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Family x site interaction in a progeny test of coastal Douglas-fir Luna-Lopez, Jose F. 1993-12-31

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FAMILY x SITE INTERACTION IN A PROGENY TESTOF COASTAL DOUGLAS-FIRbyJose Francisco Luna-LopezB. Sc. Universidad de GuadalajaraA THESIS SUBMITED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESFOREST SCIENCESWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJune 1993Jose Francisco Luna-LopezIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of ^I The University of British ColumbiaVancouver, CanadaDateDE-6 (2/88)ABSTRACTGenotype x environment interaction in coastal Douglas-fir(Pseudotsuga menziesii var. menziesii (Mirb.) Franco) wasevaluated for height at the 6th-, 7'11- and 124'. year and diameterat the 12th. year. Data collected from 15 families of theExperimental Project 708 of the BCMF were used. In addition,family stability was quantified using 4 diffent methods.Interaction was not statistically significant for any ofthe variables evaluated. These results support the findingsof a previous study made by the BCMF in another set offamilies of the same program.^Only 2 methods gave similarresults when family stability was evaluated.^In general,families kept a similar yield pattern for all the variables.The lack of statistical significance of the interactiontogether with the results obtained in the study previouslymentioned, suggest the possibility of working with only onebreeding population for this program.Table of ContentsABSTRACTList of Tables^ ivList of Figures viAcknowledgements^ vii1 INTRODUCTION 12 LITERATURE REVIEW^ 33 MATERIALS AND METHODS 134 RESULTS AND DISCUSSION-^ 235 CONCLUSIONS^ 40BIBLIOGRAPHY 44APPENDIX^ 48List of Tables3.1 Series of the Coastal Douglas-fir Breeding ProgramExperimental Proyect 708 ^  163.2^Site Localizations for Series II and III ^ 173.3^Overlapping Families in Series II and III ^ 203.4 Homogeneous Variances and Normal Distribution. . ^ 213.5 Expected Mean Squared for the Model ^ 224.1^Least-Squares Analysis of Variance. F-Values . . ^ 244.2^Components of Variance ^  254.3^Families Rank Correlation across sites ^ 274.4 Overall Mean Rank and Ranking Mean of Families . ^ 274.5 Rank Correlation of Sites ^  294.6 Duncan's Multiple Range Tests and Families Meansfor H6 ^  304.7 Duncan's Multiple Range Tests and Families Meansfor H7 ^  304.8 Duncan's Multiple Range Tests and Families Meansfor H12 ^  314.9 Duncan's Multiple Range Tests and Families Meansfor Diameter ^  314.10 Family Stability Rankings for H6 ^ 324.11 Family Stability Rankings for H7  33iv4.12 Family Stability Rankings for H12 ^  344.13 Family Stability Rankings for Diameter ^ 35vList of Figures2.1 A generalized interpretation of the familypopulation pattern obtained when the familyregression coefficients are plotted againstfamily mean yields ^  103.1 Map showing the aproximate distribution ofDouglas-fir ^  143.2 Map showing the aproximate distribution ofDouglas-fir in British Columbia ^ 153.3 Map showing the approximate localization of sitesSeries II and Series III ^  184.1 Norms of Reaction for all the variablesrepresenting 5 randomly selected families . . . . 264.2 The relationship of family regressioncoefficients (b) and family mean yield of H6. . . 36^4.3^The relationship of family regressioncoefficients (b) and family mean yield of H7. . . 364.4^The relationship of family regressioncoefficients (b) and family mean yield of H12 . . 374.5 The relationship of family regressioncoefficients (b) and family mean yield ofDiameter ^  37viAcknowledgementsI am deeply indebted to John Worrall, my researchsupervisor, and the other members of my committee, Yousry El-Kassaby, Robert Guy, Peter Marshall and Alvin Yanchuck, forall their helpful comments and patience. Special thanks tomy profesors Antal Kozak and Valerie LeMay for help withstatistics, to Denis Lavender for his help and advice, and toJ.C. Heaman from the BCMF for all the facilities and help.Thanks so much to the graduate advisors of this Faculty JackWilson, Douglas Golding and John McLean for their advice.Fellow graduate students and friends that must be recognisedfor their contribution to this thesis: Allen Balisky, CarlosGalindo, Sheldon Helbert, Mathew Koshy, Lucila Lares, GuidoMarinone, John Markham and Celia Sanchez. I thank AntonioLuna and Olivia Lopez, my parents, for everything they havedone for me. Last but certainly not least I must thankGuadalupe Estrada, my wife, and Alejandro, my son, for theirendless love, patience and support.viiCHAPTER 1: INTRODUCTIONCoastal Douglas-fir (Pseudotsugamenziesii var. menziesii(Mirb.) Franco) is one of the most economically importantspecies in British Columbia (Orr-Ewing, 1969).^In 1991, 3%of the 245 million seedlings planted on Crown land in BritishColumbia were coastal Douglas-fir^(Miller,^1992).Reforestation with Douglas-fir in the coastal area of BritishColumbia has taken place since 1930.^By the late 1950's, atree improvement program for this species was underway (Orr-Ewing, 1969).The necessity for a tree improvement program for coastalDouglas-fir in British Columbia was emphasized by anassessment of the Forest Service plantations in 1954 and ashortage of Douglas-fir seed in 1956. It began as aselection program for coastal Douglas-fir, by the Ministry ofForests of British Columbia (BCMF). Later on, variousmembers of the forest industry joined the project followingthe leading role of the BCMF (Heaman, 1967). The purpose ofthe program was to provide coastal Douglas-fir seed forreforestation projects. The program is accumulatingadditional information concerning genetic variation ofDouglas-fir (Heaman, 1977a).1Since 1972, the main emphasis of the program has been theevaluation of the genetic quality of the selected parenttrees. Such evaluation has been made with 8 differentprogeny-test series planted between 1975 and 1985 in differentsites along coastal British Columbia (Yeh and Heaman, 1987).The program had many objectives one of which was toassess the size and importance of interactions of parentsacross a sample of environments representing future plantingsites. If the variation among phenotypes in their responseto different environmental conditions or interaction patternsare sufficiently important, these tests together with theprovenance test information (Illingworth, 1976), already inthe field, will provide a basis for