshold employed. False positives areespecially frequent in the specific case in which all the follow-ing are true: there are ten experimental replicates, the popu-lation size is only 100 individuals, and there are between 32and 100 founder individuals. This elevated false-positive rate islikely due to the t-statistic used to assess significance notbeing distributed as a t-distribution, especially in the tails,when the number of replicates is small (supplementary fig.S1, Supplementary Material online). It is important that our1 Mb false-positive rate is essentially zero; otherwise, there is ahigh likelihood of identifying a false-positive CR somewhere ina genome that is several hundred Mb in size. In a genome, thesize of Drosophila melanogaster (122 Mb), the false-positiveCR detection rate necessary to achieve a genome-wide false-positive rate of 0.05 is 0.05/122 = 0.00041. This corresponds toapproximately 1 false positive in every 2,439 regions tested. Toaccurately measure the false-positive rate at low values, wegenerated 10,000 replicate simulations at each ! where s = 0.With this number of replicate simulations, any ! with four orfewer false positives has an acceptable error rate. At each !,

Table 1. Useful Terms.

Term Values Used in Simulation Description

r Number of replicates 2, 5, 10, 15, 25 The number of independent experimental populations that are usedin each trial. There are an equal number of control populations.

n Population size 100, 250, 500, 1,000 The number of diploid individuals that successfully reproduce everygeneration.

h Number of haplotypes 4, 32, 100, 500 The number of haplotypes present in each population at the start ofeach experiment. A population originally derived from one maleand one female would have four haplotypes.

g Number of generations 100, 500, 1,000 The number of generations of selection that both the control popula-tions and the selected populations have undergone before allele fre-quency calculation.

s Selection coefficient 0, 0.0005, 0.005, 0.05, 0.1, 0.2 The strength of selection at the causative locus in a particular geno-mic region.

? Parameter combination The particular set of r, n, h, g, and s used in each set of 500simulations.

MSM Most significant marker The SNP that was found to have most significantly diverged in a par-ticular simulation

CS Causative SNP The SNP that was selected upon in a particular simulation.CR detection power The fraction of studies of a particular ? that found at least one sig-

nificantly diverged SNPExact location power The fraction of studies of a particular ? in which the MSM is

the CS.Within 10 kb power The fraction of studies of a particular ? in which the MSM is within

10 kb of the CS.Top 25 power The fraction of studies of a particular ? in which the CS is one of

the 25 most significantly diverged SNPs in the region.Within 2 LOD power The fraction of studies of a particular ? in which the CS is within a

2 LOD drop of the MSMTotal Power The fraction of studies of a particular ? in which the CR is detected,

and the CS is localized according to one of the CS localizationmethods earlier. In other words, CR detection power * localizationpower

MSM-CS distance The physical distance between the MSM and the CS.CS rank The significance rank of the CS when compared with all other SNPs

in the region

1042

Baldwin-Brown et al. . doi:10.1093/molbev/msu048 MBE

at University of C

alifornia, Irvine on March 21, 2014

http://mbe.oxfordjournals.org/

Dow

nloaded from

Baldwin-Brown et al. (2014) 10.1093/molbev/msu048

simulation available from https://github.com/molpopgen/baldwin_brown_2014

https://github.com/molpopgen/baldwin_brown_2014

False positives are a problem

we found the most lenient of our chosen significance thresh-olds that produced four or fewer false positives and used it inpower calculations for the remainder of the experiment (sup-plementary fig. S2 and table S1, Supplementary Materialonline). This is a more fair comparison than choosing asingle significance threshold that is applied to all ! becausethe false-positive rate varies widely between !, so that asignificance threshold that is reasonable for some ! is un-necessarily strict for other ! and would not provide a rea-sonable estimate of the maximum power achievable in those!. !, in which an acceptable false-positive rate was notachieved by our most strict significance threshold, 10!14,were discarded. This includes all experimental designswhere r = 10, n = 100, h = 100, and g = 500 or 1,000 are simul-taneously true. Of the 208 chosen thresholds (one for eachcombination of n, h, r, and g), the distribution was as follows,with the first item in the list corresponding to 10!1, thesecond corresponding to 10!2, and so on: 0, 0, 42, 0, 7, 25,42, 62, 20, 5, 1, 1, 1, and 2. The large number of significancethresholds set to 10!3 corresponds to the ! in which r = 2; inthese !, power and false-positive rates are both extremely

low, so the selecting of a lenient significance threshold isunsurprising. The mean of the !log10 of the significancethresholds is 6.71.

