A aestiuum (2n = 6x = 42), has been described in an earlier paper (LAW 1966).

Transcription

1 THE LOCTION OF GENETIC FCTORS CONTROLLING NUMBER OF QUNTITTIVE CHRCTERS IN WHET C. N. LW Plant Breeding Institute, Cambridge, England Received February 20, 1967 technique for the location of genetic factors in the hexaploid wheat, Triticum aestiuum (2n = 6x = 42), has been described in an earlier paper (LW 1966). This technique exploited an inter-varietal chromosome-substitution line in which a single homologous pair of chromosomes in a recipient variety has been replaced by its homologues from a donor variety (SERS 1953). By using this type of genetic material, it is possible to produce single chromosome heterozygotes, the derivatives of which provide estimates of the variation created by means of crossing over. It is the study of the amount and the type of this variation which allows the location of the determinants not only for qualitative characters but also for those having effects on quantitative aspects of the phenotype. This technique has been applied to the allelic differences existing between the two homologues of chromosome 7B found in the wheat varieties Chinese Spring and Hope. For the character days to ear emergence, LW (1966) has shown that at least two factors, e, and e,, are responsible for the differences between these two homologues. Furthermore, el was shown to be closely linked to the centromere (LW and WOLFE 1966), most probably located on the short arm, whereas e, must be at least 50 map-units from the centromere but on the long arm of this chromosome. Genes controlling purple culm (Pc), mildew resistance (mz) and leaf-rust resistance (Zr) have also been located on this chromosome (LW 1966; LW and WOLFE 1966; LW and JOHNSON, unpublished). The present paper describes the use of the same experimental material to determine the positions of factors controlling the quantitative characters yield, grain weight, height, tiller number and grain number. MTERILS ND METHODS The experiments are based on the hexaploid wheat variety, Chinese Spring, designated CS, a line in which chromosome 7B of the variety Hope has been substituted for its homologue in CS, designated CS (Hope 7B), and the hybrid between CS and CS (Hope 7B). The substitution line, CS (Hope 7B), was produced by DR. E. R. SERS as a result of a backcrossing programme in which, using nullisomic-7b as the recurrent parent, chromosome 7B of Hope could be kept intact whilst the remaining 20 pairs of chromosomes could be reconstituted to form the CS background. The hybrid resulting from the cross between CS (Hope 7B) and CS should therefore be heterozygous for chromosome 7B and homozygous for the remaining 20 chromosomes. The genotypes CS, CS (Hope 7B), and the hybrid between them were then used as pollen Genetics 56: July 1967.

2 446 C. N. LW parents and crossed to CS plants mon3somic for c!iromosome 7B. Three kinds of cross were therefore involved, (i) CS mmo 7B x CS (ii) CS mono 7B x CS (Hope 7B) and (iii) CS mono 7B X [CS X CS (Hope 7B)]. The monosomic plants obtained from these crosses were selfed and the resulting families sown out in the field as a randomized block experiment in Each block consisted of 11 families from cross (i), nine families from cross (ii), and 82 families from cross (iii). Five blocks were used with plot sizes consisting of 14 plants grown as two rows spaced one foot apart and 6 inches between plants within rows. Plots were harvested on a single-plant basis and estimates made of the yield per plant in grammes, the number of fertile tillers per plant, the number of grains per ear and 250-grain weight. Height per plant, takm as the distance in cantimeters from the base of the stem to the top of the tallest tiller, was also measured. full account of the theoretical basis of this work has been given in a previous paper (LW 1966). Briefly, however, the derivatives of cross (i) and (ii) provide a sample of the two nonrecombinant chromosomes, that is chromosome 7B of the varieties CS and Hope respectively. This sample can conveniently be called the parental products. The derivatives of cross (iii), however, will be composed of plants carrying one or other of the two nonrecombinant chromos3mes and also some plants with chromosomes which have resulted from crossing over between the two parental 7B homologues. This sample is called the F, products. For any character, comparisons between the two types of product give rise to a number of informative situations. (a) If a difference in mean between the parental and F, products occurs, then either a differential transmission of genes has taken place or nonadditive genes are segregating as a result of crossing over. Where the genes behave in a completely additive manner, then the means will be the same. (b) If the derivatives of cross (i) and cross (ii) differ, i.e. the two types of parental product differ, but yet there is no distinguishable difference between the variances of the parental and F, products, then a single factor controlling the character under study is segregating. (c) If the two types of parental product differ but there is a distinguishable difference between the variances of the parental end F, products, then more than one single factor controls the character under study. Furthermore, if the variance of the F, products is less than the parental then the factors responsible are predaminantly in coupling. (d) If the two types of parental product are not different, but yet the variances of the parental and F, products differ, then more than one single factor is segregating in the population and these factors are pred3minantly in the repulsion phase. Monosomic progeny: lthough there are slight variations depending upon the particular chromosome, monosomic plants produce on average 73% monosomics, 24% euploids and 3% nullisomics among their progeny (SERS 1953). Since the plants studied in this experiment result from the selfing of a selected monosomic, then segregation will occur within plots for the monosomic, disomic and nullisomic condition of chromosome 7B. However, by far the greater proportion of these plants will be monosomic, so that the analysis will favour those genes which are active in the hemizygous state and will be biased against those genes which are hemizygousineffective. Various degrees of hemizygous expression could also be expected between different alleles at the same locus. In this way, the hemizygous condition could either enhance or reduce allelic differences compared with the more normal homozygous condition. The magnitude of the genetic variation observed could therefore be quite different from that observed when only euploids are considered. Whether this will prove to be a severe limitation to both the kind of analysis proposed and its interpretation must, of course, await an experiment based solely on euploid individuals. The genetics of chromosome 7B: Previous work carried out on the genetic variation existing between these two homologues of chromosome 7B has located a number of factors which can be used in the present analysis as markers. The location of these factors was carried out by classifying most of the derived lines used in the present experiment. This exploits one of the advantages of this kind of material. On the assumption that the genetic differences which distinguish CS from CS (Hope 7B) are all located on chromosome 7B, then each of the selected monosomics from the three crossses must breed true apart from the segregation of the disomic-monosomic

