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

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FAMILY x SITE INTERACTION IN A PROGENY TEST OF COASTAL DOUGLAS-FIR by Jose Francisco Luna-Lopez B. Sc. Universidad de Guadalajara A THESIS SUBMITED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES FOREST SCIENCES We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 1993 Jose Francisco Luna-Lopez In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of ^I The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT Genotype x environment interaction in coastal Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco) was evaluated for height at the 6th-, 7'11- and 124'. year and diameter at the 12th. year. Data collected from 15 families of the Experimental Project 708 of the BCMF were used. In addition, family stability was quantified using 4 diffent methods. Interaction was not statistically significant for any of the variables evaluated. These results support the findings of a previous study made by the BCMF in another set of families of the same program.^Only 2 methods gave similar results when family stability was evaluated.^In general, families kept a similar yield pattern for all the variables. The lack of statistical significance of the interaction together with the results obtained in the study previously mentioned, suggest the possibility of working with only one breeding population for this program. Table of Contents ABSTRACT List of Tables^ iv List of Figures vi Acknowledgements^ vii 1 INTRODUCTION 1 2 LITERATURE REVIEW^ 3 3 MATERIALS AND METHODS 13 4 RESULTS AND DISCUSSION-^ 23 5 CONCLUSIONS^ 40 BIBLIOGRAPHY 44 APPENDIX^ 48 List of Tables 3.1 Series of the Coastal Douglas-fir Breeding Program Experimental Proyect 708 ^  16 3.2^Site Localizations for Series II and III ^ 17 3.3^Overlapping Families in Series II and III^ 20 3.4 Homogeneous Variances and Normal Distribution. . ^ 21 3.5 Expected Mean Squared for the Model^ 22 4.1^Least-Squares Analysis of Variance. F-Values . . ^ 24 4.2^Components of Variance ^  25 4.3^Families Rank Correlation across sites ^ 27 4.4 Overall Mean Rank and Ranking Mean of Families . ^ 27 4.5 Rank Correlation of Sites^  29 4.6 Duncan's Multiple Range Tests and Families Means for H6 ^  30 4.7 Duncan's Multiple Range Tests and Families Means for H7 ^  30 4.8 Duncan's Multiple Range Tests and Families Means for H12^  31 4.9 Duncan's Multiple Range Tests and Families Means for Diameter ^  31 4.10 Family Stability Rankings for H6 ^ 32 4.11 Family Stability Rankings for H7  33 iv 4.12 Family Stability Rankings for H12^  34 4.13 Family Stability Rankings for Diameter ^ 35 v List of Figures 2.1 A generalized interpretation of the family population pattern obtained when the family regression coefficients are plotted against family mean yields^  10 3.1 Map showing the aproximate distribution of Douglas-fir ^  14 3.2 Map showing the aproximate distribution of Douglas-fir in British Columbia ^ 15 3.3 Map showing the approximate localization of sites Series II and Series III^  18 4.1 Norms of Reaction for all the variables representing 5 randomly selected families . . . . 26 4.2 The relationship of family regression coefficients (b) and family mean yield of H6. . . 36 ^ 4.3^The relationship of family regression coefficients (b) and family mean yield of H7. . . 36 4.4^The relationship of family regression coefficients (b) and family mean yield of H12 . . 37 4.5 The relationship of family regression coefficients (b) and family mean yield of Diameter^  37 vi Acknowledgements I am deeply indebted to John Worrall, my research supervisor, and the other members of my committee, Yousry El- Kassaby, Robert Guy, Peter Marshall and Alvin Yanchuck, for all their helpful comments and patience. Special thanks to my profesors Antal Kozak and Valerie LeMay for help with statistics, to Denis Lavender for his help and advice, and to J.C. Heaman from the BCMF for all the facilities and help. Thanks so much to the graduate advisors of this Faculty Jack Wilson, Douglas Golding and John McLean for their advice. Fellow graduate students and friends that must be recognised for their contribution to this thesis: Allen Balisky, Carlos Galindo, Sheldon Helbert, Mathew Koshy, Lucila Lares, Guido Marinone, John Markham and Celia Sanchez. I thank Antonio Luna and Olivia Lopez, my parents, for everything they have done for me. Last but certainly not least I must thank Guadalupe Estrada, my wife, and Alejandro, my son, for their endless love, patience and support. vii CHAPTER 1: INTRODUCTION Coastal Douglas-fir (Pseudotsugamenziesii var. menziesii (Mirb.) Franco) is one of the most economically important species in British Columbia (Orr-Ewing, 1969).^In 1991, 3% of the 245 million seedlings planted on Crown land in British Columbia were coastal Douglas-fir^(Miller,^1992). Reforestation with Douglas-fir in the coastal area of British Columbia has taken place since 1930.^By the late 1950's, a tree improvement program for this species was underway (Orr- Ewing, 1969). The necessity for a tree improvement program for coastal Douglas-fir in British Columbia was emphasized by an assessment of the Forest Service plantations in 1954 and a shortage of Douglas-fir seed in 1956. It began as a selection program for coastal Douglas-fir, by the Ministry of Forests of British Columbia (BCMF). Later on, various members of the forest industry joined the project following the leading role of the BCMF (Heaman, 1967). The purpose of the program was to provide coastal Douglas-fir seed for reforestation projects. The program is accumulating additional information concerning genetic variation of Douglas-fir (Heaman, 1977a). 