Breeding new sugarcane clones by mixed models under genotype by environmental interaction

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1 66 Scintia Sugarcan Agricola brding by mixd modls Brding nw sugarcan clons by mixd modls undr gnotyp by nvironmntal intraction Gustavo Mnzs Gonçalvs, Alxandr Pio Viana *, Antônio Tixira do Amaral Junior, Marcos Don Villa d Rsnd 3 Ptrobras-Bioful, Av. Rpública do Chil, Rio d Janiro, RJ Brazil. Stat Univrsity of North Fluminns Gntic and Plant Brding Lab., Av. Albrto Lamgo, Campos dos Goytacazs, RJ Brazil. 3 Embrapa Forstry, Estrada da Ribira, km, C.P Colombo, PR Brazil. *Corrsponding author <pirapora@unf.br> ABSTRACT: Sugarcan (Saccharum spp.) is on of th most important crops cultivatd in th tropics and subtropics and plays a signifi cant conomic and nvironmntal rol in Brazil. Twntyfour nw clons wr valuatd in diffrnt locations as potntial modls for rcommndation as nw varitis. Th mixd modl mthodology, using th harmonic man of th rlativ prformanc of gntic valus (MHPRVG), facilitatd th analysis of gnotypic stability and adaptability, culminating in th rcommndation of clons for ach location. MHPRVG rankd clons RB9579, RB86755, SP8-350, RB94750 and RB93530 as th bst fi v, and, additionally, clons with gratr gnotypic potntial wr idntifi d for ach tst in th six localitis. Editd by: Natalia d-lon Rcivd April 7, 03 Accptd Sptmbr 03, 03 Introduction Sugarcan (Saccharum spp.) is on of th most important spcis cultivatd in th tropics and subtropics and plays a significant conomic and nvironmntal rol in Brazil, occupying a total ara of 8.57 million hctars in th agricultural yars 0/0, according to data from th Companhia Nacional d Abastcimnto (Conab, 0) (National Supply Company). A larg numbr of clons ar valuatd vry yar in sugar can brding programs, in xprimnts conductd in diffrnt harvsts, sasons and rgions. It is bcoming incrasingly difficult to slct th bst gnotyps phnotypically. On of th most important aspcts in gntic brding is th prdiction of th gntic valus of gnotyps, which rquirs stimating varianc componnts that ar ithr known or accuratly stimatd. Thus, th optimal procdur for prdicting th bst linar unbiasd prdiction (BLUP) of gntic valus and th optimal procdur for stimating th rsidual or rstrictd maximum liklihood (REML) varianc componnts ar both associatd with a mixd linar modl. In studis on gntic brding, considration of tratmnt ffcts as random ffcts lads to gratr prdictiv accuracy. This is rlvant in gntic brding programs and allows for gntic slction. Othrwis, th slction is phnotypic rathr than gntic (Viana t al., 0; Viana t al., 0). Th simultanous considration of all nvironmnts commands th us of a univariat modl for slction, taking into account avrag productivity in th various nvironmnts. Howvr, a mor complt mthodology may allow additional infrncs, such as slction of th following: spcific gnotyps for ach location, stabl gnotyps across locations, gnotyps rsponsiv to nvironmntal improvmnt and slction on thr attributs (productivity, stability and adaptability) simultanously, Mnds t al. (0). Th prsnt study aimd to slct th most productiv clons of sugar can for a rgion in th southast of Brazil, through xprimntation on clons in th final stag of valuation, by invstigating adaptability and stability paramtrs through mixd modling. Matrials and Mthods In March and April of 005, six xprimnts wr carrid out in Campos dos Goytacazs, in th stat of Rio d Janiro (º45 5 S, 4º9 8 W - sits and ); Concição da Barra, in th stat of Espírito Santo (ES) (8º35 36 S, 39º43 56 W - sit 3); Linhars-ES (9º3 8 S, 40º04 0 W - sit 4); Itapmirim-ES (º00 40 S, 40º50 0 W - sit 5); and Srra dos Aimorés, in th stat of Minas Grais (7º46 57 S, 40º4 5 W - sit 6). Twnty-four clons wr assssd at ach sit, fiv of which wr considrd as standard, whil th othr 9 wr gnotyps with potntial for rcommndation in th rgions undr valuation, som of which hav alrady bn launchd as varitis in othr rgions of th country. Th rlationship btwn th clons is st out in Tabl. Th clons wr grown undr rainfd cultivation and rcivd managmnt tratmnts, including frtilization and wd control, in accordanc with th standard practics in forc at ach sugar mill fild. Th xprimnts wr conductd in a randomizd block dsign with four rplications, and ach plot formd consistd of four 5-m can furrows. Th xprimnts wr valuatd ovr thr agricultural yars, and th last harvst was carrid out in 008. Th plots wr

