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*ɲuGlb$7̔)%%v[C{W/?b$'I*5:=UU!b$ɫK#_ ?Cy&zEwb$Lz&qjDThe linear regression method is the most complex point analysis method, allowing different characteristics of the QTL to be investigated. Including: Additive effectskEmFFlanking marker methods have been the most popular analysis techniques over recent years, because of their accuracy and level of characterisation of the putative QTL. There are two basic techniques in the flanking marker frame work: Maximum likelihoodnHtLpIIn each method of estimation, a likelihood profile of the region between two flanking markers is produced. The log of each likelihood is then mapped against chromosome position to produce a likelihood map, like the one below: qKThe maximum likelihood estimate of map position is the highest point on the map. Whole chromosomes can be mapped by analysis of different regions, the maps can be joined producing a likelihood profile of the entire chromosome.  zT{UmThe regression method uses significantly less computational power to estimate maximum likelihood parameters. nn  ~XYMThere are four different techniques, within the multipoint mapping framework:NN Marker regression]^The idea behind marker regressions is to utilize the linear relationship between the apparent affects of a marker on a quantitative character, and the substantial effects of all related QTLs that are linked to that marker.  abComposite interval mapping uses multiple markers as additional factors in the analysis, and is an expansion of the basic interval mapping technique. Five different types of markers are considered, depending on the characteristics of the chromosome region: (Markers surrounding the QTL of interest $()cdThe standard marker trait regression approach uses properties of the regression of phenotype on marker genotype. The regression coefficients change depending on whether a QTL is present in the flanking region or not: TIf a QTL is present, the regression coefficients are significantly different to zeroUUefMultiple interval mapping uses multiple marker intervals simultaneously and aims to map multiple QTL in a single step. It is possible to detect: Epistatic QTL $ gh5QTLs have been detected in many species, for example:66 1 Arabidopsis  i Circadian rhythm  four QTL were detected through maximum likelihood $+ Kj Fruit ripening time  two QTLs were detected through regression analysis$. N/k ~Seed dormancy  four QTLs were detected by ANOVA analysis 4)?&l Tolerance to salinity  four QTL were mapped controlling different aspects$."PmhA comprehensive set of references links and further information is available on the associated web site./http://nasc.nott.ac.uk/students/qtl/frames.html00X  !0//!& ' /6:Pb ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>>+0 j(    6k P  T Click to edit Master title style! !  0\n   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0[ ``  >*  0  `   @*  0 `   D*r  ZA ޽h ?Purple mesh ̙33 Default Design0 `l(  l l 0 P    T*   l 0     V*  d l c $ ?   l 0  @  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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P ,$D  0 }+ Allelic variations are fully functional 6+ (2+ /  < TD ??@ -,$D  0 w% Individual gene effects are small 6% (2% @  < T ??` `M,$D  0 6 The genes involved can be dominant, or co-dominant 66 (26 .  < T8 ?? @,$D  0 v: Many different genotypes can produce the same phenotype ;!(2;V  < T@ ??,$D  0 2 The genes involved can be subject to epistasis 62 (22 ' H < 0޽h ? 3̙33@C 0 6(    0W ?Markers in QTL researchArial Black"`   TO ??  <6/50(2  NA  ??@,$D  0  NA ??0 @,$D  0H  0޽h ? ̙33Y `m (  ~  s *ij     <u ` ` <$6 0    T ?? 