subdividing the breedingpopulation (Heaman, 1977a).This study analyzed data obtained from a sample of 15full-sibling families that were planted on 22 sites toevaluate genotype x environment interactions.Objectives: 1. To quantify the genotype x environment interactioncomponent and its significance for height and diameteramong a subsample of families from the test which areplanted in series II and III.2. To identify and quantify the nature of stability in thefamilies for the two series analyzed.2CHAPTER 2: LITERATURE REVIEWThe selection of trees with the most desirable traits foruse as the breeding population has been a primary part of mostpresent forest tree improvement programs. Selection is madebased on the measure of the productive performance treesexhibit (Squillace, 1970).The performance trees exhibit (phenotype) is partiallydependent on the genetic potential that the trees inherit fromtheir parents (genotype) and partially on the site where theygrow (environment). In other words, there is always agenetic and an environmental component for each phenotype,since every phenotype is the result of both (Wright, 1976;Zobel and Talbert, 1984).Ideally, genotype and environment contribute to thephenotype as independent effects (Gregorius and Namkoong,1986; Wright, 1976; Zobel and Talbert, 1984). Gregorius andNamkoong (1986) stated that independence of effects simplymeans that the contribution of a particular genotype to theformation of the phenotype does not depend on environment.Conversely, a particular environment makes the samecontribution when acting on different genotypes.Nevertheless, it is quite common to find variation3between genotypes in their response to different environmentalconditions (Burdon, 1977; Shelbourne, 1972; Squillace, 1970).Shelbourne (1972), defined the genotype x environmentinteraction as the "variation between genotypes in theirresponse to different environmental conditions". Suchinteractions, according to Squillace (1970) could be assessedwhen at least two different genetic entities are tested in twodifferent sites or environments .The presence of genetic x environment interactions mayreduce genetic gains achievable in breeding programs when theselected trees are adapted to a narrow range of siteconditions and are used over a wider range (Carson, 1990;Johnson, 1992; Matheson and Cotterill, 1990). Freeman (1973)states that when interactions exist, the measures of geneticeffects apply only to the range of environments studied andvice versa.Practical consequences of these interactions are veryimportant. Such interactions may determine the subdivisionof the breeding population (Matheson and Cotterill, 1990;Matheson and Raymond, 1984; Namkoong, 1990; Shelbourne, 1972;Squillace, 1970). Furthermore, breeding regions could bedefined not only on the basis of the environmental conditionsbut also according to the performance of the trees growingthere (Carson, 1990; Matheson and Cotterill, 1990; Mathesonand Raymond, 1986; Shelbourne and Campbell, 1976; Squillace,1970).4To have just one breeding population for any improvementprogram is always desirable, but it is not always the rightalternative to achieve the goals of the breeding program(Burdon, 1977; Matheson and Raymond, 1984; Squillace, 1970).Subdivision of the breeding population results in higher costsof operation and more difficulties in managing the breedingprogram. Such factors should be compared against the yieldgains expected to be achieved to evaluate the convenience ofsuch process (Carson, 1990; Matheson and Raymond, 1984;Shelbourne, 1972; Squillace 1970). Furthermore, delineationof planting zones does not ordinarily eliminate interactions,it merely reduces them (Matheson and Raymond, 1984; Squillace1970). For these cases, choosing material which will givethe highest average yield in the whole zone is the mostdesirable (Finlay and Wilkinson, 1963; Hiihn and Leon, 1969;Matheson and Raymond, 1986; Squillace 1970).The existence of genotype x environment interactions haslong been recognized as part of the phenotypic expression ofany plant or animal (Namkoong, 1990; Wright, 1976; Zobel andTalbert, 1984). Freeman (1973) described that the earliestreference to interactions was reported in 1923, by Fisher andMackenzie (1923, original not seen). They surmised about theexistence of the interactions when they evaluated differentpotato varieties under several treatments. Since then, manyresearchers have developed various techniques to examine thestatistical nature of these interactions. For example,5Sprague and Federer (1951) showed how variance componentscould be used to separate the individual effects of thegenotypes, the environment and their interactions in theanalysis of variance to their expectations. In terms of amathematical model, the yield yijk of the kth replicate of the .itgenotype in the jth environment is made up of a general mean(p), a genotype effect di, an environmental effect aninteraction effect and a random error eijk, in a linearmodel:.170,= A + di + + gij +The statistical approach uses analysis of variance toseparate variance into components assigned to genotypes,environments, interaction, and error. These variancecomponents are then used to predict the consequences of theselection of genotypes (Gupta and Lewontin, 1982).Lewontin (1974) reported that a second approach has beenused to characterize the phenotype of a given genotype in afixed series of environments and then to compare the genotypeswith respect to their patterns of phenotypic response todifferent environments.Originally introduced by Woltereck (1909, original notseen) the concept of norm of reaction of the genotype fitsthis approach (Gregorius and Namkoong, 1986). Schmalhausen,(1949, original not seen) defined norm of reaction as: "...thearray of phenotypes that will be developed by the genotypeover an array of environments" (Gupta and Lewontin, 1987).6Evaluation of the norms of reaction can be donegraphically. Gupta and Lewontin (1984) plotted theenvironments or environmental variables against the meanyields for each genotype, to describe the norm of reaction foreach genotype plotted. The lines the genotypes describe asnorms of reaction indicate the existence of interactions whenthey cross each other (Lewontin, 1974).Gupta and Lewontin (1984) pointed out that analysis ofvariance is not sufficient to affirm or deny the existence ofthe interactions. They argue that low mean square values forthe interaction compared with the main effects, do not capturethe essential feature of the norms of reaction. Theessential feature is that they cross each other to denote theexistence of interactions. The most important differenceoccurs when interactions are not statistically significant inthe analysis of variance and the lines of the norms ofreaction cross each other.Lewontin (1974) suggested that the interpretation of theresults of the analysis of variance and their use wouldcritically depend on knowing the norms of reaction of thegenotypes evaluated. As Gupta and Lewontin (1984) indicate,both the statistical and developmental approaches havelimitations when they try to assert the interactions betweenenvironment and genome in creating the phenotype.There have been several criteria used to classifyinteractions (Allard and Bradshaw, 1964).