1 Since 1972, the main emphasis of the program has been the evaluation of the genetic quality of the selected parent trees. Such evaluation has been made with 8 different progeny-test series planted between 1975 and 1985 in different sites along coastal British Columbia (Yeh and Heaman, 1987). The program had many objectives one of which was to assess the size and importance of interactions of parents across a sample of environments representing future planting sites. If the variation among phenotypes in their response to different environmental conditions or interaction patterns are sufficiently important, these tests together with the provenance test information (Illingworth, 1976), already in the field, will provide a basis for subdividing the breeding population (Heaman, 1977a). This study analyzed data obtained from a sample of 15 full-sibling families that were planted on 22 sites to evaluate genotype x environment interactions. Objectives: 1. To quantify the genotype x environment interaction component and its significance for height and diameter among a subsample of families from the test which are planted in series II and III. 2. To identify and quantify the nature of stability in the families for the two series analyzed. 2 CHAPTER 2: LITERATURE REVIEW The selection of trees with the most desirable traits for use as the breeding population has been a primary part of most present forest tree improvement programs. Selection is made based on the measure of the productive performance trees exhibit (Squillace, 1970). The performance trees exhibit (phenotype) is partially dependent on the genetic potential that the trees inherit from their parents (genotype) and partially on the site where they grow (environment). In other words, there is always a genetic 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 the phenotype as independent effects (Gregorius and Namkoong, 1986; Wright, 1976; Zobel and Talbert, 1984). Gregorius and Namkoong (1986) stated that independence of effects simply means that the contribution of a particular genotype to the formation of the phenotype does not depend on environment. Conversely, a particular environment makes the same contribution when acting on different genotypes. Nevertheless, it is quite common to find variation 3 between genotypes in their response to different environmental conditions (Burdon, 1977; Shelbourne, 1972; Squillace, 1970). Shelbourne (1972), defined the genotype x environment interaction as the "variation between genotypes in their response to different environmental conditions". Such interactions, according to Squillace (1970) could be assessed when at least two different genetic entities are tested in two different sites or environments . The presence of genetic x environment interactions may reduce genetic gains achievable in breeding programs when the selected trees are adapted to a narrow range of site conditions 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 genetic effects apply only to the range of environments studied and vice versa. Practical consequences of these interactions are very important. Such interactions may determine the subdivision of the breeding population (Matheson and Cotterill, 1990; Matheson and Raymond, 1984; Namkoong, 1990; Shelbourne, 1972; Squillace, 1970). Furthermore, breeding regions could be defined not only on the basis of the environmental conditions but also according to the performance of the trees growing there (Carson, 1990; Matheson and Cotterill, 1990; Matheson and Raymond, 1986; Shelbourne and Campbell, 1976; Squillace, 1970). 4 To have just one breeding population for any improvement program is always desirable, but it is not always the right alternative to achieve the goals of the breeding program (Burdon, 1977; Matheson and Raymond, 1984; Squillace, 1970). Subdivision of the breeding population results in higher costs of operation and more difficulties in managing the breeding program. Such factors should be compared against the yield gains expected to be achieved to evaluate the convenience of such process (Carson, 1990; Matheson and Raymond, 1984; Shelbourne, 1972; Squillace 1970). Furthermore, delineation of planting zones does not ordinarily eliminate interactions, it merely reduces them (Matheson and Raymond, 1984; Squillace 1970). For these cases, choosing material which will give the highest average yield in the whole zone is the most desirable (Finlay and Wilkinson, 1963; Hiihn and Leon, 1969; Matheson and Raymond, 1986; Squillace 1970). The existence of genotype x environment interactions has long been recognized as part of the phenotypic expression of any plant or animal (Namkoong, 1990; Wright, 1976; Zobel and Talbert, 1984). Freeman (1973) described that the earliest reference to interactions was reported in 1923, by Fisher and Mackenzie (1923, original not seen). They surmised about the existence of the interactions when they evaluated different potato varieties under several treatments. Since then, many researchers have developed various techniques to examine the statistical nature of these interactions. For example, 5 Sprague and Federer (1951) showed how variance components could be used to separate the individual effects of the genotypes, the environment and their interactions in the analysis of variance to their expectations. In terms of a mathematical model, the yield y ijk of the kth replicate of the .i t genotype in the j th environment is made up of a general mean (p), a genotype effect di, an environmental effect an interaction effect and a random error e ijk , in a linear model: .170,= A + d i + + gij + The statistical approach uses analysis of variance to separate variance into components assigned to genotypes, environments, interaction, and error. These variance components are then used to predict the consequences of the selection of genotypes (Gupta and Lewontin, 1982). Lewontin (1974) reported that a second approach has been used to characterize the phenotype of a given genotype in a fixed series of environments and then to compare the genotypes with respect to their patterns of phenotypic response to different environments. Originally introduced by Woltereck (1909, original not seen) the concept of norm of reaction of the genotype fits this approach (Gregorius and Namkoong, 1986). Schmalhausen, (1949, original not seen) defined norm of reaction as: "...the array of phenotypes that will be developed by the genotype over an array of environments" (Gupta and Lewontin, 1987). 