2 67 harvstd and valuatd prior to dtrash with fir in commrcial plantations in th chosn localitis. Th trait tons of Pol pr hctar wr valuatd by th product of th variabl ton of can pr hctar and th prcntag of sucros in th can. Estimats of th varianc componnts and prdictions of th gntic valus wr mad using th REML/ BLUP procdur. Th simultanous slction for yild, stability and adaptability of clons was basd on th harmonic man of th rlativ prformanc of th prdictd gntic valus (MHPRVG). All ths analyss wr don using th modl blow (Mnds t al., 0). y = Xf + Zg + Qg + Tgm + Wgml + Sp + () whr "y" is th vctor of data; "f" th vctor of th ffcts of rplication-nvironmnt-yar combinations (assumd to b fixd) addd to th ovrall avrag; "g" th vctor of th gnotypic ffcts (assumd to b random); "g" th vctor of th ffcts of th intraction btwn gnotyps and nvironmnts (random); "gm" th vctor of th ffcts of gnotyp yar intraction; "gml" th vctor of th ffcts of th gnotyp nvironmnt yar tripl intraction (assumd to b random); "p" th vctor of th prmannt ffcts of th plot within nvironmnts (assumd to b random), and "" th vctor of rrors or rsidus (random). Th capital lttrs rfr to th matrics of incidnc for ths ffcts, and th adjustmnt of th modl was drivd from th following mixd modl quations: X ' X X ' Z X ' Q X ' T X ' W X ' S f ˆ X ' y Z' X Z' Z A ˆ Z' Q Z' T Z' W Z' S g Z ' y QX ' QZ ' QQ ' A ˆ QT ' QW ' QS ' gl T' X T' Z T' Q T' T A 3 T' W T' S Q' y gmˆ T' y W ' X W ' Z W ' Q W ' T W ' W A 4 W ' S gmlˆ W ' y SX ' SZ ' SQ ' ST ' SW ' SS ' A 5 pˆ S' y whr:,,, 3 g, 4 gm, 5 gml p g g whr:, th gnotypic corrlation ovr th yars was stimatd by, th gnotypic corrlation of th nvironmnts, th gnotypic corrlation of th nvironmnt yar intraction was stimatd by. Th BLUP prdiction of gnotypic avrags in ach nvironmnt was stimatd basd on th sum of th avrag valus and ffcts of gnotyps and thir intraction. Th gnotypic valus prdictd for clon i in ach nvironmnt j usd, simultanously, th data from all th nvironmnts and wr stimatd by VG ij = i + g i + g ij + gm ik + p l, whr i is th avrag of nvironmnt j. Th joint slction considring, simultanously, ton of Pol pr hctar, stability and adaptability, was givn by th statistical harmonic man of rlativ prformanc for th prdictd gnotypic valus, n MHPRVG i = n VG, whr n = numbr of nvironmnts in which ij j= clon i was valuatd, and VG ij is th gnotypic valu of clon i in th nvironmnt j, xprssd as th ratio of () (3) th avrag for this nvironmnt. For th analyss SELE- GEN softwar was usd. Rsults and Discussion Estimats of avrag hritability of clons (h m) wr mad whr avrags wr usd as th unit of valuation. This calculation of hritability is of grat intrst, sinc its prdiction is basd on th avrags of svral rplications. Th stimat of th indx found for this study was 0.65, which is considrd modrat to high, and ncourags xpctations of suprior clon slction. Th gnotypic corrlation of th rspons of clons in th nvironmnts ( r gl) provids a dgr of rliability with rgard to how constant th ranking of clons will b in ths various nvironmnts. For such, a valu of 0.38 was found, suggsting a high lvl of gnotyp nvironmnt intraction and indicats that th bst clon in on nvironmnt may not b th bst in anothr. Silva t al. (0) found this valu to b 0.635, which indicats th xistnc of a wid gnotyp nvironmnt intraction. Th gnotypic corrlation stimat of th prformanc of clons ovr th yars has providd a valu only marginally suprior to r g. Howvr, this valu (r g = 0.68) is still ratd as low, which indicats intraction btwn gnotyps and harvsts. Thrfor, clons should b valuatd in mor than on cropping sason in brding programs. Whn th stimation of th gnotypic corrlation of th bhavior of clons in nvironmnts and yars (nvironmnts) is considrd, th importanc of studis on adaptability and stability bcoms vidnt, sinc