llllllhil | i I § 1 WIN 144 417 THS PAREN?AL SELECTION BY AN. GBEEC‘WJE EDEN. n: W i-NTEF; BARLEY Thesis m the Degree cf Ni. 3. .fe‘iiCHEGN‘é SEWKYE UNZ‘JERSWY IHESXS I “@1042009 1133” 27‘ ABSTRACT PARENTAL SELECTION BY AN OBJECTIVE IDEAL IN WINTER BARLEY, by Cecil D. Nickell Twelve parents were selected and combined using the vector method to produce nineteen crosses. A subjective ideal based upon the knowledge of the population of lines and the environment was used to pick the best parents in 1960-61. The 196“ season was quite different from the 1960—61 season and the best parents chosen in 196“ were not the same ones selected in 1960-61. Also, correlations between the values of the component traits of yield and malting were zero or negative, further indicating the independence between seasons. Through the use of a set of indicator lines, the environmental differences between seasons were overcome. Multiple regression equations were calculated using the values of the indicator lines and the values of the sub— Jective ideal for a given year to determine the beta weights for each indicator. With betas averaged for five years and the current year's data for the indicator lines, an objective ideal was produced. This new ideal did pick the best lines for both 1960-61 and for l96U. PARENTAL SELECTION BY AN OBJECTIVE IDEAL IN WINTER BARLEY By Cecil D. Nickell A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of CrOp Science 1965 ACKNOWLEDGMENT The author wishes to thank Dr. J. E. Grafius for his help in conducting this research and in writing the manuscript. The financial support of the Malting Barley Improvement Association, Milwaukee, Wisconsin during the course of this investigation is gratefully acknowledged. Dr. A. D. Dickson of the U.S.D.A. Barley and Malt Labor- atory deserves special thanks for the malting quality analysis. The moral support and encouragement of the author's wife and family during the course of this investigation is deeply appreciated. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . , ii LIST OF TABLES . . . . . . . . . . . . . iv LIST OF FIGURES . . . . . . . . . . . . . v Chapter INTRODUCTION. . . . . . . . . . . . . 1 LITERATURE . . . . . . . . . . . . . 3 METHODS AND MATERIALS. . . . . . . . . . 6 RESULTS . . . . . . . . . . . . . . ll DISCUSSION . . . . . . . . . . . . . 25 Standardizing the Ideal Through Biological Indicators . . . . . . . . . . . 25 Comparison of Progeny with Calculated Mid- parents . . . . . . . . . . . . 31 SUMMARY . . . . . . . . . . .' . . . 36 LITERATURE CITED . . . . . . . . . . . . 37 iii Table 5. LIST OF TABLES Page The comparison of the unselected progeny means with the midparental mean. The per cent increase of the progeny mean over the mid- parental mean was calculated by dividing the progeny mean of each trait by the corres- ponding mean of the midparents for the same trait and multipling by 100 to give a per- centage . . . . . . . . . . . . . l2 Correlation of the bulk progeny with the mid— parental values using transformed data. The data were transformed by equation [1]. This converts all data to the same units, having a mean of 5.0 and a variance of one . 13 The correlation of the bulk progeny values for each trait with midparental values. Raw data were used since correlations were run between the values of each trait which are in the same units . . . . . . . . . . . . 1A Comparison of beta weights (standard partial regression coefficients) between 5-year data for each trait used in the selection of parents. The first two major subdivisions of the table are for the complex traits, malting quality and yield. The third major subdivision is for over-all score which includes malt quality and yield. The absolute magnitude of the 8's indicate the importance of a trait in any year . . . . . . . . 16 Comparison of beta weights using three indicator lines over five years. The average betas at the bottom of the table are averaged by using a weighting method. Nineteen traits were used to calculate the betas for 1960, 1962, and 196“ data; fourteen traits were used in the calculation of the betas in 1961 and 1963. Therefore, the betas for 1960, 1962, and 196” were all multiplied by 19; the betas in 1961 and 1963 were multiplied by ID and all added together and divided by 85 (the total number of traits for the five years) . 18 iv Table 6. 7. 8. The three indicator lines and the three ideals for the average 1960 and 1961 data. (lav = the objective ideal based upon the average betas, I6“ = ideal produced based upon 196A betas and I _ l = ideal picked subjectively for 1960—1969.§. . . . . . . . . . Correlations of all lines with the three ideals. There was a total of 31 lines of which 12 were used as parents. Comparisons with I6O—61 and with I6“ indicates poor agreement. The average ideal, however, picks the better lines in both years . . . . . . . . . Correlations between the same trait between years. Thirty-one lines were used to calcu- late the r values between 1960 and 1961 for each trait and sixteen lines were used in the correlation of each between 1960 and 196A. Page 19 23 2A LIST OF FIGURES Figure Page 1. A brief pictorial representation of the vector method which has been established previously by Grafius (5) . . . . . . . 