6 Evaluation of the norms of reaction can be done graphically. Gupta and Lewontin (1984) plotted the environments or environmental variables against the mean yields for each genotype, to describe the norm of reaction for each genotype plotted. The lines the genotypes describe as norms of reaction indicate the existence of interactions when they cross each other (Lewontin, 1974). Gupta and Lewontin (1984) pointed out that analysis of variance is not sufficient to affirm or deny the existence of the interactions. They argue that low mean square values for the interaction compared with the main effects, do not capture the essential feature of the norms of reaction. The essential feature is that they cross each other to denote the existence of interactions. The most important difference occurs when interactions are not statistically significant in the analysis of variance and the lines of the norms of reaction cross each other. Lewontin (1974) suggested that the interpretation of the results of the analysis of variance and their use would critically depend on knowing the norms of reaction of the genotypes evaluated. As Gupta and Lewontin (1984) indicate, both the statistical and developmental approaches have limitations when they try to assert the interactions between environment and genome in creating the phenotype. There have been several criteria used to classify interactions (Allard and Bradshaw, 1964).^Lambeth (1979) 7 classified only two kinds of interactions: those due to change in genetic variance between sites and those due to rank changes in genotypes. He called the former "important interactions". Matheson and Cotterill (1990) classified the interaction according to their significance in a similar way Lambeth (1979) did. They created three categories: - When interactions are not statistically significant. - When interactions are statistically significant but of no practical significance, and; - When interactions are of both statistical and practical significance. For the second case, interactions are statistically significant but of no practical significance since the rankings for the genetic components remain the same in the different environments. Matheson and Cotterill (1990) pointed out that this is the case when mere statistical significance is not sufficient evidence that interactions are important for practical purposes. The last case implies that the rankings of the genotypes change substantially from one environment to another. This is the case when one or several genotypes have higher yields in one or several environments and lower in others (Matheson and Cotterill, 1990; Shelbourne, 1972; Squillace, 1970). In addition to interactions, there is the concept of stability. A stable genotype is the one that has a constant yield in a variety of environments to which it is exposed. 8 Stability values are related to the average performance of families in each environment, but an individual family stability value would be influenced by the nature of the other families involved in the tests (Finlay and Wilkinson, 1963; Hiihn and Leon, 1984; Shelbourne, 1972; Squillace, 1970). Several authors have proposed different methods to evaluate phenotypic stability (Htihn and Leon, 1969; Morgenstern and Teich, 1969). Finlay and Wilkinson (1963) proposed that a simple linear regression used to describe various types of variety adaptability to a range of environments also can be used as a quantitative measure of phenotypic stability. Their approach is based on plantation performance to compare the adaptability of several varieties grown at several sites for several seasons. For each variety, a linear regression of individual yield on the mean yield of all varieties for each site in each year was computed. The mean yield of all the varieties at each site (site mean) provides a numerical grading of sites. Site means are proposed as a useful evaluation of the productivity or quality of the site or environment. The regression coefficient (b value) for each variety is proposed as a stability parameter. The population regression has a b value of 1.0, which is defined as the average stability of the population. Absolute phenotypic stability would be expressed as b=0. Values of b between 0 and 1 indicate that the individual family is more stable than the 9 OW >°co IL < li 0 10 0 to SPECIFICALLY ADAPTED TO FAVOURABLE ENVIRONMENTS BELOW AVERAGE STABILITY POORLY ADAPTED TO AVERAGE STABILITY WELL ADAPTED TO ALL ENVIRONMENTS ALL ENVIRONMENTS ABOVE AVERAGE STABILITY V SPECIFICALLY ADAPTED TO UNFAVOURABLE ENVIRONMENTS VARIETY MEAN YIELD Figure 2.1 A generalized interpretation of the family population pattern obtained when the family regression coefficients are plotted against family mean yields (Finlay and Wilkinson, 1963) . 