‘ ‘3’“ v.‘ .I, $¢3§¢ 3‘; ‘2‘. 2“,“. 3 : --‘ ‘iifi‘! Mti‘hkil 31.2 a? 222‘; mCfizigf‘ula .'. Thesis {re-1 {r-‘m Swim a»? .13.. S. WCHL {3fo ST A“? um‘g fzzgmr vg! 1“ L219 33311133 1;; 3:) A ‘ '_ .,4-\ . . ; K \— LIBRARY Michigan State University "—— AN ANALYSIS 01" THE COMPONENTS OF YIELD IN 18 OAT cmssns By VIIBIL D. W AN ABSTRACT Suhitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in pertiel fulfillment of the requirements for the degree of MASTER OF SCIENCE hpartnent of Penn Crops 1960 ABSTRACT VIRGIL EUEDDERS The yields of oat parents and progenies of crosses were analysed by the yield components method. The results obtained were similar to those of barley. The 3 components of yield, heads per plant (1), seeds per head (I), and kernel weight (Z), were found to be affected by different gene systems. Due to homeostasis, the variance of the F2 was less then that of the mid-perent in several instances. The higher yielding crosses can be predicted utilizing the yield components of the mid-parents, thereby eliminating the necessity for making all of the possible crosses. AN ANALYSIS OF THE COMPONENTS OF YIELD IN 18 OAT CROSSES By VIRGIL D. HIEDDERS ATHESIS Suhnitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Farm Crops 1960 ACKNWS The author wishes to express his sincere gratitude to Dr. J. I. Grefius for his guidance, encouragement, and constructive criticism during this study and in the preparation of the manuscript. Dr. 0. M. Harrison's critical review of the manuscript is greatly appreciated. TABLE OF CONTENTS INI'RONOTION.......... REVIEJOFIJTERATURE ...... MATERIAISAIDIETHON...... RESULTS............. DISCUSSION........... SUMMARI AND CONCHJSIONS . . . . . BIBLIOGRAPHY.......... Peso gamer- Tables LIST OF TABLES AND A FIGURE Heads Per Plant (1), Seeds Per Head (I), Kernel Heights (2), and Yields Bar Plant (w), OatParentsandProgeny ....... for the Correlation Coefficients for the 1’; Means vs. Mid-Parent for Heads Per Plant, Seeds Per Head, Kernel Weights, and Total Iields Per Plant . . . . Correlation Coefficients Showing the Relationship of I (Heads Per Plant), I (Seeds Per Headband Z (Kernel Weights) for the Parents, 12's and 13's lstiaates of Genetic and Environmental Variances Based on 1'2 and Parental Plants for 18 Cat Crosses Where the Genetic Variance is Equal to the Varianoeofthe rz—thelbanWarianee ofthe Parents 0 O O O O O O O O O O O O I O bans of the Cat 1' 's Compared with Their Respective Pa's' Parents . . . . . TheDominanoeRelationsofthehtP, P3CouparedtotheBarleyrlandl'z%f bans of the lad-Parents and the 12's, 1‘2, and Grafius (6) Their- Correlation, The Difference Between Then (12-15), and the Means, Standard Errors, and t-Values of the Differences for Number of Beads (1), Seeds Per Head (I), Seed Height in Centigrans (Z), all! Totallieldfil)..o............... Graphs of 12's on the Mid-Parents (M). A, Huber of Heads Per Plant (1); B, lumber of Seeds Per Bad (I); C, Average Kernel Height in Centigrans (z); and D, Total Yield Per Plant (w) 7-8 13-14 16-18 20 20 26-27 10 WIN Iield is a quantitative character and is the result of the actions and interactions of new genes throughout the life of the plant. Since yield is the end product of this sample: process, it is sore meaningful to analyse it by resolving it into its siepler parts, the oc-ponnts of yield. Intheeaseofseallgrainsandspecifieallyeats, theseccm- ponentsofyieldarethemberofheadsperplant (I), themeberof seeds per head (I), and the average weight per hernel (2). The pro- duct of these three components is the total yield per plant (x-I-z s w). This product may be represented geometrically as the volnee of a rec- tangularparallelepipedwiththeedgesx, 1, NZ. lftheedgescf this figure are not correlated, then different gene systeas are af- fecting thee and yield is an artifact. The velun ef the parallelepiped, or yield, can be increased most easily and rapidly by inereasing the shortest edge. Therefore, itshouldbepossibletogetthegreatestincreaseintheyieldofa variety by crossing so as to increase the smallest component (lengthen the shortest edge of the parallelepiped), 14., increase the nuaber ofkernelsperheadinavarietythathasalargenuberoftillers and high kernel weight so as to get the highest or maxi-In yield pos- sible. If it is possible to redme the yield-depressing effect of th liaiting factor or ccepcnent of yield, then it should be feasible to 1‘ choose parents (2 or more) that lave high values for one or more of