F ‘7 5 1’ , a ‘ ‘ 7 7‘ § ; 7 V, ,‘ ‘A ‘: —l _. 180 I,” .m-*0 I :Mtxsmmwcm 0F STEM-BRANQE-‘EENG m a, ggggm 7219.359 592' “live. {Degrees of M. 5‘. M1 CHEGAN STATE " 4% i‘z’ERE’olYY‘ Rabwi' Engagis Arxdm‘sm '3 i‘éfi JHEI‘S LIBRARY Michigan State University ABSTRACT INHERITANCE OF STEM-BRANCEJNG IN PISUM by Robert Louis Andersen In the process of developing a winter hardy culinary pea for Michigan it has been determined that the habit of plant growth necessary to accomplish over wintering is a rosette of Spreading branches with short internodes, lying prostrate on the ground. Jade and Early Perfection, which are early, upright, green seeded, culinary types, and Austrian'Winter, which is a.winter hardy field pea, were used as parents in an experiment designed to study the inheritance of stemébranching. The data suggest that the character is conditioned by two factor pairs which act in an additive, independent manner. They are designated TiltilTiztiz. INHERITANCE GE" STEM-BRANCHING IN PI SIM By ROBERT LOUIS Amman A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree MASTER OF SCIENCE Department of Horticulture 1961; ACKNOWIEDGEMEETS The author wishes to tender his sincere appreciation to Dr. D. Markarian for his patient counseling and warm encouragement throughout the course of this graduate program. DEDICATION To my family, who have endured. TABLE OF comms INIRODUCIIOR OBJECTIVES MATERIALS METHODS THECBETICAL GENETIC HIPOI'EESIS FREQUENCY DISTRIBUTIONS Emsssn IN PERCEMAGES METHOD OF ANALYSIS CHI SQUARE TEST FOR HOIOCEREITY DISCUSSION AND smmm CONCLUSIONS DESIGNATION CD? GENE PAIRS LITERATURE CITED Page .4 \O'\10\Ul 23 25 2? 28 29 INTRODUCTION The garden pea is one of the earliest of all annual vegetable crops in the northern temperate regions. However, if earlier types of arc crop can be developed there are often cultural, processing, and marketing advantages to be enjoyed. Several Russian, English, and American plant scientists are presently engaged in projects and associated experiments to obtain earlier culinary peas by developing strains that have the ability to initiate growth in the autumn, over winter, and then in the spring res'ume growth utilizing the living root system and crown that remains (5, 7, 9). The workers in all three cosmtries have been successful in developing types which will over winter. Holland and Frost (6) have also demonstrated a maturity date and quality advantage with their material in England. It was first noted by Khirchinski (7) in Russia and later by Harkarian and Andersen (9) in the United States that the habit of plant growth in the autumn that is necessary to accomplish over wintering in the more severe winters of these areas is a rosette of spreading branches with short internodes lying prostrate on the ground, as contrasted to the upright, standing habit of growth exhibited by Spring planted types (fig. 1). Marmian and Andersen (9) have made a cross between £184.13 sativum, var. Early Perfection, which is a cultivated garden pea that has an upright and usually single stemmed habit of growth, and 31.9.92 sativum, sub. arvense, var.. Austrian Winter which is a winter hardy field pea. The latter has ‘4 o F IGURE I A. Jade (P1) after 80 days. TT—Y‘ryw 2 Yvi uasossrssaussasa Note that apical dominance is evident but two secondary branches are present. 'vvh—rw .,. 'IIJIIYII ’l I Also note flower. w‘.t' 1;. F1 (P1 1 P2) after 80 days. Hots the robust stems but the lack of apical domin- anCO e HT} V'VY—v V‘V'Y‘V Islesers. . 