27 2. A pictorial representation of the extension to the vector method. The procedures are out- lined for the determination of the average betas. Using these average betas and the data of the current year for the indicator lines, a new objective ideal is constructed . 28 vi INTRODUCTION The plant breeder is faced with a large number of complexities which include the genetics of the plant and a dynamic environment. Progress in breeding programs is dependent upon solving these complexities. The plant breeder works with an organism which has a basic genetic make up, but the extent to which this basic unit manifests itself is dependent upon the ever changing environment. The complete control of this dynamic entity, environment, is impossible with our present knowledge. The next best Opportunity to solve the problem of selection in a changing environment appears to lie in develOping sets of biological indicators that can be used as a base for prediction. A primary phase of a plant breeder's work revolves around selecting parents and combining them in such a manner to produce better varieties. The more traits that a breeder works with the more complex the selection of parents becomes. Grafius (A, 5) prOposed a vector method for selecting and combining parents for maximum progress. The same author prOposed that parents could be selected using a large number of traits and that the parental means could I be used as a predictor for combining the parents. A practical ideal must be set up for successful use of the vector method. Parents then can be chosen in such a way that the progeny means of the unselected bulks will approach this ideal as closely as possible. Present information indicates that the progeny means can be pre- dicted for any given year but there is as yet no provision for increasing the reliability of prediction between years. Now, if large seasonal variations in the ideal do occur, how can a plant breeder feel sure that the ideal he uses in one particular year will pick the best parents for another environment or season? Seasons are variable and some method of selecting an ideal is needed which will answer the question, "What are the best parents, not only for this year, but for five years hence?" It will be the primary objective of this thesis to establish a method which will extend the vector method to include seasonal variation. LITERATURE Heritable traits can be classified as complex or simple. Simple traits are usually controlled by a small number of genes and are usually highly heritable. Complex traits are controlled by a large number of genes between which interactions may occur to compound the heritability of the trait resulting in relatively low predictability. Grafius (3, A, 5) defines yield as being a complex trait made up of (X) heads per unit area, (Y) kernels per head, and (Z) kernel weight in oats and barley. It was shown in space planting that X, Y, and Z were independent of each other. 'Grafius (5) points out that in the develop- ment of a plant, a rhythmic process is followed. Small grain developmental patterns consist of the laying down of tillers, floral énitiation, stem elongation, cessation of tillering, pollination and lastly, the filling and maturing of the seed. Therefore, X, Y, and Z are directly related to the life span of the plant. When competition for the existing environment ensues, the correlations become negative between X, Y, and Z. The relative values of these correlations will depend upon the particular year. Grafius (A), using X, Y, and Z in spring barley, found evidence of additivity for the three traits. Grafius (A), Leudders (7) and Whitehouse (12), using components, also found that the parents could be used in the prediction of yield. Smith (9) and Grafius (A) indicate that malting quality as a complex trait could be broken down into components of the chemical behavior and morphology of the seeds. Smith (9) used six characters: malt extract, wort nitrogen, malt nitrogen, diastatic power, beta-amylase and alpha- amylase as malting quality components. Evidence of addi— tivity for many traits was found in eleven crosses of spring X winter barley crosses. Grafius (A) using spring barley found additivity in the malting quality characters of kernel weight, plumpness, malt extract, wort nitrogen, malt nitrogen, diastatic power, and alpha-amylase. Grafius (A, 5), and Grafius and Adams (6) proposed that a vector method could be used to select and combine parents to produce populations which would closely approx— imate an ideal even when using a large set of traits. Assumptions were made that no epistasis existed, or if it did, that it was due to component interaction which could be removed by the use of components and that the vectors were all