quantitative trait loci (qtl) methods and protocols

Over the last 2 decades, leaps in genotyping technology, coupled with thedevelopment of sophisticated quantitative genetic analytical techniques, have made itpossible to dissect complex

ME T H O D S I N MO L E C U L A R BI O L O G YTM

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Quantitative Trait Loci (QTL)

Methods and Protocols

Edited by Scott A Rifkin University of Californa, San Diego, CA, USA

Scott A Rifkin, Ph.D.

University of Californa

San Diego, CA, USA

ISSN 1064-3745 ISSN 1940-6029 (electronic)

ISBN 978-1-61779-784-2 ISBN 978-1-61779-785-9 (eBook)

DOI 10.1007/978-1-61779-785-9

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For over a century, biologists have searched for the genetic bases of phenotypic variation.While this program has been quite successful for simple Mendelian traits, most traits arecomplex, shaped by context-dependent interactions between multiple loci and the envi-ronment Over the last 2 decades, leaps in genotyping technology, coupled with thedevelopment of sophisticated quantitative genetic analytical techniques, have made itpossible to dissect complex traits and link quantitative variation in traits to allelic variation

on chromosomes orquantitative trait loci (QTLs) Propelled by the genome projects andtheir spinoff technologies, QTL analyses have pervaded all fields of biology and form thebackbone for the recent explosion of studies tying specific alleles to human disease

As sequencing becomes ever cheaper and easier, QTL studies will make it possible torelatively quickly identify key genes underlying traits even in non-model organisms, pavingthe way for discovering new biology

As with any expanding field, the original QTL methodologies have been elaboratedinto a host of alternative and complementary techniques A QTL experiment has manycomponents—preparing the experimental mapping population, genotyping, measuringtraits, analyzing the data and identifying QTLs, and feeding this information to down-stream analyses—and its success depends upon each part fitting together and beingappropriate for answering the motivating question This volume contains chapters thatfocus on specific components of the entire process and also a set of case studies at the endwhere these individual components are linked together into an entire study

This book is intended to serve as a practical resource for researchers interested in linksbetween phenotypic and genotypic variation in fields from medicine to agriculture andfrom molecular biology to evolution to ecology Many of the methods are similar betweenfields QTL studies often involve multiple authors with complementary expertise, and thecase studies in particular are intended to facilitate communication between scientistsworking on different parts of a project and to give a broader perspective on how eachpiece fits into the whole QTL techniques will continue to be developed and furtherrefined and extended As phenotyping technology improves and as genotyping technologycontinues to accelerate, statistical approaches to dissecting the genotype–phenotype mapwill become increasingly important and powerful tools for biological research

v

PART I SETTING UP MAPPING POPULATIONS

Rik Kooke, Erik Wijnker, and Joost J.B Keurentjes

Matthew A Cleveland and Nader Deeb

PARTII IDENTIFYINGQUANTITATIVE TRAITLOCI

Luciano Da Costa E Silva, Shengchu Wang, and Zhao-Bang Zeng

Zhi-Liang Hu, James M Reecy, and Xiao-Lin Wu

Xiao-Lin Wu and Zhi-Liang Hu

PART III EXTENDING THE POWER OF QUANTITATIVE

TRAIT LOCUS ANALYSIS

Lin S Chen

Samprit Banerjee and Nengjun Yi

Kiranmoy Das, Zhongwen Huang, Jingyuan Liu, Guifang Fu,

Jiahan Li, Yao Li, Chunfa Tong, Junyi Gai, and Rongling Wu

vii

13 Statistical Models for Genetic Mapping in Polyploids: Challenges

Jiahan Li, Kiranmoy Das, Jingyuan Liu, Guifang Fu, Yao Li,

Christian Tobias, and Rongling Wu

PART IV CASE STUDIES

Lun Li, Xianghua Zhang, and Hongyu Zhao

Marcella Devoto and Mario Falchi

J€urgen Gadau, Christof Pietsch, and Leo W Beukeboom

viii Contents

de Compostela, Lugo, Galiza, Spain

Department of Public Health, Weill Cornell Medical College,

New York, NY, USA

Studies, University of Groningen, NL-9750 AA Haren, The Netherlands

Swedish University of Agricultural Sciences, Uppsala, Sweden;

Department of Cell and Molecular Biology, Uppsala University,

Uppsala, Sweden

LINS CHEN  Department of Health Studies, The University of Chicago,

Chicago, IL, USA

Suite 2200, Hendersonville, TN 37075, USA

Center, North Carolina State University, Raleigh, NC, USA

Pennsylvania State University, Hershey, PA 17033, USA

Philadelphia, PA, USA; Department of Pediatrics and CCEB,

University of Pennsylvania, Philadelphia, PA, USA; Dipartimento di MedicinaMolecolare, Universita’ degli Studi La Sapienza, Roma, Italy

NADERDEEB  Genus plc., 100 Bluegrass Commons Boulevard, Suite 2200,

Hendersonville, TN 37075, USA

Seattle, WA, USA

Imperial College, London, UK

Pennsylvania State University, Hershey, PA 17033, USA

JUNYIGAI  Soybean Research Institute of Nanjing Agricultural University,

National Center for Soybean Improvement, National Key Laboratory

for Crop Genetics and Germplasm Enhancement, Nanjing 210095, China

J€uRGENGADAU  School of Life Sciences, Arizona State University,

ZHONGWENHUANG  Department of Agronomy, Henan Institute of Science

and Technology, Xinxiang 453003, China

JOOSTJ.B KEURENTJES  Laboratory of Plant Physiology,

Wageningen University, Wageningen, The Netherlands;

Laboratory of Genetics, Wageningen University, Wageningen, The Netherlands

RIKKOOKE  Laboratory of Plant Physiology, Wageningen University,

Wageningen, The Netherlands

Pennsylvania State University, Hershey, PA 17033, USA

LUNLI  Hubei Bioinformatics and Molecular Imaging Key Laboratory,

Huazhong University of Science and Technology, Wuhan, Hubei, China;