3 LOCTION OF FCTORS I N WHET 44 7 condition. Indeed, by selecting euploid individuals from each derivative, pure breeding lines should result. It is thus possible to replicate this material so that more accurate estimates of the genotype can be obtained in any one environment. This corresponds to the progeny testing which THODY (1961) has used so successfully in Drosophila melunogasier. However, it is possible to go further and replicate over environments so that genotypes can be sieved through a range of different environments. In this way the genetic control of a character can be studied in environments which produce the largest differences between the expressions of the alternative alleles. n ideal example of this approach exists among the genetic material used in the present experiment. Chromosome 7B of Hope differs from chromosome 7B of CS by an allelic factor, elh, which under continuous light brings about ear emergence 17 days earlier than the alternative allele e,cs, in CS. By contrast, under the field conditions of this experiment, the effects of this allelic difference were negligible. The assay of the derived genotypes under continuous light has allowed therefore the location of the factor e,, which, although it has no detectable effects on ear emergence in the field, can nevertheless be used in these circumstances either to locate other factors by linkage or to establish pleiotropy by its influence on another character. much more penetrating study of the distribution of genes and their behaviour should thereby result. ltogether four markers have been located by sieving 73 of the derived lines through a range of different environments (LW 1966; LW and WOLFE 1966; LW and JOHNSON, unpublished). In each instance, the factors located and responsible for the control of leaf-rust resistance, mildew resistance, earliness and purple culm behaved as if they were single genes. These are symbolized Zr, ml, e, and Pc, and their approximate locations, along with the centromere, are shown in Figure 1. Since the genetic map of chromosome 7B is probably within the range ICMX110 units in length (LW and WULFE 1966), it is likely that most of the chromosome is covered by these four markers. RESULTS The description and analysis of single characters: ll the five characters studied in this experiment gave highly significant line effects. The analysis of these line differences is presented in Table 1. Grain weight: For this character the CS parental derivatives were significantly higher than those from CS (Hope 7B). However. as the analysis shows, neither the mean nor the variance of the parental products is different from the equivalent statistics obtained from the F, products. Thus, the item, parental us. F, products, gives a mean square which is similar to the error item in the total analysis. Likewise the mean squares for the variation within each of the two samples are not distinguishable from each other (V.R. = 1.10, not significant). There is no evidence, therefore, for either gene interaction or the differential transmission of genes. Nor is there clear-cut evidence that more than one factor is segregating in the population. The genetic variation can be accounted for, so far as the present analysis shows, in terms of a single factor controlling grain weight and behaving in an additive fashion. Unlike the character time to ear emergence, in which the F, products segregated as two distinct groups (LW 1966), the distribution obtained for grain FIGURE 1.-The genetic map of chromosome 7B showing the locations of the four marker genes lr, ml, e, and Pc.