these components and by the appropriate breeding techniques incorpor- ate them into one line which would have distinctly superior yield capabilities. The use of components should note the prediction of progeny expectations acre accurate and reliable, and help to change the statusofplantbreedingfronanarttcthatcfanexact science. Cats and barley are both self-fertilised and Inve a primary chromch number of I 8 7, but the cultivated cat is a hexaplcid - whereas the cultiveted barley is a diploid. Hence, one night expect cultivated cats to have gene systole built up in evolutions-y time which take advantage of the hexaplcid condition. Intra-allelic inter- action can exist in true breeding henplcids if autcsyndesis occurs, as it does in cats. Thus hetercsis could be due to both inter- and intrepallelic interactions. The fraction of heterotic effects db to the interaction of additive by additive effects and the intra—allelic interaction, due to gene action between homologous chromosomes of the three genomes, is potentially finable in the true-breeding form. If the latter is of great importance, it should interfere with the pre- diction of progelnr values from aid-parental values. The analyses and discussion in this paper are based on the following statements: the yield components method, of enlysis indi— cates why one yield might be higher than another; the components of yield are asst-ed to be independent; the same types of analyses can be used on both oats and barley, with the exception that if intra- allelic interaction is important it will interfere with yield prediction; r \ I .‘ 7 ins ’s o. e .. 1 -,._ , D a . . . . y .. . ' w ., . g, , . [ .. ‘ v ,y '1 v r ' ' r - . r r I - r‘ . ,7 ,« . . , e . I,— 1’ . .7 C A . — A ' e . m e I ' ’ .7. v r A A k F 4 " . s. , a. f ‘ . .. ~ 'I . e ' ' I \ . ~ . I r ‘ ~ '. . . . f-\ .~ s 'l I I ‘i /\ 1‘. I. it is possible to select parents which will give high-yielding progeny when crossed, and these results are assumed to be predictable; and the .72 isncrevariablethantheparents. antiserum The ccnceptofamlysing the componentsefyieldis notnewbut has not been used extensively. Frankel (3) found that the main in.- crease in yield is achieved by overcoming the limiting factors whose effects can be distinguished with a fair degree of certainty, rather than by assembling productivity genes, although this process may ac- compam the former process. As the components ef yield in wheat, he used: cars per plant, grains per car, and weight of grain; these could conceivably be further resolved but this resolution would reach a practicable end point. In a study of factors affecting the yield of barley, Iohls (12) pointed out that yield was positively correlated with the number of kernels per plant, mber of heads per plant and weight per hernel. This is not at all surprising since these are the components of yield. The yield components of cotton; bolls per plant, seed cotton per boll, seeds per boll, lint per seed, etc., have been analysed by Hutchinson (10), who found that one is increased at the expense of the others. Dinning (18) got yield increases utilising only the 3 major components of yield of cotton, nanely, bolls per plant, seeds per boll, and lint per seed. Dewey and In (2) analysed the caponents of crested wheatgrass seed production, using as the components: seed sine, spikelets per spike, fertility or seeds per spikelet and plant sise. They mglected to take one important measurenent, namely spikes per plant. Fertility 7‘ I‘ and plant sise were the nest inportant components, whereas the seed sise varied less and therefore caused less change in yield than did the other components. This relationship of seed sine to yield is inherent in the concept of yield. her (11) used bade per plant, seeds per head and weight per seed to measure the extent of heterosis in a umber of barley crosses and their progenies. Grafius (5) used a geometrical interpretation to analyse the components of yield in cats, uniquely demonstrating the relationship with the model of a rectangular parallelepiped, with the umber of panicles per unit area (I), the average number of kernels per panicle (I), and the average kernel weight (2) as the three edges and the total yield (H) as the volune. This approach was also used in his analysis of barley yields (6), except that in this case I is the mber of heads per plant. Yield is shown to he an artifact. The r, variance is separated into its environaental and genetic