Department of Epidemiology and Public Health, Yale University,

New Haven, CT, USA

YAOLI  Department of Statistics, West Virginia University, Morgantown,

WV 26506, USA

Hershey, PA, USA

Correnstrasse 3 D-06466, Gatersleben, Germany

La Jolla, CA 92093, USA

JAMESM REECY  Department of Animal Science, Iowa State University,

Ames, IA, USA

USDA-ARS Western Regional Research Center, Albany, CA 94710, USA

Hershey, PA, USA

North Carolina State University, Raleigh, NC, USA

Wageningen, The Netherlands

Pennsylvania State University, Hershey, PA 17033, USA

XIAO-LINWU  Departments of Animal Sciences & Dairy Science,

UW-Madison, Madison, WI, USA

University of Alabama at Birmingham, Birmingham, AL, USA

ZHAO-BANGZENG  Department of Statistics and Bioinformatics Research Center,North Carolina State University, Raleigh, NC, USA; Department of Genetics,North Carolina State University, Raleigh, NC, USA

University of Science and Technology of China, Hefei, Anhui, China;

Department of Epidemiology and Public Health, Yale University,

New Haven, CT, USA

x Contributors

YUAN-MINGZHANG  Section on Statistical Genomics, State Key Laboratory

of Crop Genetics and Germplasm Enhancement, Nanjing Agricultural University,Nanjing 210095, China

New Haven, CT, USA

Contributors xi

Part I

Setting Up Mapping Populations

Chapter 1

Backcross Populations and Near Isogenic Lines

Rik Kooke, Erik Wijnker, and Joost J.B Keurentjes

Key words: Near isogenic lines, Chromosome substitution strains, Heterogeneous inbred families, Bulk segregant analysis, Marker-assisted selection, Genetic mapping

1 Introduction

For many purposes, it can be very useful to swap genomic regions

of different species or species varieties For instance, one may want

to test different regions for allelic differences in a trait of interestand confirm the effect of predicted differences or breed in exoticproperties in elite lines The size and number of genomic regionsdepends on the objective, but generally a single small segment istransferred from a donor parent into the genetic background of arecipient parent The resulting lines are called introgression lines(ILs) or, because of their prevailing mode of construction, back-cross inbred lines (BILs) However, alternative ways are also in use,and we therefore prefer to use the term near isogenic lines (NILs)because of their genetic resemblance to the recipient parent.Although initially derived from heterogeneous progeny of selectedcrosses, NILs preferably are homozygous The genetic make-up isthen fixed in “immortal” lines which can be used endlessly and inmany replications in various experiments

As mentioned, NILs can be constructed through a variety ofmethods depending on the available resources In their simplest

Scott A Rifkin (ed.), Quantitative Trait Loci (QTL): Methods and Protocols, Methods in Molecular Biology, vol 871,

DOI 10.1007/978-1-61779-785-9_1, # Springer Science+Business Media New York 2012

3

form, introgression lines carry a single target locus from a donorvariety in an otherwise recurrent genetic background, i.e., isogenic

to the recipient parent In plant and animal breeding, the recipientparent is usually an enduring variety or inbred line/strain that hasthrived for decades despite the introduction of new varieties in thefield Donor chromosomal regions can be taken from any resource,like congenic species (see Note 1), advanced backcrosses (BCs),recombinant inbred lines (RILs), doubled haploids (DHs) (seeNote 2), heterogeneous inbred families (HIFs), or other mappingpopulations (F2/F3) (e.g., (1–3)) In all instances, however, thepoint of departure is a cross between two genotypes which segre-gate in subsequent generations and, in most cases, one to severalrounds of backcrossing and/or selfing are necessary to eventuallyretrieve the desired genomic constitution

NILs can serve many functions, ranging from breeding poses to genetic analyses of complex quantitative traits The ulti-mate objective of the lines determines for a large part the choice ofstarting material, crossing scheme, and eventually the genomiccomposition For instance, for the confirmation of a QTL detected

pur-in an RIL population (see Chapter3), a relatively large introgression

is sufficient which can be derived from backcrossing a selected RIL

to one of its parents On the other hand, to avoid linkage drag, i.e.,the simultaneous introgression of closely linked undesired geneticfactors, the inclusion of an exotic trait in an elite breeding linerequires a very small introgression and several generations of back-crossing after the initial F1 Other objectives such as (fine) mapping

or disentangling the genetic architecture of traits yet again requiredifferent approaches and accompanying selection criteria

Despite their different functions, the efficient generation ofsmall, targeted introgressions strongly depends on the employedselection method NILs preferably have a genomic fragment on thetargeted so-called carrier chromosome without additional donorgenomic regions on noncarrier chromosomes (4) Therefore,applying the right approaches in generating NILs is one thing,employing efficient selection methods is another Whereas in earlierdays phenotypic selection strategies were used, with the advent ofmolecular markers genotypic selection criteria are nowadays com-mon practice The choice of one selection strategy over anotherdepends on many factors including the subjected species, the cross-ing scheme applied, the desired genomic make-up, and intendedpurpose of the derived lines as well as time or cost constraints

In this chapter, we will discuss the construction and design ofNILs for a number of purposes We will take into account theconsequences of the choice of resources and crossing schemes andsuggest strategies for efficient selection of lines We will furtherillustrate the effect of differences in introgression size and popula-tion structure for several scenarios Finally, we will provide mathe-matical guidelines for the design and development of NILs

4 R Kooke et al.

2 Mendelizing

Genetic Effects

In many instances, NILs are constructed and used to confirmpreviously identified genetic loci that explain part of the variationobserved in a specific trait of interest Because many (quantitative)traits are controlled by multiple loci, each locus must be isolatedfrom its genetic background to be independently tested in a Men-delian fashion This allows for classic genetic analyses includingdominance and interaction effects Depending on the availableresources, NILs can be constructed in various ways which will beoutlined below