Power to Detect a CR as SignificantHaving controlled the false-positive rate via an individualizedstatistical threshold, we examined the ability to detect CRs. Asin traditional QTL literature, there are two issues at hand.First, is it possible to find an association between geneticfeatures and experimental treatment (this is analogous toCR detection as discussed in this section)? Second, if an asso-ciation is found, to what level of precision can the polymor-phism underlying the trait be localized (this is analogous to CSlocalization in the following sections)? As above, we consid-ered a CR detected if it contained at least one significantlydiverged SNP (P" significance threshold). Because we onlyused 500 simulations per parameter combination wheres> 0, we estimated the amount of error in estimates ofpower due to limited sampling by finding the 95% confidenceinterval around each power estimate using binomial

FIG. 1. The false-positive CR detection rate versus replication. This plot depicts the fraction out of 10,000 cases in which a region containing no CScontained at least one significantly diverged SNP for four different per SNP –log10(P value) thresholds. The black line indicates the maximum allowablefalse-positive rate (4/10,000). n represents population size, whereas h represents the number of founder haplotypes. The variable significance thresholdused in our later power analysis is also included for comparison. When two lines overlap, the line representing a more strict significance threshold is thevisible line.

1043

Power to Detect Quantitative Trait Loci . doi:10.1093/molbev/msu048 MBE

at University of C



Dow

nloaded from


Supplementary Figure 1

Sup. Fig. 1: This figure depicts a set of Q-Q plots illustrating the distribution of the t statistic used in

this study versus a theoretical t distribution. In each case, the t values were calculated from a single,

randomly chosen replicate simulation. In all cases, s = 0 so that the plots will illustrate the effect of

drift alone on the generated t values. Purple, brown, green, blue and red points correspond,

respectively, to the cases where r = 2, r = 5, r = 10, r = 15, and r = 25.


Supplementary Figure13

Sup. Fig. 13: CR detection power and false positive rate versus significance threshold. The Θ that

most closely correspond to the experimental parameters used in existing E&R experiments are

depicted. Burke et al. 2010: h = 500, n = 1000, r = 5, g = 500. Johansson et al. 2010: h = 32, n = 100, r

= 2, g = 100. Orozco-Terwengel et al. 2012 and Turner and Miller 2012: h = 100, n = 1000, r = 2, g =

100. Turner et al. 2011: h = 100, n = 250, r = 2, g = 500. When a parameter value was unknown, the

value that provided the highest power was chosen. Only s = 0.05 is shown. Any points that are not

visible are overlapping at y = 0.