portions, with the genetic variance further partitioned into additive, non-additive and interaction or epistatic effects. By means of an elegant regression model Whitehouse an a]. (21) drew conclusions sinilar to those of Grafius concerning the components of yield, but failed to designate yield as an artifact. HATERIAIS AIDMETHODS The naterial consisted of harvested seeds in envelopes, with the mber of heads per plant and the cross and plant maber recorded on the envelope. These included the 20 parents (20 different spring cat varieties), the 1‘2 of 18 crosses, and the :3 of 3 of these crosses. The crosses were flashy? of these varieties andCraigbythe other 11 varieties. _ The 18 crosses were nade by Grafius, who also planted and harvested the 12, the P3, and all of the parental varieties in 1956. These parents and progeny were space-planted 12 inches apart in the row with 12 inches between the rows in a randomised block experiment. Two replications were used. in attenpt was made to have 19 plants per plot but in nest cases there were aissing plants which were re- placed with filler plants. The actual numbers of plants harvested and subsequently analysed are reported in Table l. RESULTS The data for the parents, 12's, and 13's are given in Table l. TheaveragerzvaluesenoeedthepaxentalmeansforLT,Zandnatnp rally also for V. The average 13 value for I is significantly less, buttheIandZvaluesai-enctsignifioantlydifferentfromtheaverage oftherzaeanforthesane3crosses. The comparison of these values indicatesdominancefcrxandlackcfcratleastalcworderofdomi- nanceforTandZ. Heads Per Plant (1), 8004' Per Read (I), Kernel 51m. (2), and Tields Per Plant (11), for the at Parents and knew Table 1 I I z V In. of Conti- Parents Plants No. No. grans Grams Cherokee 75 10.688 40.378 2.721 11.609 Ajax 126 13.981. 64.140 2.46% 21.” Clintland 4.3 8.814 52.828 2.519 12.323 . 15-0-205 33 11.546 53.997 2.203 12.397 Clintafe 20 11.650 61.410 2.010 15.120 seal: 57 10.035 52.237 2.31.6 12.462 Clarion 52 9.096 50.346 2.388 11.635 Craig 137 90380 “em 20‘“ 100110 atelby 99 16.515 42.054 2.447 14.929 Beaver 28 11.607 60.846 2.678 19.048 Gerry 38 9.263 1.8.587 2.4190 10.963 Vanguard 47 16.636 45.613 2.291 18.628 Abegweit 15 14.467 56.046 2.687 21.867 Rodney 25 11.720 47.812 2.796 13.576 Jackson 24 10.750 54.779 2.625 15.363 Sincce 23 10.393 56.744 2.691 16.861 fileffcrd 37 15.162 36.267 2.960 16.646 Anus. Of All Parents 11.969 5oe752 2e 512 150250 LSD 55 Between Parents 2.522 7.567 g .238 3.982 Table 1 (continued) I I z W 5. of Centip- rz's Plants lo. lo. grams Grams Ajax 1 Cherokee 174 12.977 48.386 2.523 16.221 Ajax I Clinton 67 11.293 59.880 2.406 16.672 Ade: X cm. 117 ”068‘ 68.609” 2031‘ 21e38‘ Ajax 1 Sank 157 11.781. 61.482 2.393 17.515 ax I Clarion 156 11.651. 60.263 2.1.90” 17.569 Craig 1 Victory 79 13.127 50.276“ 2.1.33 16.062 Craig I 6.117 58 10.1.83” 54.633“ 2. 591* 15.272.. Craig I v 89 11.989 44.901. 2.339 13.569 Craig I Abegweit 23 12.367 47.813 2.778“ 16.517 Craig 1 Rodney 101 10 .614 50.308! 2.678 14.874" Craig I khan 28 12. 536 47.757 2.664“ 16.197 Craig 1 Jackson 72 10.8755 56.885* 2.650% 116.245" Craig I Simcce 109 12.982* 59.720! 2.722» 21.016“ 3111; I ””016 93 12.051 45.754" 2.832 16.063 Average of All. 12's 12.082 5!..552 2.567 17.030 m 5’ ht“ ’2'. L936 5:758 e039 3e°32 13's Ajax 1 Cherohee 878 11.1.78 52.1.21 2.608 15.932 Ajax X 011M. 373 12.721. “0915‘ Zeno 17.530 Craig I Garry 202 10.129‘ 55.63” 2.424 14.089 herage of All 1' '8 11.444 57.656 2.387 15.866 13D 5‘ Between lg 1.” 6.892 .087 2.013 *Indioates r, and 1', values are greater than the value of the high parent; does not imply significance. l'igurelccmparesther‘zwiththemid-parent. Thegraphsfor ;!and tare approximately linearbut the graph forVdoesnot fit a straight line. Hernver, this is as expected since It is the product ch, I, end send it 1. perhaps my. to expect venue. to graphas straight lines. Table 2 shows the correlation coefficients for these comparisons. The values are remarkably similar to those obtained by Grafius (6) for barley. than the barley 1'1 is cupared with the mid- parentr r: 8 .48, r’ 8 .88“, r. 8 .75", and r" 8 .45. Table 2 Correlation Coefficients for the P; ham vs. Ind-Parent fcr Beads Per Plant, Seeds re:- Head, Kernel Heights, and Total Iields Par Plant -’ -— Character Correlated - d.f. 1'; vs. Ind-Parent Beads per plant, I 16 .499" Seeds per head, I 16 . 