4 448 C. N. LW TBLE 1 nalysis of variance of the characters grain weight, height, grain number, tiller number and yield, for the parental and F, prducts Item Parental products us. F, products 1 Variation within parental products CS (Hope 7B) us. CS 1 remainder 18 Total 19 Variation within F, products 1rH : tcs 1 remainder mlh : mlcs remainder e,h : e,cs remainder remainder 71 Pc : pc 1 Total F, variation studied 81 Error 404 df Grain wt. Height *+* )* * ) Character M.S. Grain no. Tiller no. Yield *** ** 18.76' ' * P ** P *** P < weight, while showing some evidence of bimodality (see Figure 2), cannot be separated into two unequivocal groups. s a result, conventional mapping cannot be undertaken with the markers lr, mt, e, and Pc. On the other hand, if the factor for grain weight is closely linked to any of these four markers, then most of the variation within the F, products will be associated with the difference between the two alleles of the appropriate marker. If, however, grain weight is only loosely linked with the four markers then the removal of the variation relatable to each of the markers will produce only a small reduction in the overall F, products variation, The variation ascribable to each of the four markers has been calculated and is shown in Table 1. Since only 73 lines out of the 82 F, products have been fully classified for the markers, only 72 degrees of freedom are available for this marker analysis. So far as the character, grain 'weight, is concerned, it is evident that the variation remaining after removal of the variation associated with each of the markers is still large. In erery instance the variation relatable to the marker genotype is insignificant, whereas the remainder variation is significantly greater than the error. The factor controlling grain weight is consequently only loosely linked to the markers. Now, in spite of the lengthy backcrossing programme used in the production of these substitution lines, some genes from the donor variety, Hope, may still be present among the background chromosomes of the substitution line CS (Hope 7B). If this is indeed so, then some of the variation observed in this experiment could be due to genes of this nature. The markers, lr, ml, e, and Pc, have been

5 LOCTION OF FCTORS IN WHET 449 shown to occur on chromosome 7B (LW 1966; LW and WOLFE 1966; LW and JOHNSON, unpublished). The fact that grain weight has not been associated with any of the markers, could mean that the factor controlling this character resides on a chromosome other than 7B. The data from this character taken by itself cannot distinguish with certainty between these alternatives. Height: The breakdown of the variation for this character into the items which test the differences in mean and variance between the two samples indicates that in neither are these statistics different. Yet, the two parental products are significantly different from each other, the derivatives of CS being taller than those from CS (Hope 7B). This agrees with the hypothesis that only a single, segregating factor is responsible for the genetic variation observed and this factor behaves additively. In contrast to the previous character, the analysis of height for the F, products demonstrates that a significant amount of the variation is removed 'when the mean effects of the two alleles, mlh and mp, are considered. This indicates that linkage occurs between the proposed factor controlling height and m2. On the c ther hand, the variation remaining after removal of the variation associated with ml is still significantly greater than the error (V.R. 2.31, P<O.OOl), so that tight linkage with the marker can be excluded. Similarly, a simple pleiotropic effect of ml on height may also be rejected. One other feature of the analysis of height may also be usefully described here. The marker gene lr is positioned at about 31 map units distal to m2. If the factor for height is also located distally, then some linkage with lr should be detected. The analysis indicates that there is no evidence for this at all. This would suggest that the most likely position for the proposed factor for height is proximal to ml. PRENTL PRODUCTS w F. PRODUCTS FIGURE 2.-Distribution and F, products.,,,,, I,, I, l,,,,,, I GRIN WEIGHT HEIGHT GRIN NUMllER Gms. C ms. curves of grain weight, height and grain number for the parental

6 450 C. N. LW Grain number: Like the previous two characters, the observed variation in grain number can be explained in terms of the segregation of a single factor. This follows from the lack of significant differences between the means and the variances from the parental and F, products, and the highly significant differences which occur between the two parental derivatives. In this instance, the CS lines give lower grain numbers than the derivatives obtained from CS (Hope 7B). lso, there is clear evidence that this character is associated with the markers e, and Pc, since the items testing these effects are significant. Simple pleiotropy of just one of the markers can also be excluded, since in each case the remainder variation is significantly greater than the experimental error. Thus, for the marker el a V.R. = 3.09, P<O.OOl, and for the marker Pc a V.R. = 3.22, P<O.OOl are obtained. If the hypothesis is correct that only a single factor is operating, then the linkage to the two markers e, and Pc can best be explained if the factor is located between e, and Pc rather than to one side or other of them. This median location is supported by the fact that equivalent amounts of variation are associated with each of the markers, rather than the asymmetrical association expected if the factor lay outside them. Tiller number: The breakdown of the variation for this character differs from those previously described. In the first instance, there is no indication that the two parental derivatives differ in their expressions of tiller number. Secondly, the remainder variation left after the removal of the mean parental difference is significantly greater than the experimental error (V.R. 1.69, P ). For the previous three characters this remainder variation or the variation within each of the parental products was insignificant. Now the presence of a significant remainder variation could occur if the genes controlling tiller number were present on a chromosome other than 7B, and the substitution line itself was heterogeneous for these genes. However, if this is SO, such remainder variation would occur only among the derivatives from the substitution line and not from those derived from the recipient variety, CS. The breakdown of the variation in tiller number among the parental products indicates that all the residual line variation does indeed occur between the CS (Hope 7B) derivatives. Thus, the mean square measuring the variation between these derivatives gives a value of 5.13, which is significantly different from the error (P ). This compares with a mean square for the CS derivatives of only The observations therefore point to background variation as the possible cause of the tiller number differences which exist in the experimental material and that the original substitution lines differed among themselves by a gene or genes controlling tiller number. On the other hand, the analysis of the F, products indicates that at least some of the heritable variation in tiller number is determined by a factor on chromosome 7B. Thus, the item testing linkage with the marker e, is significant, indicating that those lines carrying the allele elcs give an average tiller number which is larger than those lines carrying the allele elh. lso the remainder variation is not significantly different from the estimate of background variation obtained from the parental products. Consequently, the factor responsible for tiller number