approximately the same length. A vector was used to describe a variety made up of the large number of traits. An ideal was defined as a practical Optimum based upon the population performance and the environment. The ideal was subjectively picked each year for use as a measuring stick for assigning over-all worth to the potential parents. Correlation values were calculated between the lines and the ideal in order to determine which parents to pick and combine. The vector method is dependent upon picking parents and using the parental means in making the predic- tion of the crosses. A Grafius (2, 3) found that heterosis could be explained by a multiplicative interaction. For example, yield may be increased by having a small increase in one or more of the components. Whitehouse (12) demonstrated additivity for yield components but found epistatic interaction for yield. Duarte and Adams (1), using leaflet area and leaflet number, showed extreme overdominance for leaf area but no over dominance in the components. Williams and Gilbert (1A) also found that heterosis in a complex trait could be a consequence of multiplicative interaction among the com- ponents which are additive or which could show dominance, completely or partially. Powers (8) reported a case of heterosis in yield of tomato fruit due to intra- and inter-allelic interactions between components of the fruit. Breaking the complex trait down into components simplified the mode of heterosis. METHODS AND MATERIALS Parents were selected using the vector method (A. 6) from thirty-one lines based upon the averaged data of the 1960 and 1961 seasons. Malting quality was analyzed by Dr. A. D. Dickson of the U.S.D.A. Barley and Malt Labora- tory at Madison, Wisconsin. Agronomic data were collected in the field and combined with the quality data to con- stitute twenty characters which were used to select the parents. Nineteen crosses were made in the field in 1962 using twelve parents. The F1 seed was planted in the greenhouse in the fall of 1962. The F2 bulked seed was planted in the field in early spring of 1963 to allow for vernalization and seed production. The bulked F3 seed was planted in the fall of 1963 in replicated plots, eighteen feet long and four rows wide (four feet) with the parents planted in adjacent plots. In the summer of 196“ the plots were cut back to twelve feet with the two middle rows being harvested for yield (W). Heads per three feet(X) were counted, once, in each of the two middle rows. Seed weight (Z) was determined by counting the seeds in a three gram sample. Seeds per head (Y) were calculated by the following formula: _ W Y ‘ (X)\Z W = Yield in grams. X = Heads per area multiplied by 8 to make 2“ sq feet. Z = Seed weight in gm. Disease ratings were made in the field, one being good and six poor. Lodging and winter survival are reported in percentages. Height was measured in inches from base of the head to ground level. Heading date was recorded when approximately one-half of plants were headed (head emerging from the sheath). Malt quality was evaluated on the basis of the quality analysis by Dr. A. D. Dickson. Transformed data were used in Table 2 for the corre- lation of progeny with midparents. The data for all the traits are in different units, and therefore the following equation was used to transform the data into common positive units. xi—Y; ! = e Xi C + OX“ [1] l C = A constant which is added to give a positive transformed value. Xi = The value of the transformed data. Xi = The observed value of the trait. X; = The mean value of the trait H.917 = 5.00 + (21‘5 ' 21’76) 1.82 The standard partial regression coefficients (8) in Table A for each trait were obtained by the following equation: U = U + 8w ;% rw [X,YYZ] + . . . + BHt gig rHtEAHt] t [2] U = Over—all worth of the line. B = Standard partial regression coefficient. 0U = Standard deviation of over-all worth score. OW, ch = Standard deviation of the trait in question. r = Correlation of trait between the years. AW, Amq. . . = Difference between observed value of trait and the mean of the trait. The 8's in [2] represent the weight given each complex trait and this weight is to be further apportiOned among components of the complex trait. For example, the weights for the components of the complex traits W and Mq are derived from multiple regression equations as in [3] and [A]. . _ OW OW OW W = W + BX 3—: I‘XEAX] + BY 3'— I‘YEAY] + BZ ;- PZ[AZ] X Y Z [31 W = Yield of the line. Bi = Standard partial regression coefficient. r1 = Correlation between the same trait in different years. AX, AY, AZ = Difference between observed and mean value. A _ 0/! O Mq=Mq+B Jfir[AZJ+...+s flfirm...) [u] ZOZ Z on O a a Mq = Malt quality score. 