0,$0 <7/50(2j  Td# ?? `pm ,$D  0 , Random amplified polymorphic DNA (RAPDs) 6, (2, , R   ` ?? `Y ,$D  0 2 Amplified fragment length polymorphisms (AFLPs)3!3,7  TS ?? ` ,$D  0  Microsatellites 6 (2 H  0޽h ? ̙33P  :(    4W ?Progenies in QTL researchArial Black"`pP   Tpy ??  <8/50(2  NA  ??p,$D  0  NA ??0 ,$D  0H  0޽h ? ̙33 a LD(     0x   x  B ?"   S tAT?C:\My Documents\QTL\graphics\picture2.gifP@!,$D. 0  T ?? P` <9/50(2H  0޽h ? ̙33/ aC W(     0     S nAN?C:\My Documents\QTL\graphics\lines.gifP,$D. 0  T ??  =10/50(2H  0޽h ? ̙33 @ C(    <W ?Probabilities in QTL researchArial Black"`@$i   T ??  =11/50(2  NA  ??p,$D  0   NA ??0 p,$D  0H  0޽h ? ̙331 a  Y(   ~   s *      S vAV?C:\My Documents\QTL\graphics\equation1.gif;,$D2 0   T ??  =12/50(2H   0޽h ? ̙33 `m ogH(  H~ H s *@    H S ` <$' 0  9 H Nf ?? p,$D 0 OThe resulting conditional probabilities are subsequently used in QTL detection.P(2P  H T ?? ,$D 0 =13/50(2% H T@ ?? `Z ,$D  0 m The gamete frequencies 8 (2  0 H T  ??` ,$D  0 x$ The marker genotype probabilities 8$ (2$  H H 0޽h ? ̙33@C P D7(  D D 0W ?QTL analysis techniquesArial Black"`L)  D TT  ??  =14/50(2 D NA  ??p,$D  0  D NA ??0 ,$D  0H D 0޽h ? ̙33 8J 5-pL(  L~ L s *\{    L s *<|3 <$X 0   L T} ??  =15/50(2 L T ?? PW ,$D  0  Flanking marker analysis  uses a pair of markers simultaneously D0  (2K , L T9 ??p `,$D  0  Composite multipoint mapping  uses multiple markers simultaneously D3  (2N H L 0޽h ? ̙33 @ ` H3(  H H ,W ?Single point analysisArial Black"}  H T ?? p =16/50(2 H NA  ??p,$D  0  H NA ??0 ,$D  0H H 0޽h ? ̙332 R `pZ(  p~ p s *q    p s *r3``<$X 0   p T t ??  0 =17/50(2 p Ty ??@` M ,$D  0 E ANOVA"!(2   p TȨ ??0  ,$D  0 S Multiple regression"!(2   p TD ??   ,$D  0 Q Linear regression"!(2 H p 0޽h ? ̙33PC p '(     W ?T-test analysisArial Black"c   T  ??  =18/50(2  NA  ??pr,$D  0   NA ??0 ,$D  0H  0޽h ? ̙33  N =5P (  ~  s *lc      Nff  ??  ,$D 0 b*More details can be found on the web page+(2+ *l P `@   P`@,$D: 02   A ??White marbleP `@L$D 0 !0   # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))www  ,$D 0   TLk ??  =19/50(2H  0޽h ? ̙33` } (    zW ?ANOVA Arial Black"p`   T0' ??  =20/50(2  NA  ??p,$D  0   NA ?? p,$D  0H  0޽h ? ̙33 R C;@ (  ~  s *dW       NXf  ??` p ,$D 0 b*More details can be found on the web page+(2+ 0l p0   0 p,$D: 0 2  # A ??White marblep0 L$D 0 !0  # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))www ,$D 0   T] ??  =21/50(2H  0޽h ? ̙33PC  /(    (W ?Multiple regressionArial Black"`   TT0 ??  =22/50(2  NA  ??  ,$D  0   NA ?? ,$D  0H  0޽h ? ̙33 8J C;0 (  ~  s *L     N( f  ??  ,$D 0 b*More details can be found on the web page+(2+ 0l 0 @    0@ ,$D. 0 2  # A ??White marble0 @ L$D 0 !0   # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))wwwP  ,$D 0   TQ ??  =23/50(2H  0޽h ? ̙33@  /(    (W ?Linear regression Arial Black"5   Tx9 ?? ` =24/50(2  NA  ??pr,$D  0   NA ??0 ,$D  0H  0޽h ? ̙33      * (     0t>      0@?3<$. 0    N?f  ?? ,$D 0 b*More details can be found on the web page+(2+ 0l `   `  ,$D 0 2  # A ??White marble`  L$D 0 !0  # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))wwwp ,$D 0   T E ??  =25/50(2    T` ?? ,$D  0 h Dominance effects 8 (2 2   T@ ?? 0 ,$D  0 z Epistasis 8  (2   /   T ??0 @D ,$D  0 w# Genotype/environment interaction 8# (2# H  0޽h ? ̙33C  ;(    4W ?Flanking marker methods Arial Black"   T; ??  =26/50(2  NA  ?? ,$D  0   NA ??0 ,$D  0H  0޽h ? ̙33` R (  ~  s *3     s *43<$2 0    T 6 ?? P =27/50(2O  T ? ??P p,$D  0 7 Maximum likelihood estimation through regression D)  (27 H  0޽h ? ̙33@  -(    &W ?Maximum likelihoodArial Black"0 W)   T ?? 