2.1 Phenotypic

Selection

Before the advent of molecular markers, phenotypic selection was acommon practice to create introgression lines In breeding pro-grams, phenotypic selection is still used frequently as an initialcriterion to reduce the number of individuals for molecularprofiling The starting material is always derived from a crossbetween the donor and recipient parent, but can either be a segre-gating (e.g., F2) or fixed (e.g., RIL) population From this popula-tion, a line with the desired phenotype is selected and backcrossed

to the recipient parent for several generations (Fig 1) In everygeneration, the progeny of the backcross is phenotyped and onlythose showing the desired properties are retained and further back-crossed Depending on the starting material, an isogenic recurrentbackground containing small causal donor introgressions can beachieved within two to eight rounds of backcrossing Note that noprior information about the number and genomic position of causalloci is required for this strategy That said, as selection is nottargeted to a single locus, multiple synergistically acting additiveloci might be introgressed and selected for, especially if trait valuesdepend on epistatic interactions However, the number of loci caneasily be deduced from the segregation ratios in subsequent gen-erations of backcrossing Furthermore, if the donor exhibits redun-dant loci, NILs with similar effects but different introgressions may

be obtained These can be confirmed in complementation crosses.2.2 Confirmation

of Mapped Loci

For many species, mapping populations exist or can be created (seeChapters 1–5) These populations serve to identify genomic loci(QTLs: see Note 3) that explain quantitative variation that can beobserved for traits that segregate among progeny of crosses ofdistinct parental lines Whether derived from BC, DH, RIL, orany other segregating population, all individual lines in a mappingpopulation are more or less densely genotyped This enables theselection of individuals carrying a genomic donor segment at theexact location of mapped QTLs and preferably a low proportion inthe remaining genome By selecting different lines, each QTL can

be Mendelized independently The selected lines are repeatedly

1 Backcross Populations and Near Isogenic Lines 5

backcrossed to the recurrent parent until only the desired genomicdonor segment remains and all other introgressions are lost Sincethe genomic composition of the starting material is known, only afew markers targeted at the donor introgressions are sufficient tosuccessfully monitor subsequent generations Once a single intro-gression at the desired position remains, this line can be fixed byselfing or sibling mating after which the homozygous NIL can bephenotyped and compared to the recurrent parent to confirm thepresence of a QTL in the introgressed region.

2.3 Fine Mapping

and Cloning

Upon QTL detection and confirmation, NILs can be used tofurther fine map and ultimately clone the causal gene For this,NILs spanning a QTL support interval are backcrossed to the

Fig 1 The construction of NILs through repeated backcrossing Crossing two genetically distinct parental lines results in a heterozygous offspring By backcrossing the heterozy- gote to the recipient parent, the proportion of donor parental genome is reduced with 50% In recurrent backcrosses, heterozygosity is further reduced to a small introgression followed by selfing or sibling mating to obtain a near isogenic line (NIL).

6 R Kooke et al.

recurrent parent to create lines heterozygous for the introgressedsegment Crossovers between the homologous chromosomes inthese lines result in recombinants with smaller introgression sizeswhich can be phenotyped again to establish the presence or absence

of the QTL in the reduced region In an iterative process of crossing, recombinant selection, and phenotyping, the QTL isultimately reduced to a single or a few genes which can then betested using functional genomics approaches

back-2.4 Heterogeneous

Inbred Families

A special case of inbred lines are HIFs (3) After crossing twodistinct parents, HIFs are inbred for five or six generations to createalmost complete homozygous genotypes except for a few smallregions (<5% of the genome size) (Fig 2) A collection of HIFscan be used like any other mapping population to identify QTLs.Upon detection of a QTL, however, a single line containing aheterozygous region coinciding with the QTL but otherwisehomozygous can be selected using the genotypic information ofthe population individuals Progeny of this line will segregate onlyfor the heterozygous region, creating homozygous lines with dif-ferent genotypes at the QTL region in a single generation TheseNILs can then be tested to compare the effect of the segregatingregion A hallmark of HIFs is their genomic composition which,although homozygous, is a mosaic of the two parental lines Thisoffers the advantage that often more than one HIF can be selectedwhich offers the possibility to evaluate the same locus in differentgenetic backgrounds This allows testing QTLs for epistatic inter-actions with other genomic regions which otherwise can only beachieved by crossing pure introgression lines (5)

Fig 2 The construction of heterogeneous inbred families (HIFs) A QTL detected in a RIL population can be confirmed by the use of HIFs A predecessor of a RIL which is still heterozygous for the region of interest but otherwise homozygous is selfed after which the heterozygous region segregates in a Mendelian fashion This enables the comparison of the trait of interest for that specific region for both parental genotypes in an isogenic background.

1 Backcross Populations and Near Isogenic Lines 7

3 NIL Mapping

Populations

In addition to confirming QTLs detected in mapping populations

or introducing exotic traits in elite breeding lines, NILs can be usedfor mapping purposes themselves A good indication of the pres-ence of genetic factors explaining differences in quantitative traits is

a comparison of distinct parental lines In a sense, parental linesrepresent the largest possible NILs, i.e., the genome of one parent

is completely replaced by that of another To detect which part(s) isresponsible for the observed phenotypic variation, the genomeneeds to be broken up into smaller introgressed segments dividedover multiple lines which together provide genome-wide coverage.Depending on the species involved, the available resources, and theexact purpose of the developed lines, several strategies are in usewhich will be outlined below

3.1 Bulk Segregant

Analysis

Bulk segregant analysis (BSA) is often used in combination withphenotypic selection strategies (see above) This is probably themost basic form of genetic linkage mapping as it does not require afully genotyped mapping population Usually a few rounds of back-crossing and/or inbreeding are sufficient to create a segregatingpopulation Trait values in such a genetic diverse population oftenshow a wide distribution range For qualitative traits, this will be abinominal distribution according to which the population can eas-ily be divided into two discrete classes For quantitative traits,however, the distribution will approximate normality due to thelarger number of loci involved Consequently, classifying popula-tion individuals on the basis of their phenotypes is much moredifficult and arbitrary, but two methods for bulk segregation ofquantitative distributions prevail The first method simply splitsthe population on the basis of the mean, median, or mode (depend-ing on the skewness) of the distribution The second method ismore strict and selects only the upper and lower quartile of thedistribution Both methods have their pros and cons Splitting usesall lines of the population, and therefore includes all possible varia-tion, but might misclassify individuals which reduces mappingpower Quartile classification, on the other hand, reduces the num-ber of misclassified lines, but only uses half the population size andmight only detect major effect loci In all cases, however, two bulksare formed containing lines of either one of the two designatedclasses In each bulk, all lines are pooled and the two resultingsamples can then be genotyped genome-wide with molecular mar-kers Note that markers need to be codominant to quantify allelicfrequencies; alternatively, each individual of the bulk can be geno-typed separately Genomic regions enriched for one of the twoparental genotypes in either bulk then indicate QTLs for the trait

8 R Kooke et al.

of interest In principle, all segregating populations can besubjected to BSA, but each will have their own specific properties(see Chapter4).