81 = Standard partial regression coefficient. r1 = Correlation between the values of the traits between years. AZ,. ., Aa = Difference between observed and mean values. The final equation is found by expanding [2] to include the components of the complex traits as in [2a]. . _ Ow 0W U = U + BWEBX ;— rX(AX) + . . . + BZ ;— PZ(AZ)] X Z 01W OM + s [B —49 r (AZ) + . . . + B ——9 r (Ad)] Mq Z oz Z do a O. 0U 0U + s ———— r (ATWT) + . . . + B ——— r (AHt) TWT OTWT TWT Ht OHt Ht [2a] x,,=IOO+-1—L FAX [51 .. Ci 1 i ‘ IBiB‘I X = 1 00 + r A.X [6] J 03 J J Bi = Beta weight obtained in equation [2] for the complex traits. B = Beta weight obtained in equation [3] or [A] J for the component trait. o = Standard deviation. ri or r. = Correlation between the same complex or component trait in different years. AXi or AX. = Difference of the observed value and the mean value. 10 The reason for this rather long discussion involving weighting lies in the need to establish some means of con- verting all data to the same units while at the same time recognizing that some traits are more important than others. The basic Charade here is to obtain subjective weighting first and then convert all data to common units by sub- tracting the mean and dividing by the standard deviation. This gives an array with a mean of zero and a variance of one. A constant is added to avoid negative numbers. RESULTS Data are presented in Table l for the progeny mean and midparental mean of each character measured. Also listed are the F3 bulk cross means in percentage of the midparental mean. The values for yield demonstrate heterosis as deter— mined by percentage increase over the midparent. The t-test was highly significant. The average yield of the bulk pro- genies exceeded the average of the highest parents by 2.2% further indicating heterosis for yield. High seed weight was dominant, being equal to the average of the high parents in the crosses. Seeds per head showed partial dominance. Early heading data was dominant with the average of the bulks being equal to the average of the early parents. Per cent plump, under malt quality, exceeds the midparent mean by 35.5%, which is highly significant with the t-test. The value for plumpness also exceeded the average of the highest parents by 11.7%. Both malt extract and beta-amylase show highly significant difference from the midparent, Table 1. Table 2 contains the correlation coefficients of the bulk progeny means versus the calculated midparent. Since the data were in different units for the various traits within each cross, the data were transformed as described in equation [1]. In all but one cross the r values were 11 12 TABLE l.--The comparison of the unselected progeny means with the midparental mean. The per cent increase of the progeny mean over the midparental mean was calculated by dividing the progeny mean of each trait by the corresponding mean of the midparents for the same trait and multipling by 100 to give a percentage. % Increase Mean of Midparental Over Trait Crosses Midparent Yield (W) Bus/acre 85.5 79.9 107.3** Heads per unit area (X) N0 177.6 181.0 98.1 Kernel weight (Z) mg. 33.6 31.5 106.6** Kernel per head (Y) N0 21.8 21.1 103.1 Test Weight (TWT) 1bS./bu. 47.5 46.3 102.6** Survival (So) % 8A.2 85.1 98.9 Heading date (Hd) May 19.3 20.9 108.3** Mildew (ML) Score 2.3 2.0 87.0 Lodging (LD) % 3.5 3.8 108.9 Height (HT) in. 35.“ 36.0 98.3** Barley Nitrogen (BN) % 2.20 2.21 99.5 PlumpneSS (P) % 29.“ 21.7 135.5** Color score (C) 19.1 20.2 94.6 Malt Extract (XT) % 73.8 73.3 100.8** Wort Nitrogen (WN) % .706 .684 103.2“ WN/MN 32.7 31.7 103.2 Diastase (DP) % 188 182 103.3 B-amylase (B) 611 582 105.8** a-amylase (a) units A5.2 “3.3 104.“ * significantly different as determined by t-test ** highly significant as tested by t-test 13 TABLE 2.--Corre1ation of the bulk progeny with the midparental values using transformed data. The data were transformed by equation [1]. This converts all data to the same units, having a mean of 5.0 and a variance of one. Cross d.f. Number n (n—3) r - z (n—3)z 62-431 20 17 .525* .570 —432 20 17 .393 .416 —433 20 17 .380 .400 —434 20 17 .388 .410 -435 20 17 .585** .668 -436 20 17 .645** .766 —u37 2o 17 -.155 —.157 -439 20 17 .465* .504 ~440 20 17 .297 .307 —441 20 17 .245 .251 -442 20 17 .481* .525 -443 20 17 .699** .866 -444 20 17 .253 .260 -445 20 17 .474“ .527 —446 20 17 .321 .334 —447 20 17 .548* .612 -448 20 17 .776** 1.042 —449 20 17 .175 .177 —450 20 17 .688** .845 Total 323 . 158.491 Average .455** .491 * significant at 5% level ** highly significant at 1% level positive with ten crosses showing significance at either the 1% or 5% levels. The average correlation coefficient of the set of crosses was highly significant at the l per cent level with an r = .455. The parent—progeny correlations are listed in Table 3. The r values for seeds per head and seed weight which are 14 TABLE 3.