9. AW 62-11% (P2) after 80 days. Note habit of growth is ‘7'115- prostrate ,. mult i-stemmed , small leaved, and short interned. Again apical dominance is lacking. L 3 the prostrate habit of growth when fall planted. In subsequent generations both parental types evolved, as well as, a range of intermediate types (Fig. II). This lead to the obvious conclusion that branching and the other associated morphological characters of prostrate growth, small leaves, and short internodes are heritable characters and probably correlated to hardiness. That different varieties of spring seeded peas can show differences in their ability to branch out is a comparatively well known fact amongst pea breeders. The only work that has been reported on the inheritance of branching in £39.23 was done by Lamprecht (8) in which he reported the character is controlled by polymeric genes which he designated _f_I_' and f____ru. Since different lines, which presumably had the same genetic composition at the ho branching loci, showed variation in their ability to branch he concluded that the environ- ment and the remainder of the genetic constitution of any one line may cause it to differ in degree of stem-branching from other lines which are identical to it at the branching loci. The gene f___ru resulted from x-radiation. A. 1'2 Segregate after 80 days which approaches P1 in upright habit of growth. a. 1'2 Segregate after 80 days which approaches F1 in habit of growth. Yfi‘r‘lfiV— T I '33‘55701 I E 2. F2 Segregate after 80 dws e w ‘ . which approaches P2 in hab it of growth. OBJECTIVE The Objective of this experiment was to attempt to determine the mode of inheritance of stem-branching as eXpressed subsequent to fall planting in the winter hardy material developed by Markarian and Andersen. MATERIALS In 1960 a hybridization program was started at the Michigan Agricultural.Experiment Station to determine if winter hardiness of the.Austrian Winter variety of field pea coufld be incorporated into the culinary pea variety Early Perfection. r 3 All of the plants which subsequently over wintered were multi-stemmed. bulked seed (20,000) were planted September 1, 1961. rifteen single plant selections were made in June of 1962 and the ’u 1“ seed from other unselected plants that over wintered. It was felt that some of the plant and seed types had sufficiently good seed Of these plants was retained along with over 200,000 buflhed commercial qualities to warrant continuation of the program. One of the fifteen?3 plants that was selected (designated AN 62-1“) had five stemébranches, each of which bore twelve or more pods. AW 62-1“ (Pk) was chosen as the multi-stemmed parent for this study. Jade (P1), which is an early, large, green seeded, freezing type, was chosen as the other parent because it had shown no winter hardiness and no tendency to develop stemébranches in the fall planting made in 1961. In plants of AV 62-14 were first allowed to self pollinate naturally in the greenhouse to Obtain F5 seed. The percentage of homozygosity in the P5 of a self pollinated crop like peas is 95 per cent when the number of indepently inherited gene pairs is one. (Allard, p. 55). Therefore, it was decided that the seed produced by the F plants would be screened for commercial type h and that five lines should be selected as the multi-stemmed parents 7 for this study since it could not be certain that the genes conditioning branching were in a homozygous condition. METHODS 2. and the first backcross generation to each parent. All hybridizations, to The study included the parental lines, the F1, F Obtain F1 and backcross populations, were accomplished in the green- house during the winter of 1963-196”. Hybridizations were made with- out begging the flowers. However, since the stigmas were expesed during emasculation, the greenhouses that were used were fumigated on a weekly basis to prevent an infestation of greenhouse insects. Some flowers of the parental plants were allowed to self pollinate naturally, as were some on F plants which were grown for the purpose 1 of producing 12 and backcross hybrid seeds. The seed was planted at the Michigan State University Horticulture farm on September 7, 196h, in an extremely level and uniform plot that had been fallowed during the summer of l96#. .A spacing