its valu is xtrmly low, namly, 0., which indicats a complx gnotyp nvironmnt intraction. In othr words, th classification of clons will not b th sam in diffrnt nvironmnts. Th basic supposition of th analysis of varianc and rgrssion analysis, in studis on adaptability and stability, is th indpndnc of rrors, which is a a procdur that in practic, in mor complx situations is imprcis; whil th REML mthod (rstrictd maximum liklihood) may not tak this assumption into considration and can b mor flxibl in its application. Furthrmor, th analysis of varianc shows limitations in joint analyss in th cas of htrognity of rsidual variancs btwn nvironmnts, which dos not occur in REML (Viana t al., 0; Viana t al., 0). In th cas of mixd modls with random tratmnt ffcts, th main proprtis of BLUP ar: (i) maximization of slctiv accuracy, (ii) minimization of prdiction rror in non-biasd prdiction of gntic valus, and (iii) maximization of gntic gain pr cycl of slction and maximization of liklihood of slcting th bst among svral gnotyps. BLUP is th most fficint slction indx for th us of information from rlativs. Th BLUP of th ffcts of gnotyp nvironmnt

3 68 highst gnotypic valus. Although ths two slctions ar idntical as rgards th clons slctd, th prdictions of gnotypic valus ar highr for µ + g + g m. Howvr, this supriority will only b capitalizd if th clons ar plantd in aras with th sam standards of intraction btwn gnotyps and nvironmnts as th xprimntal ntwork valuatd. Thus, th gnotypic avrags basd on µ + g ar mor rliabl. Th prdictd gntic gains with th cultivation of th fiv bst clons in ach location (undrlind valus), in rlation to th avrag, ar, 8, 9,, and % for sits,, 3, 4, 5 and 6, rspctivly. BLUP valus obtaind for ach sugar mill tak into account th information from th ntir xprimntal ntwork. Thrfor, ths stimats ar mor accurat than th calculation of BLUP valus obtaind through analyss pr nvironmnt. Th infrncs prviously found wr applid to clon slction through gnotypic valus, whthr th gnotyp nvironmnt intraction wr capitalizd or not. Howvr, whn analysing adaptability and stability, it was ncssary to apply othr mthodologis. Nowadays, thr ar numrous mthodologis that can b usd to valuat phnotypic adaptability and stabilintraction (g ) taks into account th hritability of th ffcts of th g intraction, thrby liminating nois or th rsidual ffcts of th intraction during th procss of th g prdiction. Tabl prsnts th classification of th gnotypic valus of th 4 clons valuatd for th trait tons of pol pr hctar (TPH) for th 8 nvironmnts (six localitis thr harvsts). Th clons RB9579, RB86755, SP8-350, RB94750 and RB prsnt th highst BLUP valus for gnotypic valus for th nvironmnt without capitalizing th gnotyp nvironmnt intraction (µ + g). Whn gnotypic valus (µ + g) ar usd for gnotyp classification, thy can b applid in nvironmnts diffrnt from thos whr thy wr valuatd, sinc this stimat is not capitalizd with th ffct of th gnotyp nvironmnt intraction (Bastos t al., 007; Maia t al., 009). Thrfor, th sam rspons is xpctd for th avrag in diffrnt nvironmnts. Whn th gnotyp nvironmnt intraction (µ + g + g) is capitalizd, rcommndations should b put into practic in aras of th sam xprimntal ntwork or in aras with th sam pattrn of gnotyp nvironmnt intraction. By applying µ + g + g m, th sam fiv clons sortd for µ + g ar slctd from thos with th Tabl Estimats of th gnotypic valus without capitalizing th gnotyp nvironmnt (µ + g) intraction and capitalizing th avrag gnotyp nvironmnt intraction (µ + g + g m ) and capitalizing th gnotyp nvironmnt intraction for ach location (µ + g + g) for th trait tons of pol pr hctar valuatd in six Localitis, during thr yars in 4 clons of sugarcan. µ+g. Clon Sit Sit Sit 3 Sit 4 Sit 5 Sit 6 Avrag Environmnt µ + g + g µ + g + g µ + g + g µ + g + g µ + g + g µ + g + g µ + g + g m µ + g RB RB SP RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB Avrag Gntic Gain (%) Localitis: Sits and : Campos dos Goytacazs-RJ; Sit 3: Concição da Barra-ES; Sit 4: Linhars-ES; Sit 5: Itapmirim-ES; Sit 6: Srra dos Aimorés-MG. Gntic gain wr stimatd by slction for bst fi v gnotyps ach location.