7 LOCTION OF FCTORS IN WHET 45 1 on chromosome 7B could be either the marker e, acting pleiotropically on this character or a factor tightly linked to this marker. Yield: Yield per plant is determined by the multiplication of the three subcharacters, number of grains per ear, number of fertile tillers per plant and the average weight of a single grain. ll these three subcharacters have been shown to be determined by factors segregating in the experimental population. number of factors should therefore be detectable when the character yield is examined, SO that the variation within the parental products should differ from the variation existing within the F, products. Similarly, since the character is multiplicative, then the means of the two types of product should also differ. In the present experiment both these comparisons are insignificant, although there is a suggestively high mean square for the differences between the two means. Yield, however, is similar to the character tiller number in that the remainder variation of the parental products is much larger than would be expected if genes on chromosome 7B alone were responsible for the heritable variation. Genes on other chromosomes appear to be segregating, and it is such segregation which could be responsible for the lack of significance when comparisons are made between the means and the variance of the two types of product. Indeed, there is strong evidence for stating that the proposed background variation controlling yield is determined by the same genes responsible for the similar variation in tiller number. Thus, the phenotypic correlation coefficient between yield and tiller number for the parental products gives a value of r = f 0.83 f 0.13 which is not significantly different from the value of 1. The possibility that the substitution line, CS (Hope 7R), used in this experiment was either heterozygous or heterogeneous for a gene or genes in the background and that these genes affect yield and tiller number complicates the analysis of these two characters. For tiller number there is evidence that a factor closely linked to or identical to the marker e, on chromosome 7B influences this character. For yield there is no evidence of this kind, and indeed such evidence must be difficult to obtain where the components of a complex character like yield are determined by separate factors which are not closely linked. In the present situation, at least two of the components, grain weight and grain number, are determined by factors which are not closely linked, whereas the third component, tiller number, is probably determined by factors on chromosome 7B and at least one other chromosome of the wheat complement. t least four factors are involved therefore in the control of yield so that the genetic analysis of this character must necessarily involve the isolation of these factors by analysis of the three component characters. It is only then that the genetic control of the character yield per plant can be assessed. Indeed, THODY (1967) has pointed out that a necessary step in the genetic analysis of any complex character should first be an analysis of the character expression itself. By redefining a character it is often possible not only to increase the precision of the genetic analysis but also to establish discontinuities among a segregating population so that the number of factors involved can be determined. Thus the character, steroid concentration in mice, can be assessed in terms of