4" Kernel weight, 2 16 e344“ Iield per plant, 11 16 .525” *P < .05 “P (.01 The correlation coefficients showing the relationship between I, I, and z are found in Table 3. In the parental population for the average r only I and I are significantly correlated (positive) where- as I vs. 2 and I vs. 2 show a non-significant correlation, indicating serc relationship or independence. The significant Chi square values 10 Mo 88% O . O In.“ In.“ 62 3 :2 h " 3 E g 5.. Q. \ \ I . ‘ ‘ O 3 : 8 6 6 501 6 c a ° . x ' >- b “3 A f ‘ t 44 : ° : t 1 9 IO it .4 4, so so 60 0A,: parental mean number a! My- acrenlol mean number of III heads/ciao! seeds and A B 2.800 O . . .‘V - 2|“ e . II. “N 3 a .I. Q- 3 . 3 e 3 2 Z 2.601 . 3 .5 s h 6 3 2 3 e ; 2 .2 ‘o’ .. 0 2.4OJ’ I 1' e N O '3‘ 3 2 t : l0 l2 l4 l6 l8 2:30 2:50 . 2 .70 M,-porantol mean seed welgM Hwtpcrentcl neon yleld in in oeMlgrcms grams/plant c D Figure 1. Graphs 0f Fg's on the Mid-Parents (M). A,Number of Heads Per Plant (X); B, Number of Seeds Per Head (Y); C, Average Kernel Weight in Centigrams (Z); and D, Total Yield Per Plant (W) . at the hottou of Table 3 indicate that the population of We ie nothoaogeneoueforawofthe3traite, 1,1,and2. ‘l'huetheoor- relatione my be due to either chance aeecciatione of genee or linked gene eyeteue for the 3 ccaponente in acne caeee and randu aeeooiatione in the cthere. For example, if there were allelee for differential reepcnee tohighandlownitrogeninallBgone eyetue, theninthe coupling auociation one would expect to get a pceitive correlation coefficient; a negative correlation fr. the repuleion aeeociation; and a eero correlation coefficient in the cue of random distribution of theee factore for I, for I, and for 2. All 3 typee of correlation coefficiente (poeitive, negative and eero) occur, although it not he admitted that eignificant negative values are not frequent. in overall average correlation coefficient, while not etrictly valid becauee cf the heterogeneity of the population, indicatee that onlyXandIaro aeeociatedae anaverage condition. lvenhere the aeeociation ie week, although it ie highly eignificant etatietically. The fact that zero and negative as well as positive correlation co- efficiente occur in the population of paronte indicatee that there are two eeparate gene eyetone for I and I, rather than one gene cyaton controlling both of them. However, this does not rule out the exist- ence of a third eyetea, ouch ae genes for heading date, which could poeeibly regulate both the I and I eyetene by a triggering nechaniea. For emple , the early onset of ehoot development could effectively control both the eiee of head and the nnnbor of tiuore. . . . , . . ,' e . . o O ' u ‘ v o e . l ‘ . . . o J . ' i . ‘ . . I a u . I'd . . A — a v x a e , o .— e . ~ ‘ v - . . 1 ‘ ' I- . o ’1 t ‘ i - . ., f F ' ' ' . e . , r‘ ,e I ‘ ‘ y . I. 13 Inthe rzmry Ive. Iagainshows a snallbut statistically significant positive correlation.and here the I've. z correlation is also statistically significant and negative but it is so shell that it is of little biological interest. Table 3 Correlation.Ccefficients showing the Relationship of I (Heads ror Plant), I (Seeds Per Head), and z (Kernel Weights) for the Perents, 15's and 13's 13 a 37.43 12 = 36.01 P (.01 P=.02-.01 Generation «1.x. 5119-1 11419-5 1119-1 {ants cum 72 e 121 - e 024 - e 319 u 123 0073 e 131 e 106 Clinton 16 e ‘56 "' e 001 - e 208 Olintland 40 .251 .021 .182 Ib-O-ZOS 30 .500“ .134 -.169 CW. 17 .765*‘ -.277 -.386 30.111! 5/. .374“ ”272* -.250 Clarion 49 .343" -.059 .180 can 134 .315“ -.152 «300" flol‘by 96 .333“ -.111 -.l9l Victory 33 .148 -.262 .252 Beaver 25 .037 .031 .334 “1‘17 35 e 060 -e 036 -e 13‘ V U. . 515“ .397“ .273 Abegweit 12 o ‘31 -e 148 - e 303 Rodney 22 -.170 .000 .381 khan 33 . - .181 .185 Jackson 21 .132 -.261 -.214 811000 20 .535” .650" 503* sheffcrd 34 .118 .083 .239 Average r .257" -.050 -.036 12 a 50.00 r<.01 u u r III! . ‘ . S‘."1'.V fable 3 (continued) Generation d.f. --—-'-—I vs I ____,__I vs 2 143—, Z r r 1'2 Ajax 101mm 61. 389* .010 -.220 11.: x 15.0.205 83 .204 .012 .000 Ajax IGlintafe 111. -.028 -.196 -.l76 Ada: I Glintland 115 .028 -.002 .178 1.1a: 1 San]: 154 .291“ .025 -.009 Me: I Clarion 153 .325" «261" ”174" Craig I amelby 129 .089 -.O66 «333“ Craig I Victory 76 .312“' -.028 -.423"* Craig 1 Beaver 66 .106 -.010 «453“ Craig 1 Vanguard 86 .413“ -.002 «087 Craig 1: Abegweit 20 .168 -.136 -.125 Craig 1 Rodney 93 .352“ .259” .057 0mg X mm 25 .209 -e187 -.033 cm: I JQOkQOn 69 e02]. .002 -e07‘ I Sincoe 106 .179 -.008 «274" Craig I Shefford 95 .502" «1.36” «202* Average r .235" ~03!» «146“ 12 a 42.27 12 a 50.00 12 3 1.9.58 P <.01 P (.01 P< .01 3.3. “I: IGherohe 875 e247 «“8 -0103 ”a X6113”. 