10 average. A b greater than 1 indicates that the family has a stability below the average population stability (Figure 2.1). Wricke (1962, original not seen) devised a method for thecalculation of individual family contribution to the interactions (Morgenstern and Teich, 1969). He performed an analysis of variance using the mean values to get the usual sum of squares for families, sites, family x site interactions and total. The contribution of individual varieties (VJ to the interaction is then calculated with the formula: Vi= E - xi . q) - (x.i + p) + (x.. + pq) )2 where xo is the yield of the ith variety at the jth site; xi. the sum of variety i over all locations; x.i the sum of all varieties at site j; x.. the grand total, that is, the yield of all varieties in all sites; q the number of sites and p the number of varieties. A variety contributing little to the interactions, is said to possess high stability. Plaisted (1960, original not seen) calculated interaction mean squares omitting varieties one at a time (Morgenstern and Teich, 1969). This would give different values for the sums of squares of the FxS term. The higher the sums of squares of the FxS value results, the lower is the omitted family's contribution to the FxS. A family that possesses high stability should contribute little to the sums of squares of the FxS term. 11 Hiihn and Leon (1984) used 5 different approaches to evaluate stability.^They found none of the 5 methods used gave very similar results. They concluded that the mean rank-difference previously proposed by Hiihn (1979, original not seen) showed some advantages over the others (Hlihn and Leon, 1984). Briefly, this method consists of transforming the yields of the families into ranks for each site separately. For each family, the mean of all possible, 2 by 2 absolute rank- differences between all possible pairs of different environments, is computed. Morgenstern and Teich (1969) attribute more accuracy to the method proposed by Wricke (1962). The method has the advantage of breaking out the sums of squares by families or sites of the FxS interaction. In this way families could be evaluated according to the contribution they made to the interaction. Shelbourne (1972) gave more importance to the method developed by Finlay and Wilkinson (1963), but Matheson and Raymond (1984) concluded that interacting families are not necessarily best identified by their regression on site means: the same family could be classified in several ways according to its regression coefficient (b value) and its mean yield. 12 CHAPTER 3: MATERIALS AND METHODS Experimental Project 708 of the BCMF Research Branch forms the basis of the breeding program for coastal Douglas- fir in British Columbia. Initial tree improvement work emphasized^phenotypic^selection^and^seed^orchard establishment. Phenotypically superior trees were selected until 1966 from a part of the natural distribution range of coastal Douglas-fir (Figure 3.1 and 3.2) that extends from northern California to central British Columbia (Heaman, 1977a). This population was propagated in a breeding arboretum and planted in seed orchards to meet the immediate seed requirements. Emphasis shifted to breeding of controlled pollinated progeny of the original plus trees selected, and in 1972 a decision was made to evaluate the genetic quality of the selected trees (Yeh and Heaman, 1987). A total of 372 intensively selected trees from the original selected population were crossed and produced 1109 families through a controlled cross process from 1974 to 1985 (Table 3.1).^Cross arrangement was according to a disconnected modified diallel design used for mating.^With 5 crosses per parent this produces a balanced unit of 15 crosses (Heaman, 1982). 13 Figure 3.1 Map showing the approximate distributionof Douglas-fir (Fowells, 1965). Interiorand coastal varieties are separated by a broken line. 14 Figure 3.2 Map showing the approximate distribution of Coastal Douglas-fir in British Columbia (Beaman, 1967). 15 Table 3.1 SERIES OF THE COASTAL DOUGLAS-FIR BREEDING PROGRAM EXPERIMENTAL PROJECT 708 Sowing Year Series Parents Involved Families Planted Test Sites 1975 I 60 177 11 1976 II 30 99 11 1977 III 54 165 11 1978 IV 54 170 11 1979 V 48 153 11 1980 VI 48 140 11 1981 VII 18 55 11 1985 VIII 60 150 11 The choice of trees as male or female parent was based on the availability of pollen and number of female strobili in the pollination year (Yeh and Heaman, 1987). Crosses and seeds collections were made yearly. Seedlings were raised in the Cowichan Lake Nursery and planted as 1 year-old plugs.^Progenies were established in field trials to assess their performance (Heaman, 1977a) along the coastal distribution area of Douglas-fir in southern British Columbia over eight different years (1975-1981 and 1985). Each different year represents a series.^Each series has a different number of families planted (range from 55 to 177) in 11 sites per series. All families were planted at every site (Heaman 1977b and 1988). Sites were chosen from available logging and rehabilitation sites.^The most important criteria were within site "homogeneity", and localization of the sites inside the natural distribution area of coastal Douglas-fir 16 (Yeh and Heaman, 1987).^Site location for series II and III are 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. The plantation was laid out as a randomized complete block design without sub-blocking by sets. A 3 x 3 meter spacing between seedlings was used. From the families planted each year, 15 (about 10%) were randomly selected from year to year and planted in 2 consecutive series (Yeh and Heaman, 1987; Heaman, 1977b).^Height was measured in the 6th,^7 th and 12 th year (H6, H7, and H12, respectively) in centimetres and diameter at 130 Table 3.2 SITE LOCALIZATIONS FOR SERIES II AND III Series Site: Latitude* Longitude* Elev. Forest # # Name o^'^" o^'^" (m). District II 12 Maquilla 50-04-20 126-21-10 545 Port McNeill 13 Heber 49-49-55 125-57-02 303 Campbell River 14 Sarita 48-51-23 124-52-54 364 Port Alberni 15 Jordon 48-25-00 124-00-50 45 Duncan 16 Muir 48-25-35 123-54-52 379 Duncan 17 Bamberton 48-37-32 123-34-00 212 Duncan 18 Sechelt 49-25-30 123-35-30 212 Sechelt 19 Squamish 50-12-00 123-22-00 155 Squamish 20 Chilliwack 49-05-25 121-40-35 303 Chilliwack 21 Lost Creek 49-22-13 122-14-05 424 Maple Ridge 22 Chelais 49-30-35 122-01-00 333 Maple Ridge III 23 Adam 50-24-00 126-10-00 576 Campbell River 24 Menzies 50-08-54 125-38-15 333 Campbell River 25 Gold 49-51-30 126-04-55 561 Campbell River 26 White 50-05-35 126-04-30 409 Campbell River 27 Sproat Lake 49-17-25 125-03-05 318 Port Alberni 28 Fleet 48-39-30 124-05-00 561 Duncan 29 Tansky 48-27-45 124-01-45 545 Duncan 30 Eldred 50-06-00 124-13-00 148 Powell River 31 Squamish 50-12-05 123-22-30 135 Squamish 32 Sechelt 49-25-20 123-35-27 212 Sechelt 33 Lost Creek 49-22-15 123-14-10 424 Maple Ridge * All latitudes North and all longitudes West. 17 Figure 3.3 Map showing the approximate locality of sites in series II (sites 12-22) and series III (sites 23-33) (lleaman, 1977b). 