8 452 C. N. LW whole body weight or in terms of a particular organ. Similarly it is possible to study the type of steroid so that only the concentration of a particular type is measured rather than the concentration of a whole group of steroids. By redefining the character in this way SPICKETT, STEWRT and SHIRE (1967) have shown that a single factor can clearly be shown to be segregating within a population of mice. Without character analysis the same population appeared to have a genetic control which was indistinguishable from being polygenic. Factors and genes: The evidence from the analysis of each of the three characters, height, grain weight and grain number, indicate that all three behave as if a single factor is responsible. Now, in all cases, the analysis is concerned with differences between distributions which are basically bimodal. Comparisons based on statistics calculated as if the distributions are unimodal may therefore be particularly insensitive, since most of the variation will be concerned with the differences between the two modes of two overlapping populations. Consequently, it is possible that each of the proposed factors may be composed of more than one gene, where the gene in this case is defined as a functional unit. To determine whether this is so or not, further generations are necessary, along with further replication, so that adequate progeny testing can be carried out. It may then be possible to say whether the F, products fall into two or more distinct classes. Nevertheless, in spite of these limitations, the analysis of variance has shown that these characters cannot be controlled by numbers of genes distributed evenly along a chromosome. The four markers found on chromosome 7B show varying degrees of association with each of the characters, so that the factors responsible must have different locations. For the moment, therefore, it is worth pursuing the hypothesis that each of the three characters is controlled by a single factor, whilst bearing in mind that the factor in this case could be composed of a complex of genes similar to the effective factors of MTHER (1949). In this event, the proposed single factor will be located at a point on the chromosome determined by the map distances between the constituent genes and the differences in their activity. These proposed factors can be conveniently denoted by the symbols, gn for grain number, gur for grain weight, and ht for height. factor determining tiller number has also been located on chromosome 7B. Whether this factor is the same as the marker e, cannot from the present evidence be stated conclusively. For the moment, therefore, the factor affecting tiller number will be designated, tl. The degree of association with the four markers enables a rough ordering to be made between the four factors. For gn and ht there is evidence that they are linked to the markers, Pc and e,, and ml respectively. This places ht on the long arm of this chromosome and, because of its lack of association with Zr, proximal to ml. The factor, gn, on the other hand, must be located on the short arm and possibly at a position which is distal to e, but proximal to Pc. For tl, as stated in the previous paragraph, the close association with e, could indicate pleiotropy of this marker or close linkage, in which case tl could lie on either arm of the chromosome but close to the centromere. The factor gw, however, shows little association with any of the markers. This

9 LOCTION OF FCTORS IN WHET 453 could suggest that gw is located outside the regions delimited by the markers. Now, it has been suggested that the distance between the two outside markers, lr and Pc, is close to the expected map distance for this chromosome. If this is SO, then gw cannot occur distal to either lr or Pc. This leaves two possibilities: either gw is located on another chromosome to 7B, or gw is situated within a region of this chromosome which is not closely marked, that is the region between ml and e,. The analysis presented so far cannot distinguish between these alternatives. The analysis of the characters together: The study of the single characters has, of course, been based on the differences between univariate distributions. HOWever, there is no difficulty in making comparisons between bivariate distributions based on pairs of characters. The customary way of measuring the variation present when two independent variables are involved is that of the correlation coefficient. The parental products provide a sample of the nonrecombinant chromosomes so that the correlation coefficient between two characters calculated from this sample will give a measure of the degree of association when recombination has not taken place. The F, products, on the other hand, give a measure of the degree of association between characters when recombination might have occurred between the factors responsible for their control. significant difference between these two correlation coefficients must therefore indicate that some recombination has taken place. For example, with close linkage the correlation coefficients for both the parental and F, products will tend to be the same. With loose linkage then the two characters will tend in the F, products to show independence and a correlation coefficient of zero. Furthermore, it is apparent that the difference observed between the parental and F, products is not just the means by which recombination can be detected, the magnitude of the difference must be related in some way to the distance the two factors (say) are apart on the chromosome. Indeed, assuming only single factors, the difference between the correlation coefficients of the parental and F, products can provide an estimate of p, the recombination value itself. Suppose two factors, one affecting character and the other character B. Let the factor effects be additive so that the expression of the two alleles affecting character will be * d, and the expression of the two alleles affecting character B will be * db. The parental products can consequently be defined as follows, where the two alternative alleles for characters and B are -a and B-b respec- tively. Genotype Character Character B Frequency B m+d, m+db Y2 ab m-d, m-db % Similarly, the F, products can be depicted as Genotype B ab b ab Character Character B Frequency m+d, m+db %(I-?) m-d, m-db X(1-P) m+d, m-db Y2P m-d, m+db %P

10 454 C. N. LW where p stands for the recombination frequency between the two characters and m for the general mean for each character. The correlation coefficient for the parental products (rp) must of course equal 1. The coefficient for the F, products (rp) simplifies readily to give so that p = (rp- rf)/2. This relationship applies to situations where both the alleles on each of the nonrecombinant chromosomes act in either a positive or a negative direction. If they oppose each other, then of course r, will equal -1 and rp becomes 2-1. In this event ( rp - rp) /2 will equal p, the recombination fre- P quency. This approach may be applied to the measurements for the four characters grain weight, height, grain number and tiller number, already analysed separately. The presence of an association with the four markers has shown that the factors responsible for a number of these characters can be separated. It now remains to see whether or not the analysis by means of correlation coefficients can produce a similar separation. In each instance, the genetic correlation coefficients (KEMPTHORNE 1957) rather than the phenotypic values have been used in making the comparisons between the two types of product. The standard error of each coefficient has been obtained using the formula given by ROBERTSON (1959): u(h2.) u(h2,) U(,) =- - r2 2% [ hzs I" h2, and the sampling variance of the heritability estimates by the method indicated by OSBORNE and PTERSON (1952). TBLE 2 Genetic correlation coefficients between the characters, grain weight, tiller number, height and grain number for the parental products (rp) and for the F, products (IF) Height Tiller no. Grain weight Parental products (rp) Grain number t 0.13 t 0.35 t 0.02 Grain weight f 0.09 f Tiller number t Height F, products (rf) Grain number c 0.12 t 0.17 f 0.14 Grain weight f 0.11 f 0.26 Tiller number t Height