370 on, .061 -.002 Craig I Garry 199 . .103 -.115 Average r .236" -.002 ”079" 12 a 6.27 12 a 10.3 12 a 2.95 1’.’= 05-.02 r < .01 P=.30-.20 31m .05 “P'<.01 p. O 15 The I vs. 25 negative correlation is too mall to interpret biologically since it explains less than 15 of the variation. at.- tistical significance is possible because of the very large nuaber of degrees of freedom. The positive correlation betwen tiller nuaber and the number of kernels is difficult to explain satisfactorily and was capletely unexpected. It was expected that as the number of tillers increased the lumber of kernels per head would decrease. This 1ine of reasoning 1. supported by Iabanaukas and Duncan (13), who found that the tillers declined in yield fro- the first one for-ed tcthe last, the-ainstenyieldingluchacrethantheindividual tillers. However, the total. yield of 5 tillers was acre thn twice aslnchasthatoftheprincipalstu. Table I. shows the estinates of the genetic and environ-ental variances for the different crosses. Some of these values for genetic variance are negative, indicating that the parents are acre variable than the 12's, but this isdiaaetrieally opposed to the genetical nodel. Those discrepancies any have been due to chance because of slall nuabers or to honecstasis. Develop-entel hoaeostasis see-s to be the acre likely explana- tion to this made. On the average, the r, asansare greater than theaid-perontelaeansfcrx, I, andZ. Thevariancocfanrz is 1/2 D+l/I,H+ll, where Dis the additive genetic variance, H is the non-additive genetic variance, and I is the onvircnental variance; whereas the variance of the parents is entirely I or environlental. Kyl- ,9 Table l. 16 lstintes of Genetic and hvircmental Variances Based on 1‘ and Parental Plants for 18 Oat Crosses more he Genetic Variance is equal to the variance of the Fz—the lbanYarianco of the Parents Cross 1 I z W 12.8515 166.71 £12525 22.6353- 3.5351 16.31. .018467 8.1021 Ajax ICIinton 8.0137 252.62 .044750 37.74.37 2225225 221.57 .028700‘ M -15.l.257 31.05 .016050 4.6.9027 Ajax I 110-0-205 12.0313 212.81 .042637 61.6114 1212259. M M 521222 -.2635 8.40 «01821.0 16.3589 Ajax 1 emu:- 24.7652 250.80 .060465 69.5397 1 .zgé M ,92178 52.8021 14.4006 -18.66 .021287 23.7376 10.6182 209.12 M 1.0.5225 e92‘9 "9e25 0037‘10 5.23% Ajax 1 Sauk 9.3090 230.46 .078711. 46.4152 10.4586 196.33 .050845 4.2029 4.11.96 34.13 .027869 2.2123 Ajax 1 Clarion 11.6573 235.49 .0672.“ 50.9990 19.2227 M .050061 59.5539 4.5651. 20.95 .017183 4.5430 13.7236 143.13 .038087 25.2991. 8.0649 43.84 .045407 27.0575 Table 4 (continued) 17 Gross I I z W m X '10W” 190 1%? 228089 e 052019 5708630 10.9708 1 1.5 .062692 22.2197 8.1359 77.34 -.010673 3/» 5433 Craig I Beaver 15.3881 173.18 .089267 42.3673 7.7433 187.17 .049587 29.9330 7.6448 -13e99 com 12.10343 , 12.6502 216.22 M ' 26.6756 -l.9534 190.63 .002467 28.8000 Craig I Vanguard 22.8249 262.67 .066033 58.sz 28.2081 18mg 2242212 60.0622 -504832 74e78 .0162fl -2e0171 Craig 1 115.3611: 3.3.1.795 195.63 .033461. 49.963? 101255 122,62 M 22,0662 2.9441 35.98 -.008194 26.8975 cm. 1 Rodney 10.4354 308.79 .066983 44.1283 22.7188 ' 260.22 .060028 22.7082 -30283‘ 47.87 em6955 20e‘201 'Oraig x Erban 18.6247 223.43 .061180 59.8652 12.0568 1.52225 M 22.9107 6. 5679 80.09 .014753 29.9545 Craig I Jackson 9.3591 126.21 .047450 32.0780 2.5.2121 121.92 . 6 M16 -5.1530 -64.88 «012646 -2.3776 II Table 4 (continued) Cross I I z W Craig I Simcce 8.9838 235.95 .050392 52.0959 10.8082 189.08 .060798 32.8222 -1.8245 45.87 -.009906 19.2723 Craig I Shefford , 10.7755 144.30 00869“ 45o8933 15.0968 160.00 .057901 40.1484 -4.3213 -15.20 .029003 5.7449 Average 0—: 0.3217 32.516 .012950 11.1625 Hence the 12 variance should exceed that of the parents. If the loans of the 1'2 were less than that of the mid-parent, then theoretically it would be possible for the variance of the mid-parent to exceed that of the 1'2, since the size of the mean and of the variance is correlated. However, the 12 aeans are larger’than the aid-parental.neans, and in addition the heritabilities for I, I, and Z are .4995, .884", and .844“, respectively. These heritabilities are shown in Table 2, where the correlation coefficients are equal to the standard partial regression coefficients of the 1'2 on the mid-parent. Heritability values of this magnitude indicate large values of D in relation to H and E. Therefore, the inescapable conclusion is that the 1'2 varied less than the model predicted it would. 