NONALLELIC GENE INTERACTIONS IN THE INHERITANCE OF QUANTITATIVE CHARACTERS IN BARLEY

Transcription

1 NONALLLIC GN INTRACTIONS IN TH INHRITANC OF QUANTITATIV CHARACTRS IN BARLY A. C. FASOULAS AND R. W. ALLARD Uniuersity of California, Dauis, California Received March, 96 TH possibility that nonallelic interactions of genes play a role in the often unpredictable behavior of populations has stimulated many attempts to specify and measure epistasis. As early as 98 FISHR included an epistatic parameter in the genetic model which he proposed for the description of the action of genes controlling continuously varying characters, and in 9 WRIGHT constructed a model in which he expressed deviations from an optimum in terms of interactions of loci in pairs. More recently other workers have proposed epistatic models, among which those of COCKRHAM ( 94), ANDRSON and KMP- THORN (94) and HAYMAN and MATHR (9) differ most from previous models in that they provide for orthogonal subdivision of the epistatic deviations and variance. Basically this subdivision is into interactions of homozygous loci with homozygous loci, heterozygous loci with heterozygous loci, or combinations of homozygous with heterozygous loci. In the case of two equally frequent alleles at each of n diploid loci, -I parameters are required to specify the genotypic value (if position effects, cytoplasmic effects and other special conditions are ignored). Among these parameters n represent additive effects of genes, n represent dominance effects and the remainder represent interactions of nonalleles. Thus, great complexity is possible with respect to epistatic deviations in ordinary populations, which are presumably heterozygous at many loci. One way around the difficulties this complexity causes in the analysis of quantitative genetic variability is to study extraordinary model situations of reduced complexity. As an example, segregation is expected to be much less complex in populations derived from crosses between homozygous lines that are isogenic except for specific marker loci (and adjacent segments of chromosome) than in ordinary populations, and experiments based on such materials may be useful in measuring epistatic deviations and variance. This does not imply that study of such model situations can substitute for direct approaches. However, information gained from study of simplified situations may serve a complementary role in increasing our knowledge of real populations. The present paper reports the results of a study of interactions among small chromosomal segments which differentiate certain otherwise isogenic lines of barley. This study was supported in part by a grant-in-aid (G4Q4) from the National Science Foundation. The authors are grateful to C. A. SUNSON, ARS, United States Department of Agriculture, who made available the stocks on which this study was based. Present address: Aristoleleian University of Thessalonike, Thessalonike, Greece. Genetics 47: July 96.

2 9 A. C. FASOULAS AND R. W. ALLARD TH ISOGNIC LINS The four isogenic lines on which this experiment was based were developed and kindly made available to the authors by C. A. SUNSON. In developing these lines Atlas 46 barley (white lemma, rough awn) was crossed to a variety with orange lemmas () and to another variety with smooth awns (rr). Parallel and independent backcrosses were then made to Atlas 46 during which loci o (linkage group VI) and r (linkage group VII) were held heterozygous. In the case of r 9 backcrosses were made, the first to Atlas and the final six to Atlas 46. Atlas 46, a backcross derived variety resistant to certain foliar diseases, was substituted for Atlas as the recurrent parent when it became available in 946. Six backcrosses to Atlas 46 were made in the case of. One or more generations of selfing followed each backcross in the two series. Intense selection was practiced for the Atlas 46 phenotype during all stages of this program of backcrossing and selfing. After the final backcrosses, the homozygotes oorr and OOrr were extracted by selection during two generations of selfing and crossed to obtain the double heterozygote OoRr. The four possible homozygotes were then obtained by selection in appropriate homozygous F, families derived from a single plant of the double heterozygote OoRr. The crosses were made in such a way that Atlas 46 cytoplasm occurred in all four lines. These four homozygous lines are expected to be isogenic, or nearly so, for all loci except the marker loci and closely linked segments on either side of the marker loci. The expected length of segment introduced in a backcross series has been shown by BARTLTT and HALDAN (9) to be l/t crossover units, with sampling variance l/t crossover units, on each side of the marker locus after t cycles of backcrossing with enforced heterozygosity at the marker locus. Selfing reduces the length of heterozygous segment at twice the above rate because, under self-fertilization, effective crossing-over can occur in both male and female gametogenesis. More recently, HANSON ( 99) has presented exact distributions for heterozygous half lengths, taking chromosome length into consideration. For a chromosome of unit map length the limiting values given by BARTLTT and HALDAN are adequate approximations after the equivalence of about eight generations of backcrossing. The expectations assume that the marker locus is neither terminal nor subterminal, which is the case for the o and r loci. If the selection practiced during the development of the isogenic lines is not taken into account, the estimated half lengths of chromosome segment associated with o and r on either side can be computed to be of the order of.9 f.9 and.o 4.O crossover units, respectively. However, small differences are easily discerned between and within highly homozygous families and selection can be highly effective during a program of backcrossing and selfing of the type by which the present lines were developed. It is probable, therefore, that the map length of the associated segments is substantially smaller than indicated by computations which do not take selection into account. This experiment depended on the testing of stocks in which the two pairs of homologous segments occurred in all possible combinations. The question there-