11 ~ ~~ ~~~~ LOCTION OF FCTORS IN WHET 455 The correlation coefficients for each pair of characters for the parental products ( rp) and the F, products ( rf) are given in Table 2. The estimates of recombination (p) obtained from these coefficients are shown in Table 3. Grain weight and height: The scatter diagrams produced by plotting against each other the means of five replicates for each of these characters are shown in Figure 3. Two diagrams are given: (a) the scatter produced by the parental products and (b) the distribution obtained by plotting the F, products. Both distributions are similar so that some linkage between ht and gw occurs on chromosome 7B. The genetic correlation coefficients, rp and rp, are however significantly different from each other. The factors, ht and gw are therefore separable and give a recombination value of p = 0.27 t This is significantly different from both 0.5 and 0.0, so that linkage occurs, but not close linkage. The analysis of grain weight and height on their own demonstrated that ht was linked to ml and therefore must be located on chromosome 7B. On the other hand, gw showed no linkage with any marker, so that gw could be located on another chromosome of the complement. The present evidence indicates that gw by virtue of its linkage to ht must be located somewhere on chromosome 7B. Grain weight and grain number: The scatter diagrams for these two characters are also given in Figure 3. The parental products show a negative genetic correlation which is very close to the expected value of -1. The F, products, however, give a scatter diagram in which the points are distributed at random, rf = 0.09 * The difference between rp and rf is highly significant (P < 0.001). NOW, gn has been closely linked with the markers, e, and Pc, so that both gn and gw are located on this chromosome. The difference in scatter must therefore reflect the results of recombination between the two factors. The high recombination value of p = 0.56 f 0.07 demonstrates therefore that gn and gw are separated by a distance along the chromosome which is either close to 50 map units or greater. TBLE 3 Estimates of the recombination values between the factors controlling the characters grain weight, tiller number, height and grain number Characters Recombination value p =O p=0.5 Height and grain number 0.55 *** ns Grain weight and grain number 0.56 *** ns t 0.07 Height and tiller number 0.38 * ns i 0.17 Grain number and tiller number 0.32 ns ns t 0.19 Grain weight and height *** *** Grain weight and tiller number 0.21 ns ns t 0.19 * P ** P *** P <

12 456 c. iy. LW 8.4, b' 82 F 80 I 3 p e D O r= ? , I. 4.. r = to height [cmsl r t r7 E 0Q. L c a. L (I, m... *t r=+0~0826+0~1114 * b IO7 r=+0*2867? 0, I a r= groin number FIGURE 3.-Scatter diagrams between the characters grain weight and height (top), grain weight and grain number (middle), and grain number and height (bottom), for (a) the parental

13 LOCTION OF FCTORS IN WHET 45 7 Grain number and height: The bivariate distributions relating to these two characters are given in Figure 3. Once again the parental products give a negative rp which is not significant from the expected value of -1. The F, products also appear to be scattered at random, rf = 0.34 f The factors, ht and gn, are consequently segregating independently to give a recombination value of p = It follows therefore that both ht and gw must be located at map distances from gn which are quite large. lso, the calculated recombination values between ht and gn and between gw and gn are almost identical so that it is not possible to state from the evidence provided so far whether the order is ht gw gn or gw ht gn. The character tiller number: The earlier analyses of tiller number suggest that at least two factors are responsible for control of this character. One of these factors (tl) is situated on chromosome 7B and the other on another chromosome of the complement. Consequently, the first factor (tl) would segregate among the F, products only, whereas the second factor would segregate amongst both the parental and F, products. The differences between the two kinds of product must therefore be influenced by the segregation of the factor present in the background. This segregation will act in such a way as to increase the range of genotypes among the F, products as well as among the parental products, but to a much greater extent. This follows simply from the fact that only the substitution line derivatives among the parental products can carry such a factor, whereas all the F, products are open to such background effects. This increased variation will influence the correlation coefficients between tiller number and another character in two ways. First, the rp values will depart from the expected value of 1 or -1 and second, the difference between rp and rf will depart, in some cases considerably, from that expected when only the factor, tl, on chromosome 7B was segregating. The degree of this departure will depend upon a number of variables, but in general if low values of p, the recombination value between tl and the factor responsible for a second character, are involved, then the difference between rp and r,. will be such as to give an inflated estimate of p. On the other hand, if high values of p occur then the estimates will be smaller. In the present experiment, each of the rp values involving tiller number show large departures from the expected values. lso, only one of the calculated recombination frequencies, that between ht and tl, is significantly different from zero. Because of the high standard errors involved, all the other estimates of recombination show no significant departures from either p = 0 or p = 0.5. On the other hand, the estimates given in Table 4 point to an ordering along the chromosome which is ht gw t2 gn. This is clearly brought out in Figure 4 in which the recombination between any pair of factors is shown. lso, the location of the factors obtained by using correlation coefficients agree closely with those obtained and (b) the F, products. Solid circles represent those families resulting from the cross CS mono 7B x CS (Hope 7B). Open circles to the cross CS mono 7B x CS. The phenotypic correlation coeffilent of each distribution is shown.