19 Adana and Shank (1), Lewis (15, 16, 17), Ierner (11.), among others, have proposed that this is exactly what would be expected if the hybrids are better buffered or better canalised in their develop- aent than the homozygote. Adams and Shank found that inbred lines of corn were acre variable than hybrids and also noted differences in buffering mcng inbreds and among hybrids at the same level of hot- erosygcsity. Thus, though tin haseostasis observed was highly re- lated (approximately 80%) to the expected levels of heterozygcsity in the hybrids, intrinsic hetero sygosity was not a sufficient explanation of homeostasis in mains. Iewis (17), working with 2 species of tcaatces and their re- ciprocal crosses, found that the hybrids were auch acre stable (lower variance of height) than the parents when grown under several combina- tions of light intensity and temperature. Therefore in a variable environ-out the heterozygote 111; scans to be acre stable and superior to either A1A1 or A2A2. This apparently is true in cats as well as in ccrn.and tomatoes. Theocaparisoneftheaeanscfthecatparents, the 1'2, andthe 1'3 is given in Table 5. These include only those parents and 12's that are represented in the 1'3 and therefore, these aeans are not the seas as those found in Table l. The doainance relationships between the 1’1, 1'2, and 1'3 of cats are compared to the ’1 and 1'2 of barley (data from Grafius, 6). The doainanee in.cate was estiaated from the values of the F2, assming that the doaimnce is reduced by 1/2 in each generation. . . e r , a e . v \ . n - . I I - \ . t - _ . C 7 'v C ' I ' O n . -7 5 v . , . w 0‘ I I' v . I P ' n C l O . ‘. _ Q . 1 . ,_ . . 20 Table 5 lbans of the cat 13's Compared with Their Respective Fz‘s and Parents x I z m =1! lumber Ember Milligraas Grams MI!“ 11049 53e75 2.423 15e23 1'2 12.58 57.21 2.476 17.63 15 11444. 57.66 2.387 15.87 Table 6 The Dominance Relations of the Dot 1'1, 1'2, and P Ccapared to the Barley 1'1 and 1’2 of Grafius (6 bans Expressed as Percentagg of the Mid-Parent I I 2 I12 2 U Barley r1 126.25 107.82 103.50 141.00 Barley r2 119.48 103.91 102.00 126.64 or. r1 («0.) 1.16.28 113.40 104.18 137.37 Oat 13, 108.14 106.70 102.09 117.80 Oat r, 100.32 108.03 98.19 106.40 21 Both the cats and barley show dominance for I, although the demo of dominance for barley is higher than for cats. This dif- ference could be due to sapling, or to actual response differences in the 2 crops. In barley, denim for I decreased by exactly 1/2 fra the 1'1 to the 1‘2, but the dcaimnce in cats apparently increased slightly fro- the !2 to the 13, instead of decreasing to approxilately 103.35 as expected. This discrepancy is probably due to sampling error. For 2, both cats and barley exhibit a very low order of or a complete lack of dominance. Thus here again cats and barley behave similarly, which is not unexpected since the components of yield seen to be affected by similar gene systems in both species. DISOUSSIW Perhaps the nest interesting finding in these analyses is the fact that the hexaploid cat and the diploid barley react in a siailar aanner. The correlation coefficients for I, I, and z for the progeny versus the aid-parents are alnost identical for the two species. This indicates that the aaj or forces of heterosis are epistatic in nature and result from the interaction of additive I additive, additive I non- additive , and non-additive x non-additive rather than acume- or overdoainance. Turtheracro, the hexaplcid does not exhibit an intrin- sic type of heterosis due to hetercsygcsity. The doainance values for the 1'2 did not exceed 8.2% for an coapcnent, which indicates that it is aainly an additive systoa of gene action. lbst of the genetic variances were positive as expected but several of then were negative. These negative variances would perhaps not have been so surprising if one had been actively thinking about hcaecstasis at the tine. Homeostasis scene to be a logical and good biological explanation or interpretation for this phenomenon, which aay be acre canon or ubiquitous and acre closely related to heterosis than is ordinrily suspected. It was suggested that these negative genetic variances aay have been due to the presence of several dif- ferent genotypes in the original parental varieties but since these were purelined