18 cm height in the 12 th year in millimetres. Twenty-two different parents were involved to produce 15 families (Table 3.3).^Parent provenances extended from Vancouver Island (Gold River and Knight Inlet sites) to the Snoqualmie 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 data unbalanced.^The data were evaluated according to the following model: ;kir=^+ R1 +^+ FixRi + Sol + B (1 bq^Fi X S^FjXB(i 0,1^Eo i 1 q)r where: Yijlqr Ri FjxRi Soo Bo oq F^xS(;)1 FjxBo = 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 interaction EO. Or = Residual or individual effect of r th tree (r=4) All effects except the overall mean (g) were considered random. Statistical analysis of the data was performed on the UBC mainframe computer using several procedures of the 19 Table 3.3 OVERLAPPING FAMILIES IN SERIES II AND III Family a Number Parentsb 9^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 West in 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, namely homogeneous 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 normality was met and the variances were within the acceptable range and therefore assumed homogeneous (Table 3.4). Sums of squares and the expected mean squares were calculated with the General Linear Model Procedure (GLM Proc) using type III sums of squares as well as the Duncan's multiple range test for the 20 Table 3.4 HOMOGENEOUS VARIANCES AND NORMAL DISTRIBUTION Variable^Variances (x2)* T Value** 116^13.95Ns^0.71887 H7 14.18 NS 0.76850 H12 13.46Ns^0.74041 D1AM^13.87Ns 0.77153 NS = 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 then there is not sufficient evidence to declare the variances heterogenous (Morrison, 1976). ** T value obtained from the Kolomogorov D statistic to test normal distribution. If value calculated < to 0.775 the sample is considered normally distributed (Stephens, 1974) means. The expected mean squares for the model are given in Table 3.5. For sources of variation for which there was not a direct error term to test against, pseudo-F tests were constructed and the appropriate degrees of freedom calculated according to the Satterthwaite's (Hicks, 1982) approximation. Evaluation of family stability across sites was done by 4 different methods: the Finlay and Wilkinson (1963) approach; the Wricke (1962) method; excluding one family at a time in the analysis of variance (Plaisted, 1960); and, with the mean rank-difference method (HUhn and Leon, 1969). The Regression Procedure (Reg Proc) was used for the first, the Analysis of Variance (Anova Proc) for the second and third, and a simple spread sheet for the last. Scattergrams of family norms of reaction were constructed plotting family means against sites. Rank correlations for 21 Table 3.5 EXPECTED MEAN SOUARES FOR THE MODEL Source^Expected Mean Squares Repetition (R) VE +C IVF*13 +C2VF*S ±C3VB +c4VB -1-05VFMR^-I-c7VB Family^(F) VE +C 117F4S ±C2VF•S^ +CSVF*R +c 6VFFxR VE +C 1VF*13 +C2VF*S +c514.a Site^(S) VE +CIVF•B + C2VF*S +c3VB +c4VB Block (B) VE ±CIVF*B^-1-c3VB FxS VE +C 1VpIS ±C2VF•S FxB^VE ±CIVF*B Error VE Range of the Coefficients (ca ) : Variable H6^H7 H12 DIAM c 1 low 3.81 3.83 3.74 3.72 high 3.87 3.89 3.83 3.82 c2 low 15.25 15.35 15.01 14.92 high 15.34 15.42 15.12 15.04 C3 low 57.22 57.59 56.33 56.01 high 57.29 57.64 56.44 56.12 c4 low 228.91 230.38 225.39 224.11 high 228.96 230.42 225.51 224.24 C5 low 167.82 168.91 165.26 164.32 high 168.03 169.08 165.46 164.53 c6 335.85 337.99 330.72 328.85 C7 2517.50 2533.70 2479.00 2464.90 families across sites were performed using the Kendal approximation (W) and Friedman's chi-square (V) to evaluate ranking as suggested by Siegel (1967). Kendal approximation (W) and Friedman's chi-square (M), or Spearman's regression coefficient (1'0 were also used to compare rankings of the results observed. 22 CHAPTER 4: RESULTS AND DISCUSSION Analysis of variance for the variables is summarized in Table 4.1. Table 4.2 shows the components of variance for all the sources of variation. The largest variation for every variable was due to site (Vs). Sampling error (VE) was the second largest source of variation for all variables. Variance components kept a similar proportion for H6, H7 and H12. For all the variables the FxB interaction was significant (P0.01). The significance of this factor could be due to the poor homogeneity within sites, and/or the relatively small number of blocks (i.e. four). The FxS interaction was not significant for any variable, but FxR was significant for H7 and H12 (P<0.05), and highly significant for diameter (P<0.01). The FxS interaction on was not statistically significant.^However, as was shown by the rank changes the interaction does exist.^Norms of reaction of five families randomly selected were plotted. The occurrence of crossed lines indicates the existence of interactions (Figure 4.1). Rankings were evaluated with the V, rsand/or W coefficients. The V determines whether the ranks totals 23 Table 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*R R 1^0.38Ns F*R 14^1.68Ns 0.10Ns 2.12 * 0.01Ns 2.03 * 0.17Ns 2.25 ** VF*B +Vs —VF*B VF*S S^20^58.70 ** 55.95" 57.40 ** 71.20" Vs -I-I/Fos —VF.B B 66^2.28** 2.57 ** 2.28 ** 1.93" VF*B F*S^280^1.13Ns F*B 924^1.87** 1.15Ns 1.96" 1.14Ns 2.10" 1.08Ns 1.82 ** VF*B VE **= Highly Significant (P5.0.01) *= Significant (1D0.05) NS= Not Significant differ significantly from one family to another.