of four inches between seeds was used to allow easy observation of the stem- branching habit. The only weed control measure was to carefully hoe a small patch of Convolvulus arvensis that appeared after about two weeks. .Approximately one inch of irrigation was applied by sprinkler system on the day after planting. Subsequently, frequent light rains kept a plentiful moisture supply present. Counts to determine the. number of stem4branches per plant were taken on OctOber 20 through 25, 196“, when plants were of the approximate size shown in Figure I and II. All visible branches over approximately one half inch long were counted. These data are shown in Table I. Ultimately only .o .n .m nommupwaoum one u m.m I m.H .aopu no nonmep on e m.a I m.o N .opHsHH anode human one .opo .n.m .m.~ .n.H H “Na R Hanan am Duo 9...: I. I. H mm m: cm e I. .I mg a 3 cm mm.o No.m I: I. I. II n am as am a NHH Ame a HHVHM_HM am :3 2.: .I a :H 3 «H SH SH mm H HS 9383 we mN.H Ha.a I: n m mm mm on as a I: amH “Hm a man «a 24 men I H e Hm R as H mm H an “as in H3 ms mm.o es.a I: u. N om ma mm m In a: eOH AHm a wee He 36 Him .I I. m Hm em a H .I I. 2. Ame u Haw Ha Ha.o Hw.m I- In mH am an a H In an HaH Away aHINe :4 inc wHJ I. I. I. .I I. I. an ow mm SH “Hay each. .m mam m.m m.a n.» w.m .w.a mqmlw m.~1¢ w.H “mammm quauuuquu upmoam cam Ho muoHuoaeaow ameuoumwn how acoam Hem monomoumiseam no moanppanunan homQAdeuh 2" eHnmE I ...... O 0-. e v a II I I ‘ I A II D 1.. I: I- " III. II III {I III. ‘III little ll: 1'! III. I: sill I l I .‘IJ'UI ...-..-I.|'ll',lt 'O-l‘.llsl‘llll 9 Line Two was chosen for analysis because it showed the least total variance and was therefore thought to be derived from the most homozygous F line of the five that were chosen originally. 5 The experimental design used for this material is adequate to illustrate the method of analysis and give a preliminary suggestion of the number of genes conditioning the branching character, but a more extensive genetic design is desirable as a basis for final genetic conclusions. Adequate design would include randomization, replication, a more highly inbred Pb, and reciprocal backcrosses. The data used in the computations involve the actual number of stemébranches observed for each plant in the parent, Fl, 12, and backcross generations grown in the same year (September through November 196“). The estimate of genetic differences in this cross was based on a comparison of the observed and hypothetical means and a chi square test of I'goodness of fit' of the observed frequency distributions of the segregating populations to theoretical frequency distributions calculated using the hypothetical means and an estimate of the environmental variance. THEORETICAL GENETIC HYPOTHESIS It is now necessary to develop a genetic hypothesis against which the obtained frequency distribution may be tested. Frequency distributions expressed in percentages First,_the observed frequency distributions are converted to percentages. For example, the Jade parent has 28 plants in the one 28 branch class. The percentage is then computed: IE? 1 100 I 19.0“ 10 .mamonpomzn oHuocow Hooaponoon» mo moaooassuom ma oompoaw moummao osmoweqa mumxomam commemoouem cw moaaspueauan hocoadoeh commoumxo moose aaumw 3<_H each a no umoflpm .mowopcooeofl no Homom amouoxoop .aeonmm we came womfioaco Ho mmouespfinpmae hosonvonh .w canoe H SH I- .35 .r 9.3, #0.? I35 86 I. I. «a 3 8 NH. I. I. I. weeks > $.le 3.3 $93 P mass... Hm 2. 3 HS . $6 NNVN RS . Exam 3.0m 3.3.. .35 » Neal 938$ mm 3H Ami; £0: 8.3”. mném RAN meamm 3%.: > I... AHm a «.3 Na Rm lens SW and... 3.9... Hm.mm Rim $5 > TWIN. hum a HAS Na 3H .I kumH aflmm HHJN $4.. 2.6 I. I. “may Ham 5 SH I. I. I. I. I. :13 $6: 3.3 Am: :3. 358 Tm VIN mew Tn In: Tm mqm THU 3 H38 .83 so 23H .33: II. Ind I ll.‘ in.-. 