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Generation Means Analysis of the Twin-Ear Trait in Maize T. E. Frank and A. R. Hallauer The twin-ear trait in maize (Zea mays L_) is defined as having two separate ears, each enclosed within separate husks and separate shanks attached to the same node. The objective of this study was to evaluate the genetic effects for twin-ear penetrance and expressivity by using generation means analysis for twin-ear inbreds A and B, each crossed to Inbreds B79 and Mo17. Progeny generation means suggested twin-ear shoot formation was recessive to single-ear shoot formation. Additive and dominance effects for penetrance were adequate In explaining the variation of genetic effects for A x B79, A x Mo17, B x B79, and B x Mo17 because the additive and dominance model accounted for 97%, 97%, 94%, and 95% of the total variation in genetic effects, respectively. All four crosses had positive additive effects and negative dominance effects estimates for penetrance that were significant and unique due to the relative unimportance of epistatic effects. Genetic effects estimates are considered unique when epistatic effects are not Important Twin-ear ear formation also was recessive to single-ear ear formation. B x B79 expressivity had a significant and unique positive estimate of additive genetic effects. Significant and unique positive estimates of additive and dominance genetic effects were found for A x B79 expressivity. A x Mo17 and B x Mo17 additive and dominance genetic effects estimates for expressivity were not unique. Twin-ear penetrance and expressivity fit the definition of a threshold trait or character in this study. From the Department o( Agronomy, 1515 Agronomy Hall, Iowa State University, Ames, IA 50011-1010. This U Journal Paper no. J-l 6866 of the Iowa Agriculture and Home Economic! Experiment Station, Ames, Iowa; project no. 3082. This article was part of a thesis submitted by T. E. Frank In partial fulfillment of the requirements for an M.S. degree. Journal of Heredity 1997;88:46ft-474; 0022-1503/97/J5.00 Distinct and unique maize (Zea mays L.) ear phenotypes have been reported. Collins and Doyle (1911) described a true breeding variety named Quachi, in which branching of the ear occurs above a single shank and one husk encloses the doubleeared maize. Ramosa-type ears were first reported by Gernert (1912) as a mutation in a strain of the Learning variety at the University of Illinois. Gernert defined ramosa as "a cone-shaped ear In outline that gives the appearance externally of being composed of a mass of kernels borne on numerous irregular branches." Gernert observed that ramosa was reproduced faithfully in progeny, covered with one normal husk, and attached to the node by a single shank. Bearsfoot, or imperfect fasciated ear phenotypes, are two ears fused from the butt to near the tip of the ear that arise from a single shank and are enclosed by common husks (Kempton 1923). Kempton (1923) also described a partially bifurcated ear, where the ears appear fused cylindrically from the base to near the tip, but the tip shows two distinct ears that are enclosed by a single husk. Kempton (1923) also reported a form of branching that is common among sweet corn cultivars in which a branch arises at the base of the ear inside the innermost husk. The branch is also enclosed in several husks, but rarely has well-developed seeds, although the rows are extremely distinct. Frontispiece, a maize variety that originated from the Pawnee Indians of Nebraska, typically has ears consisting of four-rowed branches arising from the base of the ear, with fully developed seeds, but sometimes revealing only glumes and lacking fully developed seeds (Kempton 1923). The branched ears are enclosed by common husks and attached to the node by a single shank. Hallauer (1984) characterized a unique maize ear-branching trait independently in an S2 progeny of BS10(FR)C2-2388-10 and in an S5 progeny of BSAAo.2 and named the trait twin-ear. Twin-ear is defined as having two separate ears, each enclosed with separate husks and separate shanks attached to the same node. Twin-ear expression for the S2 progeny per se was 67%. Twin-ear expression of S2 progeny 469 crosses to BSAAo2, B37o2, and Oh43o2 was 5.4%, 18.2%, and 0%, respectively. The S2 progenies were self-pollinated to the S7 generation. Twin-ear expression of the S7 generation was 16%, but progenies ranged from 0-42.1%. Expression of twin-ear in S8 progenies was 37.9%, with a range among progenies from 0-85%. Additional evaluations of twin-ear for estimates of penetrance were conducted in 1985 and 1986 with 65 progeny rows, 25 plants/row (Hallauer 1988). Penetrance averaged 83% and 79% in 1985 and 1986, respectively, and ranged from 64-100% in 1985 and from 56100% in 1986. Testcrosses of twin-ear plants by Hallauer (1988) to B77, B79, B88, B90, B91, and Mol7 did not produce progenies exhibiting the twin-ear trait, except for three plants in the Mol7 testcross. Hallauer (1984) was unable to isolate a pure strain with 100% expression of twin-ear upon continued self-pollination of the twin-ear plants. Estimates of genetic effects can by used to assist in the interpretation of phenotypic variation (Hayman and Mather 1955). Estimation of genetic effects that control a plant trait can be accomplished with a generation means analysis. Generation means analysis is a very useful tool because genetic information is lacking regarding the twin-ear trait in maize. Our objective was to evaluate the genetic effects for twin-ear penetrance and expressivity by using generation means analysis. Materials and Methods Parental Material Background and Hybridization Twin-ear inbred lines used in this study were developed by two separate crosses of an S5 BSAAo2 line by an S2 BS10(FR)C22388-10 line. The two twin-ear S8 inbred lines were derived using ear-to-row selection and are designated as A and B. Additional inbreds included in the study were the prolific Reid Yellow Dent inbred line B79, derived from BS10(FR)C 10-98, and the predominantly single-ear Lancaster Sure Crop inbred line Mo 17, derived from CI187-2 X C103. Crosses made during the summer of 1991 for the development of the progeny generations for field evaluations were A x B79, A x Mol7, B X B79, and B X Mol7. The F,, F2, BC(P1), and BC(P2) generations were produced for each of the four crosses during the 1992 and 1993 summers. PI always refers to the twin-ear inbred line and P2 to either B79 or Mo 17 in any one cross. The F2 was developed by selfing the F, generation. 4 7 0 The Journal erf Heredity 1997:88(6) BC(P1) and BC(P2) refer to the backcrosses of the F, to the PI and P2, respectively. Field Plot Methods Field evaluations for the 20 entries were grown in a randomized complete-block design with three replications at the Agronomy and Agricultural Engineering Research Center near Ames, Iowa, in 1993 and 1994. In the 1993 growing season rainfall was above normal and summer temperatures were relatively cool. The 1994 growing conditions were favorable and nearly ideal for maize development. The experimental unit was a four-row plot for the PI, P2, and F, generations, a six-row plot for the BC(P1) and BC(P2) generations, and an eight-row plot for the F2 progeny generation. The length of the rows, including 61 cm alleys, was 5.49 m with 76 cm between rows. Four-, six-, and eight-row plots were used to reduce intergenotyplc competition between plots of different generations and to sample adequately the genetic variability within generations. Data were not collected from the two outside rows of a plot. End plants from the interior plot rows were sampled. Plots were machine-planted and thinned to 20 plants/row at the five-leaf stage. All ear trait data were identified by plot, row within plot, plant within row, and finally, nodal location on the plant to maintain data recorded on an individual plant node basis. When mature, the plots were hand harvested, air dried, and shelled, keeping each individual plant node Identity separate. Data were collected for four traits: the total number of shoots (ST) found at the top three ear nodes on each plant after flowering; the total number of ears (ET) hand harvested at the top three ear nodes on each plant; penetrance (PE) (Figure 1A), defined as the total number of plants having at least one twin-ear shoot during pollination divided by the total number of plants in which shoot total data were recorded; and expressivity (EX) (Figure IB), defined as the total number of plants expressing at least one twin-ear ear after pollination divided by the total number of plants expressing at least one twin-ear shoot during pollination. For penetrance and expressivity to occur, the plants must have the twin-ear allele(s). B79 and Mo 17 do not have the allele(s) for twin-ear, and no plants of B79 and Mo 17 were observed with twin-ear shoots or ears. Statistical Analyses Analysis of variance (ANOVA) of a randomized complete-block design with three replications for each year was conducted by considering replications and environments as random effects and generations as fixed effects. The combined ANOVA and pooled error mean squares were obtained by using an unweighted means analysis. The pooled linear additive model is K1|k = p. + e, + r,(0 + & + (ge)ik + e^ where yijk denotes the ftth generation (g) in the yth replication (r) at the rth environment (e) where / = 2, y = 3, and k = 6. Generation means analysis was conducted using the model of Hayman (1958,1960) for each cross pooled across environments. The linear additive model for the feth generation is gk = m + (a)a + (0)d + (pF)aa + (2ap)ad + (ff)dd (Hayman 1960; Mather and Jinks 1982), where a and fi are the coefficients for the genetic effects for the particular generation being estimated (Hayman 1958). Notation of parameters for the model used were those of Gamble (1962), where m is the mean based on the F2 population, a is the pooled additive genetic effects, d is the pooled dominance genetic effects, aa is the pooled additlveby-additive genetic effects, ad is the pooled additive-by-dominance genetic effects, and dd is the pooled dominance-bydomlnance genetic effects over all loci. Genetic effects were fit sequentially beginning with the additive model and then the additive and dominance model. A model was deemed adequate when the lack-of-fit (LOF) mean square was not significant when tested against the generation-by-environment interaction mean square. Unique estimates of additive and dominance effects exist when the LOF is found to be nonsignificant for the additive and dominance model because LOF represents the additive-by-additive, addltive-by-domInance, and dominance-by-dominance digenic epistatic effects (Hayman 1960). Estimates of additive and dominance genetic effects were calculated for each cross by using least squares regression analyses. In matrix notation, p = (X'X)-'(X'Y), where P is the column vector of genetic effects being estimated, X is the matrix of genetic effects coefficients, and Y is the column matrix of observed generation means for a cross. Standard errors of the estimated genetic effects were calculated as the diagonal elements of the solution equation, SE(/9) = [(XTQ-'^OS, where a2 is the error variance for each cross estimated by the generation-by-environment interaction mean square (Steel and Torrie 1980). B Figure 1. Maize twin-ear inbred line A. (A) Twin-ear shoots during pollination in early July are used to calculate penetrance. Penetrance is the total number of plants having at least one twin-ear shoot during pollination divided by the total number of plants in which shoot total data were collected. (B) Twin-ear ears in late August after pollination was completed are used to calculate expressivity. Expressivity is the total number of plants expressing at least one twin-ear ear after pollination divided by the total number of plants expressing at least one twin-ear shoot during pollination. Frank and Hallauer • Maize Twin-Ear Trait Generation Means Analysis 4 7 1 Results and Discussion cent of SSGMA A ** • a D d BLOF • 80.0 70.0 *• in 10 50.0 30.0 | »* • •• 60.0 • I • • a> a. 40.0 SS Model Twin-Ear Penetrance Mean penetrance for the twin-ear parents were 0.83 and 0 for B79 and Mol7, respectively (Table 1). Generation means were similar between the A x B79 and A x Mol7 crosses, as were generation means between B x B79 and B x Mol7 generations. Progeny means for B twin-ear line crosses to B79 and Mol7 tended to be less than progeny means for A twin-ear line crosses to B79 and Mol7. B x Mol7 BC(P2) plants did not produce any plants with twin-ear shoots. Backcrosses to the twin-ear parent tended to Increase penetrance means for all four crosses. Progeny generation means indicate that twin-ear shoot formation was recessive to singleear shoot formation. Highly significant (P £ .01) differences were detected among penetrance generation means for all four crosses. Least significant differences (LSD) among generations within a cross ranged from 0.04-0.08. No significant interactions of generations by environments were found for A x B79, A x Mol7, B x B79, and B x Mol7 (data not shown). The generation-by-environment mean squares were smaller than error mean squares for A x Mo 17 and B x B79 penetrance (data not shown). Regression of the additive and dominance effects model determined that additive and dominance effects mean squares were highly significant for the four crosses (Figure 2A). LOF mean squares were significant (P rs .05) for A x B79 and highly significant for A x Mol7, B x B79, and B x Mol7, indicating that the additive and dominance effects model was not adequate in explaining the genetic effects. Additive genetic effects, however, accounted for 81%, 77%, 68%, and 69% of the total genetic effects variation for A x B79, A x Mol7, B X B79, and B X Mol7, respectively. Dominance genetic effects vary an ad- = I 20.0 10.0 ^^H 0.0 L** AxB79 AxMo17 AxB79 A x Mo17 ~ H him 1 I n B x B79 B x Mo17 B o V) (A c 0) a 0) Q. "5 •a o V) V) BxMo17 BxB79 Figure 2. Percentage distribution of the generation means analysis (GMA) using six generations [PI P2, F,, F,, BCl (PI), and BCl (P2)] to calculate pooled additive genetic effects (a), pooled dominance genetic effects (d), and lack-of-fit (LOF) sum of squares (SS) for four maize crosses (A X B79, A X Mol7, B X B79, and B X Mol7), where A and B are twin-ear maize lnbreds. *,** are significance probability levels of 0.05 and 0.01, respectively, for a, d, and LOF mean squares In the combined ANOVA. Mean squares In the combined ANOVA which do not have significance probability levels of 0.05 and 0.01 are considered not significant (ns). (A) Twin-ear penetrance (PE). (B) Twin-ear expressivity (EX). Table 1. Means for twin-ear penetrance (PE) In four maize crosses for the six generations used for the generation means analysis Cross A X A X B X B X Generation B79 Mol7 B79 Mol7 PI 0.83 0.00 0.07 0.11 0.46 0.02 0.02 0.08 0.83 0.00 0.01 0.10 0.49 0.03 0.01 0.04 0.83 0.00 0.00 0.04 0.28 0.01 0.02 0.06 0.83 0.00 0.00 0.04 0.29 0.00 0.02 0.07 n F, F, BC(P1) BC(P2) SE' LSD (0.05) • SEs of the generation means for each cross. 4 7 2 The Journal of Heredity 1997:88(6) Table 2. Estimates of genetic effects on generation means and their standard errors (SE) for twin-ear penetrance (PE) In fonr maize crosses when additive (a) and dominance (d) effects are Inclnded In the model Genetic effects ± SE Cross A A B B X B79 X Mol7 X B79 X Mol7 0.215** 0.2O9** 0.156** 0.158** ± 0.010 ± 0.004 ± 0.007 ±0.008 0.414** 0.423** 0.387** 0391" ± ± i ± 0.015 0.007 0.010 0.012 -0356** -0.403** -0.448** -0.447** ± ± ± i 0.028 0.013 0.019 0.023 • m = mean of the F, generation; a = pooled additive effects; d • pooled dominance effects over all loci. ' significant at the 0.05 and 0.01 probability levels, respectively. Table 3. Means for twin-ear expressivity (EX) in fonr maize crosses for the six generations used for the generation means analysis Cross Generation A X A X Mol7 B x B79 B X Mol7 PI P2 F, F, 034 0.00 0.68 0.14 0.61 0.47 0.10 035 034 0.57 0.00 0.00 050 0.60 033 0.10 036 057 0.00 0.00 0.42 0.72 0.00 0.07 0.25 BC(P1) BC(P2) SELSD (0.05) 0.00 0.00 0.48 0.65 0.13 0.10 0.35 " SEs of the generation means for each cross. ditional 16%, 20%, 26%, and 26% of the total genetic effects variation for A x B79, A x Mol7, B x B79, and B x Mol7, respectively. The additive and dominance effects model seemed adequate in explaining the genetic effects for A x B79, A x Mo 17, B x B79, and B x Mol7 because the model accounted for 97%, 97%, 94%, and 95% of the total variation, respectively. Although statistically significant in some instances, LOF, or epistasis, was relatively unimportant for penetrance of twin-ear. Estimates of additive genetic effects were highly significant for all crosses (Table 2). Additive genetic effects estimates were positive for all crosses and ranged from 0.387-0.423. All crosses had highly significant negative estimates of dominance genetic effects that ranged from -0.356 to -0.448. The negative dominance effects indicate that twin-ear penetrance is a recessive trait. All estimates of additive and dominance genetic effects for the four crosses are unique In the absence of epistasis, but they would be confounded with epistatic genetic effects if LOF mean squares are significant. Twin-Ear Expressivity Mean expressivity for twin-ear parents A and B was 0.34 and 0.57, respectively, and 0 for B79 and Mol7 (Table 3). Means for twin-ear expressivity were zero for the B x Mol7 BC(P2) and the A X Mol7, B x B79, and B x Mol7 crosses, suggesting re- cessiveness for twin-ear ear formation. Backcrosses to the twin-ear parent tended to increase the BC(P1) expressivity means for all crosses similarly, whereas backcrosses to the B79 and Mol7 parents had varying effects on the BC(P2) expressivity means. Expressivity is a function of plants producing twin-ear ears from twin-ear shoots. The A x B79 F,, A x Mol7 F2, and all BC(P1) crosses simply had a higher percentage of plants that produced twinear ears from twin-ear shoots than the twin-ear parents. Effects of inbreeding on the twin-ear parents are inferred from the larger but not statistically different means reported for the A x B79 F,, A X Mol7 F2, and all BC(P1) generations. LSD for twinear expressivity was higher than twin-ear penetrance LSD due to the larger standard error (SE) among generation means. A x B79, A X Mol7, and B x B79 exhibited significant differences among generations, and highly significant differences among generations were detected for B x Mo 17. No environment-by-generation interactions were present when F tests were conducted for the four crosses, indicating additivity of genotypic and environmental effects (data not shown). Regression of the additive genetic effects model detected a highly significant additive effects mean square and a nonsignificant LOF mean square for B x B79 (Figure 2B). Additive genetic effects explained 52% of the total genetic effects variation for B x B79. The Table 4. Estimates of genetic effects on generation means and their standard errors (SE) for twin-ear expressivity (EX) In four maize crosses when additive (a) and dominance (<f) effects are Included in the model Genetic effects ± SE Cross m- A A B B 0.416" ± 0.040 X X X X B79 Mol7 B79 Mol7 0.261" ± 0.041 0320" ± 0.042 0.267" ± 0.029 0.163* 0.239* 0.281" 0370** + 0.061 ±0.061 ±0.063 ± 0.044 0.509" -0.150 -0.165 -0.200 ± 0.114 ±0.115 ± 0.119 ± 0.082 • m = mean of the F, generation; a = pooled additive effects; d •• pooled dominance effects over all loci. ' significant at the 0.05 and 0.01 probability levels, respectively additive and dominance genetics effects regression model detected significant LOF mean squares for A x Mol7 and B x Mo 17. Therefore epistatic effects are important in explaining the genetic effects for A x Mol7 and B x Mol7. Fitting of the additive and dominance genetics effects regression model detected a significant additive effects mean square, a highly significant dominance effects mean square, and non significance for the LOF mean square for A x B79. Additive and dominance genetic effects explained 18% and 51% of the total genetic variation, respectively, for A x B79. A x Mol7 and B x Mol7 additive and dominance genetic effects estimates for expressivity are not unique, but are confounded with epistatic effects because the LOF mean squares are significant (Figure 2B). A x B79 had a significant unique additive effect estimate of 0.163 and a highly significant unique dominance effect estimate of 0.509 (Table 4). Detection of the dominance genetic effect for A x B79 occurred because twin-ear ears were found in the F, generation (Table 3). The unique additive genetic effects estimate for B x B79 is 0.281. Presence of significant, unbiased additive effects in A x B79 and B x B79 indicate that accumulation of favorable alleles is possible for twin-ear ear development. Lack of dominance effects, except for A x B79 suggest that dominance did not have a role in twin-ear ear formation. Dominance effects were important in all crosses for the twin-ear shoot formation. Therefore the dominance effects detected for A x B79 twin-ear ear formation are possibly controlled by the same allele(s) that control twin-ear penetrance. Implications Twin-ear penetrance was controlled mainly by additive genetic effects and partially by dominance genetic effects, although confounding with epistatic effects can occur in some instances. Additive genetic effects are important for B x B79 twin-ear expressivity, but primarily dominance genetic effects and some additive genetic effects were responsible for controlling A x B79 twin-ear expressivity. Examination of the generation means per se (Tables 1 and 3) and genetic effects estimates (Tables 2 and 4) for each cross indicate that twin-ear is a recessive trait and that non-twin-ear is almost completely dominant to the twin-ear trait. Hallauer (1988) also found the twin-ear phenotype to be masked in twin-ear line test crosses with six non-twin-ear inbreds. Twin-ear Frank and Hallauer • Maize Twin-Ear Trait Generation Means Analysis 4 7 3 p e n e t r a n c e a n d expression s e e m s t o de, ,_ .... , Falconer DS and MacKay TFC, 1996. Introduction to quantitative genetics, 4th ed Essex, England: Longman. dltive and dominance variation In generation means H. Genetlca 31:133-146. Gamble EE, 1962. Gene effects In corn. Part 1. SeparatlOn and relative Importance of gene eflects lor yield can j Plant Sd 42:339-348. ^ ^ m m 2 AnewsubspeciesofZeamo)sLAm Nat 46:616-622. Ha]lauer ^ 1 9 8 4 T w t l > < a r expression. Maize Genet Newsi 58:27-22. HaUauer AR, 1988. Penetrance and expressivity of twin ears. Maize Genet Newsl 62:2-3. Hayman Bl, 1958. The separation of eplstatlcfrom addltive and dominance variation In generation means. H<:redlt I 2 : 3 7 1 3 9 0 y - Hayman Bl, 1960. The separation of eplttatlc from ad- Hayman Bl and Mather K, 1955. The description of genlc Interactions In continuous variation. Biometrics 11: 69-82. ^mpton JH, 1923. Heritable characters of maize. Part ^ Branched ears. JHered 14:243-251. Ma her K g ' , ^Jlnks ^J^2' ^ ^ !T e t ' ( ? : h t h e ^ i S " "" S t e e ] R G D ^d Torrie JH, 1980. Principles and proced u r e s , n s t a O s U c s . a biometrical approach, 2nd ed. N e w York: McGraw-Hill. Received May 30 1996 Accepted November 29, 1996 Corresponding Editor Susan Gabay-Laughnan pend on some specific conditions of gene e x p r e s s i o n d u r i n s t h e o n t o c e n v of t h p cApressioii u u n n g m e o n t o g e n y 01 m e plant, which agrees with the observation made by Hallauer (1984). Twin-ear penetrance and expressivity in this Study fit t h e definition of a threshold trait or character as defined by Falconer and MacKay (1996). References Collins CN and Doyle CB, 1911. Note, on southern MexIco. Natl Geog Mag 22:301-320. 4 7 4 The Journal of Heredity 1997:88(6)