Fig 3 Genome-wide coverage NIL populations Different population designs can substantially affect population sizes, resolution, and power Shown are three different designs, a reciprocal chromosome substitution library, a library with adjacent large introgressions, and a library with small overlapping introgressions.

1 Backcross Populations and Near Isogenic Lines 9

larger population sizes, i.e., more lines, are needed to maintaingenome-wide coverage Especially for species with large genomesizes, this can considerably increase the number of lines to bemaintained and hence experimentation costs An alternative designconsists of a population of NILs with overlapping introgressions insuch a way that each genomic region is covered twice (or more).Such a population offers the experimenter the choice to exclude theoverlapping lines at the cost of decreased power and resolution, butwithout losing genome-wide coverage (Fig 3) Finally, one canchoose to develop a one-way or a reciprocal population, i.e., eachparental line serves both as recipient and donor parent in twoseparate collections of lines.

Once a certain design has been selected, NILs need to bedeveloped in a concerted action After generating an F1, this willusually take several rounds of backcrossing (depending on thegenome size, crossover frequencies (see Note 5 on heterochiasmy),and desired introgression sizes) followed by one or two generations

of selfing or sibling mating Eventually, NILs are selected by typing genomic regions using molecular markers The efficiency ofNIL construction can considerably be enhanced by using thesemarkers in what is called marker-assisted selection (MAS) Differentselection strategies have been defined based on marker selectionapplied to carrier and noncarrier chromosomes (7, 8) Two-stageselection is based on selection for the targeted segment on thecarrier chromosome (foreground selection) and against donorgenomic regions on noncarrier chromosomes (background selec-tion) Three-stage selection involves one more step that selects forthe amount of recombination between the target locus and itsflanking markers and between the flanking markers and the telo-meres on the carrier chromosome (8) Although in principle adesired genotype can be selected from a BC1 population, thisusually requires large population sizes, which exponentiallyincreases with the genome size (see Subheading 4) Therefore,having more backcrosses is generally advantageous over genotypingmore lines Because the level of heterozygosity is highest in earliergenerations, the number of backcrosses can substantially decreasegenotyping costs However, with each backcross, the average intro-gression size decreases, which needs to be considered when design-ing MAS strategies

geno-An example of using MAS in a crossing scheme could be to usetwo-stage selection in BC1and three-stage selection in advanced BCgenerations, minimizing both genotyping costs and the levels ofdonor parental DNA on noncarrier chromosomes (8) On noncarrierchromosomes, one can increase the number of markers in advancedgenerations and only use markers at the telomeres in early generations

to reduce genotyping costs Eventually all selected lines need to begenotyped at a resolution high enough to detect double crossovers(usually 10–20 cM) Finally, all desired lines which are still

10 R Kooke et al.

heterozygous for the introgressed region after backcrossing should beinbred to obtain a homozygous immortal mapping population.3.3 Chromosome

Substitution Strains

A special case of NILs are chromosome substitution strains (CSS):these carry the largest possible introgression of a single stretch ofDNA into a recipient background In such a strain, one of thechromosome pairs of the recipient parent has been substitutedwith that of another (donor) parent Reasons for CSS constructionmay be multiple: First, a complete set of CSSs provides a crudemapping population for QTLs, assigning QTLs to whole chromo-somes Second, a CSS removes a lot of background noise from thepopulation that greatly facilitates identification and fine mapping ofQTLs ((9) and see above) Finally, a CSS provides an excellentstarting point for the generation of smaller NILs A CSS can bebackcrossed to the recipient parent, introducing heterozygosity ononly one chromosome pair By subsequent backcrosses, the intro-gressed segment can be shortened until fixed by inbreeding.The general approach in constructing CSSs is very similar tothat described for NILs above An alternative approach that workswell for species with small genomes and large numbers of offspring

is selecting lines carrying a nonrecombinant chromosome 1,screening the selected lines for a nonrecombinant chromosome 2,and so on for all chromosomes This results in the elimination ofapproximately 50% of the individuals at every genotyping round,leaving a BC1population from which all CSS can be derived in thenext generation (10)

4.2 Minimal Distance

Between Markers

The genotype of individual lines at specific positions can be identified

by molecular markers (see Chapter5) The genotype at every otherposition, the marker intervals, needs to be estimated from its sur-rounding markers To reliably estimate the genotype between twoadjacent markers, their required maximal distance can be calculated.Incorrect estimates can result from double crossovers between adja-cent markers which consequently will not be observed The occur-rence of double crossovers is therefore dependent on therecombination frequency between markers, which can be calculatedusing Haldane’s mapping function:r¼1

2ð1  eð2d=100ÞÞ where d isthe distance between markers in cM From this formula, it can easily

be deduced that the probability of a single crossover event in a 20 cMregion is 17% and a double crossover less than 3% For a distance of

10 cM, the latter will be even less than 1% For most purposes, agenetic distance of 10–20 cM between markers is therefore sufficient

to reliably determine genome-wide genotypes Note that the tionship between genetic and physical distances is not constant overthe genome and can vary significantly between species

between two loci with a given probability again depends on thegenetic distance The relationship is given by the formula:

N ¼ Logð1rÞð1  PÞ, where N is the number of backcrosses, r isthe recombination frequency, andP is the probability of separation

To have 95% certainty that a crossover has occurred in a 20 cMinterval would then take 17 generations of backcrossing Equivalently,the probability of a crossover to occur between two loci at a givendistance and number of backcrosses would read asP ¼ 1  ð1  rÞN.The chance of a single crossover after four backcrosses over a distance

of 50 cM can then be calculated as 78% Over a distance of 1 cM, thiswould be 4% (11) The examples given here of course representrandom selections of single individuals In practice, however, multi-ple individuals are often selected which increases the probability ofcrossover occurrence and therefore decreases the number of back-crosses needed This is shown by the formula P ¼ 1  ð1  p1Þn

wherep1is the probability for a single individual andn the number

of selected individuals The chance that at least one out of tenindividuals carries a crossover in a 1 cM interval after four genera-tions of backcrossing would then be 34% (compare to 4% for a singleindividual)