0 =28/50(2  NA  ??p,$D  0   NA ?? ,$D  0H  0޽h ? ̙33xi ]U(    6M ?"P {CThere are three different methods of maximum likelihood estimation:D(2D   s *r3 @` ,$(# 0 n Single marker maximum likelihood! !  Nyf  ?? ,$D 0 The power of detection increases from simple single marker to order restricted. Flanking marker maximum likelihood probably has the most applications.(2   T6 ?? p =29/50(21  T ??`P ,$D  0 y% Flanking marker maximum likelihood 8% (2% 0  TK ??` ,$D  0 x$ Order restricted interval mapping 8$ (2$ H  0޽h ? ̙339 a a(  ~  s *,@     S ~A ^?C:\My Documents\QTL\graphics\likelihoodmap.gif@p,$D: 0  T. ??  =30/50(2H  0޽h ? ̙33W  (  ~  s *     63 ?"p[ ,$D: 0 There is one major problem with maximum likelihood estimation, the intense computational nature of calculation. The method requires specialist software and is therefore inappropriate in some cases.  2   N(!f  ?? P ,$D 0 b*More details can be found on the web page+(2+ 0l ` p   `p,$D' 0 2   # A ??White marble` pL$D 0' !0   # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))www t,$D 0  T% ?? p =31/50(2H  0޽h ? ̙33U  }(    vW ?Maximum likelihood estimation through regression analysisArial Black"Pl%   T ?? @ =32/50(2  NA  ??@,$D  0   NA ??0 p,$D  0H  0޽h ? ̙33  b     (   ~   s *4P      63 ?",$D(# 0 The regression is calculated from character values of the individual genotypes, the resulting regression values are then plotted to produce a graph similar to that produced by maximum likelihood. 2   6 ?" ,$D' 0 There have been arguments as to the accuracy of estimation under some circumstances. However, the computational simplicity has made the regression method the standard choice over recent years. 2   Nf  ?? p *,$D 0 b*More details can be found on the web page+(2+ 0l  P   P,$D' 0 2   # A ??White marble PL$D 0 !0   # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))wwwPP ~,$D 0   TD ?? @ =33/50(2H   0޽h ? ̙33-@  U(    NW ?Composite multipoint mapping methodsArial Black"@N   T ??  =34/50(2  NA  ?? ,$D  0   NA ?? ,$D  0H  0޽h ? ̙33 U :2(  ~  s *@P     s * 3@0@<$(# 0    T ??  =35/50(2)  T ??@ ,$D  0 q Composite interval mapping 8 (2 0  T ??@@pT ,$D  0 x$ Standard marker-trait regressions 8$ (2$ (  T ?? @ ,$D  0 p Multiple interval mapping 8 (2 H  0޽h ? ̙33@C  ,=(  , , 6W ?Marker trait regressions Arial Black"`e  , T ??  =36/50(2 , NA  ??@r,$D  0  , NA ??0 p,$D  0H , 0޽h ? ̙33M 0u 0u(  0~ 0 s *h    0 63 ?"P` ,$D. 0 Differences in the distance between the QTL and the markers alter factors in this relationship. Therefore markers can be used as beacons, from which these relative effects can be measured. 2  0 NPf  ?? p ,$D 0 b*More details can be found on the web page+(2+ 0l `    0`  ,$D. 0 2  0 # A ??White marble`  L$D 0 !0  0 # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))wwwP ~,$D 0 0 T8 ?? pp =37/50(2H 0 0޽h ? ̙33P  LA(  L L  6W ??Composite interval mappingArial Black`  L T8 ?? 0 =38/50(2 L NA  ??pr,$D  0  L NA ??0 ,$D  0H L 0޽h ? ̙33(  XC    PP (  P~ P s *١    P S ١` <$: 0    P Nhۡf  ?? ,$D 0 b*More details can be found on the web page+(2+ 0l p   P ,$D 0 2 P # A ??White marblep L$D 0 !0  P # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))www  ND,$D 0  P T ??  =39/50(22  P T ??0 `0 ,$D  0 z( Linked markers within the QTL region 6( (2( 3 P T4' ??P ` = ,$D  0 {) Linked markers outside the QTL region 6) (2) 4 P TP ??p `],$D  0 |* Unlinked markers within the QTL region 6* (2*  P T ??   ,$D  0 f* Unlinked markers outside the QTL region +!(2+H P 0޽h ? ̙33+@   TS(  T T  HW ??Standard marker trait regressionsArial Black@  T T ??  =40/50(2 T NA  ?? r,$D  0  T NA ??0 p,$D  0H T 0޽h ? ̙33  }C H @  X(  X~ X s *ǡ    X S ǡ@<$. 0   X NLɡf  ?? p ,$D 0 b*More details can be found on the web page+(2+ 0l   X ,$D 0 2 X # A ??White marble L$D 0 !0 X # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))wwwP ~t,$D 0 X Nf ??