^Lambeth (1979)7classified only two kinds of interactions: those due to changein genetic variance between sites and those due to rankchanges in genotypes. He called the former "importantinteractions". Matheson and Cotterill (1990) classified theinteraction according to their significance in a similar wayLambeth (1979) did. They created three categories:- When interactions are not statistically significant.- When interactions are statistically significant but of nopractical significance, and;- When interactions are of both statistical and practicalsignificance.For the second case, interactions are statisticallysignificant but of no practical significance since therankings for the genetic components remain the same in thedifferent environments. Matheson and Cotterill (1990)pointed out that this is the case when mere statisticalsignificance is not sufficient evidence that interactions areimportant for practical purposes.The last case implies that the rankings of the genotypeschange substantially from one environment to another. Thisis the case when one or several genotypes have higher yieldsin one or several environments and lower in others (Mathesonand Cotterill, 1990; Shelbourne, 1972; Squillace, 1970).In addition to interactions, there is the concept ofstability. A stable genotype is the one that has a constantyield in a variety of environments to which it is exposed.8Stability values are related to the average performance offamilies in each environment, but an individual familystability value would be influenced by the nature of the otherfamilies involved in the tests (Finlay and Wilkinson, 1963;Hiihn and Leon, 1984; Shelbourne, 1972; Squillace, 1970).Several authors have proposed different methods toevaluate phenotypic stability (Htihn and Leon, 1969;Morgenstern and Teich, 1969). Finlay and Wilkinson (1963)proposed that a simple linear regression used to describevarious types of variety adaptability to a range ofenvironments also can be used as a quantitative measure ofphenotypic stability. Their approach is based on plantationperformance to compare the adaptability of several varietiesgrown at several sites for several seasons. For each variety,a linear regression of individual yield on the mean yield ofall varieties for each site in each year was computed. Themean yield of all the varieties at each site (site mean)provides a numerical grading of sites. Site means areproposed as a useful evaluation of the productivity or qualityof the site or environment.The regression coefficient (b value) for each variety isproposed as a stability parameter. The population regressionhas a b value of 1.0, which is defined as the averagestability of the population. Absolute phenotypic stabilitywould be expressed as b=0. Values of b between 0 and 1indicate that the individual family is more stable than the9OW >°coIL <li0100toSPECIFICALLYADAPTED TOFAVOURABLE ENVIRONMENTSBELOWAVERAGE STABILITYPOORLY ADAPTED TOAVERAGE STABILITY WELL ADAPTED TOALL ENVIRONMENTS ALL ENVIRONMENTSABOVEAVERAGE STABILITYVSPECIFICALLY ADAPTEDTO UNFAVOURABLEENVIRONMENTSVARIETY MEAN YIELDFigure 2.1 A generalized interpretation of thefamily population pattern obtained whenthe family regression coefficients areplotted against family mean yields(Finlay and Wilkinson, 1963) .10average. A b greater than 1 indicates that the family has astability below the average population stability (Figure 2.1).Wricke (1962, original not seen) devised a method forthecalculation of individual family contribution to theinteractions (Morgenstern and Teich, 1969). He performed ananalysis of variance using the mean values to get the usualsum of squares for families, sites, family x site interactionsand total. The contribution of individual varieties (VJ tothe interaction is then calculated with the formula:Vi= E - xi . q) - (x.i + p) + (x.. + pq) )2where xo is the yield of the ith variety at the jth site; xi. thesum of variety i over all locations; x.i the sum of allvarieties at site j; x.. the grand total, that is, the yieldof all varieties in all sites; q the number of sites and p thenumber of varieties. A variety contributing little to theinteractions, is said to possess high stability.Plaisted (1960, original not seen) calculated interactionmean squares omitting varieties one at a time (Morgenstern andTeich, 1969). This would give different values for the sumsof squares of the FxS term. The higher the sums of squares ofthe FxS value results, the lower is the omitted family'scontribution to the FxS. A family that possesses highstability should contribute little to the sums of squares ofthe FxS term.11Hiihn and Leon (1984) used 5 different approaches toevaluate stability.