11 per cent, and so on, in a similar manner, for the other percentage values. These data are complied in Table II. 1 Examination of the F2 frequency distribution expressed in percent- ages indicates a single mode that falls between the modes of the parental generations. The simplest genetic hypothesis which could be based on this fact would be that a single factor pair expressing no dominance is causing this situation. One reciprocal F2 generation (P: x P1) would appear to approximate a 25%:50%:25% proportion if the 3 and under classes are added to Obtain 27.32 per cent, the h and 5 classes are similarly grouped to obtain 5h.12 per cent, and the 6 and above classes are grouped to give 18.62 per cent. Calculations accomplished in a similar manner on the reciprocal F2 (P1 x PE) are inconsistent with this hypothesis, however. Inapection of the back- cross generations reveals that a single factor hypothesis would appear to also be invalid in these segregating populations because it is impossible to derive a 1:1 ratio from them. This indicates at least two factor pairs condition the branching character in the F2. Since the frequency distribution of the F2 generations have been shown to have intermediate modes between those of the two parents, the simplest two factor hypothesis that would be consistent with this fact would be that of additivity because the 12 mode (and mean) of a character conditioned by 2 additive factor pairs should fall intermediate to those of the parents. The percentages of the total frequency distribution theoretically should form five classes in the F2, viz., 6.25 per cent Egbb, 25.00 per cent 9.332.220 Aggy, 37.50 per cent A3333, £592, 9%, 25.00 per cent AABb, AaBB, and 6.25 per cent AABB (Table III). Grouping by adding Table 3. Complete genetic hypothesis expressed as percentages and ratios; including lwpothetical means for 1'2 and backcross populations. Proportion g_f_ :2 Population _ Genotype Groups Percent Ratio X 1) aabb» .25 1 2.180 2) aaBb, Aabb 25.00 1) 3.090 3) mm mm, aaBB 37.50 6 3.995 1+) AABb, AaBB 25.00 4 h,900 5) was 6.25 1 5.810 Proportion of Backcross Population - to Jade 6_) aabb 25.00 1 2.180 7) Aabb, aaBb 50.00 2 3.090 8) AaBb 25.00 1 3.995 Proportion of Baclocross Population toAW62-lh _ 9) AaBb 25.00 1 3.995 10) AABb, AaBB 50.00 2 “.900 11) AABB 25.00 1 5.810 *b‘fi F... ~ . ~- _.,‘.. _ 7 in---‘ ' v H g - u - -.._ 1 ‘ §-.—‘-- _... -._. .- .. -' -- -1 ‘s . ‘.. - .. ..... -- . -». - -w-u. - - . ur-V-r' ' --- - o-- ' .- .. -— 4 an... - i - ---,_q - ~‘-----__~-., ---_-. _‘-~,‘..-.“~- . n H ‘W "~_-*._- ‘ ' " . . -"""-O..-.-. - C q ‘ ~-.- in.--\‘“- I . 9"-5—.-_,A __,->_‘ ‘ . (0 Q H.-m..-.-- -_ ‘~ h..- --——-o. 0"- -.-~. . C H--. “H-o—C - _ -‘---- .h‘---- ‘u‘ov ~u—-.--—.—-—- w--~-- a.-- c--- v».- ~'—‘.. . -- v“-— 13 Observed percentages in the F2 (P1 x Pb) as follows: classes one and two combined total 8.66 per cent, class three 2“.73 Per cent, class four 33.21 per cent, class five 20.58 per cent and class six and above combined total 10.11 per cent: it can readily be seen that an additive scheme is approximated. The same grouping in the reciprocal F2 (P2 x P1) shows inconsistency with this hypothesis. However, similar grouping of the pooled F2 again yields an approximation of the 1:“:6:“:1 ratio. Again, as in the case of the one gene hypothesis, examination of the back- cross data should yield support of this hypothesis if any is available. A 25%:50%:25% proportion is expected in backcross generations in an additive 2 factor scheme. If the observed percentages of the frequency distribution of the backcross to F1 are grouped and added it yields: classes one and two 32.1“ per cent, class three “1.96 per cent, and classes four and five 25.89 per cent. Grouping and adding the back? cross to AW 62-1“ it yields: classes three and four 25.“9 per cent, class five “8.0“ per cent, and classes six and seven combined total 26.