^The rs shows if the two rankings compared are significantly correlated.^The W coefficient shows the association among several rankings.^If the W value is high the rankings are statistically similar. The W coefficients were low for every variable when computing the families rank correlation across sites. This means that family ranks were different from site to site. In addition, the x,2 values were highly significant, denoting differences among families (Table 4.3). These results support the existence of the crosses of the lines of the norms of reaction. Besides the families rank correlation across sites, two more rankings were calculated. One of them ranks families according the family overall mean for each variable and the other was the ranking mean or the sum of ranks of every family in every site divided by the number of sites. When 24 Table 4.2 COMPONENTS OF VARIANCE Source Variables: H6^%^H7 VR 0.00^0.00 0.00^0.00 VF 73.85^1.43^146.89^1.63 VF•R 19.40^0.37 49.14^0.55 Vs 2344.57 45.25^4323.90 48.08 VB 86.45^1.67 180.47^2.01 VFss 32.99^0.64^61.63^0.69 VF*B 470.97^9.09 849.10^9.44 VE 2153.42 41.55^3382.92^37.60 Source H12^%^DIAM VR 0.00^0.00 0.00^0.00 VP 723.42^2.07^11.19^1.06 VF*R 184.88^0.53 6.18^0.59 Vs 16423.15 47.05^493.83 46.86 VB 608.74^1.74 12.88^1.22 VF*s 241.69^0.69^3.59^0.34 VF*B 3792.64^10.87 95.33^9.05 VE 12932.26^37.05^430.78^40.88 these two rankings of every variable were compared with rs they were highly correlated. When any pair of rankings of the height variables was compared, the rs was very high (rs > 0.935). When a ranking of any of the height variables was compared with the ranking of 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 the rs coefficient. The x12 was significant too, denoting the differences in ranking among families (Table 4.4). Overall site rankings were computed for every variable to see if the variables were good estimators of site quality as 25 H7 Fam. Mean (cm.) 500 H12 Fain. Mean (cm.) 1000 400 - 300 200 100 Fain. Mean (cm.) 3C0 H6 50 12^14^16^18^20^22^24^26^28^30^32 13^15^17^19^21^23^25^27^29^31^33 S ites 800 600 200 0 0 12^14^16^18^20^22^24^26^28^30^32 13^15^17^19^21^23^25^27^29^31^33^ Sites Fam . Mean (tam.) 140- 120 103 so 60 40 20 0 12^14^16^18^20^22^24^26^28^ 30^32 13^15^17^19^21^23^25^27^29^ 31^33 S ites12^14^16^18^20^22^24^26^28^30 32^Sites13^15^17^19^21^23^25^27^29^31^33 Figure 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). 250 200 150 103 Table 4.3 FAMILIES RANK CORRELATION ACROSS SITES H6^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 FAMILIES Variables Family H6^a*^b* H7 a^b H12 a^b DIAM a^b 2 15^14 15^14 15^14 14^14 12 6^5 6^5 7^7 1^1 15 12^12 12^12 12^12 3^3 18 5^4 4^4 4^4 7^6 21 11^9 9^9 8^8 11^11 39 13^13 13^13 13^13 13^12 44 9^10 10^10 10^9 8^8 67 3^3 3^2 2^2 5^5 68 8^7 8^7 6^5 10^9 69 10^11 11^11 11^11 12^13 73 7^8 7^8 9^10 9^10 74 14^15 14^15 14^15 15^15 88 1^1 1^1 1^1 2^2 89 2^2 2^3 5^3 4^4 94 4^6 5^6 3^6 6^7 rs^(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 the variable. b= Rank according to the sum of rankings of every family divided by the number of sites, or ranking mean. ** = Values computed using the overall mean of the family rank. ++ = Values computed using the overall mean of the family rank for the height variables only. 27 suggested by Finlay and Wilkinson (1963): xr2 was significant denoting the differences in ranking among sites. The W value was high denoting that the differences among variables in the overall 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 were 15, 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 (Table 4.13). The most stable families according to the method of Finlay 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 diameter 21, 39, 74, 18 and 2 (Table 4.13). Families closer to the average stability according to Finlay 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); for 28 Table 4.5 RANK CORRELATION OF SITES FOR HEIGHT VARIABLES^FOR ALL THE ONLY^ VARIABLES xr2^60.45" 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 of this study, sites are discussed as they relate to family yields. As mentioned before, Finlay and Wilkinson (1963)proposed site mean as an evaluation of the environment productivity. Therefore, comparing the means of the poor sites with the family means in these sites, would reveal the families with better yields in poor sites when their means in these sites were above the site mean. A similar comparison for the rich sites would delineate the families with better yields in rich sites. For H6, there were 12 sites with means below the overall mean or poor sites, and 10 sites with means above the overall mean or rich sites; for H7 were 12 poor sites and 10 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 with better yields in all sites (b.-.,. 1 and mean > p) for H6 were 88, 89, 67, 94, 18 and 12; for H7 were 88, 89, 67, 18, 94, 12 and 73; for H12 were 88, 67, 94, 18, 89, 68, 12 and 21; for diameter were 12, 88, 15, 89, 67, 94, 18 and 44. Families which tended to have better yield in poor sites 29 Table 4.6 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANS FOR H6 Ranking Family Mean P<0.01* P<0.05* 1 88 178.02 A A 2 89 176.10 A AB 3 67 173.26 A AB 4 94 170.25 AB B 5 18 169.79 AB B 6 12 168.89 AB CB 7 73 161.74 B CB 8 68 161.54 CB CD 9 44 158.16 CD D 10 69 157.34 C D D 11 21 156.07 CD E D 12 15 155.99 CD E D 13 39 148.98 CD E F 14 74 148.54 D E F 15 12 148.07 D F Overall 162.27 * Families with the same letter are not significantly different at the P level shown. Table 4.7 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANS FOR H7 Ranking Family Mean P<0.01* P<0.05* 1 88 247.03 A A 2 89 238.88 A AB 3 67 237.36 AB AB 4 18 231.07 ABC CB 5 94 229.88 ABC CB 6 12 225.27 DBC CD 7 73 220.29 DEC E D 8 68 219.82 DEC E D 9 44 215.52 DE E^F 10 21 215.08 DE E^F 11 69 213.57 DEF E^F 12 15 209.15 GEF G F 13 39 202.49 G^F H G 14 74 199.74 G H 15 2 199.37 G H Overall 220.07 * Families with the same letter are not significantly different at the P level shown. 