^They found none of the 5 methods usedgave very similar results. They concluded that the meanrank-difference previously proposed by Hiihn (1979, originalnot seen) showed some advantages over the others (Hlihn andLeon, 1984).Briefly, this method consists of transforming the yieldsof the families into ranks for each site separately. Foreach family, the mean of all possible, 2 by 2 absolute rank-differences between all possible pairs of differentenvironments, is computed.Morgenstern and Teich (1969) attribute more accuracy tothe method proposed by Wricke (1962). The method has theadvantage of breaking out the sums of squares by families orsites of the FxS interaction. In this way families could beevaluated according to the contribution they made to theinteraction.Shelbourne (1972) gave more importance to the methoddeveloped by Finlay and Wilkinson (1963), but Matheson andRaymond (1984) concluded that interacting families are notnecessarily best identified by their regression on site means:the same family could be classified in several ways accordingto its regression coefficient (b value) and its mean yield.12CHAPTER 3: MATERIALS AND METHODSExperimental Project 708 of the BCMF Research Branchforms the basis of the breeding program for coastal Douglas-fir in British Columbia. Initial tree improvement workemphasized^phenotypic^selection^and^seed^orchardestablishment. Phenotypically superior trees were selecteduntil 1966 from a part of the natural distribution range ofcoastal Douglas-fir (Figure 3.1 and 3.2) that extends fromnorthern California to central British Columbia (Heaman,1977a). This population was propagated in a breedingarboretum and planted in seed orchards to meet the immediateseed requirements. Emphasis shifted to breeding ofcontrolled pollinated progeny of the original plus treesselected, and in 1972 a decision was made to evaluate thegenetic quality of the selected trees (Yeh and Heaman, 1987).A total of 372 intensively selected trees from theoriginal selected population were crossed and produced 1109families through a controlled cross process from 1974 to 1985(Table 3.1).^Cross arrangement was according to adisconnected modified diallel design used for mating. ^With5 crosses per parent this produces a balanced unit of 15crosses (Heaman, 1982).13Figure 3.1 Map showing the approximate distributionof Douglas-fir (Fowells, 1965). Interiorand coastal varieties are separated bya broken line.14Figure 3.2 Map showing the approximate distribution ofCoastal Douglas-fir in British Columbia (Beaman,1967).15Table 3.1 SERIES OF THE COASTAL DOUGLAS-FIR BREEDING PROGRAMEXPERIMENTAL PROJECT 708SowingYearSeries ParentsInvolvedFamiliesPlantedTestSites1975 I 60 177 111976 II 30 99 111977 III 54 165 111978 IV 54 170 111979 V 48 153 111980 VI 48 140 111981 VII 18 55 111985 VIII 60 150 11The choice of trees as male or female parent was based onthe availability of pollen and number of female strobili inthe pollination year (Yeh and Heaman, 1987).Crosses and seeds collections were made yearly.Seedlings were raised in the Cowichan Lake Nursery and plantedas 1 year-old plugs.^Progenies were established in fieldtrials to assess their performance (Heaman, 1977a) along thecoastal distribution area of Douglas-fir in southern BritishColumbia over eight different years (1975-1981 and 1985). Eachdifferent year represents a series.^Each series has adifferent number of families planted (range from 55 to 177) in11 sites per series. All families were planted at every site(Heaman 1977b and 1988).Sites were chosen from available logging andrehabilitation sites.^The most important criteria werewithin site "homogeneity", and localization of the sitesinside the natural distribution area of coastal Douglas-fir16(Yeh and Heaman, 1987).^Site location for series II and IIIare listed in Table 3.2 and shown in Figure 3.3.The field design comprised of four replications of four-tree-row-plots of the families in each test site. Theplantation was laid out as a randomized complete block designwithout sub-blocking by sets. A 3 x 3 meter spacing betweenseedlings was used. From the families planted each year, 15(about 10%) were randomly selected from year to year andplanted in 2 consecutive series (Yeh and Heaman, 1987; Heaman,1977b).^Height was measured in the 6th,^7th and 12th year (H6,H7, and H12, respectively) in centimetres and diameter at 130Table 3.2 SITE LOCALIZATIONS FOR SERIES II AND IIISeries Site: Latitude* Longitude* Elev. Forest# # Name o^'^" o^'^" (m). DistrictII 12 Maquilla 50-04-20 126-21-10 545 Port McNeill13 Heber 49-49-55 125-57-02 303 Campbell River14 Sarita 48-51-23 124-52-54 364 Port Alberni15 Jordon 48-25-00 124-00-50 45 Duncan16 Muir 48-25-35 123-54-52 379 Duncan17 Bamberton 48-37-32 123-34-00 212 Duncan18 Sechelt 49-25-30 123-35-30 212 Sechelt19 Squamish 50-12-00 123-22-00 155 Squamish20 Chilliwack 49-05-25 121-40-35 303 Chilliwack21 Lost Creek 49-22-13 122-14-05 424 Maple Ridge22 Chelais 49-30-35 122-01-00 333 Maple RidgeIII 23 Adam 50-24-00 126-10-00 576 Campbell River24 Menzies 50-08-54 125-38-15 333 Campbell River25 Gold 49-51-30 126-04-55 561 Campbell River26 White 50-05-35 126-04-30 409 Campbell River27 Sproat Lake 49-17-25 125-03-05 318 Port Alberni28 Fleet 48-39-30 124-05-00 561 Duncan29 Tansky 48-27-45 124-01-45 545 Duncan30 Eldred 50-06-00 124-13-00 148 Powell River31 Squamish 50-12-05 123-22-30 135 Squamish32 Sechelt 49-25-20 123-35-27 212 Sechelt33 Lost Creek 49-22-15 123-14-10 424 Maple Ridge* All latitudes North and all longitudes West.17Figure 3.3Map showing the approximatelocality of sites inseries II (sites 12-22)and series III (sites 23-33)(lleaman, 1977b).18cm height in the 12th year in millimetres.Twenty-two different parents were involved to produce 15families (Table 3.3).^Parent provenances extended fromVancouver Island (Gold River and Knight Inlet sites) to theSnoqualmie site in the interior of the State of Washington(latitude 47°10' to 51°05' N, longitude 121°30' to 126°07').The seedling survival varied from site to site making the dataunbalanced.^The data were evaluated according to thefollowing model:;kir=^+ R1 +^+ FixRi + Sol + B(1 bq^Fi X S^FjXB(i 0,1^Eo i 1 q)rwhere:YijlqrRiFjxRiSooBo oqF^xS(;)1FjxBo= observation of the ijlqr th tree= overall mean= Year effect (i=2)= Family effect (j=15)= Family x year interaction= Site effect nested in year (1=11)= Block effect nested in site and year (q=4)= Family x site interaction= Family x block interactionEO. Or = Residual or individual effect of rth tree (r=4)All effects except the overall mean (g) were consideredrandom. Statistical analysis of the data was performed onthe UBC mainframe computer using several procedures of the19Table 3.3 OVERLAPPING FAMILIES IN SERIES II AND IIIFamily aNumberParentsb9^Lat. Long.^Elev. d Lat. Long.