For s = 0.05


Questions






1.0


SNP location

0.8 1.0

Alle

le fr

eque

ncy 0.8

0.6

0.4

0.2

0.0

1.0

Alle

le fr

eque

ncy

mea

sure

d by

CA

PS

0.8

0.6

0.4

0.2

0.0

a

b


0.5X

2L

2R

3L

3R

0.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.00.50.40.30.20.10.0


Het

eroz

ygos

ity

20 25



LETTER RESEARCH

0 0 M O N T H 2 0 1 0 | V O L 0 0 0 | N A T U R E | 3








7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210


20 25



RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0



Time and strength of selection







7X

2L

2R

3R

3L

L 10F

ET5%

Q

654321076543210765432107654321076543210


20 25



RESEARCH LETTER

2 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 0



sampling. We found that the mean width of the 95% confi-dence interval for all nonzero power estimates was 4.64%,the standard deviation of these widths was 3.31%, and therange of widths was 0.052–8.94%. The power to detect aCR increased with increasing r, n, and s, slowly decreasedwith increasing h, and was maximized at g = 500 whens = 0.05 and at g = 100 when s! 0.1 (fig. 2). When r = 2, weobserved a power of near zero in all cases. For several simu-lated parameter combinations, power was quite high, espe-cially when n was large and the s associated with the CS was!0.05. As expected from standard population genetic theory,as decreasing s approached the reciprocal population size,power to detect a CR decreased substantially. Interestingly,although smaller numbers of starting haplotypes are associ-ated with the greatest power to detect a CR, this effect wasweak (a feature of E&R experiments that will be important inidentifying CSs). Below, we disregarded parameter valueswhere CR power with that parameter value was alwaysbelow 35%; specifically, we disregarded all ! wheres" 0.005, r = 2, n" 100, or the specific case where n" 250and r" 5.

Power to Identify a CSThe goal of an E&R study is CR detection followed by theidentification of a CS within the detected CR. To determinemost effective method of CS localization, we examined thedistance from the most significant marker (MSM) to thecausative SNP (MSM-CS distance) in each simulated regionin which at least one SNP was significant (fig. 3). A largefraction of MSM-CS distances were equal to zero for casesof ! where CR detection power was high, indicating thatprecise localization is possible under some circumstances.The nonzero MSM-CS distances appeared to be skewed,such that a large fraction of MSMs were within 100 kb ofthe CS, indicating that these MSMs are likely driven to highlevels of divergence by linkage to the CS, rather than drift.Indeed, if we take, for example, the (relatively moderatelypowered, drift-heavy) case in which s = 0.05, n = 500, h = 32,r = 10, and g = 500, 95% of all nonzero MSM-CS distanceswere less than 59 kb when only significant regions were con-sidered. For a large portion of the ! cases with high CRdetection power (i.e., n = 500, s! 0.05, r! 10, h! 100,except where n = 500, h = 32, r = 10, and g = 1,000), the

FIG. 2. CR detection power. This plot depicts the power to detect regions containing one or more significantly diverged SNPs. The ! in which all thefollowing are true simultaneously: r = 10, n = 100, h = 100, and g = 500 or 1,000 would be omitted due to high false-positive rates, but only g = 100 isshown for ease of viewing. n represents population size. h represents the number of founder haplotypes. The P-value threshold for significance wasdetermined for each ! by finding the most lenient threshold that sufficiently limited false positives. Each point represents 500 independently replicatedsets of populations. All lines that are not visible overlap with s = 0.005. The black lines indicate power levels of 50% and 80%.

1044


at University of C



Dow

nloaded from


How do we get power?

The false-positive localization rate, equal to 1 – (localiza-tion power), can be considered the fraction of CRs inwhich the CS is not correctly localized. At least one of thelocalization false-positive rates calculated is below 5% in 123of our simulated !, including but not limited to the en-tire simulated parameter space where h! 500, n! 500,r! 10, and s! 0.05. It is not possible to calculate agenome-wide false-positive localization rate because thenumber of expected CRs in a genome is unknown. Notethat this false-positive rate is distinct from the false-positiveCR detection rate. The false-positive CR detection rate indi-cates specifically the frequency with which CRs are detectedwhere they do not exist, whereas the false-positive localizationrate indicates the fraction of the time that a true CR has itsCS incorrectly localized. This value may be of special interestto researchers attempting to assess the chance that a signif-icant SNP in a study is likely to be a CS or merely a neighborof a CS.

Total PowerTotal power is the product of CR detection power and CSlocalization power given CR detection. Total power is thenthe fraction of all CSs that, starting from no prior knowledgeabout the data, can be detected and localized successfully.Figure 5 gives the total exact power, total top 25 power, andCR detection power as functions of ! when g = 100. Therange where h = 4 is excluded because the CS localizationpower conditional upon CR detection in these ! is lessthan 80% for all statistics except the within 2 LOD power,and few E&R experiments use only four founder haplotypes.Total power is highest when s, n, h, and r are maximized, and gis at a value of 100. The parameters necessary to achieve atleast 80% exact location power for the s = 0.1 case aren! 1,000, r! 25, and h! 500 (fig. 5, supplementary fig. S6,Supplementary Material online). This is a sobering result be-cause it is experimentally difficult (in a system like Drosophila)to achieve values of ! that reach a total exact location power