before crossing this is probably not part of the cause. The dcaimnce relationships appear to be quite siailar for cats and barley. The values in Table 6 are averages for the doainences 23 of the 3 crosses, and there were differences in the degree of duinaace between the crosses. The environ-eat and genotype interact to produce various effects and Iewis proposes that dcainance is also affected, especially by teaperature. Iewis (15) grew toaato plants under high and low temperatures and found that the dominance of genes affecting low flower amber is alaost ccaplete in the high expression environent and absent in the low expression envircment. Thus in cats and barley the different genotypes could possibly have different dominance responses (for the sane trait) to the environent. The heritabilities for I, I, and z are .50, .88 and .84, re- spectively, so that selection should be quite effective, especially for I and z. This selection is usually thought of as being applied totheprogeny,butcanalsobeusedtochcosetheparerrtstobe crossed. The regression of the 1'2 on the aid-parents shows that it is pcssibletcpredictIandZonthebasiscftheaid-parent. Inthe case of I, the prediction is not as precise although the regression coefficient is significant. It I, I, and I can be predicted, then the approxinate yield can also be predicted. If the variety aeans are expressed as percentages of the overu- all aean, then the relative aagnitude of the expected yields for the various crosses can be calculated. This is done by estiaating the relative values of I, I, and 2 for the aid-parents. Thus the product of 1.8.2 will be the relative aagnitude of the expected yield. The 24 hats over the letters indicate estiaated values. These are obtained by using the aethod cf Grafius and 111.0. (8), naaely, ’x‘ . 'i +AIh2, wbre ’1‘ 1. the .nmua value of x, 'x" 1. the population aean :6:- x, Axummmnmm. overallnean (2-x), andhz 1. the heritability. Therefore the crosses to be actually made would be those with relatively high I-I-Q values for the specific aid-parents. Thesewouldbeexpectcdtcpreducehigheryieldingprogenythanthose crosses involving the parents with a low ’I‘oI‘o’Z‘ value. Theabove calculationswereaadefcrtheZOparentsusedia this experiaent, and these results ccapared to.th_e 1'2 canbe used as evidence for the validity of the aethcd. The estiaated or expected order of the 1'2 yields involving the cc-cn parent Ajax are: Clinton) Clintafe>Ho-0-205>Clintland>8auk>0herokee0-Claricn. The actual ob- served erder 1. 011ntafe>llo—G-205>Clintland>01arion>8mk‘>¢lintcn> Cherokee. The Clinton cross was a distinct aiss but the others are in good order. No special significance is attached to the one aber- rant casewhichcculdwellbeduetothe .11th (19 101.110.). There were 11 crosses involving Craig as the canon parent. The 5 of 11 crosses that were predicted to have the highest yield were the seas 5thatdid showthehighcstyieldsintherz, althoughtheerder is not the cane. However, here the order aay not be iaportant because only one of the 5 values is significantly different from the rest and it ranked first instead of fourth as expected. Thus it is possible to eliainate those crosses which will not result in high yielding progeny and the breeder can concentrate his " '\ 25 efforts to crossing only those parents which have a higher probability of producing high yielding progeny. Since the heritability for the nuabcr of heads is lower, selection for I aay not be as successful as that for I and 2. Pray (4.) agrees that yield coaponcnt analyses can be used to select parental combination and to predict high yielding segregates, however he does not give any aothod for selection or prediction. Padrhons (9) found that the nest productive ferns of .all grains were derived from crosses of those with good tillering capacity and aany grainspcrearbythcse with-anygrainsper oarandhigthOO-grain weight. Whitehousc gt .1. (21) are skeptical about this, and 0.11... that attempts to raise yield by combining large grains and numerous grains per spikelct would very likely reach a biological limit so that some other character, perhaps oar umber, would be reduced. Be— cause cf this linitation there is very little prospect of discerning which pairs of varieties will combine advantageously without actually making the crosses. However the progeny do outyicld the parents, even the high parents in some cases, so that if some biological liait does exist, it apparently has not been reached as yet, and it could more than likely be some other character (perhaps straw strength) as well as one of the yield components. Table 7 compares the aeans of the aid-parents and the F2, the difference between them, and also the means, standard errors, t-valucs and the significance of the differences. 