14 45 8 C. N. LW by using the four markers, lr, ml, e, and Pc. It will be recalled that ht was linked closely to ml, tl to e,, and gn to both e, and Pc. In other words, the order was ht tl gn along the chromosome. The factor gw was the only one not to show any evidence of linkage to a marker. Since gw has now been shown to be definitely located on chromosome 7B, then following earlier suggestions the most reasonable location for gw would appear to be within a region not closely marked, probably the region between ml and e,. The correlation coefficient analysis does indeed show that gw maps in this region. However, the estimates of recombination obtained in the present analysis give higher values than those indicated by the use of markers. Thus, using the recombination values obtained by the means of the correlation coefficient analysis, the distance between ht and gn would appear to be in the region of 90 units long. In contrast, the marker analysis demonstrated that ht was probably located proximally to ml whereas the most likely position for gn was between e, and Pc. This gives a map distance between ht and gn which is of the order of only 50 units long, so that large differences occur between the WO types of analysis. The most likely reason for this discrepancy is that the estimates of recombination are inflated because of background effects whenever tiller number is investigated as a character. By allowing for this, all four factors, ht, gw, tl, and gn would be much closer together, although by how much is by no means certain until the background effects can be removed from the analysis. linkage with markers 1 Marker-map Correlation map Final map FIGURE 4.-The approximate locations of the factors ht, gw, tl and gn. These locations have been obtained by combining the evidence from the marker and correlation maps.

15 LOCTION OF FCTORS IN WHET 459 DISCUSSION In an earlier paper (LW 1966), the location of factors responsible for the control of the days to ear emergence was described. The comparative ease with which these locations were achieved was ascribed in part to the high heritability of this character. However, the prediction was also made that since the technique allows each derivative to be replicated, it should also be possible to locate the factors responsible for characters with much smaller heritabilities. This prediction has been wholly vindicated in the present work. Support is also provided for THODY S (1961) view that with adequate techniques it is possible to handle experimentally the individual genetic components which determine a continuously variable character. In so doing it is possible to achieve the location of the factors responsible, to measure their individual contributions and to determine their inter-relations with other components of the genetic system (GIBSON and THODY 1962; SPICKETT and THODY 1966; THODY 1967). The analysis of chromosome 7B has benefitted from the presence of four markers Zr, mz, e, and Pc, segregating in the population. The close agreement between the marker analysis and the results obtained using correlation coefficients suggests, however, that even in the absence of markers, the locations of factors responsible for the expression of quantitative characters can still be achieved. Genetic mapping by means of correlation coefficients could therefore be of considerable value where whole chromosome substitution lines are concerned, since adequate genetic markers are rarely available in wheat. n important aspect of the genetic control of the characters studied is that in each instance simple pleiotropy in which one factor affects the expression of two characters has been excluded. ll the characters are controlled by factors which can be separated by genetic analysis and are not tightly linked. This of course assumes that each of the factors is composed of a single gene. If this is not so, then some pleiotropy may occur and will not be detected until the constituent genes are located. However, despite this limitation, the present analysis must indicate that some of the genes are separate both in terms of action and position. Linkages which can be broken by crossing over have therefore been definitely established; as yet there is no conclusive evidence for either tight linkage or pleiotropy. The absence of tight linkage between some, if not all, the genes responsible for the control of the characters under study is of obvious importance to plant breeding. The factors responsible for the control of yield, that is the factors, gw, tl and gn, controlling the three components of yield, lie near to each other on the chromosome, but the map-distance encompassed is at least 40 units long. It is thus possible to recombine these factors quite readily and achieve the positive coupling linkages upon which an increase in yield depends. In the present experiment, chromosome 7B of CS carries allelic factors which act to give ++- expressions for the three component characters, grain weight, tiller number and grain number respectively. Chromosome 7B of Hope must of