FIG. 4. Localization power conditional on regional significance. In other words, the fraction of all significant SNP containing regions in which the CScould be either exactly identified or localized to a small number of candidate SNPs. For clarity, only cases where s = 0.1 are shown, but similar patternsoccur for s = 0.05 and s = 0.2. This set of plots shows the fraction of experiments that correctly identified the location of the CS out of all experiments inwhich at least one SNP was significant. Exact location power refers to cases in which the MSM is the CS, top 25 power refers to cases in which the CS isamong the 25 most significant SNPs, within 10 kb power refers to cases in which the MSM is within 10 kb of the CS, and within 2 LOD power refers tocases in which the CS is within 2 LOD of the MSM. The population size is represented by n, whereas the number of founder haplotypes is representedby h. Nonvisible within 10 kb power points overlap with top 25 power points. The black lines indicate 80% power and 95% power.

1046


at University of C



Dow

nloaded from


Localization

Counter-intuitive observations

As noted earlier, the effect of g on the total power to detectand localize CSs was small in the parameter space wherepower was high, so g was omitted from several plots for sim-plicity. It was apparent that there was a strong interactionbetween g and s with respect to power. At s = 0.05, an inter-mediate g (500) appeared to be superior to either high (1,000)or low (100) g values in terms of the power to detect CS-containing regions and the total power to localize CSs (fig. 6);at s = 0.1 and s = 0.2, the relationship between g and powerwas generally negative. One possible explanation for thisresult is that, when s = 0.05, selection had largely fixed anyCS’s by generation 500, but drift continued to influence allelefrequencies at linked markers past generation 500 resulting inincreased noise after 500 generations, whereas CSs with higherselection coefficients, that is, s = 0.1 or 0.2, were mostly fixedby generation 100, causing power to decrease when s> 100due to genetic drift. We found that the number of fixed orlost CS alleles in populations where s = 0.05 increased fromapproximately 25% fixed or lost when g = 100 up to approx-imately 100% fixed or lost when g = 500 (fig. 7; see supple-mentary fig. S8, Supplementary Material online, for allelefrequencies), but that the total number of fixed alleles con-tinued to increase even when g = 1,000, implying that

functional standing genetic variation in fitness was largelyexhausted by generation 500, but that drift at linked neutralmarkers continued to occur. This result seems to confirm thatrapid selection and slow drift cause intermediate numbers ofgenerations to be ideal for CS detection and localization.

We used multiple linear regression to attempt to create amodel that predicts exact location power as a function of thes, r, g, h, and n (supplementary table S2 and fig. S9,Supplementary Material online). We generated a table oftotal exact location power and the five experimental designvariables of interest, then censored it in R to only contain the! where 10! r! 25, 250! n! 1,000, 32! h! 500,0.05! s! 0.2, and 100! g! 1,000 to focus on modelingthe power curve in the area where power is highest. Wethen used the lm function in R to fit the linear model below:

0:245" log10ðsÞ+ 0:668" log10ðrÞ+ 0:437" log10ðnÞ+ 0:179" log10ðhÞ % 0:0001559

" g% 1:594¼ total exact location power

Before calculating the slopes, we modified s, r, h, and n byapplying the log10() function to them as this improved the fitof the model. In the limited parameter space examined, the

FIG. 6. The total power to detect and localize SNPs when s' 0.05 and h = 100 versus the number of generations of selection. For simplicity, only CRdetection power and total exact location power are shown. Variation in h is not shown because there are no visible interactions between h and g. Theblack lines indicate 50% and 80% power.

1048


at University of C



Dow

nloaded from


Moving away from discrete traits

−5 0 5 10

0.0

0.1

0.2

0.3

0.4

N = 250 Bandwidth = 0.286

Den

sity

PhenotypeFitness

Science

Vivo vitrothingamajig