30 Table 4.8 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANS FOR H12 Ranking Family Mean P<0.01* P<0.05* 1 88 247.03 A A 2 67 623.98 A B A B 3 94 617.85 A B C A B C 4 18 616.85 A B C A B C 5 89 615.93 A B C A B C 6 68 605.87 D B C D B C 7 12 598.44 DBCE D^C 8 21 596.38 D^C E D 9 73 586.95 D F^E D E 10 44 586.42 D F^E D E 11 69 573.91 F G E E F 12 15 564.82 H F G G^F 13 39 552.97 H^G I G H 14 74 540.84 H I H 15 2 538.44 I H Overall 590.40 * Families with the same letter are not significantly different at the P level shown. Table 4.9 DUNCAN'S MULTIPLE RANGE TESTS AND FAMILIES MEANS FOR DIAMETER Ranking Family Mean P<0.01* P<0.05* 1 12 86.45 A A 2 88 84.85 A B A B 3 15 84.59 A B A B 4 89 84.25 A B A B 5 67 83.29 A B C A B C 6 94 82.67 A B C B C D 7 18 81.71 ABCD EBCD 8 44 81.44 B C D EBCD 9 73 80.37 B C D EFCD 10 68 80.23 B C D EFCD 11 21 79.08 C D E F^D 12 69 78.65 C D E F 13 39 77.53 E^D F 14 2 73.88 E F G 15 74 71.44 F G Overall 80.70 * Families with the same letter are not significantly different at the P level shown. 31 Table 4.10 FAMILY STABILITY RANKINGS FOR H6 Fam A B C D E 2 15 15 4 8 12 12 4 4 8 3 14 15 1 1 7 2 3 18 10 10 5 5 11 21 7 7 1 15 15 39 9 9 3 12 7 44 5 5 6 1 10 67 12 12 9 4 6 68 8 8 11 7 13 69 6 6 15 13 8 73 3 3 14 11 4 74 2 2 2 14 1 88 11 11 13 10 2 89 13 13 10 6 5 94 14 14 12 9 9 x12 = 13.05 NS^W=0.233 Ns= Not significant A = 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. 32 Table 4.11 FAMILIES STABILITY RANKINGS FOR H7 Fam A 2 13 13 4 9 12 12 3 3 6 2 6 15 1 1 9 4 3 18 12 12 5 5 13 21 8 8 1 15 15 39 11 11 2 13 11 44 4 4 8 3 7 67 10 10 10 6 4 68 6 6 11 7 5 69 5 5 15 14 9 73 7 7 14 11 10 74 2 2 3 12 1 88 9 9 13 10 2 89 14 14 7 1 8 94 15 15 12 8 14 X12 = 17.00 NS ^W=0.243 NS= Not significant A = 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. 33 Table 4.12 FAMILIES STABILITY RANKINGS FOR H12 Fam A B C D E 2 15 15 4 9 9 12 2 2 5 6 7 15 4 4 7 3 6 18 9 9 8 1 12 21 8 8 1 15 14 39 12 12 2 12 5 44 3 3 12 8 4 67 10 10 9 2 10 68 6 6 11 7 8 69 5 5 15 14 3 73 13 13 14 13 15 74 1 1 6 4 1 88 7 7 10 5 2 89 11 11 3 11 13 94 14 14 13 10 11 X1.2 = 20.87 NS ^W=0.298 NS= Not significant A = 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. 34 Table 4.13 FAMILIES STABILITY RANKINGS FOR DIAMETER Fain^A B C D E 2 15 15 5 5 7 12 3 3 10 6 3 15 5 5 14 11 4 18 9 9 4 8 12 21 11 11 1 15 15 39 14 14 2 13 14 44 4 4 11 7 6 67 13 13 8 3 10 68 1 1 6 2 2 69 7 7 15 14 11 73 10 10 12 9 9 74 2 2 3 12 1 88 6 6 13 10 5 89 8 8 7 1 8 94 12 12 9 4 13 Xr2 = 11.73 Ns^W=0.168 NS= Not significant A = 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). 35 1.15 44 X 18 X 21 X .4^1.1 Z3 aw 1.05 0 0 1 0 U) 0.95- C) P4 0.9— 2 X 39 X 0.85— 74 X 0.8— 69 X^73X^ 8894^ X X 68 X^ 67^8912^X X 15^ X X 73 X 94 X 88 1.15— 69X 0 1.05 _ 68 X^ 67 X O L.) 1— Z 0U) cyj 0.95— 0 C4 0.9— 0.85— 0.8— 15^44 8912 X X 18 X 2 X 74 X 39 X 21 X 1.25 1.2— 0.75 145^ 110 ^155^160^165^130^175^180 Family Means Figure 4.2 The relationship of family regression coefficients (b) and family mean yield of H6 variable. 1.25 1.2— 0.75 190 ^ 21)3^210 ^210^zip^240 Family Means Figure 4.3 The relationship of family regression coefficients (b) and family mean yield of H7 variable. 36 0.75 510 560^540^580^590^690^610 Family Means 630530 620 1.2- 1 . 15 - 69 X 73 X 44 68 X 94 X 88 1.05 - 74 X 15 X is^67 x X 12 X 2 X^39^ 89 0.85- 0.8- 21 X 69 X1.15- 73 'd^1. 1 - x 44 12 X94 67X x1.05-0 0 68^89 2 X 18 X 74 X 39 X0.85- 21 X 0.8- 1.25 11- 1.25 Figure 4.4 The relationship of family regression coefficients (b) and family mean yield of H12 variable. 0.75 70 ^ 716^78^80^82^84 Family Means Figure 4.5 The relationship of family regression coefficients (b) and family mean yield of Diameter variable. 37 (b < 1 and mean < p) for H6 were 21, 39, 74 and 2; for H7 were 21, 39, 74 and 2; for H12 were 39 and 2; for diameter were 21, 39 and 74. Nevertheless, the analysis of the results did not support this criterion in the majority of the cases. The attribute of better yield in poor sites was quite notable for family 21 in variables H6, H7 and diameter, but the other sets of families did not show this quality, especially family 2 which had means below the site means in almost every case for H6, H7 and H12. Finlay and Wilkinson (1963) explained their low mean yields as a consequence of high phenotypic stability: they are so stable that they are unable to exploit high yield environments. The Finlay and Wilkinson (1963) approach suggests that families 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; for H12 were 73, 44 and 69; for diameter were 73 and 69. Again, as in the case of the families with better yields in poor sites, the analysis of results did not support this criterion for H6 and H7. However, this attribute was appropriate for the set of families mentioned for the H12 variable, especially family 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). 38 Family rankings for stability gave low W values for all the variables denoting the significant differences existing among rankings. Xr2 values were not significant for any variable either: the lack of significance may be associated to the considerable differences among rankings that made it impossible to detect any significant difference among families. 39 CHAPTER 5: CONCLUSIONS Family rankings for H6 and H7 were very similar: only 2 pairs of families interchanged positions. This similarity is obviously due to the proximity in time in which the data were taken.^Comparing the rankings of H6 and H7 with H12, more notable differences appeared.