3 PISTASIS 9 fore arises whether each of the four marked segments was the same in each of the parental lines, and hence in each of the nine possible homozygous and heterozygous combinations; if not, interaction effects might be confounded with the effects of segregation. In appraising this question it is convenient to consider that each of the four isogenic lines was derived from a pair of identical gametes produced by a single doubly heterozygous individual. If the two segments are about six and two crossover units long, as calculated above, the probabilities that no crossovers occurred in the o and r segments are about.94 and.98, respectively, assuming complete interference; and the probability of no crossovers in all four pairs of gametes is approximately (.94) (.98) = /. Conversely, the expected numbers of crossovers in a six-unit and two-unit segment are.6 +., or approximately % in all four lines. Thus, even ignoring the intense selection that was practiced during the development of the isogenic lines, the probability that the integrity of the corresponding segmental pairs was maintained in the final selection of the four parents considerably exceeds the probability that the segments were not identical. Nevertheless, the possibility that crossing-over occurred such that the segments were not the same must be kept in mind in interpreting the results of this experiment. XPRIMNTAL PROCDURS The experimental materials upon which measurements were taken were obtained by crossing the four isogenic lines OORR, OOrr, oorr, and oorr in all possible combinations (including selfs but excluding reciprocal crosses), to produce the genotypes OORR, OORr, OOrr, OoRR, OoRr (oorr X OORR), Oorr, oorr, oorr, and oorr. All crosses, iiicluding selfs, were made in the same manner and under similar environmental conditions to minimize nongenetic differences amongst genotypes. To obtain good stands and synchronous start of the plants, seeds were sown in flats and transplanted to the field at the second leaf stage. The basic field design was of a randomized complete-block type with tea replications in which individual plants, spaced 8 inches apart within and between rows, were the experimental unit. Six sets of the basic design were sown at each of three planting dates approximately one month apart (November, December 8, February ). Hence each of the nine genotypes was represented by a maximum of 6 plants for each planting date, or 8 plants in total. RSULTS DifJerences among genotypes: The significance of observed differences among genotypes was tested by standard analyses of variance for each of the eight characters (Table ). The variance ratio for genotypes was significant for seven of these characters but nonsignificant for the character straw weight. This indicates that the chromosome segments marked by the o and/or I loci were genetically active with respect to seven of the characters but inactive (or that genes within each segment cancelled each other in effect) with respect to straw weight. The straw weight character was consequently not analyzed further.

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5 PISTASIS 9 Variance ratios for planting dates and for sets within planting dates were significant for all characters. This provides evidence that the environment differed from planting date to planting date and from set to set within the three planting dates. Further the frequently significant variance ratios for replications within sets indicates that microenvironmental differences occurred in the experimental area. It should be noted, however, that the item genotypes x sets within planting dates was uniformly nonsignificant. The responses of the various characters were therefore consistent in the differing environments represented by the six sets planted at each of the three dates. This was not always the case, however, over planting dates. In two cases (heading time and spike length) the item genotypes x planting dates was significant, indicating that for these two characters certain genotypes did not respond in the same way in the different environments represented by the planting dates. The general pattern was, however, one of stability of performance over the different environments. Partition of the phenotypic variance: In analyzing the genetic and environmental factors affecting the traits measured in this experiment, it is useful to partition the observed phenotypic variance into three general components as follows: () an environmental component, U;, reflecting random dant to plant variability, including errors of measurement; () a genotypic component, U; ; and () a component, or components, aix,, reflecting interactions of genotypes with the various environments in which the genotypes were grown. The partition of degrees of freedom and the derivation of expectations of mean squares in terms of the relevant population parameters followed standard procedures ( KMP- THORN 97). stimates of the parameters were then obtained by equating observed mean squares to mean square expectations and solving the resulting equations. These estimates of the relevant components of phenotypic variance (Table ) show that the genotypic component of variance was generally much larger than the components of variance due to genotypic-environmental interactions but smaller than the Component of variance due to random plant-to-plant variability. The genotypic components of variance, as expected, were much smaller than have been observed previously for some of the same characters in nonisogenic materials. Partition of the genotypic variance: The next step in the analysis is to partition the genotypic component of variance for each character into component parts. The present experiment provides the three possible genetic phases at locus, i.e., and ; and also the three possible genetic phases of locus r, namely, RR, Rr, and rr-. Considering both loci simultaneously, all nine possible combinations of the phases occur. The situation is thus parallel to a factorial experiment in which two factors (loci) occur at three levels each (COCKRHAM 94; ANDRSON and KMPTHORN 94; HAYMAN and MATHR 9). There are nine observations; consequently eight degrees of freedom are available, two of which can be assigned to linear comparisons, two to quadratic deviations from the linear, and four to interactions. In genetic terminology, additive and domi-