4.4 Chromosome

Substitution Strains

The generation of CSSs requires the transmission of whole mosomes, and hence, depends upon the absence of crossovers Thechance of a certain chromosome not recombining is given by thefunction eðd=100Þwhered is the length of the chromosome in cM,while assuming no crossover interference (9) The chance of finding

chro-a specific nonrecombinchro-ant donor chromosome in chro-a BC1then equals

1

12 R Kooke et al.

nonrecombinant donor chromosome with a certainty of q, therequired number of individuals can be calculated by solving

2ð1  eð2d=100ÞÞ where d is the genetic distance in cM) (12).This probability can estimate the number of individuals that need

to be genotyped in BC1 to immediately obtain a pure CSS.The probability of obtaining a CSS is Pða non - recombinanttarget chromosomeÞ  P ðall other chromosomes recurrentÞ ¼

1

2eðd=100Þ1

2ð1  rÞðc1Þ From this formula, it can be easilydeduced that the number of individuals to be screened increasesrapidly with the chromosome number of the species For a specieswith only five chromosomes, fewer than 5000 BC1individuals need

to be screened to obtain all possible CSSs For a species with tenchromosomes, this would require millions of BC1individuals, andmultiple generations of backcrossing and selection are thereforeneeded

4.5 Fixing Heterozygous

Segments

After backcrossing, all introgressed regions are heterozygous, andtherefore selected lines require inbreeding to obtain immortalhomozygous lines The probability that a progeny carries a homo-zygous introgression after selfing is given by

P ¼ ð1  rÞ2=4 where r¼1

2ð1  eð2d=100ÞÞwhen assuming no interference The required population size toobtain the desired genotype with a probability of successq can then

be calculated as:n¼ lnð1  qÞ= lnð1  pÞ (13) For an introgressedsegment of 20 cM, this means that more than 36 individuals (n)need to be screened to obtain 99.9% confidence (q) of selecting thedesired homozygous line

5 Notes

1 Congenic strains in animals

In animals, isogenic lines are often termed congenic strains.Especially in vertebrates, congenic strains are far more difficult

to produce than, e.g., NILs in plants for a number of reasons.Vertebrates generally have a much longer generation time withlower numbers of offspring, suffer from inbreeding depression,and breeding is more costly These drawbacks make it almostimpossible to genotype a huge number of individuals and select

1 Backcross Populations and Near Isogenic Lines 13

the most promising ones for further generations Therefore, inanimal research often more generations and intermediate selec-tion are required to obtain a desired genotype.

2 Doubled haploids

A number of organisms, mostly plants but also certain animalspecies (e.g.,Drosophila and certain fish species), allow for theproduction of doubled haploids (DHs) These are homozy-gous offspring derived from haploid individuals who under-went chromosome doubling The unique properties of DHs lie

in the fact that they allow for the direct fixation of the geneticcontent in (micro- or macro-) spores (gametes) DHs produceimmortal lines and eliminate heterozygosity from offspring,thereby tremendously decreasing costs for genotyping DH-production diminishes inbreeding steps and therefore therecovery of heterozygotes in inbreds The use of DHs is wide-spread in agriculture where protocols have been developed formany crops (14)

3 Quantitative trait loci

Within plant and animal species, natural selection acting uponadaptations to different environmental conditions has led to awide range of natural variation in quantitative traits Mostagronomical traits, such as yield, nutritional value, and bio-mass, are quantitatively inherited These complex traits areaffected by a large number of genes, by environmental variationand by genotype-by-environment interactions For plant andanimal breeding, it is of high importance to identify the geno-mic regions (QTLs) and genes that contribute to variation inthese traits and use this knowledge to create new crop or strainvarieties QTL mapping is a powerful tool that can give a goodindication of the different genomic regions contributing to thetrait variation, the size of their effects, and epistatic interac-tions Most often, QTL mapping is performed on crossesbetween two strains or accessions that vary strongly for aparticular trait In offspring populations, genomic regions ofboth genotypes segregate With molecular markers, polymor-phic for the two parents, each individual line can be genotyped.Statistical analyses then associate the genomic regions betweenthe markers with the phenotypic trait under study (see alsoChapter3)

4 Interspecific crosses

In many breeding programs, attempts have been made to reference lines with their wild relatives to map or introgresstraits Such crosses inherently cause a number of distinctproblems which have been well documented (see (1) for

cross-an example in tomato breeding) Interspecific crosses ccross-ancause sterility and lethality problems in offspring caused byDobzhansky-Muller incompatibilities This may complicate

14 R Kooke et al.

RIL construction or lead to RIL populations showing strongsegregation distortions NILs may then provide viable alterna-tives since in NILs the introduced donor genome fraction ismuch smaller.

Apart from zygote inviability, sequence divergence or mosome rearrangements (such as inversions) can affect themeiotic behavior of chromosomes Crossover recombination

chro-is less likely to occur between homeologous chromosome ments than between homologous chromosome segments.Again, work on tomato introgression lines is worth consulting(15) When small, homeologous chromosome segments are to

seg-be introgressed, selection should initially seg-be aimed at obtainingthe largest introgressions, and not (as one might intuitivelythink) for the smallest introgressions The reason is that findingrecombinants close to the locus of interest in later generations

is much higher when the homeologous segment is large ler introgressions may show strong suppression of crossoverformation For a review on crossover behavior, see (16)

Smal-5 Heterochiasmy

It may be worthwhile to pay attention to sexual differences incrossover frequencies since, depending on the species, thesemay vary (strongly) between sexes In Arabidopsis thalianafor example, the number of crossovers during microsporogen-esis is twofold higher as compared to megasporogenesis Thiscan have large consequences for the efficiency of breedingprograms When crossover incidence is to be maximized

in the offspring of anArabidopsis heterozygote, as is the case

in the shortening of introgressed segments in backcross lations (NILs), the heterozygote should preferably be used

popu-as the male parent in crosses When crossovers are not desired

in a line, e.g., when constructing chromosome substitutionlines, the heterozygote should be used as the female parent,which increases the chance of finding the required allele com-binations twofold

References

1 Eshed Y, Zamir D (1995) An introgression line

population of Lycopersicon pennellii in the

cultivated tomato enables the identification

and fine mapping of yield-associated QTL.