-—The correlation of the bulk progeny values for each trait with midparental values. Raw data were used since correlations were run between the values of each trait which are in the same units. d f. Trait n n-2 r Yield l9 17 .3776 heads per unit area 19 17 .0973 seeds per head 19 17 .4748* seed weight l9 17 .6849** Test Weight 19 17 .2887 Survival l9 17 .1550 Heading Date l9 17 .2709 Mildew 19 17 .6116** Lodging l9 17 .4288 Height 19 17 .3834 Barley Nitrogen 19' 17 .7334** Plumpness 19 17 .4224 Color Score 19 17 .3059 Malt Extract l9 17 .5330* Wort Nitrogen l9 17 .7205** WN/MN 19 17 .4231 Diastase 19 17 -8422** B-amylase l9 17 .8117** a-amylase 19 17 .3567 * significant at 5% level ** highly significant at 1% level part of yield are significant and highly significant, respectively. The malt quality components are all .3 or above indicating positive correlation with the midparent. Barley nitrogen, malt extract, wort nitrogen, diastase, and beta—amylase are significantly correlated with the parental means. The weakest correlation is for X and for survival. Presumably there is a severe interaction between winter survival and tillering. 15 Table 4 contains the beta weights (standard partial regression coefficients) occurring from year to year for the individual traits. Equation [2] was used to calculate the beta weights for complex traits that make up the over-all score. Equation [3] was used to calculate the betas for the components of malting quality using equation [4]. The listed beta weights indicate the changes from year to year due to the environment. It should be pointed out that the absolute values of the betas indicate the importance of the trait in the particular year. Comparing 1960 with 1964, malting quality had approximately the same emphasis. The importance of lodging, however, changed drastically due to far less lodging in 1964. As mentioned before, the ideal for any particular year is based upon the population's performance in a given environment. To determine if the performance of progeny in 1964 can be related to the predictions made in 1960-61, three lines were picked as indicators of the season. Using these three lines and the ideal picked for 1964, a multiple regression equation was calculated. 0 H O H __ 01 “813.3"; AAWB .13. AB + BC 3— A9 [71 Q B I = Established ideal for the particular year and is a multivariate vector. The ideal vector is made up of component traits of yield and malting quality and simply inherited traits such as height and disease reaction. Since all the traits that make up the ideal are in different units they are transformed to a common base by equations [5] and [6]° l6 mmoo. somo.n sesa.s ammo. mmmo.u pemfimm :Aoo. emzm. eemm. momm. weflweoq omqa. mmmo.n msmfi. warm. maam. zmefiaz moom. mmOH. :mmo.- some. ammo. Essa mamemmm :mmo.- mmza.u mzao. mmea.n emem.n efima. Hm>fi>ssm Hemo.- omma.n ms:a.- oaeo.u AHHH.I emmo.u pewfimz paws memm.u mmmm.u meoe.u mmmm.u Hmmm.u mmmfi.u eamfim ammo. mmmm. mamm. ommz. mmme. mmom. spmfimse was: whoom HlecHON/O eemm. mmmfi. mmmm. :emm. pemfimz Hmesmg mmmm. _ mHom.H emmm. memo. cemE\memmm mmoe. emem. mmmm. mmom. mmsm\memmm efimflm mmmm. moem. m:am.- mmom.u mmmm.u mm::.u mmmflsemua ammo.mu mam:.- momm.u e:me.- wome.u mmmfl.u mmmpmefia some. mooo. mesa. :mzm. morn. Hamm.- atmospfiz paw: :osa.- qum.- mafia. semo.u aqmm. mmsm.u emmoppfiz use; emmm.n mazm.- :mmo.- mmflm.u Hmao.u momm.u pomspxm pfimz :moo.- Hmmm.u mmmo.- m:mo.- mmflo. mmmo. msoom soaoo Hemm.- mem:.- mmmm.u mmmm.u omem.u mmea. Emmeeesam ommH. s:ms.- mmmm.u mfimo. smzo. memm.u pewfimz Hmesmg spfiaese Baez :mma moma mwma Hmlommfi mea coma prLB .pmoz mcm CH pampp m mo mocwp ILOQEH ocp cpmoaocfi m.m map no oo3pflcwme mpofiomnm ace .oamflm one hpfiamov paws moosaocm cums: opoom Hamspo>o pom mm commm>flpoom LOWGE opflcp one .ofimfiz pom mpflamsv mammawe amufimsp meQEoo map Log ope mfinmp on» mo mCOHmH>fiooom momma ozp pmpmm one .meOLmo mo soapomfiom map :H pom: pfimmp comm Log memo pmomlm cmospoo AmBCOHOHmmooo coflmmopmmp Hemppmo opmocmpmv mpzwmoz moon mo QOmHLmQEoonl.: mqmde 17 B’ BC = The standard partial regression co— efficients which govern the amount contributed to the ideal by the indi— cator line A (410-1), line B (414-80), and line C (Hudson). A) I = Standard deviation of the ideal. It is important to note that OI refers to variation within the ideal. OA’ OB, CC = Standard deviation of the biological indicators. These statistics refer to variation within vectors A, A, and Q. A = Difference from the mean of a line and ' the observed value of a given trait. A is a vector made up of many traits as are B and g. It is assumed that AA = (A - A) = (A - 1) since A = the mean magnitude of vector A which is assumed to be an estimate of l. A numMerical example using data calculated by equations [5] and [6] is used in equation [7] as follows: 1.06 = 1.034..A (f%%§)(.99-1.00)+8B (f%§§)<.98—1.0u)+ sc< 90- 98) 1.09 = 1.03+BA(f%%§)(.9u-1.ooi+sB (f%%%)(.99-1.04)+ ec(f%%§)(.97-.98) 1.13 = 1.03+BA(1.06—1.00)+8B(f%%§)(1.06—1.0u)+ .048 BC(T045)(°97-'98) The above example explains how the beta-weights are calculated in Table 5. Using the beta-weights calculated in equation [7] and the three lines in the 1960-61 population, a new ideal was calculated. 18 TABLE 5.