6 ~ 94 A. C. FASOULAS AND R. W. ALLARD nance replace linear and quadratic, respectively. Thus the eight degrees of freedom can be assigned as follows: A A D D = additive effect of locus o = additive effect of locus r = dominance effect of locus o = dominance effect of locus r A A = interaction additive in o x additive in r A D = interaction additive in o x dominance in r D A = interaction dominance in o x additive in r D D interaction dominance in o x domifiance in r. In computing the portion of the total genotypic variance corresponding to each degree of freedom, it is convenient to use orthogonal sets (SNDCOR 946). The eight possible partitions of the variance correspond to those of COCKRHAM (94) when gene frequency is / at both loci and the coefficient of inbreeding (F) is /. stimates made in the present experiment can be used to compute expected variances for populations in which gene frequency is not $$ and F f: / only if there is no interaction between the various components of variance and the gene frequencies and coefficients of inbreeding. Mean phenotypic values for each of the nine genotypes are given in Table and the mean squares corresponding to each of the eight degrees of freedom are in Table 4. Assuming that both genotypes and environments are fixed sets, the appropriate denominator for the variance ratio for the test of the significance of genetic effects associated with individual degrees of freedom is the error mean square value from Table. Under the assumption that the genotypes and environments are random sets, the denominator for the variance ratio is the appropriate interaction term in this table. The asterisks in Table 4 refer to the first of these tests of significance; however, both tests lead to nearly identical conclusions regarding the significance of the individual additive, dominance and epistatic effects of genes. Thus, additive effects (A and A )were significant in among 4 cases, i.e. individual additive effects were significant in 79 percent of cases. Additive x additive interaction effects were significant in six out of seven or 86 percent of cases, followed by dominance x dominance effects (7 TABL Phenotypic values for all characters. ach ualue is the mean of 8 plants Rlem phenotypic values OOri OoRR OoRr Oorr Cltar acter Heading time Plant height Number of spikes Yield of spikes Spike length Spike weight Spike density OOHR ,6 OORr ,6.6,46. oorr oorr oorr ,8,4

7 PISTASIS 9 percent), dominance effects (4 percent), and additive x dominance effects (4 percent) of cases. The foregoing analysis shows in a direct way which among the additive (A', A"), dominance (D', D"), and epistatic effects (A"'', A'D", D'A'', D'D'') were significant and which were not. It would aid in interpretation, however, to know the relative magnitudes of the variances associated with the various additive, dominance, and epistatic effects under study. Appropriate estimates of components of variance associated with individual degrees of freedom can be obtained from the data of Table 4 in a manner analogous to that by which U:, ~, and uix were estimated earlier. The mean squares which appear in Table 4 were calculated from phenotypic values, and they consequently are inflated by components in U; and U; ' which must be removed to obtain unbiased estimates of genotypic variance. stimates of the components of genotypic variance, expressed in percent of the total genotypic variance, appear in Table. The following conclusions can be reached from these estimates: () For some characters (e.g., plant height) segment o was the more active genetically and for other characters (e.g., spike density) segment I was the more active; () The TABL 4 Mean square ualues for each of eight components of genotypic variance Heading Plant Number of Yield of Spike Spike Spike time height spikes spikes length weight density A' 8.89" 4.** 8." *' 9.78" A" 4.'* 8.*' 69.' '' 7.6'* D' 7.9" ' 4. 8.".6 D" 7.9' 6.6' A'"'.47" 6.4" 78." 66.67'.".7 A'"' ' D'A" 9.6** D'D'' ** 8.6''.7** * P=.. ** P=O.Ol (for degrees of freedom versus 9s). o.ooooo.8**.4.69*.66"..848 *.7648' TABL Components of genotypic variance expressed in percent of total genotypic uariance Heading Plant Number of Yield of Spike Spike Spike Variance height spikes spikes length weight density A' A" D' D'' A'A" A'"' D'A'' D'D''