4 69 ity, but th simplst intrprtation procdurs hav bn mor apprciatd. Thus, masurs that incorporat both stability and adaptability in a singl statistical figur ar th prvailing ons. Most procdurs for th analysis of adaptability and stability us phnotypic avrags aftr prforming th analysis of varianc, including th mthodologis of Ebrhart and Russll (966) and Lin and Binns (988), which stimat adaptability and phnotypic stability. In turn, th MHPRVG mthod, proposd by Mnds t al. (0), is basd on gnotypic valus prdictd via mixd modls, whr th trm adaptability and gnotypic stability can b usd, which aggrgats productivity, stability and adaptability into a singl statistical datum. As for th infrncs for xpctd productivity, gnotypic valus should b usd as follows (Pdrozo t al., 0): i) for planting in th fild of ach sugar mill: considring gnotypic valus by using th gnotyp nvironmnt intraction for ach nvironmnt (µ + g + g); ii) for planting in othr placs with th sam standard of gnotyp nvironmnt intraction as th xprimntal ntwork: considring gnotypic valus by using th gnotyp avrag nvironmnt intraction (µ + g + g m ) or th adaptability of gnotypic valus (PRVG); iii) for planting in othr unknown nvironmnts or whn using a standard of gnotyp nvironmnt intraction diffrnt from th xprimntal ntwork or with high nvironmntal htrognity within th nvironmnt that taks into account gnotypic valus without capitalizing gnotyp nvironmnt intraction (µ + g) or th stability of gnotypic valus (MHVG); iv) and for planting in svral othr nvironmnts with diffrnt standards of gnotyp nvironmnt intraction: considring stability and adaptability of gnotypic valus (MHPRVG). Th MHPRVG mthod was adoptd for this study. Tabl prsnts th rsults for th stability of gnotypic valus (MHVG), adaptability of gnotypic valus (PRVG and PRVG x µ) and th stability and adaptability of gnotypic valus (MHPRVG and MHPRVG x µ) for th trait TPH, as prdictd by BLUP analysis for 4 clons of sugar can. Th harmonic man of gntic valus (MHVG) classifis gnotyps for gnotypic valus (productivity) and stability, th lowr th standard dviation of th gnotypic prformanc btwn nvironmnts, th highr th MHVG valu. Thus, slction basd on this valu implis simultanous slction for yild and stability, (Mnds t al., 0). Bastos t al. (007) valuatd 70 clons and two controls of sugarcan in svn nvironmnts and found high corrlation btwn th gnotypic valus by capitalizing th gnotyp nvironmnt intraction with th valus prdictd by MHPRVG, which wr ffctiv for gnotyp slction. Tabl Stability of gnotypic valus (MHVG); adaptability of gnotypic valus (PRVG and PRVG µ); stability and adaptability of gnotypic valus (MHPRVG and MHPRVG µ) for th trait tons of pol pr hctar prdictd by BLUP analysis for 4 clons of sugarcan. Clon MHVG Clon PRVG PRVGxµ Clon MHPRVG MHPRVGxµ RB RB RB RB RB RB RB SP SP SP RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB RB936. RB RB RB RB RB MHVG: harmonic man of gnotypic valus; PRVG: rlativ prformanc of gnotypic valus; MHPRVG: harmonic man of th rlativ prformanc of gnotypic valus; µ: ovrall avrag.