16 460 C. N. LW course act in the reverse manner, --+. It should therefore be possible to select out those chromosomes which have undergone a crossover between tl and gn and obtain the two coupling linkages +f+ and ---. These derivatives should then give higher and lower values of yield than either of the parental products. Unfortunately, although there are lines which appear to give higher and lower yields than the parental products, the analysis of yield was complicated by the presence of a factor or factors not on chromosome 7B and segregating in the population. Under these circumstances, the effects of recombination within chromosome 7B are obscured. To establish whether or not an increase in yield can be achieved by selecting such recombinants among the PI products, further backcrosses need to be carried out to remove the effects of the background variation. The large number of factors located on chromosome 7B could suggest that the number of alleles which distinguish one variety of wheat from another will be very large. On the other hand, the variety Hope derives from a cross between a spring, hexaploid wheat, Marquis, and a tetraploid, vernal emmer (CLRK and BYLES 1935). The variety Marquis is white stemmed and is susceptible to both leaf rust and mildew, whereas vernal emmer is purple stemmed and is resistant to both these diseases. This would suggest that the genes Pc, lr and ml on chromosome 7B of the variety Hope derive initially from the tetraploid. Chromosome 7B of Hope could therefore have arisen either directly from the tetraploid, or, alternatively, from a double crossover condition, in which the distal regions stem from the tetraploid and the proximal regions from the hexaploid variety, Marquis. In either event, it is probable that some of the allelic differences observed between chromosome 7B of CS and Hope represent differences which occur between two long-isolated populations, the tetraploid and hexaploid wheats. If this is so, then a large number of allelic differences are not unlikely. study of the allelic differences distinguishing varieties more closely related, a situation which is applicable to many of the varieties now in agricultural use, may give a totally different picture. It need hardly be emphasized that the recognition of genetic factors controlling different phases in the development of the wheat plant will be of great value in the study of the physiological differences for which these factors are ultimately responsible. lso, the study of the relationships which exist between these factors, in terms of biochemistry and physiology, could provide an important approach to the understanding of differentiation in higher plants. I would like to thank MR.. J. WOUND and MR. M. J. COTTON for their help in carrying out these experiments and also MB. VICTOR CHPMN for the assistance he has given in the preparation of the manuscript. SUMMRY Techniques based on the use of intervarietal substitutions in wheat were used to locate factors controlling a number of quantitative characters. Chromosome 7B of the variety Hope differs from that of Chinese Spring by four factors, ht, gw, gn and tl, determining the characters height, grain weight, grain number and tiller number. By establishing significant associations between these characters

17 LOCTION OF FCTORS IN WHET 46 1 and four genetic markers previously located on this chromosome, the approximate positions were obtained of three of the factors, ht, gn and tl. lso, using a method based on the correlation coefficients between any two' of the four characters, estimates of recombination between the factors were derived. This provided strong evidence that the order was ht gw tl gn along the chromosome. The recombination frequencies obtained by this method agree closely with those established by the use of the genetic markers. Since two of the markers are located on the long arm and two on the short arm of this chromosome, the location of the factors in relation to the centromere could be ascertained. In this way, ht and gw were found to be situated on the long arm and gn on the short arm, whereas tl could be on either arm but close to the centromere. CLRK, J.., and B. B. BYLES, 1935 States. U.S. Dept. gr. Bull. 459: KEMPTHORNE, O., 1957 LITERTURE CITED LW, C. N., 1966 The location of genetic factors affecting a quantitative character in wheat. Genetics 53: LW, C. N., and M. S. WO Location of genetic factors for mildew resistance and ear emergence time on chromosome 7B of wheat. Can. J. Plant Sci. 8: MTHER, K., 1949 OSBORNE, R., and W. S. B. PTERSON, 1952 On the sampling variance of heritability estimates derived from variance analyses. Proc. Roy. Soc. Edinb. B 64: ROBERTSON,., : SERS, E. R., 1953 Classification of wheat varieties grown in the United GIBSON, J. B., and J. M. THODY, 1962 Effects of disruptive selection. VI. second chromosome polymorphism. Heredity 17: n Introduction to Genetic Statistics. Chapman and Hall, London. Biometrical Genetics. Methuen, London. The sampling variance of the genetic correlation coefficient. Biometrics Nullisomic analysis in common wheat. m. Naturalist 87: SPICKETT, S. G., and J. M. THODY, 1966 Regular response to selection. 3. Interaction between located polygenes. Genet. Res. 7: SPICKETT, S. G., J. STEWRT, and J. SHIRE, 1967 Genetical variation in adrenal and renal structure and function. Mem. Soc. Endocrinol. 15: THODY, J. M., 1961 Location of polygenes. Nature 191: Genes in the study of continuous variation. Proc. Intern. Genet. Symp. (Brazil), 1966 (in press).