“? per cent. The fact that three segregating populations out of four seem to support the hypothesis of branching being conditioned by 2 factor pairs, plus the fact that pooling the data from the F2 reciprocals also yields an approximation of the expected ratio constitutes the basis for examining this possibility further. METHOD OF ANAEYSIS Before this genetic hypothesis can be tested, one must compute the means for the genotype groups (Table III). The designation of Jade as aahb and of AW 62-1“ as AABB is done solely as an expedient 1“ to facilitate clarity and ease of discussion. The plus (capital letter) values are assigned to At 62-1“ because it can be noted that partial dominance is expressed by the means of the F1 and F2 populations in the direction of this, the multi-stemmed, parent. Further discussion of this fact will follow in the Discussion. Assuming additivity, the mean of the heterozygous F1 genotype and both of the other genotypes with exactly two plus alleles is calculated by taking the average of the two parental means. This gives the mid point, or in this case, the hypothetical mean of Genotype Group 3. In a similar manner, the hypothetical means of Genotype Groups 2 and “ are calculated respectively as follows: 2.18 + 3.991 = 3.09 and 3.9251: 5.81 = “.900. 2 2 "t“ tests are then performed to determine if these hypothetical means correspond to those of the observed segregating F2 and back- cross generations. The data from these tests can be found in Table IV. The "t“ tests for the F2 (P1 x P2) and the pooled F2 show there is no significant differences between the observed means of 3.99 and “.10, respectively, when they are compared with the calculated mean of 3.995 at the 5 per cent level of signifigance. The F2 (P: x P1) shows significant difference between the observed mean of “.“l and the calculated mean 3.995. The "t" tests for the backcrosses to P1 and Pb show there is no significant difference between the observed means of 2.92 and “.98 when they are compared with their respective hypothetical means of 3.09 and “.90. The final analysis of interest that can be completed using these data is to estimate the number of gene pairs acting. This is accomplished 15 Table “. 't' test comparing Observed and hypothetical means for segregating populationsl. Population Opp. Hyp. Obs. 333.2 X _ M 32 Q; ‘9 t4025.. r2 (1:1 1 P2) 3.990 3.995 1.1416 1.117 0.05 _ 1.960 12 (P2 1 P1) 0.010 3.995 1.660 1.117 3.05" __ 1.960 BC to Pi 2.920 3.090 0.903 0.935 1.30 1.980 130 to p2 0.930 0.900 . 0.533 0.935 0.66 __ 1.980 ‘ Signifigant at the 5 percent level 1. t ‘3 i "' 3.2 2 2 where sp is the pooled estimate of the given by Zed—62 306' 32' 2 0p2 3 (NI-l) s1 +(N2-l) 522 —S .. ' “P.1-hl ‘15 N2 and the degrees of freedom 3: 11 +112 - 2 taken from.Dixon and Massey (2) ea {midragge - class center)2 (7’2. 'O'oztd’nz These formulas are taken from Allard (1) and were used to calculate the hypothetical variance. .__- - ---- ..-,‘ -.-. 7--..__—.—-.—-a-__-e-——~——..g _ -_---.‘c..._.-. .._. C .- --_-- --.----.._-._. .--..—-._..-._-----_..--..-—_.-_-,--.-_ D l v I C h ‘ t l n I e v - — Vu '- 9 h 0-- d O C - ..—. G v c It i O . a I O I Q Q ——~ . . _- ---_.-_..-- pH---—~-‘-o---'*--‘_.—'.~~vC’H-‘I—v-’ol..-~..-------. " b e ._... ... ~ .— . . _. H-—..—-,~ , . . F. _..r .— .— ..._ _- 1’..- A--. .0 '-~-‘- L--H..’. _ . .- __._ d — ~ -M--..-.M7----.~-....4—-7--..-,.. —. - .— _--—. --.... '4 .... . . . ‘ . . . a ‘ ' O 1 6 by determining if the observed frequency distributions of the segregating populations will fit an estimated theoretical frequency distribution constructed by applying the observed environmental variance 0.525 to the hypothetical means of the various genotypes. This is the best available estimate of the environmental variance expected for each genotype (10). The theoretical values are calculated by the method suggested by Powers, et.al. (11). Table V contains an example of this method. Calculations were accomplished in the manner described below. The upper class limit is subtracted