^Elev.2 (158) 247 (47-10; 121-30;1220) * 418 (51-05; 125-35; 400)12 (161) 418 (51-05; 125-35; 400) * 101 (48-52; 124-06; 550)15 (156) 440 (49-22; 123-13; 620) * 101 (48-52; 124-06; 550)18 (159) 495 (48-45; 124-10; 200) * 573 (50-12; 124-36; 70)21 (157) 107 (48-47; 123-56; 210) * 287 (48-05; 124-00; 850)39 (151) 67 (48-49; 124-07; 180) * 452 (50-04; 123-20; 370)44 (162) 28 (48-56; 124-07; 680) * 452 (50-04; 123-20; 370)67 (163) 73 (48-50; 124-10; 180) * 56 (49-52; 126-07; 240)68 (153) 73 (48-50; 124-10; 180) * 581 (48-52; 123-49; 180)69 (150) 73 (48-50; 124-10; 180) * 48 (49-33; 125-03; 700)73 (152) 49 (49-17; 124-33; 470) * 48 (49-33; 125-03; 700)74 (164) 102 (48-48; 124-00; 210) * 56 (49-52; 126-07; 240)88 (155) 83 (49-18; 122-34; 370) * 32 (48-50; 124-05; 460)89 (160) 32 (48-50; 124-05; 460) * 423 (49-26; 123-32; 530)94 (154) 152 (48-55; 124-05; 490) * 70 (48-35; 123-58; 400)Total: 15 families and 22 different parents.a: Numbers in parenthesis correspond to series III in the original plan.In this analysis, only the numbers for series II were used.b: 2=Seed or Female parent; d=Pollen or Male parent; Lat.=latitude Westin grades and minutes; Long.= longitude North in grades and minutes;Elev.= elevation in meters above the sea level.6.07 version of SAS (1990a, b, c).Assumptions for the analysis of variance, namelyhomogeneous variances and normal distribution of observations(Walpole, 1982) were checked with the Discriminate Functions(Discrim Proc) and the Univariate Normal Procedures(Univariate Proc), respectively. The assumption of normalitywas met and the variances were within the acceptable range andtherefore assumed homogeneous (Table 3.4). Sums of squaresand the expected mean squares were calculated with the GeneralLinear Model Procedure (GLM Proc) using type III sums ofsquares as well as the Duncan's multiple range test for the20Table 3.4 HOMOGENEOUS VARIANCES AND NORMAL DISTRIBUTIONVariable^Variances (x2)* T Value**116^13.95Ns^0.71887H7 14.18NS 0.76850H12 13.46Ns^0.74041D1AM^13.87Ns 0.77153NS = Not significant. x2critical value = 29.141* Bartlet's X2 test to compare variances. If value calculated< that value of tables at the probability level tested thenthere is not sufficient evidence to declare the variancesheterogenous (Morrison, 1976).** T value obtained from the Kolomogorov D statistic to testnormal distribution. If value calculated < to 0.775 thesample is considered normally distributed (Stephens, 1974)means. The expected mean squares for the model are given inTable 3.5.For sources of variation for which there was not a directerror term to test against, pseudo-F tests were constructedand the appropriate degrees of freedom calculated according tothe Satterthwaite's (Hicks, 1982) approximation.Evaluation of family stability across sites was done by4 different methods: the Finlay and Wilkinson (1963) approach;the Wricke (1962) method; excluding one family at a time inthe analysis of variance (Plaisted, 1960); and, with the meanrank-difference method (HUhn and Leon, 1969). The RegressionProcedure (Reg Proc) was used for the first, the Analysis ofVariance (Anova Proc) for the second and third, and a simplespread sheet for the last.Scattergrams of family norms of reaction were constructedplotting family means against sites. Rank correlations for21Table 3.5 EXPECTED MEAN SOUARES FOR THE MODELSource^Expected Mean Squares Repetition (R) VE +C IVF*13 +C2VF*S ±C3VB +c4VB -1-05VFMR^-I-c7VBFamily^(F) VE +C 117F4S ±C2VF S^ +CSVF*R +c6VFFxR VE +C 1VF*13 +C2VF*S +c514.aSite^(S) VE +CIVF B + C2VF*S +c3VB +c4VBBlock (B) VE ±CIVF*B^-1-c3VBFxS VE +C 1VpIS ±C2VF SFxB^VE ±CIVF*BError VERange of the Coefficients (ca) :VariableH6^H7 H12 DIAMc1 low 3.81 3.83 3.74 3.72high 3.87 3.89 3.83 3.82c2 low 15.25 15.35 15.01 14.92high 15.34 15.42 15.12 15.04C3 low 57.22 57.59 56.33 56.01high 57.29 57.64 56.44 56.12c4 low 228.91 230.38 225.39 224.11high 228.96 230.42 225.51 224.24C5 low 167.82 168.91 165.26 164.32high 168.03 169.08 165.46 164.53c6 335.85 337.99 330.72 328.85C7 2517.50 2533.70 2479.00 2464.90families across sites were performed using the Kendalapproximation (W) and Friedman's chi-square (V) to evaluateranking as suggested by Siegel (1967). Kendal approximation(W) and Friedman's chi-square (M), or Spearman's regressioncoefficient (1'0 were also used to compare rankings of theresults observed.22CHAPTER 4: RESULTS AND DISCUSSIONAnalysis of variance for the variables is summarizedin Table 4.1. Table 4.2 shows the components of variance forall the sources of variation. The largest variation forevery variable was due to site (Vs). Sampling error (VE) wasthe second largest source of variation for all variables.Variance components kept a similar proportion for H6, H7 andH12.For all the variables the FxB interaction wassignificant (P0.01). The significance of this factor couldbe due to the poor homogeneity within sites, and/or therelatively small number of blocks (i.e. four).The FxS interaction was not significant for anyvariable, but FxR was significant for H7 and H12 (P<0.05), andhighly significant for diameter (P<0.01).The FxS interaction on was not statisticallysignificant.^However, as was shown by the rank changes theinteraction does exist.^Norms of reaction of five familiesrandomly selected were plotted. The occurrence of crossedlines indicates the existence of interactions (Figure 4.1).Rankings were evaluated with the V, rsand/or W coefficients.The V determines whether the ranks totals23Table 4.1 LEAST-SOUARES ANALYSIS OF VARIANCE. F-VALUES.Source^D.F.^H6 H7 H12 Diam. Test Term.F^14^4.38" 4.07" 4.81 ** VF*RR 1^0.38NsF*R 14^1.68Ns0.10Ns2.12 *0.01Ns2.03 *0.17Ns2.25**VF*B +Vs —VF*BVF*SS^20^58.70** 55.95" 57.40** 71.20" Vs-I-I/Fos —VF.BB 66^2.28** 2.57 ** 2.28 ** 1.93" VF*BF*S^280^1.13NsF*B 924^1.87**1.15Ns1.96"1.14 Ns2.10"1.08Ns1.82 **VF*BVE**= Highly Significant (P5.0.01)*= Significant (1D0.05)NS= Not Significantdiffer significantly from one family to another. ^The rsshows if the two rankings compared are significantlycorrelated.^The W coefficient shows the association amongseveral rankings.