—-Comparison of beta weights using three indicator lines over five years. The average betas at the bottom of the table are averaged by using a weighting method. Nineteen traits were used to calculate the betas for 1960, 1962, and 1964 data; fourteen traits were used in the calculation of the betas in 1961 and 1963. Therefore, the betas for 1960, 1962, and 1964 were all multiplied by 19; the betas in 1961 and 1963 were multiplied by 14 and all added together and divided by 85 (the total number of traits for the five years). Indicator lines Year 410-1 414—80 Hudson 1960 .6534 .0728 .2890 1961 -.1086 .2720 -.4293 1962 .2444 -.3596 .7505 1963 .1861 .7235 -.3816 1964 .0972 .1942 -.0148 Average .2350 .1310 .1021 The new ideals in Table 6, based upon the average beta weights and three indicators, were calculated using the following equation: 0 I . .— '_-(C-C) [81 B C 0C — O H O H i = I + B -—— (ArK> + SE ——(§—E) + 8 II:- Equation [8] is based on data standardized by the equations [5] and [6] so that each trait has a mean of l, a variance of 1, and a standard deviation of 1. This in- cludes the proposed ideal. Therefore, equation [8] reduces to: 19 m.00 0.00 0.00 m.00 0.Hm m.Hm sewed: pate 0.0m 0.00 0.0m 0.0m 0.0m 0.0m eewflem H.0m 0.0a 0.0m 0.00 0.mm 0.00 mesmeoa 0.m m.m 0.m 0.0 0.0 0.H zeeaaz H.0m 0.0m 0.0m 0.0m 0.0m 0.0m meme wefleeem m.00 0.00 0.00 0.00 0.m0 0.00 mte H0>H>Esm m.0m 0.00 0.00 0.00 0.00 0.00 pm: He>a>tsm . Hm>H>p5m 0.00 m.00 0.m: 0.H0 m.m: 0.m: mmemsee eeafia 0H0 0H0 0A0 msm mme 0mm mmefisee 000m 00H 00H 00m 00H 00m mmm easemeae 00.m 00.m :0.H :0.m 00.m 00.m cemeteae pass 000. 000. 00m. mme. 000. mme. demoseae etoz 0.0m m.mm 0.mm 0.0m m.0m 0.05 seepage 0H0: 0.mm m.0m 0.0m m.mm 0.0m 0.:m meoem toaoo 0.00 m.m0 0.00 m.H0 0.0: 0.00 mmeeeeafim m.mm m.mm 0.0m 0.Hm m.mm :.mm 000mm; Hesteg m0.m m0.m 00.H 00.m 00.m 00.m cemetefie mafieem sefifiese 0H0: m.mm m.mm 0.0m 0.Hm m.mm :.mm unwed; Heeteg H.mm 0.mm 0.mm m.0m m.Hm 0.0m 0000\00000 m.m0e 0.mefl 0.00H 0.0mH 0.0mm 0.00H eee0\meeem efieam 00H 00H H0 00H 000000 00-0H0 m10ae paste ”~6me mmflwd LOUMOHUCH A. 0H lemma pom ham>flpommnom chOHQ ammow u #mlomH bum mmpoo :mma coo: bemmo Umoooomo amoefl n :mH .mmpmn owmgo>m 02p coo: comma Hmoofl o>woommoo ecu u >mHV .MBQU Hmma pom coma owmpo>m map mom mammofi moms» esp cam mOCHH Loomompcfl oopcp 0391:.0 mum ll HI + m A ”F bl + m A CD I ml v + m If BA, 8 , and BC are known, I can be calculated for any year. But to do this,.vectors A thru 9 must be in standard measure. Convert the data for each trait by , - 8:2 ' . 1;: x - 1.00 + leil °x rx or XJ 1.00 + leiejl °x x "S Calculate i from converted data Biological Indicators A B C Ideal x 1.017 ' 1.090 1.060 1.045 Y 1.060 .958 .916 1.032 2 .989 .983 .895 1.061 The 8 values for several years may be averaged algebrai— cally. These average values can operate in current years from the biological indicators to give an average ideal. However A thru 9 are vectors and the data should be con- verted to standard measure. ] ' I _ X-K or xj - 1.00 + leiejl ;;— rX The new ideal is then calculated using average betas and current data. I = a + b (A) + b I The above data may be changed back to original units by the reverse process. (A) + 00(9) A B O O X t — X - X = —— X - 1.00 + X X = - . + X Ttglrx < 1 > or TEZEET rX(XJ 1 00) FIGURE 2.-—A pictorial representation of the extension to the vector method. The procedures are outlined for the determination of the average betas. Using these average betas and the data of the current year for the indicator lines, a new objective ideal is constructed. 29 upon the knowledge of the population and the environment. Evidence was presented indicating that the subjective ideal is only good in the year in which it was established. This can be attributed to environmental changes between seasons and the response of the population to these environmental changes. Even though the parents are selected by this ideal, they will only perform as expected in the year of selection, not in other environments. Using several lines which are good indicators of the environmental changes, an ideal can be calculated as stated previously in this thesis. The ideal will fluctuate with the season due to the environ- mental changes. This ideal will pick parents which will perform over several sets of environments. The selected parents can then be combined as described by Grafius (5) using the vector method which will produce unselected bulks having a mean performance approaching an ideal based on the indicator lines. With the ability to select parents and combine them to produce the best crosses in the future, the selection of lines from the unselected bulks after a few generations of selfing becomes simplified. Since the emphasis on particular traits can change between years, a long time average is desirable in order to give any predictability to parental means in the vector method. Five years data were collected and used to calculate the average beta weights. Between the time of crossing and 30 the time the performance trials on the unselected bulks are complete, another three years will have passed. Using the ideal based on the current data for three