from the mean of the particular genotype being considered. This difference is then divided by the standard deviation (‘T5:5§3). The quotient is the value t.which is used to enter the Table of Areas, Ordinates, and Derivatives of the Normal Curve of Error (“). The values of the area.under the curve from the ordinate at‘t'= 0 to the ordinate for the values of t.can thus be read in the area column. Calculation of §.values and deriving of the area located under the particular class interval for the ggpb_genotype 0f the 32 (Pooled) data would be as follows: the upper class limit of the first class is 1.5. It ie_eubtracted from 2.18, the genotypes' hypothetical mean, 2.18 - 1.50 : 0.68. Dividing 0.68 by 0.725 yields the value 3, Reading from the table of areas we find the correspmnding area to be 0.326“. This value must be subtracted from 0.5000 to arrive at the area under the curve to the left of 1.5, which is the ordinate of interest. In this case the area under the 1.5 class is thus calculated to be 1? Ho.o u mo.o u m m~.o a mu . .m~.o Ho.o am.o mo.o Ho.e .oaoo\mo so.mom me.” «n.3mfi we.m mm.o- mo mo.aH -.H mm.HH meta mm.eH .oo as: so .NHH «ea .oHH mm A..so >v paoo an: .0: ea we. NHH Nee oHH ulnmwerluau. .uso as: Hm.oe ma.oHH on.mm~ em.HHH no.5: .oHso r ooflpsoo Has .moo.o mm.o om.o -.om. oa.o~a om.mma oo.aHH .wqumlrnaqo. .oaso ooH aooo.o ao.o nm.~ on.m mm.mm Ho.~m ne.m~ Ha.m we.” oH\a oooH. Ho.o eo.H ~w.- Ha.ema oo.oam oo.amn mo.omm om.mma o~.m~ Hosea ooH Ho.o mo.o NH.oH mm.oe no.o~ oe.m ao.o I: u: Hm.m was. own. mm<< oom so.o oo.~ wo.am oa.aoa mm.mm om.m oH.o us oo.o mma. mmm. mma< N ooH us mo.o mm.H ~m.mm mo.om mm.- om.~ mo.o oo.m mms. mmn. p944 oom no.0 ow.m oo.em oH.HoH mm.mm om.m oH.o as oo.o was. own. pmqq N ooe .. an.o oe.a w~.om mo.mom oe.ao oa.a NH.o oo.m mes. mam. pmq< a oom 1: a: oo.o o~.m Ne.Hm om.HoH eo.mm ow.~ mo.m mms. men. pps< N ooH us mo.o no.” mm.~m mo.on mm.-, em.H mo.o oo.m mma. awn. mass oom u- an mo.o ofl.n No.am om.HoH oo.mm mo.~ oo.m mmu. own. ammo N ooH s: as u- ao.o em.m om.o~ oo.oe on.a~ ma.~ mus. mun. been a a o to 3 so so a... um so 3 m am New 3388 .noupmasmOm Acoaoomv Nh_ma seem Mo mmflnosmup mafiaouuaosoo modem anew mo hopes: no moanedpoaeo mo camsmwn 0“ afipma I." ‘I. -PII."|II‘.O--II.II0.I-:‘ lo....~01 1". le..0|lv~l’t'e.‘4‘III..0C.O. A..|3 ('0‘ I: I! Ill. O I...- vllll h ’ I- II. III! a i - II. b u 3 III. .lvl c i .Iul a I e t a O I 0.1.7.1 ‘.‘I.".L'O D. 0.10-1.1" it? 0'11 .| 0 '1' a I'.’ a 9 .o n C v I 0 e a .— a I. :‘.'Un.'l‘l so ..'I"C."l'I’.\I‘-’-tl'l‘,‘ti¥ U‘ ell l..l .llllll‘e'Yl .1004".-. VIII: I10I’o"--.l - O I!....". 1091‘)‘.I"-Ill" Hull: [1.13 l u I \ .I.“ 0.0.1:! “ "l‘l 0"- Oil'l‘lul'id {0-.Ot C lle-‘a- i}.’l’\'e- -90 .I"-'| III" 6 a 9 b + a e e e 1 t d ‘ _‘ .0 d I O 1” e 6 e e l l I I w I 0 ll: l i I e i 'II t e r O r .l.‘ I 0 I'll i t I.-- 91‘ . VI A I VII 0 O I...'I."l!s n It‘ll; | 'ti 0 n v i 1 .1 i e a .9, I V e. 4 e e e s v a e c . _ + t I l 0:-uc -..¢J . .0 .91 . 1 I- 0:1 0 4 0| a H“ o u 18 0.5000 - 0.3“6“ - 0.1736. The next upper class limit is similarly subtracted and the difference again divided by the standard deviation, 2,: - 2.18 u'2‘2§_u 0.““. The area corresponding to 0.““ as Obtained 0.725 0.725 from the table is 0.1700. In this case the area 0.1700 is added to the area 0.326“ which was obtained previously. This is necessary because 0.1700 represents the area from the ordinate at 3.: 0 to the ordinate value 2.5, and similarly 0.3“6“ represents the area from the ordinate at t_- 0 to the ordinate value 1.5. The difference between the next upper class limit and the mean is 3.5 - 2.18 = 1.32. When it is divided by the standard deviation of 0.725 the resulting t.va1ue is 1.82. The area 0.“656 corresponding to 1.82 is again obtained from the table. In this case it is necessary to find the difference between this value and the area value 0.1700 which was previously determined because O.