^If the W value is high the rankings arestatistically similar.The W coefficients were low for every variable whencomputing the families rank correlation across sites. Thismeans that family ranks were different from site to site. Inaddition, the x,2 values were highly significant, denotingdifferences among families (Table 4.3). These resultssupport the existence of the crosses of the lines of the normsof reaction.Besides the families rank correlation across sites, twomore rankings were calculated. One of them ranks familiesaccording the family overall mean for each variable and theother was the ranking mean or the sum of ranks of everyfamily in every site divided by the number of sites. When24Table 4.2 COMPONENTS OF VARIANCESourceVariables:H6^%^H7VR 0.00^0.00 0.00^0.00VF 73.85^1.43^146.89^1.63VF•R 19.40^0.37 49.14^0.55Vs 2344.57 45.25^4323.90 48.08VB 86.45^1.67 180.47^2.01VFss 32.99^0.64^61.63^0.69VF*B 470.97^9.09 849.10^9.44VE 2153.42 41.55^3382.92^37.60Source H12^%^DIAMVR 0.00^0.00 0.00^0.00VP 723.42^2.07^11.19^1.06VF*R 184.88^0.53 6.18^0.59Vs 16423.15 47.05^493.83 46.86VB 608.74^1.74 12.88^1.22VF*s 241.69^0.69^3.59^0.34VF*B 3792.64^10.87 95.33^9.05VE 12932.26^37.05^430.78^40.88these two rankings of every variable were compared with rsthey were highly correlated.When any pair of rankings of the height variables wascompared, the rs was very high (rs > 0.935). When a rankingof any of the height variables was compared with the rankingof the diameter variable, the values were lower (rs > 0.76).Nevertheless, every pair compared had significant values (P >0.01) and all rankings were considered statistically similar.When all the rankings were compared using the W coefficient,it was significant, supporting the results obtained with thers coefficient. The x12 was significant too, denoting thedifferences in ranking among families (Table 4.4).Overall site rankings were computed for every variable tosee if the variables were good estimators of site quality as25H7Fam. Mean(cm.)500H12Fain. Mean(cm.)1000400 -300200100Fain. Mean(cm.)3C0 H650 12^14^16^18^20^22^24^26^28^30^3213^15^17^19^21^23^25^27^29^31^33 S ites80060020000 12^14^16^18^20^22^24^26^28^30^3213^15^17^19^21^23^25^27^29^31^33^SitesFam . Mean(tam.)140-120103so6040200 12^14^16^18^20^22^24^26^28^30^3213^15^17^19^21^23^25^27^29^31^33 Sites12^14^16^18^20^22^24^26^28^30 32^Sites13^15^17^19^21^23^25^27^29^31^33Figure 4.1 Norms of Reaction for all the variables representing 5 randomly selectedfamilies. Site numbers in the x axes and family means (in centimetres forH6, H7, H12 and in millimetres for Diam) in the y axes (See appendix).250200150103Table 4.3 FAMILIES RANK CORRELATION ACROSS SITESH6^H7^H12^DIAM)6-2^85.482**^96.536"^95.591"^72.582"W^0.278 0.313 0.310 0.236** = Highly significant (13 0.01)Table 4.4 OVERALL MEAN RANK AND RANKING MEAN OF FAMILIESVariablesFamily H6^a*^b* H7 a^b H12 a^b DIAM a^b2 15^14 15^14 15^14 14^1412 6^5 6^5 7^7 1^115 12^12 12^12 12^12 3^318 5^4 4^4 4^4 7^621 11^9 9^9 8^8 11^1139 13^13 13^13 13^13 13^1244 9^10 10^10 10^9 8^867 3^3 3^2 2^2 5^568 8^7 8^7 6^5 10^969 10^11 11^11 11^11 12^1373 7^8 7^8 9^10 9^1074 14^15 14^15 14^15 15^1588 1^1 1^1 1^1 2^289 2^2 2^3 5^3 4^494 4^6 5^6 3^6 6^7rs^(a & b)^0.971 0.982 0.988 0.989**rs H6-H7^0.996**rs H6-H12^0.936**rs H7-H12^0.948**rs H6-DIAM 0.754**rs H7-DIAM 0.754**rs H12-DIAM 0.682**w^0.884++W 0.975**Xr2^49.53++Xr2^40.93* a= Rank according to the overall mean of the family for thevariable.b= Rank according to the sum of rankings of every familydivided by the number of sites, or ranking mean.** = Values computed using the overall mean of the familyrank.++ = Values computed using the overall mean of the family rankfor the height variables only.27suggested by Finlay and Wilkinson (1963): xr2 was significantdenoting the differences in ranking among sites. The W valuewas high denoting that the differences among variables in theoverall site mean rankings were not statistically significant(Table 4.5).The best families for variable H6 were 88, 89, 67, 94,18, and 12^(Table 4.6); for variable H7 were 88, 89, 67, 18,94^and^12^(Table 4.7);^for H12 were 88,^67,^94, 18 and 89(Table 4.8); for diameter were 12, 88, 15, 89, 67, 94, and 18(Table 4.9).The most stable families as determined by the Wricke(1962) method and omitting one family at a time for H6 were15, 74, 73, 12 and 44 (Table 4.10); for H7 were 15, 74, 12,44, 69 and 68 (Table 4.11); for H12 were 74, 12, 44, 15 and 69(Table 4.12); for diameter were 68, 74, 12, 44, and 15 (Table4.13).The most stable families according to the method ofFinlay and Wilkinson (1963) for H6 were 21, 74, 39 and 2(Table 4.10); for H7 were 21, 39, 74, 2 and 18 (Table 4.11);for H12 were 21, 39, 89, 2, and 12 (Table 4.12); for diameter21, 39, 74, 18 and 2 (Table 4.13).Families closer to the average stability according toFinlay and Wilkinson (1963) for H6 were 44, 15, 12, 67, 18,and 89 (Figure 4.2); for H7 were 89, 12, 44, 15, and 18(Figure 4.3);for H12 were 18, 67, 15, and 74 (Figure 4.4); for28Table 4.5 RANK CORRELATION OF SITES FOR HEIGHT VARIABLES^FOR ALL THEONLY^ VARIABLESxr2^60.45" 79.85"W^0.960 0.951" = Highly significant (P5.0.01)diameter were 89, 68, 67, 94, 2, and 12 (Figure 4.5).Since the evaluation of site yields is not the goal ofthis study, sites are discussed as they relate to familyyields. As mentioned before, Finlay and Wilkinson(1963)proposed site mean as an evaluation of the environmentproductivity. Therefore, comparing the means of the poorsites with the family means in these sites, would reveal thefamilies with better yields in poor sites when their means inthese sites were above the site mean. A similar comparison forthe rich sites would delineate the families with better yieldsin rich sites. For H6, there were 12 sites with means belowthe overall mean or poor sites, and 10 sites with means abovethe overall mean or rich sites; for H7 were 12 poor sites and10 rich sites; for H12 were 10 poor sites and 12 rich sites;for diameter there were 12 poor sites and 10 rich sites.According to Finlay and Wilkinson (1963), families withbetter yields in all sites (b.-.,. 1 and mean > p) for H6 were88, 89, 67, 94, 18 and 12; for H7 were 88, 89, 67, 18, 94, 12and 73; for H12 were 88, 67, 94, 18, 89, 68, 12 and 21; fordiameter were 12, 88, 15, 89, 67, 94, 18 and 44.Families which tended to have better yield in poor sites29Table 4.6 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANSFOR H6Ranking Family Mean P<0.01* P<0.05*1 88 178.02 A A2 89 176.10 A AB3 67 173.26 A AB4 94 170.25 AB B5 18 169.79 AB B6 12 168.89 AB CB7 73 161.74 B CB8 68 161.54 CB CD9 44 158.16 CD D10 69 157.34 C D D11 21 156.07 CD E D12 15 155.99 CD E D13 39 148.98 CD E F14 74 148.54 D E F15 12 148.07 D FOverall 162.27* Families with the same letter are not significantlydifferent at the P level shown.Table 4.7 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANSFOR H7Ranking Family Mean P<0.01* P<0.05*1 88 247.03 A A2 89 238.88 A AB3 67 237.36 AB AB4 18 231.07 ABC CB5 94 229.88 ABC CB6 12 225.27 DBC CD7 73 220.29 DEC E D8 68 219.82 DEC E D9 44 215.52 DE E^F10 21 215.08 DE E^F11 69 213.57 DEF E^F12 15 209.15 GEF G F13 39 202.49 G^F H G14 74 199.74 G H15 2 199.37 G HOverall 220.07* Families with the same letter are not significantlydifferent at the P level shown.30Table 4.8 