HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Related articles in Crop Science Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Butruille, D. V. Articles by Coors, J. G. Search for Related Content PubMed Articles by Butruille, D. V. Articles by Coors, J. G. Agricola Articles by Butruille, D. V. Articles by Coors, J. G. Related Collections Germplasm Enhancement Maize Crop Genetics

CROP BREEDING, GENETICS & CYTOLOGY

Response to Selection and Genetic Drift in Three Populations Derived from the Golden Glow Maize Population

^a Monsanto Company, Ankeny, IA
^b Universidade Federal de Uberlândia, Uberlândia, Brazil
^c Dep. of Agronomy, 1575 Linden Drive, Univ. of Wisconsin, Madison, WI 53706

^* Corresponding author (jgcoors{at}facstaff.wisc.edu).

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Reciprocal recurrent selection (RRS) in maize (Zea mays L.) is used to develop populations with superior combining ability, and it is usually assumed that these populations must be genetically distinct for RRS to be effective. Starting from two randomly derived subpopulations, GG(A) and GG(B), of the open-pollinated maize population ‘Golden Glow’ (GGC0), we conducted six cycles of full-sib RRS for grain yield and moisture. Our objectives were to (i) document selection response; (ii) evaluate inter and intrapopulation genetic diversity; and (iii) review selection response relative to gene action, heterosis, inbreeding, and genetic drift. We performed a generation means analysis (GMA) using GG(A), GG(B), and a third population of Golden Glow developed by 21 cycles of mass selection for prolificacy, GG(MP). Field performance was evaluated at four environments in Wisconsin. We analyzed allele frequency changes using simple sequence repeats (SSRs) and amplified fragment length polymorphisms (AFLPs). Selection response for grain yield of GG(A) x GG(B) population crosses was 5.3 g plant^–1 cycle^–1. Grain moisture and root lodging decreased by –0.5% cycle^–1 and –5.2% cycle^–1, while prolificacy increased by 0.03 ears cycle^–1. After six cycles of RRS, GG(A) and GG(B) diverged genetically from each other, as well as from GG(MP)C21 and Golden Glow. Gene diversity within GG(A) and GG(B) decreased. However, total gene diversity over both GG(A) and GG(B) did not change over cycles of RRS. Genetic drift did not appear to seriously impede selection response. Most of the selection response, regardless of trait, selection method, or subpopulation, was attributed to additive genetic effects.

Abbreviations: AFLP, amplified fragment length polymorphisms • GG, Golden Glow • GMA, generation means analysis • RRS, reciprocal recurrent selection • SSR, simple sequence repeats

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
DEVELOPMENT OF SUPERIOR GERMPLASM requires selection, which can be applied in a recurrent fashion to a genetically heterogeneous population to increase the frequency of favorable alleles cycle after cycle (Hallauer, 1985). Reciprocal recurrent selection was proposed to simultaneously improve population per se and population-cross performance by increasing frequencies of alleles with favorable additive and dominance effects at the same time (Comstock et al., 1949).

One of the best-known RRS programs is that involving the BSSS and BSCB1 populations started at Iowa State University in 1949 (Penny and Eberhart, 1971). Selection response has been studied both at the phenotypic level (Keratinijakal and Lamkey, 1993a, 1993b; Schnicker and Lamkey, 1993) and at the molecular marker level (Labate et al., 1997, 1999). The BSSS x BSCB1 RRS system has led to dramatic yield increases in the population crosses, but genetic drift due to small effective population size may have decreased gene diversity at the molecular level. Genetic drift may also have increased inbreeding depression within each population as well as reduced additive and total genetic variance, thereby reducing the potential for future selection.

To examine the effect of RRS on genetic diversity, J.H. Lonnquist started a selection program at the University of Wisconsin in 1971 in which the open-pollinated maize population Golden Glow was randomly subdivided into GG(A) and GG(B) substrains that were then used for six cycles of full-sib RRS to increase grain yield and decrease grain moisture at harvest. This is the only known long-term RRS program in maize that has been initiated with a single population. All other RRS programs have used genetically distinct populations to capitalize on dominance variance between populations because of differences in initial gene frequencies. The Golden Glow RRS program, therefore, provides a unique opportunity to examine how heterotic groups might evolve as a result of selection for combining ability. The concept of heterotic group is a relatively recent development (Tracy et al., 2003). While heterosis requires genetic diversity between parents, the source of that diversity does not necessarily require great initial genetic diversity based on phylogenetic divergence. Heterotic groups may be mostly created by breeders and genetic diversity enhanced by both selection and genetic drift.

Lonnquist also used the same source population of Golden Glow to initiate a mass selection program for increased ear number (referred to as prolificacy), a trait that is highly correlated to grain yield (Maita and Coors, 1996; de Leon and Coors, 2002). Thirty cycles of mass selection for prolificacy have been completed in this Golden Glow subpopulation, GG(MP).

We used the selected populations derived from Golden Glow to analyze the impact of these different selection methods on agronomic performance, molecular diversity, and genetic divergence of the three selected populations. Our objectives were to (i) document response to selection; (ii) evaluate changes in inter- and intrapopulation genetic diversity; and (iii) review selection response relative to gene action, heterosis, inbreeding, and genetic drift.