5 70 Out of th fiv bst clons for MHVG (RB9579, RB86755, RB93530, SP8-350 and RB94750), four ar among th fiv bst clons classifid by joint analysis of gnotypic valus (xcluding clon RB93530). In rlation to typ of studis, Bastos t al. (007) concludd that th MHVG mthod is a slction that is sufficintly rliabl whr th aim is stability and productivity. Howvr, Mnds t al. (0) rportd that this mthodology cannot b considrd rliabl for analyzing information from unbalancd xprimnts whr not all clons ar prsnt in all nvironmnts. Th mthod of rlativ prformanc of gnotypic valus (PRVG) stimats th adaptability of gntic valus in diffrnt nvironmnts. In this mthodology, th prdictd gnotypic valus ar xprssd as a ratio of th ovrall avrag of ach location. Thn, th avrag valu of this ratio is obtaind through th nvironmnts (Mnds t al., 0). It is possibl to obsrv that th fiv bst clons ratd by MHVG wr also th bst using PRVG. Estimats of MHVG, and PRVG and MHPRVG in cashw plants mad by Maia t al. (009) allowd for slction of mor productiv gnotyps. Thy concludd that ths mthodologis can b usd in brding programs for this crop. Th MHPRVG mthod (harmonic man of th rlativ prformanc of gntic valus) proposd by Mnds t al. (0) is among th mixd modls and allows simultanous slction for productivity, stability and adaptability. Clons RB9579, RB86755, SP8-350, RB94750 and RB93530 stood out in simultanous slction for productivity, stability and adaptability and wr ratd in th fiv first positions. It is possibl to obsrv crtain maintnanc of th ordr of matrials in ths thr mthodologis, which indicats that th mthods MHVG, PRVG and MHPRVG hav a crtain dgr of agrmnt in th positioning of gnotyps. For diffrnt stratgis, a comparison btwn th mthodologis of Lin and Binns (988) and MHPRVG, with th slction of th tn bst clons, as sortd by MHPRVG, showd that ight clons slctd by MH- PRVG coincid with th tn clons slctd using th mthodology of Lin and Binns (988). Howvr, thr was also som rvrs ordr among som ovrlapping clons. Nvrthlss, high corrlation is obsrvd btwn th two mthods, also rportd by Bastos t al. (007). Mnds t al. (0) showd that th MHPRVG mthodology has th advantag of providing rsults in th vry scal usd for masuring th trait, which allows for calculating gntic gain with simultanous slction for yild, adaptability and stability. Svral clons wr rankd among th fiv bst for mor than on of th six localitis tstd (Tabl 3), which dmonstrats grat productiv potntial. Clons RB9579 (fiv localitis), RB86755 (four localitis) and clons RB758540, RB93530, SP8-350 and RB94750 stood out and wr among th most productiv in thr out of th six localitis valuatd. As th ffcts of tratmnts (clons) wr accptd as random, tsts for multipl comparisons of tratmnt mans ar inappropriat (Viana t al., 0; Pipho, 998). REML/BLUP (tratmnts as random ffcts) should b usd, instad of a comparison of mans (tratmnts as fixd ffcts). RB9579, RB86755, SP8-350, RB94750, RB and RB93530 wr th bst suitd clons for planting in othr nvironmnts with th sam pattrn of intraction btwn gnotyps and th nvironmnt of th xprimntal ntwork (Tabl 4). Ths clons wr rcommndd for planting in othr unknown nvironmnts, or whr thr is a pattrn of th intraction btwn gnotyps and diffrnt nvironmnts of th xprimntal ntwork or high nvironmntal htrognity within th nvironmnt. Clons RB9579, RB86755, Tabl 4 Clons includd among th bst fi v gnotypic valus for itms ii, iii and iv for th six localitis valuatd for th trait tons of pol pr hctar for 4 clons of sugarcan. Managmnt Suggstd ii iii iv µ + g + g m PRVG µ + g MHVG MHPRVG RB9579 RB9579 RB9579 RB9579 RB9579 RB86755 RB86755 RB86755 RB86755 RB86755 SP8-350 SP8-350 SP8-350 RB93530 SP8-350 RB94750 RB93530 RB94750 SP8-350 RB94750 RB RB94750 RB RB94750 RB ii: planting in othr nvironmnts with th sam pattrn of intraction btwn gnotyp and nvironmnt of xprimntal ntwork, iii: planting in othr unknown nvironmnts or with pattrn of gnotyp nvironmnt intraction diffrnt from that of th xprimntal ntwork or with high nvironmntal htrognity within th nvironmnt; iv: planting in many othr nvironmnts with diffrnt pattrns of gnotyp nvironmnt intraction. PRVG: rlativ prformanc of gnotypic valus, MHVG: harmonic man of gnotypic valus, MHPRVG: harmonic man of th rlativ prformanc of gnotypic valus. Tabl 3 Clons includd in th fi v highst gnotypic valus for sugarcan, capitalizing th gnotyp nvironmnt intraction (µ + g + g), for th six localitis valuatd for th trait tons of pol pr hctar. Sit Sit Sit 3 Sit 4 Sit 5 Sit 6 RB9579 RB86755 RB9579 RB9579 RB9579 RB9579 RB86755 RB RB86755 SP8-350 RB94750 RB86755 RB RB93530 SP8-350 RB94750 RB93530 SP8-350 RB93530 RB9606 RB94750 RB95597 RB95597 RB88698 RB9865 RB8555 RB RB95696 RB88698 RB7454 Localitis: Sits and : Campos dos Goytacazs-RJ; Sit 3: Concição da Barra-ES; Sit 4: Linhars-ES; Sit 5: Itapmirim-ES; Sit 6: Srra dos Aimorés-MG.