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANSFOR H12Ranking Family Mean P<0.01* P<0.05*1 88 247.03 A A2 67 623.98 A B A B3 94 617.85 A B C A B C4 18 616.85 A B C A B C5 89 615.93 A B C A B C6 68 605.87 D B C D B C7 12 598.44 DBCE D^C8 21 596.38 D^C E D9 73 586.95 D F^E D E10 44 586.42 D F^E D E11 69 573.91 F G E E F12 15 564.82 H F G G^F13 39 552.97 H^G I G H14 74 540.84 H I H15 2 538.44 I HOverall 590.40* Families with the same letter are not significantlydifferent at the P level shown.Table 4.9 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANSFOR DIAMETERRanking Family Mean P<0.01* P<0.05*1 12 86.45 A A2 88 84.85 A B A B3 15 84.59 A B A B4 89 84.25 A B A B5 67 83.29 A B C A B C6 94 82.67 A B C B C D7 18 81.71 ABCD EBCD8 44 81.44 B C D EBCD9 73 80.37 B C D EFCD10 68 80.23 B C D EFCD11 21 79.08 C D E F^D12 69 78.65 C D E F13 39 77.53 E^D F14 2 73.88 E F G15 74 71.44 F GOverall 80.70* Families with the same letter are not significantlydifferent at the P level shown.31Table 4.10 FAMILY STABILITY RANKINGS FOR H6Fam A B C D E2 15 15 4 8 1212 4 4 8 3 1415 1 1 7 2 318 10 10 5 5 1121 7 7 1 15 1539 9 9 3 12 744 5 5 6 1 1067 12 12 9 4 668 8 8 11 7 1369 6 6 15 13 873 3 3 14 11 474 2 2 2 14 188 11 11 13 10 289 13 13 10 6 594 14 14 12 9 9x12 = 13.05 NS^W=0.233Ns= Not significantA = As determined by Wricke (1962) method.B = Omitting one family at a time.C = As determined by Finlay and Wilkinson (1963) method b = O.D = As determined by Finlay and Wilkinson (1963) method b = 1.E = As determined by Hiihn (1979) method.Rank position of the family according to that criterion:1 the most stable, 15 the less stable.32Table 4.11 FAMILIES STABILITY RANKINGS FOR H7Fam A2 13 13 4 9 1212 3 3 6 2 615 1 1 9 4 318 12 12 5 5 1321 8 8 1 15 1539 11 11 2 13 1144 4 4 8 3 767 10 10 10 6 468 6 6 11 7 569 5 5 15 14 973 7 7 14 11 1074 2 2 3 12 188 9 9 13 10 289 14 14 7 1 894 15 15 12 8 14X12 = 17.00 NS^W=0.243NS= Not significantA = As determined by Wricke (1962) method.B = Omitting one family at a time.C = As determined by Finlay and Wilkinson (1963) method b = O.D = As determined by Finlay and Wilkinson (1963) method b = 1.E = As determined by 'Tiffin (1979) method.Rank position of the family according to that criterion:1 the most stable, 15 the less stable.33Table 4.12 FAMILIES STABILITY RANKINGS FOR H12Fam A B C D E2 15 15 4 9 912 2 2 5 6 715 4 4 7 3 618 9 9 8 1 1221 8 8 1 15 1439 12 12 2 12 544 3 3 12 8 467 10 10 9 2 1068 6 6 11 7 869 5 5 15 14 373 13 13 14 13 1574 1 1 6 4 188 7 7 10 5 289 11 11 3 11 1394 14 14 13 10 11X1.2 = 20.87 NS^W=0.298NS= Not significantA = As determined by Wricke (1962) method.B = Omitting one family at a time.C = As determined by Finlay and Wilkinson (1963) method b = 0.D = As determined by Finlay and Wilkinson (1963) method b = 1.E = As determined by Hiihn (1979) method.Rank position of the family according to that criterion:1 the most stable, 15 the less stable.34Table 4.13 FAMILIES STABILITY RANKINGS FOR DIAMETERFain^A B C D E2 15 15 5 5 712 3 3 10 6 315 5 5 14 11 418 9 9 4 8 1221 11 11 1 15 1539 14 14 2 13 1444 4 4 11 7 667 13 13 8 3 1068 1 1 6 2 269 7 7 15 14 1173 10 10 12 9 974 2 2 3 12 188 6 6 13 10 589 8 8 7 1 894 12 12 9 4 13Xr2 = 11.73 Ns^W=0.168NS= Not significantA = As determined by Wricke (1962) method.B = Omitting one family at a time.C = As determined by Finlay and Wilkinson (1963) method b = O.D = As determined by Finlay and Wilkinson (1963) method b = 1.E = As determined by Hlihn (1979) method.Rank position of the family according to that criterion:1 the most stable, 15 the less stable (See appendix).351.1544X18X21X.4^1.1Z3aw 1.0500 10U)0.95-C)P4 0.9—2X39X0.85—74X0.8—69X^73X^8894^ XX68X^ 67^8912^X X15^ XX73X94X 881.15— 69X01.05_68X^ 67XOL.) 1—Z0U)cyj 0.95—0C4 0.9—0.85—0.8—15^448912 XX18X2X74X 39X21X1.251.2—0.75 145^110^155^160^165^130^175^180Family MeansFigure 4.2 The relationship of family regressioncoefficients (b) and family mean yieldof H6 variable.1.251.2—0.75190^21)3^210^210^zip^240Family MeansFigure 4.3 The relationship of family regressioncoefficients (b) and family mean yieldof H7 variable.360.75510 560^540^580^590^690^610Family Means630530 6201.2-1 . 15 -69X73X4468X94X881.05 -74X15Xis^67x X12X2X^39^ 890.85-0.8-21X69X1.15-73'd^1. 1 -x 44 12X94 67X x1.05-0068^892X18X74X39X0.85-21X0.8-1.2511-1.25Figure 4.4 The relationship of family regressioncoefficients (b) and family mean yieldof H12 variable.0.7570^ 716^78^80^82^84Family MeansFigure 4.5 The relationship of family regressioncoefficients (b) and family mean yieldof Diameter variable.37(b < 1 and mean < p) for H6 were 21, 39, 74 and 2; for H7 were21, 39, 74 and 2; for H12 were 39 and 2; for diameter were 21,39 and 74. Nevertheless, the analysis of the results did notsupport this criterion in the majority of the cases. Theattribute of better yield in poor sites was quite notable forfamily 21 in variables H6, H7 and diameter, but the other setsof families did not show this quality, especially family 2which had means below the site means in almost every case forH6, H7 and H12. Finlay and Wilkinson (1963) explained theirlow mean yields as a consequence of high phenotypic stability:they are so stable that they are unable to exploit high yieldenvironments.The Finlay and Wilkinson (1963) approach suggests thatfamilies with better yields on rich sites (b > 1 and mean < p)for H6 were 88, 94, 73, 68 and 69; for H7 were 68 and 69; forH12 were 73, 44 and 69; for diameter were 73 and 69. Again,as in the case of the families with better yields in poorsites, the analysis of results did not support this criterionfor H6 and H7. However, this attribute was appropriate forthe set of families mentioned for the H12 variable, especiallyfamily 44, and in the diameter variable for family 73.The most stable families according to the mean rank-difference for H6 were 74, 88, 15, 89, and 73 (Table 4.10);for H7 were 74, 88, 15, 67 and 68 (Table 4.11); H12 were 74,88, 69, 39 and 44 (Table 4.12); for diameter were 68, 74, 12,44 and 15 (Table 4.13).38Family rankings for stability gave low W values for allthe variables denoting the significant differences existingamong rankings. Xr2 values were not significant for anyvariable either: the lack of significance may be associated tothe considerable differences among rankings that made itimpossible to detect any significant difference amongfamilies.39CHAPTER 5: CONCLUSIONSFamily rankings for H6 and H7 were very similar: only 2pairs of families interchanged positions. This similarity isobviously due to the proximity in time in which the data weretaken.