indicators and the average betas, the best bulks can be selected and selections made from within these crosses. Two to three years will ordinarily pass by until replicated performance trials have been conducted on the selected lines. Further selection of the outstanding lines can be made again based upon the average betas and the current data from three indicator lines. One would, of course, use the actual average performance data too. But in addition to this average data there are average data for a ten to eleven year period collected on the parents which will also help in selection of the new varieties. To simplify the picture, the following outline gives the steps in a breeding program which used the vector method and the objective ideal: 1. Data are collected for two or three years on a population of potential parents. Each year indicator lines are grown with the population. An ideal is picked each year subjectively to evaluate the lines. Beta weights are determine for each year for each of the indicators and average the betas for the three years. 2. Using the average betas and the current data from indicator lines, an ideal is calculated by which parents are selected and combined to produce unselected bulks. 3. Grow the parents and the unselected bulks in plot trials for two or three years until homo- zygosity is approached within the crosses. 3l 4. Again determine the average betas for the parents. The data now spans six years. Calculate the ideal and select the best unselected bulks. 5. Make selections from the best bulks. Grow the parents and bulks until the selected lines can be tested. 6. Using the average betas and the current data from the indicator lines, the objective ideal is determined and will be used to select the best lines. It may be feasible to use two or three years data to pick the parents in spring cereals with the calculated ideal, which would shorten the cycle by three years. This would allow collection of data on the parents for eight years. With the great potential of hybrid cereals, the use of the objective ideal will become more important. In the case of hybridization, dominance will be experienced; but since the ideal will pick parents which will perform better over several environments, the hybrids should also show maximum adaptation. The vector method along with the objective ideal and estimates of dominance can be used to construct hybrids which will approach an ideal and will thus eliminate many unnecessary crosses. Comparison of Progeny with Calculated Midparents The average yield of the bulk progenies exceeded the midparental value by 7.3% in the F generation and exceeded 3 that of the average high parents by 2.2%. Since yield is 32 broken down in components, X (heads per unit area), Y (seeds per head), and Z (seed weight), and the product of X, Y, and Z equals yield, then if any one or more of the components exceed their midparent, the multiplication of the dominant effects may give heterosis. In this case, X = 98.1%, Y = 103.1% and Z = 106.6%. These are all in per cent of the midparent and the product X, Y, and Z equals 107.8%. As shown, even with the reduction in one component and an increase in the other two, heterosis does exist if measured as an increase over the midparental values. The increase in the components may be due to dominance even though these components exhibit additivity as indicated in Table 3 where seeds per head and seed weight are shown to be significantly correlated with the midparent. Interaction between traits presents a third source of possible deviation from the midparent. Heads per unit area decreased by two per cent between the progeny and mid- parent means. At the same time, heading date become earlier than the midparent. Now the development of a biological organism is such that the various stages follow one another in a certain sequence. Tillers are put down until such time that floral initials start to form. Floral initiation tapers off when elongation starts. Since an earlier heading date leaves less time for tiller formation, the bulk progenies being earlier should also have fewer tillers. Time then influences tillering, 33 and eventually affects kernel weight and kernels per head as explained by Grafius (5). Per cent plump exceeded the midparent by thirty-five per cent and exceeded the average highest parent by 11.7%. Seed weight and plumpness are highly correlated with an r = .83. With the earlier heading date perhaps more energy was left to produce larger seeds? Plumpness increase, even though it exceeded the average of the highest parent, may be due to the early heading date. An argument may arise about the difference of just two days in heading date, but a statistical difference does exist and the early heading date does coincide with the reduced tillering and greater kernel weight. With the reduced tiller number and earlier heading date, the rainfall was great enough to boost the extra filling of the seeds. Malt extract is closely associated with seed size and