26 The data in this table were used to construct Figure 1, and the correlation coefficients found in Table 2 are the ones presented in this table. Table 7 bans of the Mid-Parents and the 12's, Their Correlation, The Difference Between Thea (r2431, and the lbans, Standard Errors, and t-Values of the fercnces for Number of lbads (I), Seeds for Head (I), Seed Uei in Centigrens (Z) , and Total Iicld (U I I Mid-Parent ’2 rz-P. P‘ ’2 rz-P‘ Ajax 1 Cherokee 12.095 12.977 .882 52.259 48.384 -3.875 “n I Clinton 12e624 11.298 -1e326 58e086 ”e880 1e794 Ajax 1 Clintland 11.399 11.034 -.365 58.481. 63.432 4.91.8 Ajax 1 110-0-205 12.265 13.430 1.165 59.069 63.498 4.429 “a X fink 12.010 11cm "e226 ”cm 61cm 3e293 Craig I Shelby 11.948 12.712 .764 42.937 “0439 1.502 01118 I Beaver 100494 11.399 1.405 52.333 53.901 1. 563 Craig I Vanguard 130008 11.939 “14019 415.717 “e90‘ e187 Craig I Ahegweit 11.924 12.347 .1023 49.933 47.813 -2.120 Craig I Erban 11.898 12.536 .633 46.299 47.757 1.458 Craig 1 Jackson 10.065 10.875 .810 1.9.299 56.885 7.586 Craig I Sincoe 9.887 12.982 3.095 50.282 59.720 9.433 cm; x surfers 12.270 12.051 -.219 40.048 45.751. 5.754 hens 11c 5‘5 120m o 537 51e058 S‘e 552 3e49,. Correlation .499“ . 884*“ mm Errors 1.239 i1.177 t-Values 2.2413 2.968" Table '7 (continued) 27 Z __...... W .— Mid-Parent 112 12.11,. r. :2 r243 Ajax I mm. 2.593 2.523 -.070 16.705 16.221 -.‘84 “I! 1 Clinton 20438 20M -0032 13.421 160672 -10749 Us: XOlintland 2.1.97 2.534 0037 17.062 18.039 .977 14.: x 110-0-205 2.334 2.415 .081 17.099 20.955 3.896 “a I Olintafo 2e237 2e3u .077 18.460 21.38‘ 2092‘ 13.2 x Clarion 2.1.26 2.1.90 .061. 16.718 17.569 .851 01113 I 3101” 2.458 2.701. .246 12.520 15.151 2.631 0mg I Victory 2e‘78 2e438 -0050 new 16e0‘2 20963 Craig I Beaver 2.574 2.726 .152 14.579 17.238 2.659 Craig 1 Vanguard 2.380 2.339 -.Ol.1 14.369 13.569 -.800 Craig 1 Jackson 2.547 2.650 .103 12.737 16.245 3.5“ Craig I Sinooe 2.580 2.722 .142 13.486 21.016 7.530 0011311111011. 0 8““ e 52 5* Standard Errors 1'. 021 1'. 521 197.1110! 30‘81“ 7.804“ *2 (.05 "24.01 M AND GOMLUSIONS The average 1'2 values exceeded the parental aeans for all 3 of the yield components and also for total yield. The mid-parent vs. 1'2 correlations were all positive and significant, and approximately the same magnitude as those observed for barley. The significant Chi squares indicate that the populations were not homogeneous. The oc- currence of negative, serc, and positive correlations for I vs. I, I vs. 2, and I vs. 2 in the parental and r2 generations indicates that separate gene systens are affecting each of the 3 components. Most of the genetic variances were positive, however some of them were negative; this phenomenon in believed to be the result of developmental homeostasis. Both oats and barley shew dominance for I, a low order'cf dominance for I, and lack of dominance for Z. The heritabilities are high for I and z and intermediate for I, thus in- creasing the confidence with which one can select favorable parental combinations for crossing and predicting the approximate relative re- sults by the yield components method. It is concluded that: the yield components method of analysis is the best now available and nay be used on both oats and barley; the 3 components of yield are affected by 3 essential]: independent gene systems; in general, the 1'2 is more variable than the parents, but with homeostasis the 1'2 nay be less variable than the parents; and, a breeder can select high-yielding parental combinations and pre- dict the relative results by the use of the components method. 1. 2. 3. 4. 5. 9. 10. ll. BIBIIOGRAPHY Adams, 14. W. and Shank, D. B. The relation of heterozygosity to homeostasis in maize hybrids. Genetics 44:777-786. 1959. Dewey, D. R. and In, K. H. A correlation and path-coefficient analysis of components of crested wheatgrass seed produc- tion. Agmne Jaure 513515-518e 1959e Frankel, K. J. The theory of plant breeding for yield. Heredity 1‘1m‘1200 1947e Frey, K. J. Yield components in cats. III. Their contribution to the variety I location interaction for grain yield. Agron. 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