^Comparing the rankings of H6 and H7 with H12, morenotable differences appeared.^However, the Spearman'scorrelation coefficients (rs) were very high for any pair ofrankings compared, showing the similarity of rankings for allthe variables.In all cases, it was possible to distinguish 3 sets offamilies:- The top class: 18, 67, 88, 89 and 94.- The middle class: 12, 21, 44, 68, 69 and 73.- The lower class: 2, 15, 39 and 74.Of the top 5 families, family 88 was highest for the 3variables. According to the Duncan's multiple range test,there were not statistically significant differences amongthem (P<0.01).The families of the middle group showed more changes intheir rankings. There were different rankings for eachvariable, but most of the changes were only 1 or 2 places inthe ranking.40The lower 4 families (15, 39, 74 and 2) kept the sameranking for the 3 variables. According to the Wricke method(Morgenstern and Teich, 1969), family 2 was among the lesserof the stable families. In contrast, the Finlay andWilkinson (1963) method classified this family as one of themost stable families for all variables. Given the poorconcordance between what Finlay and Wilkinson (1963) suggestedand the results obtained, it seems that the Finlay andWilkinson (1963) method is not the most suitable to evaluatestability, as Matheson and Raymond (1984) suggest.For diameter, the families in general kept the samepattern as the ones showed for height variables. Theexceptions were families 12 and 15 that were among the middleand low families for height increments and were ranked as 1and 3, respectively, for diameter. Height and diameter weregood estimators of site quality as suggested by Finlay andWilkinson (1963), given the similarity of the ranking forsites for the 4 variables.The significance of the FxR interaction for the H7, H12and diameter variables could be due to the environmentaldifferences from one year to the next. Sites were locatedwithin the same general climatic area, but different weatherconditions in different years could produce such significantinteraction. Squillace (1970) suggested that given the longlife span of most trees, this kind of interaction becomesnonsignificant over a period of 30 years. In this study, a41peak value of the FxR interaction for height was attained atthe 7th year, but for the whole study the maximum was fordiameter which was measured at the 12th year.The lack of significance of the FxS interaction in thissample of families supports Yeh and Heaman (1987), and theprospect of working with only one breeding population seemsappropriate.The high correlation between the ranking of the familymeans and the ranking mean of the families reinforce theobserved lack of significance of the FxS term. In spite ofthe results of the rank correlation of families across sitesthat showed the significance in the change of the familyrankings from site to site, other results suggest that evenwith the significance of changes in rankings site, suchchanges are not statistically significant with other methods.Four different methods were used to calculate familystability. They gave very different family stability ranks.The W values were very low showing no relation or similarityamong the ranks. The xr2 were not significant in any case, anddid not show any significant differences among the families.Only the method suggested by Wricke (1962) and the oneomitting one family at a time for the calculation of the FxSinteraction, gave similar rankings' results . Comparingrankings of both methods the correlations were 1 for everyvariable because rankings were identical.The methods suggested by Finlay and Wilkinson (1963) and42by Hiihn (1979) gave very different results. The mean rank-difference expresses only the rank changes of the familiesfrom site to site, but it does not take account of any sitevalue and the possible links with the stability of thefamilies.^In this study, the Finlay and Wilkinson approachalways classified as the most stable families the lessproductive ones.^Considering the regression coefficient of1 (average stability) to rank families, the differences inrankings with the other methods to evaluate stability, stillpersisted. Considering the family means and the regressioncoefficient together, to classify family stability, was alsonot very consistent. Families with mean values greater thanthe overall mean and stability values (b) close to 1 were onaverage the most productive families for all variables.Families that were classified as with better yields in poor orrich sites did not exhibit any consistency for such traits.This study did not show genotype x environmentinteraction for the families and sites evaluated. 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New York. 505 p.47APPENDIX4 8An example of the data used to calculate the stability rankings:FAMILY STABILITY VALUES FOR DIAMETERFain A C (*) (&) D2 1913.13 15 15614.32 15 0.953 5 5 318.95 712 615.74 3 17004.39 3 1.047 10 6 193.45 315 883.64 5 16717.36 5 1.110 14 11 224.00 418 1353.94 9 16213.45 9 0.932 4 8 405.05 1221 1383.84 11 16181.42 11 0.778 1 15 472.77 1539 1853.94 14 15677.75 14 0.848 2 13 439.27 1444 782.46 4 16825.75 4 1.063 11 7 296.77 667 1574.31 13 15977.35 13 1.039 8 3 360.36 1068 453.76 1 17177.94 1 0.996 6 2 186.77 269 1105.36 7 16479.79 7 1.154 15 14 373.45 1173 1383.50 10 16181.79 10 1.071 12 9 351.45 974 519.14 2 17107.88 2 0.870 3 12 114.00 188 1103.70 6 16481.58 6 1.102 13 10 230.95 589 1260.14 8 16313.96 8 0.996 7 1 323.86 894 1477.44 12 16081.14 12 1.041 9 4 416.77 131.000(**)A = Contribution to the FxS SS according to Wricke (1962) method.B = FxS SS omitting one family at a time.C = Regression Coefficient (b) according to Finlay and Wilkinson (1963) method.Families were ranking according closeness to the b value of 0(*) and 1(&).D = Mean-rank deviation according to Hain (1979) method.Rank position of the family according to that criteria: 1 the most stable, 15 theless stable.(**) 1.00 is the average regression coefficient for the whole sample.14012010080 -DIAMETER20Sites12^14^16^18^20^22^24^26^28^30^3213^15^17^19^21^23^25^27^29^31^33Figure to show the norms of reaction of the 15 families for the variable diameter (Sitesnumbers in the x axe, and family means in the y axe in millimetres).


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