@ @p ,$D 0 j2Position and effect can subsequently be calculated3(23  X TPѡ ?? P =41/50(23  X T ??  ,$D  0 {? If a QTL is not present the regression coefficients are zero @!(2@H X 0޽h ? ̙33@ 0 \?(  \ \  4W ??Multiple interval mappingArial Black0)  \ T ?? P` =42/50(2 \ NA  ??r,$D  0  \ NA ?? @,$D  0H \ 0޽h ? ̙33*  }    `R (  `~ ` s *    ` S <$' 0  I ` N䵡f ??  ,$D 0 aThe method is an extension of standard interval mapping and tends to be more powerful and preciseb 2b ` Nĺf  ?? p ,$D 0 b*More details can be found on the web page+(2+ 0l   ` ,$D 0 2 ` # A ??White marble L$D 0 !0 ` # > WdF ?8| 0'<P]?QTL Times New Roman ___H!___5H)))wwwP ~t,$D 0  ` T ?? p =43/50(2#  ` T<' ?? ,$D  0 k Individual QTL values 6 (2 U  ` T ' ??0  ,$D  0 ) Heritabilities of Quantitative traits 6) (2) H ` 0޽h ? ̙33C @ d?(  d d  4W ??Examples of QTL detectionArial Black0@  d TL ??  =44/50(2 d NA  ??pr,$D  0  d NA ??0 p,$D  0H d 0޽h ? ̙33; hB hc(  h~ h s *P    h S  @@<$ 0   h Tp ?? 0 =45/50(2 h T% ??P@P ,$D  0 F Tomato" !(2   h Txf' ??  ,$D  0 ] Barley 8  (2    h TH,' ?? 0* ,$D  0 [ Rice 8 (2  H h 0޽h ? ̙33  N aYp l(  l l S  p @ <$ 0   l  W ??ArabidopsisArial Black * l N ??P,$D 0 x(QTLs have been detected associated with:) 2) $v l N ??" l C tA ZC:\My Documents\QTL\graphics\arabidopsis.jpg,$D 0  l T ??  =46/50(2  l TT' ??@ 0,$D 0 D Trichome spacing  a single QTL was detected through the use of RILs and maximum likelihood08! 2+ 2c,=H l 0޽h ? ̙33   NC ? 7 ` p(  p p S @ <$ 0   p  W ??TomatoArial Black 0* p N0{ ??,$D 0 x(QTLs have been detected associated with:) 2) %v p N ??77  p C jAPC:\My Documents\QTL\graphics\tomato.gif,$D 0  p T\~ ??   =47/50(2  p Tm' ??P ,$D 0 . Resistance to bacterial wilt  two QTLs were detected through interval mapping D9  (2V $.  p T' ?? 0,$D 0 H Comparison with wild type  166 QTLs were detected through single point regression analysis D- 6 (2c !>H p 0޽h ? ̙33  ] @ 8 P t(  t t S ho<$ 0   t  W ??BarleyArial Black   t Nq ??P ,$D 0 ]'QTL have been detected associated with:( 2( v t N ??cxc t C jAPC:\My Documents\QTL\graphics\barley.gifq,$D 0  t Tu ??  =48/50(2  t T' ?? 0,$D 0 0 Disease resistance  loci for a number of different diseases mapped as single QTLs D9 " (2[U  t TԞ' ?? 0w,$D 0 b Drechslera teres resistance  12 QTLs were mapped by composite interval mapping d. ) (2C ,1H t 0޽h ? ̙33 ] XP@ x(  x x S 0 <$ 0   x   W ??RiceArial Black   x N e ??P,$D 0 ]'QTL have been detected associated with:( 2( v x N ??JsJ x C fALC:\My Documents\QTL\graphics\rice.jpg,$D 0  x Th ??  =49/50(2  x TT' ?? ` ,$D 0  Development of tiller number  15 QTL were mapped by composite interval mapping D. ) (2W \  x T' ??P d ,$D 0 P Heading date  two QTL 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"CJB"``g`gafa```aa뒒쒒쒒쒒쒒쒒쒒뒒`a`g```aaf``f```=a`a``a``af``a`g```aaf``f```=a`a``a``af``a`g```aaf``f```=a`a``aJJr"Cn!C"f``fa`af`af=af`a``f``af``f`>f``fa`af`af=af`a``f``af``f`>f``fa`af`af=af`a``f``af``f`>f``fa`af`af=af`a``f``af``f`>f``fa`af`af=af`a``f``af``f`>f``fa`af```a````=``````a```````````````a````=``````a```````````````a````=``````a```````````````a````=``````a```````````````a````=``````a```````````````a````=``````a`````=```=`=``g`a=```=```=<===`=`=```=`=``g`a=```=```=<===`=`=```=`=``g`a=```=```=<===`=`=```=`=``g`a=```=```=<===`=`=```=`=``g`a=```=```=<===`=`=```=`=``g`a=```=`` "--&TNPP & ՜.+,D՜.