Genetics 141:1147–1162

2 Alonso-Blanco C, Bentsink L, Hanhart CJ,

Vries HBE, Koornneef M (2003) Analysis

of natural allelic variation at seed dormancy

loci of Arabidopsis thaliana Genetics

164:711–729

3 Tuinstra MR, Ejeta G, Goldsbrough PB (1997) Heterogeneous inbred family (HIF) analysis: a method for developing near-isogenic lines that differ at quantitative trait loci Theor Appl Genet 95:1005–1011

4 Hospital F (2002) Marker-assisted backcross breeding: a case study in genotype building theory In: Kang MS (ed) Quantitative genet- ics, genomics and plant breeding CAB Inter- national, New York

1 Backcross Populations and Near Isogenic Lines 15

5 Loudet O, Gaudon V, Trubuil A, Daniel-Vedele

F (2005) Quantitative trait loci controlling root

growth and architecture in Arabidopsis thaliana

confirmed by heterogeneous inbred family.

Theor Appl Genet 110:742–753

6 Keurentjes JJB, Bentsink L, Alonso-Blanco C,

Hanhart CJ, Blankestijn-De Vries H, Effgen S

et al (2007) Development of a near-isogenic

line population of Arabidopsis thaliana and

comparison of mapping power with a

recombi-nant inbred line population Genetics

175:891–905

7 Frisch M, Bohn M, Melchinger AE (1999)

Comparison of selection strategies for

marker-assisted backcrossing of a gene Crop Sci

39:1295–1301

8 Falke KC, Miedaner T, Frisch M (2009)

Selec-tion strategies for the development of rye

introgression libraries Theor Appl Genet

119:595–603

9 Koumproglou R, Wilkes TM, Townson P,

Wang XY, Beynon J, Pooni HS et al (2002)

STAIRS: a new genetic resource for functional

genomic studies of Arabidopsis Plant J 31:

12 Visscher PM, Haley CS, Thompson R (1996) Marker-assisted introgression in backcross breeding programs Genetics 144:1923–1932

13 Frisch M, Bohn M, Melchinger AE (1999) Minimum sample size and optimal positioning

of flanking markers in marker-assisted crossing for transfer of a target gene Crop Sci 39:967–975

back-14 Forster BP, Heberle-Bors E, Kasha KJ, Touraev

A (2007) The resurgence of haploids in higher plants Trends Plant Sci 12:368–375

15 Canady MA, Ji Y, Chetelat RT (2006) ologous recombination in Solanum lycopersi- coides introgression lines of cultivated tomato Genetics 174:1775–1788

Home-16 Wijnker E, de Jong H (2008) Managing otic recombination in plant breeding Trends Plant Sci 13:640–646

mei-16 R Kooke et al.

Chapter 2

F2 Designs for QTL Analysis

Yuan-Ming Zhang

Abstract

This chapter covers the procedure of mapping quantitative trait loci (QTLs) in an F2breeding design.

I describe genetic design, general methods and software, and several commonly used approaches The genetic design section includes F2population construction Widely used methods and software are introduced in the section of general methods and software Finally, composite interval mapping, penalized maximum likeli- hood, and empirical Bayes are described in detail Some issues related to the F 2 design are discussed Key words: F 2 design, Quantitative trait locus, Composite interval mapping, Penalized maximum likelihood, Empirical Bayes, Multiple quantitative trait loci model, Segregation analysis

1 Introduction

In modern quantitative genetics, phenotypic values, populationstructure, and marker information are used to infer the number ofquantitative trait loci (QTLs) and to estimate their positions andeffects One key advance in QTL mapping was the introduction ofinterval mapping in a population from a cross between two inbredlines (1) Many variants of this approach have been developed, andthey mainly focus on segregation populations such as F2, backcross,double haploid (DH), and recombinant inbred line (RIL) popula-tions ((2–7), Chapter3)

F2populations play an important role in the genetic dissection

of quantitative traits for several reasons First, all kinds of geneticeffects (additive, dominant, and all kinds of epistatic effects) can beestimated Second, many genetic populations and designs arederived from the F2, including the F2:3 design, RIL, advancedintercross lines (AILs), and triple testcross (TTC) design Third, alarge F2 population derived from two near-isogenic lines isfrequently used in the fine mapping of QTL In this chapter, wefocus on the essential F2design for QTL analysis

Scott A Rifkin (ed.), Quantitative Trait Loci (QTL): Methods and Protocols, Methods in Molecular Biology, vol 871,

DOI 10.1007/978-1-61779-785-9_2, # Springer Science+Business Media New York 2012

17

2 Genetic Design

Several methods exist to construct an F2 population Theseapproaches are described as below using plants as an example

1 A female parent (inbred line, homozygous genotype) is crossed

to a male parent (inbred line, homozygous genotype) The F1

plants are selfed to develop F2seeds (Fig.1) All F2seeds areplanted to construct an F2plant population and these F2plantsare genotyped for molecular markers and phenotyped for thetrait These phenotypic values along with molecular markerinformation are used to detect QTLs for quantitative traits.This is the most widely and commonly used method in coarsemapping of QTLs

2 Immortalized F2(IF2)population: This idea was first presented

by Gardiner et al (8) The heterozygosity of the F2population

is “immortalized” by pooled random mating in the F3 andsubsequent generations, because the genotype of the F2 ismaintained in each pooled IF2 family The procedure is asfollows Forty F3seeds from each F2plant are planted in tworows On successive pollinating days, pollen from five F3plants

in one row is bulked and the bulked pollen is used to pollinatefive F3 plant in the same IF2 family A minimum of 20 earsare bulked to immortalize the F2 Recently, another design forthe IF2was proposed by Hua et al (9) according to a doublehaploid (DH) or recombination inbred line (RIL) population(Fig.2) In this design, all the DH lines or RILs are randomlydivided into two groups with same sample size The lines ineach group are randomly numbered The ith line in the firstgroup is crossed to theith line in the second group Each ofthese lines is used only once in each round of pairing and

Fig 1 Construction of an F2 population.