^However, the Spearman's correlation coefficients (rs) were very high for any pair of rankings compared, showing the similarity of rankings for all the variables. In all cases, it was possible to distinguish 3 sets of families: - 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 3 variables. According to the Duncan's multiple range test, there were not statistically significant differences among them (P<0.01). The families of the middle group showed more changes in their rankings. There were different rankings for each variable, but most of the changes were only 1 or 2 places in the ranking. 40 The lower 4 families (15, 39, 74 and 2) kept the same ranking for the 3 variables. According to the Wricke method (Morgenstern and Teich, 1969), family 2 was among the lesser of the stable families. In contrast, the Finlay and Wilkinson (1963) method classified this family as one of the most stable families for all variables. Given the poor concordance between what Finlay and Wilkinson (1963) suggested and the results obtained, it seems that the Finlay and Wilkinson (1963) method is not the most suitable to evaluate stability, as Matheson and Raymond (1984) suggest. For diameter, the families in general kept the same pattern as the ones showed for height variables. The exceptions were families 12 and 15 that were among the middle and low families for height increments and were ranked as 1 and 3, respectively, for diameter. Height and diameter were good estimators of site quality as suggested by Finlay and Wilkinson (1963), given the similarity of the ranking for sites for the 4 variables. The significance of the FxR interaction for the H7, H12 and diameter variables could be due to the environmental differences from one year to the next. Sites were located within the same general climatic area, but different weather conditions in different years could produce such significant interaction. Squillace (1970) suggested that given the long life span of most trees, this kind of interaction becomes nonsignificant over a period of 30 years. In this study, a 41 peak value of the FxR interaction for height was attained at the 7th year, but for the whole study the maximum was for diameter which was measured at the 12th year. The lack of significance of the FxS interaction in this sample of families supports Yeh and Heaman (1987), and the prospect of working with only one breeding population seems appropriate. The high correlation between the ranking of the family means and the ranking mean of the families reinforce the observed lack of significance of the FxS term. In spite of the results of the rank correlation of families across sites that showed the significance in the change of the family rankings from site to site, other results suggest that even with the significance of changes in rankings site, such changes are not statistically significant with other methods. Four different methods were used to calculate family stability. They gave very different family stability ranks. The W values were very low showing no relation or similarity among the ranks. The xr2 were not significant in any case, and did not show any significant differences among the families. Only the method suggested by Wricke (1962) and the one omitting one family at a time for the calculation of the FxS interaction, gave similar rankings' results . Comparing rankings of both methods the correlations were 1 for every variable because rankings were identical. The methods suggested by Finlay and Wilkinson (1963) and 42 by Hiihn (1979) gave very different results. The mean rank- difference expresses only the rank changes of the families from site to site, but it does not take account of any site value and the possible links with the stability of the families.^In this study, the Finlay and Wilkinson approach always classified as the most stable families the less productive ones.^Considering the regression coefficient of 1 (average stability) to rank families, the differences in rankings with the other methods to evaluate stability, still persisted. Considering the family means and the regression coefficient together, to classify family stability, was also not very consistent. Families with mean values greater than the overall mean and stability values (b) close to 1 were on average the most productive families for all variables. Families that were classified as with better yields in poor or rich sites did not exhibit any consistency for such traits. This study did not show genotype x environment interaction for the families and sites evaluated. 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New York. 505 p. 47 APPENDIX 4 8 An example of the data used to calculate the stability rankings: FAMILY STABILITY VALUES FOR DIAMETER Fain A C (*) (&) D 2 1913.13 15 15614.32 15 0.953 5 5 318.95 7 12 615.74 3 17004.39 3 1.047 10 6 193.45 3 15 883.64 5 16717.36 5 1.110 14 11 224.00 4 18 1353.94 9 16213.45 9 0.932 4 8 405.05 12 21 1383.84 11 16181.42 11 0.778 1 15 472.77 15 39 1853.94 14 15677.75 14 0.848 2 13 439.27 14 44 782.46 4 16825.75 4 1.063 11 7 296.77 6 67 1574.31 13 15977.35 13 1.039 8 3 360.36 10 68 453.76 1 17177.94 1 0.996 6 2 186.77 2 69 1105.36 7 16479.79 7 1.154 15 14 373.45 11 73 1383.50 10 16181.79 10 1.071 12 9 351.45 9 74 519.14 2 17107.88 2 0.870 3 12 114.00 1 88 1103.70 6 16481.58 6 1.102 13 10 230.95 5 89 1260.14 8 16313.96 8 0.996 7 1 323.86 8 94 1477.44 12 16081.14 12 1.041 9 4 416.77 13 1.000(**) 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 the less stable. (**) 1.00 is the average regression coefficient for the whole sample. 140 120 100 80 - DIAMETER 20 Sites 12^14^16^18^20^22^24^26^28^30^3213^15^17^19^21^23^25^27^29^31^33 Figure to show the norms of reaction of the 15 families for the variable diameter (Sites numbers in the x axe, and family means in the y axe in millimetres).

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