plumpness. All three traits show a statistically highly significant difference from the midparent. Extract difference can be explained by increased seed weight and plumpness since significant difference occurred in both traits. It is not surprising that in the F generation such 3 differences exist between the midparent and progeny. Heterozygosis exists in these early generations and since we are working with normally self pollinating organism, 34 originating from lines which are homozygous,even modest degrees of heterozygosis may be noted. When comparisons were made between individual charac— ters of the bulks and midparents, high correlations were found. Correlations for seeds per head and extract were significant at the 5% level; and for seed weight, disease reaction, barley nitrogen, wort nitrogen, diastase and beta-amylase were highly significant. Even with signifi- cant differences from the midparent, kernel weight still was highly correlated with the midparent. Heads per unit area was independent of the midparental values, which may be due to the difference in heading date and possibly to differences in winter hardiness. Since heading date notes were taken on unselected bulks, any early lines in the population will tend to cause the observer to give an earlier reading than may really be true. Survival may have some effect on heading date, but with the small difference in survival, no definite con- clusion can be made. Also, survival may be broken into components which may be more additive than the complex trait winter survival (4). The components of malt quality all are positively correlated with the midparents. Barley nitrogen, extract, wort nitrogen diastase, and beta—amylase all are staticti- cally significantly correlated. In general, additivity was experienced in the malt quality characters. 35 When comparisons were made between the bulk progeny and the midparents, ten of the nineteen crosses were significantly or high significantly correlated. Table 2 shows only one bulk with a negative correlation value with the midparents. The average correlation value for the nineteen lines as calculated, using Z transformation in Snedecore (10), giving r = 295% which was highly signifi- cant. SUMMARY A method is presented in which an ideal may be cal- culated by using average standard partial regression co- efficients averaged for five years and the current data from three biological indicator lines. It was also established that this ideal would pick lines which would perform well under several environments. The new objective ideal coupled with the vector method will give a more accurate evaluation to the predictability of the crosses and also will lend itself to better selection of parents. The new ideal will compensate for seasonal variation auto- matically through the indicator lines. The objective ideal will pick the best parents, and also will help in the selection of the best unselected bulks and finally will help in the selection of lines from these bulks. Additivity was demonstrated in general for all com- ponent traits of malting quality and yield even though dominance was demonstrated in the component traits and heterosis for yield. Yield increase can attributed to multiplicative interaction of the components X, Y, and Z. These bulks were in the F generation, and enough hetero- 3 zygosity was still present to account for the dominance and heterosis. 36 10. 11. 12. LITERATURE CITED Duarte, R. A., and Adams, M. W. 1963. Component interaction in relation to expression of a complex trait in a field bean cross. [Crop Science 3:185-186. Grafius, J. E. 1956. Components of yield in oats. A geometrical interpretation. Agron. Jour. 48:419—423. . 1959. Heterosis in Barley. Agron. Jour. 51:551-554. . 1964. A geometry for plant breeding. Crop Science 4:241-146. 1965. A geometry of plant breeding. Research Bull. 7 Michigan State University Ag. Exp. Station. , and Adams, M. W. 1960. Eugenics in crops Agron. Jour. 52:519—523. Leudders, V. D. 1960. An analysis of the components of yield in 18 oat crosses. M. S. Thesis, Michigan State University. Powers, L. Gene. 1952. Recombination and heterosis. Heterosis. Edited by John W. Gowen. Iowa State College Press. ' Smith, D. H. 1963. Relationship of winter habit and malting quality in winter x Spring barley crosses. Ph. D. Thesis, Michigan State University. Snedecor, G. W. 1946. Statistical Methods. Iowa State College Press. Thompson, J. B., and R. N. H. Whitehouse. 1962. Studies on the breeding of self pollinating cereals. 4. Environment and the inheritance of quality in spring wheats. Euphytica 11:181-196. Whitehouse, R. N. H., Thompson, J. B., and Dovalle Ribeiro, M. A. M. 1958. Studies on the breeding of self pollinating cereals. 2. The use of a diallel cross analysis in yield production. Euphytica 7:147- 169. 37 38 13. Williams, W. 1959. Heterosis and the genetics of complex characters. Nature 184:527-530. 14. , and Gilbert, N. 1960. Heterosis in the tomato. Heredity 14:133-149. 1lu11111111111111