18 Y.-M Zhang

crossing In order to increase the sample size of the IF2, theabove procedure may be repeated multiple times This popula-tion resembles an F2population in that the compositions andfrequencies of single- and multilocus genotypes are similar tothose of an F2population.

3 Residual heterozygous line (RHL): The RHL design was posed by Yamanaka et al (10) for fine mapping QTLs Itincludes two steps (Fig.3) First, a line is selected from an F4

pro-population such that its genome contains a heterozygous ment around a major QTL, but is homozygous in otherregions, including other QTLs

seg-Fig 3 Construction of an F2 population using residual heterozygous line.

Fig 2 Construction of an “immortalized F2” population (a) The IF2 population is derived from a DH or RIL population; (b) the construction procedure; and (c) pairing between two RILs from different groups.

2 F2Designs for QTL Analysis 19

Second, the selected RHL is selfed to construct a large gating F2population at the target region This design is similar tothe heterogeneous inbred family of Tuinstra et al (11) However,the purpose of the latter is to develop near-isogenic lines thatdiffer at the detected QTLs in order to confirm the QTLs.

segre-4 The F2:3design: In the most widely used F2design above, all F3

seeds from one F2plant are planted to construct an F2:3familyand each F2:3family is phenotyped for quantitative trait Thus,the strategy of using F2 marker genotypes and F2:3 averagephenotypes for QTL mapping is named as the F2:3design (12)

3 General Methods

and Software

There are a series of methods available for detecting QTLs in an

F2 population, such as interval mapping (1), composite intervalmapping (13–15), multiple interval mapping (16), Bayesian analysis(5, 17), and penalized maximum likelihood (PML) method(18) Several packages (cataloged at: http://www.stat.wisc.edu/

~yandell/statgen/software/biosci/qtl.html) have been developed

to implement these methods, such as Windows QTL CartographerV2.5_005 ((19), http://statgen.ncsu.edu/qtlcart/WQTLCart.htm), R/qtlbim v1.7.7 ((20), http://www.qtlbim.org), and QTLNetwork 2.0 ((21),http://ibi.zju.edu.cn/software/qtlnetwork/).Here we introduce three methods: composite interval mapping, thePML, and empirical Bayes ((22),http://www.statgen.ucr.edu/)

4 Composite

Interval Mapping

popula-tion Let us define the three possible genotypes by QQ, Qq, and qq.The phenotypic value of quantitative trait for theith F2plant,yi,may be described as below

i ¼ 0 for QQ, x

i ¼ 0 and z

for Qq,xi ¼ 1 and z

i ¼ 0 for qq, and similar definition for xikand

zik; and eiis a residual error with an assumedNð0; s2Þ distribution

20 Y.-M Zhang

a ¼Xn

i¼1

ðp 1i p

i¼1

ðp 1iþ p 3iÞ,

d ¼X

n i¼1

p2iðyi XiBÞ Xn

i¼1

p2i,

Xn i¼1

½p 1iðyi XiB  aÞ2þ p

2iðyi XiB  dÞ2

þ p 3iðyi XiB þ aÞ2

(3)

where Xi is the ith row of matrix X, Ps ¼ ðp

siÞn1(s ¼ 1; 2; 3),Y ¼ ðyiÞn1and

The hypotheses to be tested are H0: a ¼ d¼ 0 and

H1: a6¼ 0; d6¼ 0 The likelihood ratio statistic is

LOD¼ lg Lða; d; B; s2Þ

Lða¼ 0; d¼ 0; ~B; ~s2Þ (4)where

~B ¼ ðX0XÞ1X0Yand

~s2 ¼1

nðY  XBÞ0ðY  XBÞ:

2 F2Designs for QTL Analysis 21

The critical value for the LOD score obtained from 1,000imputation experiments is often used to declare the presence of aputative QTL in a given genomic region The QTL confidenceinterval (90–95%) is often defined as a map interval that corre-sponds to one LOD decline on either side of the peak.

This approach can be performed by Windows QTL pher V2.5_005

recip-ðg  2Þth family population of the kth cross (i ¼ 1;    ; nr2;

g¼ 3; ; ~G;k¼ 1; 2), yiðr2Þk, may be described by the followingmodel:

½xijxiðR1þ2l1ÞðaeÞjl þ xijxiðR1þ2lÞðdeÞjl

GC¼Xm

l¼1

½xcxiðR1þ2l1ÞðacÞl þ xcxiðR1þ2lÞðdcÞlwhere R and m are the numbers of environments and QTL,respectively, a is additive effect, d is dominant effect, ae isadditive-by-environment interaction effect, de is dominant-by-environment interaction effect,ac is additive-by-cytoplasm interac-tion effect,dc is dominant-by-cytoplasm interaction effect, and x is

a dummy variable for various effects To reflect the genetic ship among various generations, the value ofx for a heterozygous

relation-Fgfamily is two times that for heterozygous Fg 1family If the dataare involved only in one of direct or reciprocal crosses, the

22 Y.-M Zhang

cytoplasmic and cytoplasm-by-QTL interaction effects cannot beconsidered in the model (5) If the data are involved only in oneenvironment, the environmental and environment-by-QTL inter-action effects cannot be considered in the model (5).