+,H    On-screen Shown-sj2 4Times New RomanDefault DesignPowerPoint PresentationQuantitative traits are continuous characters. Variation in continuous characters is due to a number of loci each of which have a small yet variable effect. Quantitative genetics attempts to characterize quantitative traits in terms of:Quantitative trait locus (QTL)Quantitative trait locus (QTL)The basic theory of QTL mapping is to score a population for a trait according to the marker genotype. Statistics are then used to identify differences associated with the markers and the trait of interest. QTLs have the following characteristics:PowerPoint PresentationThe study of QTLs relies on the availability of segregating markers that can be used to divide up the population. The availability of markers limited QTL research before the emergence of DNA markers such as:PowerPoint PresentationQTL analysis can be classified by the type of progeny used. All of the different progenies are derived from the same reference population, produced by crossing two inbred lines, shown below:From this reference population seven progenies are produced, with different uses, in different QTL analysis techniques. The derivation of these progenies is shown below:PowerPoint PresentationThe conditional probability that the QTL genotype can be deduced from the known marker genotypes, is the basis on which QTL analysis operates. The conditional probability equation is shown below:HIt is possible to calculate the conditional probability in an F2, from:PowerPoint Presentation7There are three basic techniques used in QTL analysis:PowerPoint PresentationUIn the point analysis framework, there are four techniques that have been developed:PowerPoint PresentationThis method uses the simple students T-test to evaluate the presence of a QTL, through statistical differences between marker genotypes. The T-test can only be used in experimental designs where two marker genotypes are present.PowerPoint Presentation The ANOVA method is used to detect marker differences when there are more than two marker genotypes. It essentially produces a ranking of genotypes, in order of phenotypic effect for the trait of interest, and tests for significant differences between each genotype.PowerPoint PresentationThe multiple regression method is a simple remodelling of the ANOVA technique in regression terms, with the same ranking and testing for differences.PowerPoint PresentationThe linear regression method is the most complex point analysis method, allowing different characteristics of the QTL to be investigated. Including:PowerPoint PresentationFlanking marker methods have been the most popular analysis techniques over recent years, because of their accuracy and level of characterisation of the putative QTL. There are two basic techniques in the flanking marker frame work:PowerPoint PresentationPowerPoint PresentationIn each method of estimation, a likelihood profile of the region between two flanking markers is produced. The log of each likelihood is then mapped against chromosome position to produce a likelihood map, like the one below:The maximum likelihood estimate of map position is the highest point on the map. Whole chromosomes can be mapped by analysis of different regions, the maps can be joined producing a likelihood profile of the entire chromosome.PowerPoint PresentationnThe regression method uses significantly less computational power to estimate maximum likelihood parameters. PowerPoint PresentationNThere are four different techniques, within the multipoint mapping framework:PowerPoint PresentationThe idea behind marker regressions is to utilize the linear relationship between the apparent affects of a marker on a quantitative character, and the substantial effects of all related QTLs that are linked to that marker.PowerPoint PresentationComposite interval mapping uses multiple markers as additional factors in the