8 96 A. C. FASOULAS AND R. W. ALLARD proportions of the genetic variance associated with the eight individual degrees of freedom varied strikingly from character to character; () Averaged over all characters the additive variance was the largest (6 percent), followed by epistatic variance ( percent) and dominance variance (three percent) ; (4) Among the epistatic components the additive x additive and dominance x dominance Components were larger than the two additive x dominance components. which were always small and were frequently zero. DISCUSSION This experiment was based on two short chromosome segments which had been placed in an otherwise isogenic background by a combination of backcrossing and selfing. One of these segments () was probably not longer than six crossover units and the other (r) was probably not more than two crossover units in length. The linkage map of barley indicates that six of the seven pairs of chromosomes of this species are at least crossover units in length and some chromosomes are considerably longer than crossover units. Only chromosome VI is so incompletely mapped that statements concerning its minimal length are meaningless. Consequently the o and r segmental pairs together probably represent less than one percent of the total map length of the species. Due to the isogenicity of background genotype, these two segmental pairs can be regarded as representing a genetic system in themselves. Perhaps the main conclusion of the experiment is that a substantial part ( percent averaged over seven quantitative characters) of the genotypic variance attributable to these two short chromosome segmental pairs was associated with interactions of a nonallelic type. Since there is no reason to believe that these segments represent a biased sample among the or more equivalent segments which constitute the entire genotype of barley, it seems likely that two-segment epistasis of the type associated with the o and r segments may be a common feature of quantitative genetic systems. It follows that epistatic interaction systems may be very complicated in ordinary hybrids which are presumably heterozygous for many such segments. The present experiment provides no direct evidence on higher order interactions. But even if they do not occur, the many two locus types which are suggested by the present results could in themselves lead to bewildering complexity without the further complications of multilocus interactions. SUMMARY Intercrosses among four homozygous isogenic lines of barley differing with respect to two pairs of short chromosomal segments were used to study the relative importance of additive, domillance, and epistatic gene action in the inheritance of eight quantitative characters. These two chromosomal segments were found to be genetically active for seven among the eight characters. On partitioning the phenotypic variance into components associated with environment ( U:), genotype (U;), and genotypic-environmental interaction (U: ) it was found

9 PISTASIS 97 > uix. The component uix was small enough for each of the that U; > U: characters to indicate that different genotypes performed in a reasonably consistent manner in each of the environments in which the experimental materials were grown. The intercrosses among the isogenic lines provided nine genotypes and eight degrees of freedom which were used to obtain estimates of components of genoty-pic variance as follows: U:, U:, (representing the additive genetic variance associated with the two segmental pairs) ; U:, and U;, (representing the dominance variance) ; and U;,,,,, U;, U;, and u,,,,,(representing the additive X additive, additive x dominance, and dominance by dominance intersegmental interactions). Averaged over seven characters, the additive variance (U:, +U;,,) accounted for more than half of the total genotypic variance (6 percent). The epistatic variance (u:,~,, +U;, + U, + U:,) accounted for most of the remainder ( percent), and the dominance variance for only a small part of the total (three percent). The observation that epistatic variance constituted a major part of the total genetic variance for these randomly-chosen segmental pairs suggests that epistatic gene action may also be a feature of the many comparable segmental pairs which might segregate in ordinary hybrids. Consequently if the r and o segments are a typical sample of these segmental pairs an enormous number of different epistatic situations may be possible. Apparently genetic analysis of hybrids which segregate simultaneously for several or many chromosomal segments will be extremely complex. LITRATUR CITD ANDRSON, V. L., and. KMPTHORN, 94 A model for the study of quantitative inheritance. Genetics 9: BARTLTT, M. S., and J. B. S. HALDAN, 9 The theory of inbreeding with forced heterozygosis. J. Genet. : 7-4. COCKRHAM, C. C., 94 An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 9 : FISHR, R. A., 98 The correlation between relatives on the supposition of Mendelian inheritance. Trans. Roy. Soc. dinburgh : 994. HANSON, W. D., 99 arly generation analysis of lengths of heterozygous chromosome segments around a locus held heterozygous with backcrossing or selfing. Genetics 44: HAYMAN, B. I., and K. MATHR, 9 The description of genic interactions in continuous variation. Biometrics : KMPTHORN, O., 97 An introduction to Genetic Statistics. John Wiley and Sons. New York. SNDCOR, G. W., 946 Statistical Methods. Fourth edition. Iowa State College Press. Ames, Iowa. WRIGHT, S., 9 The analysis of variance and the correlations between relatives with respect to deviations from an optimum. J. Genet. : 4-6.