Because all kinds of effects in model (5) are treated in the sameway under the PML, model (5) can be rewritten for the sake ofclarity as:

yu¼X

p l¼1

zulblþ ei ðu ¼ 1;    ; nÞ (6)

where p¼ ðR þ 1Þð2m þ 1Þ, and n ¼ 3  504 ¼ 1; 512 Thepseudomarker approach uses the multimarker analysis with a slightmodification by inserting virtual markers into all marker intervals

>5 cM Because of incomplete genotypic information in the realdata analysis, multiple permutations for incomplete marker geno-types (23) can be adopted to simulate the incomplete genotypes.This requires multiple analyses of the data, one for each imputeddataset Ten to fifty imputed datasets are usually sufficient For eachsample, the complete genotypes sampled are used to construct thedesign matrix for QTL effects in model (6)

If an IF2population is available, the molecular marker tion of all the IF2plants is not needed, because the marker infor-mation for each IF2plant can be derived from its parents (Table1).Therefore, the phenotypic values for IF2 plants along with thededuced marker information are available in QTL mapping Thegenetic model and corresponding methods are same as those in the

informa-F2design

If RHL is available, the RHL is selfed to construct a new F2population In the F2population, we scan only the target region ofgenome Therefore, the information of markers on the targetregion along with the phenotypic value of a complex trait is used

to perform fine mapping of QTL The genetic model andcorresponding methods are same as those in the F2design

zulbl; s2Þ

p l¼2

Xn u¼1

ðyuX

p l6¼t

Xn u¼1

ðyuX

p l¼1

> 2 compared to the total number of imputed samples (30) would

be considered real The QTL position is an average weighted by thetotal genetic variance of QTL detected The reported result is themean of estimates for each imputed data set When marker density istoo high, choosing one marker from the cluster of markers avoids ahigh degree of multicollinearity When the markers are too sparse,virtual markers (treated as missing data) may be inserted When thenumber of effects in the model (6) is much larger than sample size(e.g., 20 times), a two-stage method is proposed In the first stage, afull model including all effects is divided into many reduced models,

24 Y.-M Zhang

each with about 2,000 effects (or ten times sample size) In thesecond stage, the genetic model is modified so that only effectsthat have passed the first round of selection are included in themodel, and PML can be used to reanalyze the data.

where b is the non-QTL effect vector (e.g., the year effect),X is thecorresponding design matrix, gl is a vector of genotypic effect forlocusl, and Zl is the corresponding incidence matrix determined bythe genotypes of locusl The residual error vector e is assumed to

be distributed as e N ð0; s2InÞ, where In is an n  n identitymatrix and s2is an unknown residual error variance

lZl0V1ðy  XbÞ and var(glÞ ¼Is2

to the classical F2:3design (12).

The second design is TTC design It entails crossing the ithindividual of an F2 population to the same three testers, the twoinbred lines (P1and P2), and their F1, to produce 3n families (L1i,

L2i, andL3i) The design provides separate tests for, and estimates

of, the additive, dominance, and epistatic components of variability.Recently, we have developed a two-stage approach, which providesunbiased estimates for all the QTL effects

There are some shortcomings for the F2 design First, the

F2 population is temporally limited and used only one time Toovercome this problem, the RIL population by single-seed descentand the IF2design are available Second, there is rarely recombina-tion in F2 populations between closely linked loci because thegametes have undergone only a single cycle of recombination.AILs increase the number of recombination events Recently, Kaoand Zeng (24) have developed a statistical method for QTLmapping in advanced populations derived from two inbred lines,such as AILs In molecular biology, SNP marker can be also used toovercome this issue Third, most triploid endosperm trait locimapping methods do not produce unbiased estimates of the twodominant effects of endosperm trait loci A random hybridizationdesign is an alternative method that may be used to overcome thisproblem (25) In addition, in any highly heterozygous outbredspecies, such as most trees and livestock, inbred lines cannot bedeveloped and the cross between two heterozygous individuals isoften named as pseudotestcross This is because many markers areheterozygous in one parent, null in the other, and therefore segre-gate 1 : 1 in their F1progeny following a testcross configuration Ifmany markers are heterozygous in the two parents, their F1prog-eny will follow a F2configuration In theory, it is more similar tofour-way cross (26)

26 Y.-M Zhang

at least 24-model combinations are considered to select one modelthat best explain the quantitative trait variation by using bothAkaike’s information criterion and a set of tests of fitness Finally,the estimates of genetic parameters are calculated from the esti-mates of component distributions in the optimal genetic model Allformulae and analytical procedures have been established for asingle segregating population with or without its parents, including

F2and F2:3; for five generations of P1, P2, F1, F2, and F2:3; and forsix generations of P1, P2, F1, BC1, BC2, and F2(29) This approachhas been widely applied in China However, this is a phenotypicanalysis method, the major genes detected cannot be localized onchromosomes, and the estimates of genetic parameters have largererrors relative to QTL mapping

7.3 Multi-QTL Joint

Analysis

In interval mapping, the estimated position and effect of a putativeQTL may be biased by the presence of other QTLs linked withinthe same chromosome, especially if the linkage is tight In theextreme situation when the two linked QTLs have effects in oppo-site directions, the QTLs can cancel each other out and neither ofthem will be detected On the other hand, if the two linked QTLshave effects in the same direction, a “ghost” QTL may be detectedbetween the two real QTLs To overcome the above issues, it isnecessary to use a multi-QTL genetic model to estimate all QTLeffects simultaneously in a single model Jansen and Zeng indepen-dently proposed composite interval mapping (13–15) Thereafter,Kao et al developed multiple interval mapping (16) Recently,various multi-QTL analyses have been successively developed,such as PML approach (18) and the empirical Bayes method (22)

2 F2Designs for QTL Analysis 27

The multi-QTL joint analysis approach differs from the classicalmethods First, the joint analysis approach can jointly analyze adataset with multiple environments or replicates This increasessample size so that more QTLs can be detected using the newmethods than for the classical methods (22, 30) Second, mainand environmental effects and environmental and epistatic interac-tions are simultaneously considered in a single genetic model.

A single-QTL model with the choice of markers to include ascofactors is tested once in composite interval mapping, while inmultiple interval mapping a multi-QTL and interaction geneticmodel is studied In other words, no interaction is included in thegenetic model of composite interval mapping, and two commonkinds of interactions—QTL-by-environment and interactionbetween the loci without main effects—are not evaluated in multi-ple interval mapping Results show that the joint analysis seems to

be more powerful Therefore, we recommend the joint analysisapproach

Acknowledgments

The work was supported by the National Natural Science tion of China (30971848 and 30671333), the 111 Project(B08025), NCET (NCET-05-0489), and the FundamentalResearch Funds for the Central Universities (KYT201002).References

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28 Y.-M Zhang