analysis, and is an expansion of the basic interval mapping technique. Five different types of markers are considered, depending on the characteristics of the chromosome region:PowerPoint PresentationThe standard marker trait regression approach uses properties of the regression of phenotype on marker genotype. The regression coefficients change depending on whether a QTL is present in the flanking region or not:PowerPoint PresentationMultiple interval mapping uses multiple marker intervals simultaneously and aims to map multiple QTL in a single step. It is possible to detect:PowerPoint Presentation6QTLs have been detected in many species, for example:PowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationiA comprehensive set of references links and further information is available on the associated web site.  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;: 9  765   4 3  2 1 0/  . - , 8  + *  )  (' & % $ # <(R$=VYjL#=/}> R$ &-d9 ) b$BIợZUG$R$Fv *ɲuGlb$7̔)%%v[C{W/?b$'I*5:=UU!b$ɫK#_ ?Cy&zEwb$Lz&qjDThe linear regression method is the most complex point analysis method, allowing different characteristics of the QTL to be investigated. Including: Additive effectskEmFFlanking marker methods have been the most popular analysis techniques over recent years, because of their accuracy and level of characterisation of the putative QTL. There are two basic techniques in the flanking marker frame work: Maximum likelihoodnHtLpIIn each method of estimation, a likelihood profile of the region between two flanking markers is produced. The log of each likelihood is then mapped against chromosome position to produce a likelihood map, like the one below: qKThe maximum likelihood estimate of map position is the highest point on the map. Whole chromosomes can be mapped by analysis of different regions, the maps can be joined producing a likelihood profile of the entire chromosome.  zT{UmThe regression method uses significantly less computational power to estimate maximum likelihood parameters. nn  ~XYMThere are four different techniques, within the multipoint mapping framework:NN Marker regression]^The idea behind marker regressions is to utilize the linear relationship between the apparent affects of a marker on a quantitative character, and the substantial effects of all related QTLs that are linked to that marker.  abComposite interval mapping uses multiple markers as additional factors in the analysis, and is an expansion of the basic interval mapping technique. Five different types of markers are considered, depending on the characteristics of the chromosome region: (Markers surrounding the QTL of interest $()cdThe standard marker trait regression approach uses properties of the regression of phenotype on marker genotype. The regression coefficients change depending on whether a QTL is present in the flanking region or not: TIf a QTL is present, the regression coefficients are significantly different to zeroUUefMultiple interval mapping uses multiple marker intervals simultaneously and aims to map multiple QTL in a single step. It is possible to detect: Epistatic QTL $ gh5QTLs have been detected in many species, for example:66 1 Arabidopsis  i Circadian rhythm  four QTL were detected through maximum likelihood $+ Kj Fruit ripening time  two QTLs were detected through regression analysis$. N/k ~Seed dormancy  four QTLs were detected by ANOVA analysis 4)?&l Tolerance to salinity  four QTL were mapped controlling different aspects$."PmhA comprehensive set of references links and further information is available on the associated web site./http://nasc.nott.ac.uk/students/qtl/frames.html00X  !0//!& ' /6:Pbr  |j