6 7 SP8-350, RB94750 and RB wr slctd for planting in svral othr nvironmnts with diffrnt pattrns of gnotyp nvironmnt intraction. In conclusion, th mixd modl mthodology provd adquat for valuating adaptability and stability, as wll as for slcting gnotyps with rsponsiv supriority in assssmnts of various plantation nvironmnts. Rfrncs Bastos, I.T.; Barbosa, M.H.P.; Rsnd, M.D.V.; Ptrnlli, L.A.; Silvira, L.C.I.; Donda, L.R.; Fortunato, A.A.; Costa, P.M.A; Figuirdo, I.C.R Assssmnt of gnotyp nvironmnt intraction in sugar can sugar by mixd modls. Psquisa Agropcuária Tropical 37: (in Portugus, with abstract in English). Companhia Nacional d Abastcimnto [CONAB]. 0. Monitoring of th Brazilian can sugar harvst, crop 0/. Availabl at: [Accssd Spt 9, 0] Ebrhart, S.A.; Russl, W.A Stability paramtrs for comparing varitis. Crop Scinc 6: Lin, C.S.; Binns, M.R A supriority masur of cultivar prformanc for cultivar x location data. Canadian Journal of Plant Scinc 68: Maia, M.C.C.; Rsnd, M.D.V.; Paiva, J.R.; Cavalcanti, J.J.V.; Barros, L.M Simultanous slction for yild, adaptability and gnotypic stability in cashw clons by mixd modls. Psquisa Agropcuária Tropical 39: (in Portugus, with abstract in English). Mnds, F.F.; Guimarãs, L.J.M.; Souza, J.C.; Guimarãs, P.E.O.; Pachco, C.A.P.; Machado, J.R.A.; Mirlls, W.F.; Silva, A.R.; Parntoni, N. 0. Adaptability and stability of maiz varitis using mixd modls mthodology. Crop Brding and Applid Biotchnology : -7. Pdrozo, C.A.; Barbosa, M.H.P.; Silva, F.L.S.; Rsnd, M.D.V.; Ptrnlli, L.A. 0. Rpatability of full-sib sugarcan familis across harvsts and th fficincy of arly slction. Euphytica 8: Pipho, H.P Empirical bst linar unbiasd prdiction in cultivar trials using factor analytic varianc-covarianc structurs. Thortical and Applid Gntics 97: Silva, G.A.P.; Gouvêa, L.R.L.; Vrardi, C.K.; Rsnd, M.D.V.; Scalopi Junior, E.J.; Gonçalvs, P.S. 0. Gntic paramtrs and corrlation in arly masurmnt cycls in rubbr trs. Availabl at: http//link.springr.com/articl/0.007%fs [Accssd May 0, 03] Viana, J.M.S.; Faria, V.R.; Silva, F.F.; Rsnd, M.D.V. 0. Combind slction of progny in crop brding using bst linar umbiasd prdiction. Canadian Journal of Plant Scinc 9: Viana, J.M.S.; Faria, V.R.; Silva, F.F.; Rsnd, M.D.V. 0. Bst linar unbiasd prdiction and family slction in crop spcis. Crop Scinc 5: