Reciprocal Recurrent Selection Research Articles

Genetic Changes Associated with Different Methods of Recurrent Selection in Five Maize Populations: I. Directly Selected Traits

Several methods of recurrent selection have been developed in maize (Zea mays L.), but information is lacking on which is most effective. A confounding factor is that progress may be hindered by inbreeding depression associated with random changes of allelic frequencies due to the constraints of small effective population sizes. The objectives of this study were to (i) compare the effectiveness of four selection methods in five maize populations (CGSynA, CGSynB, CGG, CGN, and CGW) improved for performance indices involving grain yield, grain moisture, and plant lodging, (ii) separate effects of selection from those due to random drift, and (iii) estimate additive and dominance gene effects contributing to response to selection. Four selection procedures were compared: modified ear‐to‐row (ME) in CGSynA, CGSynB, CGG, and CGN; half‐sib family (I‐IS) in all five populations; seffed progeny (S) in all five populations; and reciprocal recurrent selection (RRS) in CGSynA and CGW. In general, performance indices increased with concomitant increases in yield and decreases in moisture and lodging. Generally, S was the most effective selection procedure and HS was second best. Response to selection was attributed to changing the frequencies of alleles with mostly (i) dominance effects. in ME selection, (ii) additive effects in S and, (iii) either dominance or additive effects in HS and RRS. Estimates of genetic drift effects were predominantly of the opposite sign from the direction of response to selection. The S procedure resulted in the greatest genetic drift in three of the five populations, whereas HS suffered minimal genetic drift effects. This study indicated that there is no selection method that is best under all circumstances.

Genetic Changes Associated with Different Methods of Recurrent Selection in Five Maize Populations: II. Indirectly Selected Traits

Recurrent selection in a population can result in changes in traits other than those used directly as selection criteria. Such changes usually are not easily predicted or understood because they do not occur in a consistent manner. This study was conducted to compare changes in indirectly sdected traits (plant height, ear height, tassel branch number, and days to anthesis and silking) in five maize (Zea mays L.) populations (CGSynA, CGSynB, CGG, CGN, and CGW) that were selected for performance indices based on grain yield, grain moisture, and standability. Four selection methods were compared: modified ear‐to‐row (ME) in CGSynA, CGSynB, CGG, and CGN; half‐sib family (HS) in all five populations; selfed progeny (S) in five populations; and reciprocal recurrent selection (RRS) in CGSynA and CGW. Generally, response to indirect selection depended on (i) the selection method used, (ii) the initial mean value of a trait the original population, and (ii) correlations between indirectly and directly selected traits. The combination of these factors seems to determine whether an indirectly selected trait will increase, decrease, or remain constant in advanced cycles of selection. No general trend for response to indirect selection was observed for ear height, plant height, or tassel branch number. Days to anthesis and silking were mainly reduced. This uniform response of days to tlowering was partly due to non‐documented selection against later flowering plants in initial cycles of selection. Genetic drift generally acted in the opposite direction from response to selection, and I‐IS resulted in the least genetic drift. Generally, it seems that the indirectly selected traits changed in the way that would most efficiently contribute to the desirable changes of the directly selected traits.

Genetics of Tolerance to Soil Acidity in Tropical Maize

Maize (Zea mays L.) is grown on approximately eight million hectares of acidic soils, where yields are low because of the toxicity of AI and Mn and deficiency in Ca, Mg, and P. Maize cultivars tolerant to soil acidity would increase yields on such soils. A diailel study was conducted involving six soil‐acidity tolerant and two susceptible segregating populations to identify superior germplasm to develop cultivars for acidic soils. The eight populations and their 28 crosses were evaluated in seven acidic soil environments. Tolerant populations averaged higher in yield (2.19 vs. 1.58 Mg ha−1; P < 0.01), ears per plant (0.79 vs. 0.64; P < 0.05), and ear height (61.6 vs. 51.4 cm; P < 0.01), and fewer in days to silk (68.8 vs. 69.7 d; P < 0.05) than the susceptible populations. Mean squares of parents vs. crosses were highly significant for yield, ear height, and ears per plant, and significant for days to silk, indicating beterosis for these traits. Crosses between tolerant populations tended to yield higher (3.00 Mg ha−1) than those between tolerant and susceptible populations (2.40 Mg ha−1) and between susceptible populations (2.01 Mg ha−1). General combining ability (GCA) was highly significant for all traits, but specific combining ability (SCA) was significant only for ears per plant. Reciprocal recurrent selection would be effective in developing superior cultivars for acidic soils and should include populations 90SA‐3 and 90SA‐4 or CMS‐36 for yellow endosperm cultivars and 90SA‐6 and 90SA‐7 for white endosperm cultivars.

Recurrent Selection for Maize Grain Yield: Dry Matter and Nitrogen Accumulation and Partitioning Changes

Recurrent full‐sib family and reciprocal recurrent selection have resulted in significant increases in grain weight of crosses between the varieties of maize (Zea mays L.) Jarvis Golden Prolific and Indian Chief. The objectives of this study were to (i) compare increases due to 14 cycles of recurrent full‐sib family selection, and reciprocal recurrent selection for yield in maize and (ii) determine whether increased grain weights were accompanied by parallel increases in total dry matter and total N accumulation. Unless total dry matter acquisition increases in parallel with grain weight during selection, sustained root and shoot functions would be restricted by excessive diversion of carbohydrates to grain. After 14 selection cycles on sandy soils of the North Carolina coastal plain, grain weight, dry matter accumulation, and N accumulation in the population hybrid increased 23, 12, and 4%, respectively, with full‐sib family selection and 27, 21, and I0%, respectively, with reciprocal recurrent selection. Greater proportions of the dry matter and N accumulated were partitioned to grain after full‐sib family selection than after reciprocal recurrent selection. Therefore, photosynthate production after full‐sib family selection was not sufficient to fully satisfy both the demand by grain and the requirements for root and shoot processes. Reciprocal recurrent selection resulted in a greater increase in photosynthate production, so that the hybrid population was able to meet the demand for carbohydrate by higher grain yield and still sustain N acquisition by roots. The conclusions were also supported by heterosis for grain weight, total dry matter, and total N accumulation, which was greater after reciprocal recurrent selection than after full‐sib family selection. Selection to increase grain weight will result in efficient N acquisition only when the greater grain weight is supported by an adequate increase in photosynthate production.

Change in ribosomal DNA intergenic spacer-length composition in maize recurrent selection populations. 1. Analysis of BS13, BSSS, and BSCB1

Five different ribosomal DNA (rDNA) intergenic spacer-length variants (slvs) were detected among the maize inbreds which were the progenitors of Iowa Stiff Stalk Synthetic (BSSS). One rDNASstI restriction site polymorphism in the 3' region of the 26S gene was detected. Nine different rDNA intergenic spacer (IGS) hybridization fragment patterns (assigned letter designations A-I) were observed among the BSSS progenitors. Following 7 cycles of half-sib recurrent selection in BSSS using the Ia13 double cross as a tester, hybridization fragment pattern E became predominant in the population. In contrast, 11 cycles of reciprocal recurrent selection in BSSS with the Iowa Corn Borer Synthetic No. 1 (BSCB1) population resulted in hybridization pattern D becoming predominant. Hybridization pattern E is present in the elite inbreds B14, B37, B73, and B84, which were derived from different cycles of the BSSS half-sib recurrent selection program with Ia13. Hybridization pattern D is present in the elite inbreds B89 and B94, which were derived from different cycles of the BSSS reciprocal recurrent selection program with BSCB1. Therefore, two different forms of recurrent selection on BSSS resulted in different hybridization patterns becoming predominant in the selected populations and present in elite inbreds derived from the populations. These results also suggest that rDNA IGS hybridization fragment patterns D and E, which both have the longest slv detected, may have a selective or adaptive advantage in BSSS materials grown in the Corn Belt.

Interpopulation Genetic Variance after Reciprocal Recurrent Selection in BSSS and BSCB1 Maize Populations

Reciprocal recurrent selection is a breeding procedure designed to improve two populations simultaneously by selecting for performance in the interpopulation cross. The objective of this study was to evaluate the effects of II cycles of selection on the mean, genetic variance, and correlations amongtr aits in the interpopulationc ross of the Iowa Stiff Stalk Synthetic (BSSS) and Iowa Corn Borer Synthetic no. 1 (BSCBI) maize (Zea mays L.) populations. Oneh undredr eciprocal full‐sib families from Cycle 0, Cycle 5, and Cycle II of the interpopulation cross between BSSS and BSCBI were evaluated at two locations in 1989 and three locations in 1990. Grain yield increased 0.25 Mg ha‐1 per cycle (6.46%) after II cycles of selection, grain moisture increased 0.85 g kg‐1 per cycle, root lodging decreased 0.23%, and stalk lodging decreased 1.64% (all changes significant at P = 0.01). Estimates of genetic variance for all traits were significantly different from zero, except for root lodging in Cycle II. Genetic variance for grain yield decreased after II cycles of selection, although the differences among cycles were not significant. Root lodging, stalk lodging, anthesis date, and silking date had significant decreases in genetic variance after II cycles of selection. Changeisn heritability generally paralleled changes in genetic variance. Genotypic and phenotypic correlations were seemingly unchangeda cross cycles of selection. The results indicate that reciprocal recurrent selection has been effective in increasing the mean performance of the population cross while maintaining genetic variance.

Genetic Effects Associated with Reciprocal Recurrent Selection in BSSS and BSCB1 Maize Populations

Reciprocal recurrent selection (RRS) was designed to capitalize on both additive and nonadditive genetic effects for improvement of the cross between two populations by complementary changes in allelic frequencies between populations. Eleven cycles of RRS have been completed in the Iowa Stiff Stalk Synthetic (BSSS) and Iowa Corn Borer Synthetic No. 1 (BSCB1) maize (Zea mays L.) populations. The objectives of this study were to partition the response to selection into that due to additive and dominance genetic effects and to evaluate the effects of genetic drift. A population diallel of the CO, C4, C7, C9, and Cll cycles of BSSS(R) and BSCB1(R) the C8 and C10 inte rpopulation crosses of BSSS(R) and BSCB1(R) were evaluated. The populations per se selfed and interpopulation crosses selfed of the CO, C4, C7, C8, C9, CI0, Cll cycles also were included in the study. The study was evaluated at four locations in 1988 and three locations in 1989. The response of the interpopulation cross for grain yield was 0.28 ± 0.04 Mg ha‐1 cycle‐1 and was primarily due to dominance effects. Responses in the populations per se, adjusted for the effects of genetic drift, were similar to the direct effects in the interpopulation cross. Improvementin BSSS(R) was due to both additive and dominance effects, but only dominance ffects were important in BSCBI(R). The results showed that selection response occurred at loci with alleles with partial to complete dominance with no evidence for overdominant alleles contributing to selection response. There were no significant changes in grain moisture, and the responses for root and stalk lodging were in the desired direction. It is concluded that RPS was effective for improving the interpopulation cross and inbreeding depression from genetic drift limited the observed response in the populations per se.

Responses to Reciprocal Recurrent Selection in BSSS and BSCB1 Maize Populations

Improvement of germplasm as a parental source for developing inbreds has been an important part of most maize (Zea mays L.) breeding programs. Reciprocal recurrent selection is a cyclical breeding procedure designed to improve the interpopulation cross of two base populations. The objective of this study was to evaluate the direct and indirect responses of 11 cycles of reciprocal recurrent selection in the BSSS(R) (Iowa Stiff Stalk Synthetic) and BSCB1(R) (Iowa Corn Borer Synthethic no. 1) maize populations. The populations per se, populations per se selfed, interpopulation crosses, and interpopulation crosses selfed corresponding to C0, C4, C7, C8, C9, C10, and C11 of the populations were evaluated. Testcrosses of the original and advanced cycles of the populations per se with inbreds B73 and Mo17 and with BSSS(R)C0 and BSCB1(R)C0 also were evaluated in the study. Response in grain yield of the BSSS(R) × BSCB1(R) interpopulation cross was 6.95% (or 0.28 Mg ha‐1) cycle‐1. Grain yield of BSCB1(R) increased 1.94% (or 0.06 Mg ha‐1) cycle‐1, but grain yield of BSSS(R) did not change significantly. Midparent heterosis of the interpopulation cross increased from 25.44 to 76.04% from C0 to C11. Inbreeding depression in the population crosses increased from 1.01 to 2.32 Mg ha‐1 after 11 cycles of selection. The frequency of heterozygotes for grain yield in the population crosses seems to have increased with cycles of selection. Testcrosses to the C0 populations and the inbreds showed linear increases in grain yield, indicating that selection Improved general and specific combining ability of the populations. Selection was effective in reducing root and stalk lodging. No changes in grain moisture were observed. changes in other agronomic traits were in the desired direction.

Reciprocal recurrent selection applied to Coffea canephora Pierre. I. Characterization and evaluation of breeding populations and value of intergroup hybrids

Two breeding populations have been identified with Coffea canephora, based on geographical and genetic differences: the Guinean group from West Africa and the Congolese group from central Africa. A reciprocal recurrent selection programme based on these groups was initiated in Cote d'Ivoire in 1984. Genotypes of both groups available in field collections are either of cultivated or wild origin.

Reciprocal recurrent selection applied to Coffea canephora Pierre

Genetic parameters were estimated in trials planted in connection with a reciprocal recurrent selection programme applied to Coffea canephora in Cote d'Ivoire. Narrow sense heritability values, estimated from a breakdown of the analysis of variance, were high for architectural characters (0.22 to 0.78) and medium for tree vigour (0.13 to 0.40) and for bean weight (0.15 to 0.28). Calculated heritability values for the first two harvests were high (h2>0.7), but much lower for the following harvests (less than 0.2). Heritability estimates by parent-offspring regressions gave variable results, though they were often similar to those obtained by variance analysis, especially for bean weight. Phenotypic and genetic correlations between tree vigour traits and productivity were high. Bean weight was not correlated with vigour or production. Canopy diameter of 4 year-old trees was closely correlated with cumulated productivity from 2 to 5 years in the absence of development competition between trees, but the correlation was low if trees were in competition with each other. The consequences of the results for the choice of characters to be selected among intergroup hybrids or the parents of both populations are discussed.

Variation of growth rhythm among families and correlation between growth rhythm and growth Rate in Betula pendula roth

Growth rhythm, including growth initiation, growth cessation, growth period, and growth rate for Betula pendula were observed on two full‐sib trials of reciprocal recurrent selection and polycross. The results indicate that most of the characters of growth rhythm show significant differences among families and mating patterns. The variations of the characters of growth rhythm are more strongly under genetic control than those of growth rate. The correlations between most characters of growth rhythm and growth rate are highly significant.

Five Years of HOPE: The Hierarchical Open‐Ended Corn Breeding System

The hierarchical, open‐ended corn (Zea mays L.) breeding system (HOPE) is designed to enhance genetic diversity and breeding potential by continually introgressing a wide range of germplasm into breeding populations concurrently subjected to increasingly stringent recurrent selection procedures. This research evaluated the response to selection after 5 yr. The HOPE breeding system involves two heterotic (A and B) sets of four open‐ended populations based on a hierarchy of performance: elite (E), high (H), intermediate (I), and low (L). The 5 yr of selection included two cycles of reciprocal recurrent selection (RRS) at the E level, five cycles of modified ear‐to‐row (ME) selection at the H and I levels, and five cycles of stratified mass selection at the L level. Selection was for performance index (PI) = grain yield ÷ grain moisture. About 90% of the 408 introductions added to HOPE during this period were to the L level. In EA, RRS reduced grain moisture 2.7% per year relative to CO; this was offset by a decrease in grain yield of 3.2% per year. In EB, PI and grain yield increased by 2.0 and 2.7% per year, respectively. In the cross EA × EB, only grain moisture was improved. At the H level of performance, ME selection produced increases of 2.8 and 4.6% per year for PI, 1.4 and 6.9% per year for grain yield, and −0.9 and 1.8% per year for grain moisture, relative to C0, in HA and HB, respectively. At the I level, ME selection improved PI by 3.2% per year and reduced grain moisture by 2.2% per year in IA relative to C0. In IB, only grain moisture was improved. At the L level, mass selection increased PI by 4.0 and 2.1% per year and reduced grain moisture by 2.2 and 1.0% per year relative to C0 in LA and LB, respectively. Five years of HOPE resulted in genetic gains, suggesting that selection in open‐ended populations, arranged in a hierarchical structure, is a viable breeding strategy.

Three-Way and Four-Way Recurrent Selection in Plant Breeding

Three or four-way recurrent selection is proposed for the development of three or four-way crosses. In term of genetic effects, it could be justified if there are interactions between more than three genes, whether alleles or not, if autopolyploids are also considered. For autotetraploids, in particular with tetragenic interaction, four-way recurrent selection could be more effective than reciprocal recurrent selection (two-way selection). According to the types of progenies used to develop the tests, different selection procedures are considered, the two extremes being called method 1 and method 3. With method 1 (selection for three or four-way general combining ability) a plant from a population is used to produce three-way or four-way progenies with the other populations used as testers. With method 3 (selection for three or four-way specific combining ability) three-way or four-way crosses are developed with one plant from each population. To study the genetic advance, the theory is developed to consider either diploidy or autotetraploidy. It is shown that method 3 will allow a greater genetic advance than method 1 for low heritability and low selection intensity. The way towards hybrid development with three and four-way pedigree selection is discussed: again selection can be for general or specific three or four-way combining ability. It is emphasized that an advantage of recurrent selection for three or four-way specific combining ability is that it allows direct varietal development with pedigree selection on three or four-way specific combining ability. Some other practical aspects are also considered.

Cumulative inbreeding in commercial White Leghorn lines under long‐term reciprocal recurrent selection

Abstract 1. Cumulative inbreeding attributable to selection in a finite population after long‐term reciprocal recurrent selection (RRS) and modified RRS (MRRS) was studied in two White Leghorn lines. 2. Pedigree information was analysed for a period of 24 generations. In one generation, progeny of full‐sib, half‐sib and unrelated pure‐line as well as reciprocal cross‐line matings were produced. 3. The structure of the two pure lines, which have been consistently used as part of the commercial cross, was documented in terms of numbers of sires and dams mated to produce sons and daughters, and variance of family size. On average, 87 sires and 870 dams per generation were mated to produce offspring. 4. Cumulative inbreeding values determined from pedigree data were compared with estimates from effective population size and variation of family size. 5. The increase in average inbreeding over 23 generations was 11.9% for line A and 10.8% for line B or 0.49% per generation, based on pedigree data. 6. Estimates ...

Inbreeding and heterosis effects on quantitative traits in a White Leghorn population under long‐term reciprocal recurrent selection

1. Inbreeding and heterosis effects for quantitative traits were estimated in two White Leghorn lines selected with reciprocal recurrent selection (RRS) since 1950. 2. Pedigreed progeny were produced from full-sib, half-sib and unrelated pure line as well as reciprocal cross line matings to estimate inbreeding and heterosis effects "within sires". 3. Inbreeding effects estimated as linear regressions agreed well with estimates considering inbreeding as fixed effect. The inbreeding depression per 10% inbreeding was highest for hatchability (6-7%), intermediate for production-related traits (3%), and about 1% for shell quality, body weight and egg weight. 4. Heterosis effects were estimated by comparing pure line and cross line progeny of the same sires. 5. Results indicate considerably less heterosis for egg production than found earlier, which is interpreted as a consequence of pure line selection.

Frequency of the transposable elementUqin Iowa stiff stalk synthetic maize populations

SummaryTheUqtransposable element is one of two transposable elements consistently found in maize (Zea maysL.) populations. Populations developed from two independent recurrent selection programs initiated in the Iowa Stiff Stalk Synthetic (BSSS) maize population were tested for the frequency ofUqtransposable elements to determine howUqfrequency has changed with cycles of recurrent selection. In the first programme, 13 cycles of half-sib and S2progeny recurrent selection [BSSS(S)C13] have been completed and 10 of the 13 cycles were assayed for activeUqelements. In the second programme, 11 cycles of reciprocal recurrent selection [BSSS(R)C11] have been completed and five of the 11 cycles were assayed for activeUqelements. The frequency ofUqwas different for the two recurrent-selection programmes. The percentage of plants containing activeUqelements increased from 19% (BSSS) to 91% [BSSS(S)C13] at a linear rate after 13 cycles of half-sib and S2progeny recurrent selection, whereas the percentage of plants containing activeUqelements decreased from 19% (BSSS) to 0% [BSSS(R)C11] after 11 cycles of reciprocal recurrent selection, with extinction of theUqelement occurring between the fifth and sixth cycles of selection. Our data suggest that the increase in frequency ofUqwith half-sib and S2progeny recurrent selection was predominantly due to random genetic drift coupled with a selective advantage possibly associated with a region of the genome linked toUq. Neither replicative transposition or chromosome assortment and segregation can be invoked to explain the change in frequency ofUqin these populations. The extinction ofUqafter reciprocal recurrent selection was best explained by random genetic drift.

Performance and Genetic Variance among S1 Lines and Testcrosses of Iowa Stiff Stalk Synthetic Maize