“656 represents the total area from the ordinate t_: O to the ordinate 3.5 and it is only desired to know the area between the ordinates 2.5 and 3.5. This is repeated for the remaining upper class limits until a value of zero is obtained for the area under a subsequent class. This step>by step process is accomplished for each genotype. The total area under each class interval is then Obtained and converted to per cent. The theoretical number of individuals that should lie within this class interval is then obtained by multiplying the percentage of individuals lying within a class interval times E. Similar calculations are accomplished for the F2 (P1 1 Pi), F2 (P2 x P1), BC to P1, and BC to P2. Figure III and Figure IV show the comparison of these theoretical frequency distributions to the observed frequency distributions. . ., wJ-Le'... '1, (be 19 FIGURE III m Graph shows the observed frequency distribution of the F2 (P2 x P1) population in solid line as compared to the theoretical computed frequency distribution in intermitt- ent line. A "poor fit' is obtained when these 2 distributions are compared by chi square test. 1.2323 9.13.2.1}. shows the observed frequency distribtuion of the F2 (P1 1 P2) population in solid line as compared to the theoretical com- puted frequency distribution in intermittent line. A. 'good fit” is obtained when these 2 distributions are compared by chi square test. 20 , noun III 7 4 5 STEM- BRANCHES 3 80- 70- 00- b b - O O O 5 4 3 ruzuDOuxu 3 4 5 6 STEM - BRANCHES 2 21 FIGURE IV Eppg£_§g§ph shows the Observed frequency distribution of the BC to P2 population in solid line as compared to the theoretical com- puted frequency distribution in intermittent line. A ”good fit" is obtained when these 2 distributions are compared by chi square test. ‘§2!g£_§£§ph shows the observed frequency distribution of the BC to P1 population in solid line as compared to the theoretical com- puted frequency distribution in intermittent line. A.'good fit' is obtained when these 2 distributions are compared by chi square test. FREQUENCY FIGURE IV a O I FREQUENCY N u b u- o o o o l T l 1 O T O u z s 4 5 e ; s‘rsu - BRANCHES 2 <.3 4 5 6 7 STEN-BRANCHER ' 22 23 Chi Square Test for Hemogeneity It is now desirable to test for homogeneity of agreement between the data of the original observed F2 frequency distributions and those of the theoretical 12's and backcrosses calculated in the manner explained in the last paragraph. The tail classes of the distributions are grouped. A chi square (12) test approximation for homogeneity is used in order to determine "goodness of fit' of the various observed and theoretical frequency distributions as suggested by Fisher (3). Table VI shows the chi square tests for the segregating generations. An acceptable fit is Obtained in all instances except the F2 (Pb x P1). 2“ Table 6. Chi square test for homogeneity of data for observed and theoretical F2 and backcross frequency distributions. Population Class Obs. Cale. o-c 0-02/0 df P F (P x P ) 2.5 2“ 28.15 “.15 0.61 2 1 2 3.5 76 65.79 10.21 1.58 “.5 92 90.33 2.79 0.03 5.5 57 65.15 8.15 1.02 3.25 “ 0.50-0.30 12 (P 1 Pi) 2.5 9 19.71 10.71 5.82 2 3.5 1+“ “6.08 2.08 0.09 “.5 50 63.26 13.26 2.78 5-5 55 “5.63 9.37 1.92 — 2“.99 4 (0.01" 22 (Pooled) 2.5 33 “7.85 1“.85 “.61 3.5 110 111.86 1.86 0.03 “.5 143 153-59 11.59 0.87 5.5 112 110.78 1.22 0.01 6.5 6“ “6.91 17.09 6.23 3.5 29 25.3“ 3.66 0.53 “.5 “7 “3.05 3.95 0.36 5.5 2“ 29.67 5.67 1.08 6.5 5 8.26 3.26 1.29 W ——— w3.57 —“ “ ' 0.50-0.30 30 to 22 3.5 6 7.79 1.79 0.111 “.5 20 27.37 7.37 1.98 505 “9 39.09 9.91 2.51 6.5 27 27.85 0.85 0.03 “.93 3 0.20-0.10 ‘1 . HI. I - - ' , ‘- - n a a. - . e P‘ -- ‘ - n . — '7‘ - ‘ - - — - - ‘p— - ‘ -- D. -- - — - r . - — n - 1 4 v . I V ‘ e . , -. —- 4 A . vow -- . w .-1 -- -- . .. .--—»‘-‘r—-->-§~- - _-_-,.4, —..—. .-..--. u 4- . It I Q 4 ~ D I . 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