Iowa Stiff Stalk Synthetic (BSSSC0) maize (Zea mays L.) population has been used in two long‐term recurrent selection programs: reciprocal recurrent selection (R) and half‐sib followed by S2‐progeny (S) recurrent selection. Advanced populations after nine cycles of reciprocals recurrent selection [BSSS(R)C9] and seven cycles of half‐sib and three cycels of S2 progeny selection [BS13(S)C3] were evaluated. Objectives of this study were to compare performance and amount of genetic variation present among S1 lines from BSSSC0, BSSS(R)C9, BS13(S)C3, and BSSS(R)C9 ✕ BS13(S)C3(C3 ✕ C9) and, also, to compare performance and genetic variation among testcrosses of the S1 lines by using two testers of different heterotic background, B73 and Mo17. The S1 lines from BSSS(S)C9 and BS13(S)C3 showed significant increases in grain yield compared with S1 lines from BSSSC0. The C3 ✕ C9 S1 lines showed high‐parent heterosis for grain yield. Genetic variance component estimates of S1 lines were significant in all four populations, and C3 ✕ C9 reflected midparent estimates between the estimates for C3 and C9. Mean grain yield for Mo17 testcrosses was significantly greater than for B73 testcrosses within each of the four populations. Testcrosses involving C3 and a related inbred, B73, showed a nonsignificant grain yield variance estimate. The average yield for the testcrosses of S1 lines from C3 ✕ C9 for both testers was intermediate between the testcrosses of S1 lines from C3 and C9; thus, the high‐parent heterosis observed for C3 ✕ C9 S1 lines was not observed for the testcross means.

Heterotic Patterns among Mexican Races of Maize

Collection and description of the maize (Zea mays L.) germplasm complexes of Mexico began in 1943, and efforts toward the potential utilization of the 25 recognized Mexican races were initiated in 1961. This study was conducted to determine the performance of the 25 Mexican races and 300 interracial crosses evaluated in three environments identified as high (2249 m), intermediate (1800 m), and low (1300 m) elevations. Data were analyzed with the Gardner‐Eberhart model, Analysis II. At the high elevation the races Cónico, Cónico Norteño, and Chalqueño had high mean yields per se and in crosses. Cacahuacintle and Maiz Dulce had equally high yield in crosses but had lower per se yield. At the intermediate elevation, the best yielding races in crosses and per se were Comiteco, Harinoso de Ocho, Celaya, Maiz Dulce, Tabloncillo, and Tuxpeno. At the low elevation, the highest per se yields were exhibited by Harinoso de Ocho, Celaya, Pepitilla, and Tabloncillo. Across all elevations, the best general combiners were Cacahuacintle, Harinoso de Ocho, and Maiz Dulce. Results of this study could be used to (i) introgress the heterotic patterns found among races into new commercial varieties or populations, (ii) search for race collections with better agronomic type that belong to the racial heterotic pattern, (iii) improve gene pools based on racial heterotic patterns and geographical origins, (iv) establish reciprocal recurrent selection between two races that exhibited heterosis when crossed, or (v) develop hybrids based on lines derived from the collections studied in each environment.

The three C's — competition, coexistence and coevolution — and their impact on the breeding of forage crop mixtures

The role of competition, coexistence and co-evolution in the formation of plant communities is discussed, particularly in relation to the breeding of improved grass/legume mixtures. Competition occurs whenever the demand for a particular resource outstrips supply, with the pressures generated within a species expected to exceed those between species. These pressures must be withstood before populations can coexist within a community. This is accomplished by a process of niche diversification, arising from temporal or spatial differences between the populations, that enables them to draw on resources not readily available to their competitors. Coexistence is crucial to the success of any breeding programme designed to raise the productivity of grass/ legume pastures, because it enables components to adapt not only to the environment which they share, but also to each other. A strategy that improves the "general ecological combining ability" of one or both components by a process of recurrent or reciprocal recurrent unilateral adaptation may prove successful, particularly if existing niche differences are increased thereby. Although both processes may give rise to populations which have apparently coevolved, only those resulting from reciprocal recurrent selection will meet the criteria of specificity and reciprocity.

Inter‐ and Intracultivar Effects of Selection on Heterosis

The effect of selection on heterosis depends on the gene action and the type of selection. Intracultivar (W) selection, full‐sib family selection within each of two cultivars, and intercultivar (R) selection, reciprocal recurrent selection between the two cultivars, were contrasted for their effects on heterosis. The cultivars were considered to be random replicate populations from an ancestral population. The relatedness of individuals within cultivars and the degree of divergence between cultivars were formalized in terms of identity by descent (IBD) measures for two, three, two‐pair, and four genes a locus and joint IBD measures for genes at each of two loci. Quantitative genetic components for a model that is general for additive, dominance, and additive by additive (a ✕ a) effects with an arbitrary number of alleles were defined for the ancestral population, and selection responses were formulated for the cultivars and the hybrid for each selection method with the aid of the IBD measures. A further analysis was made utilizing a biological building block model of gene effects. The contribution of a ✕ a effects was such that they reduced heterosis from W selection, but slightly increased heterosis from R selection. It was concluded that R selection always increased heterosis while W selection could increase or decrease heterosis, but decreased heterosis for a preponderance of the genetic parameters considered.