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Population Development—RRS
At the beginning of the 20th century, R.A. Moore derived the Golden Glow dent maize variety from strains related to Minnesota No.13 and Toole's North Star (Moore and Albertz, 1924). In 1971, J.H. Lonnquist started both the RRS and the biparental mass selection programs from Golden Glow. Both selection programs started with the same source population. Strains GG(A) and GG(B) were randomly derived substrains for Golden Glow that were subsequently selected via RRS. During each of the first two cycles, C1 and C2, a single prolific plant in GG(A) was self pollinated and crossed with a single prolific plant in GG(B). The GG(B) plant was also self pollinated and crossed back to the GG(A) plant. The two ears representing the cross were combined. This process was repeated to create a number of full-sib crosses for evaluation. Grain yield and grain moisture of the crosses were determined the following summer. Crosses with high grain yield and low grain moisture were identified, and the corresponding parental plants within each strain were recombined with remnant selfed (S₁ family) seed. Plants within each recombined strain were intermated for two generations before initiating the next cycle of RRS.

During the first two cycles, prolific plants were required to make both self and full-sib pollinations, and this made it difficult to create large numbers of full-sib families for evaluation. For cycles C3 to C6, S₁ families were first developed by selfing plants within each strain. These S₁ families were used to make crosses between strains the following season. There was no intentional per se selection among or within S₁ families. The GG(A) x GG(B) crosses were evaluated over the following 2 yr, and the best crosses were selected on the basis of grain yield and grain moisture. The corresponding S₁ families were used for recombination. For cycles C3 to C6 there was only one recombination generation per cycle.

While the number of crosses evaluated in yield trials varied from cycle to cycle, the number of S₁ families recombined was always greater than 20 to maintain genetic variation and reduce genetic drift. The proportion selected in the first three cycles was relatively high, although the number of crosses evaluated was low [i.e., 33% (25/75) in C1, 30% (23/77) in C2, 39% (33/85) in C3, respectively]. Selection intensified during cycles C4, C5, and C6 when 13% (20/153), 15% (20/137), and 13% (20/159) were selected because many more crosses were evaluated during these three cycles.

Population Development—Mass Selection for Prolificacy
For each cycle of biparental mass selection for prolificacy, the subpopulation GG(MP) was planted in an isolated plot. Before silk emergence, the top-most ear shoot of plants showing early development of two or more ear shoots and good silk synchronization was covered with a shoot bag. After prolific plants were shoot-bagged, all other plants were detasseled. One day later, shoot bags were removed to allow pollination from other prolific plants. At harvest, the top-most ears from approximately 100 to 300 plants were selected on the basis of prolificacy and a visual assessment of plant health, root strength, stalk length, and grain moisture. A balanced composite was made from all selected ears for the next cycle of selection. Selection intensity ranged from approximately 0.5 to 5.0% for the first 21 cycles.

Field Experiments
Seventy-nine unique entries and 22 duplicate entries were used for generation means analysis (GMA) analysis. The entries were as follows: populations per se- C0, C1, C2, C3, C4, C5 for GG(A) as well as GG(B) and C0, C6, C12, C21 for GG(MP); S₁ bulks of populations—same as above with exception of GG(MP) C6 and C12; population crosses C0 x C0, C1 x C1, C2 x C2, C3 x C3, C4 x C4, C5 x C5, C0 x C3, C0 x C5, C3 x C0, C5 x C0 for GG(A) x GG(B), and C0 x C21, C3 x C21, C5 x C21 for GG(A) x GG(MP) and GG(B) x GG(MP); S₁ bulks of population crosses—same population crosses as above; random-mated population crosses—same population crosses as above. Due to a planting mistake, GG(MP)C6 was planted only in 1998, while GG(MP)C12 was planted only in 1999. Nearly all entries involving GGC0 as well as those involving the most recent cycles of RRS and mass selection for prolificacy [GG(A)C5, GG(B)C5, and GG(MP)C21] were duplicated because of the large influence these entries have on GMA. We used balanced bulks by sampling at least 100 plants to make each entry (100 plants from each population in the case of population crosses).

Entries were planted in a triple 10 x 10 lattice design at two locations (Madison and Arlington, WI, USA) in 1998 and 1999. The soils at both sites are Plano silt loam (fine-silty, mixed, mesic Type Arguidoll). Two-row plots (6.1 x 0.8 m) were machine planted at a density of 41 000 plants ha^–1. All plots were bordered on both sides by two rows of an early maturing (CRM 89), commercial hybrid, Pioneer 3897 (Pioneer Hi-Bred Intl., Johnston, IA). Plots were fertilized according to soil test recommendations, and weeds were chemically and mechanically controlled. Before harvest, root lodging was recorded as the percentage of plants in each plot leaning more than 30° from vertical. In the two 1998 environments, the number of ears in each plot were counted. An ear was defined as a female inflorescence with one or more fully formed seeds. The number of ears was divided by the number of plants in each plot. In all four environments, plots were harvested by machine, and grain yield and moisture were recorded.

Entry means were calculated within each environment (year-location combination), considering the lattice design by SAS PROC MIXED (SAS, 2001). Blocks and replications were considered as random, and entries as fixed, variables. These were then used to derive least square estimates of entry means over all environments with SAS PROC GLM, considering the entries as fixed effects and the environments as random effects (SAS Institute, 2001). Duplicate entries were averaged for the GMA, and, for simplicity of analysis and presentation, we ignored the resulting lower standard error of these means in subsequent analyses. Thus, least square estimates of the mean of each entry were used in the GMA study.

Generation Means Analysis
The GMA model we used (see Appendix) was similar to the one developed by Smith (1979) to estimate A0, AL, D0, DL, DQ, and HQ. Since all subpopulations were derived from cycle 0, the definitions of the above terms are: A0 = contribution of additive effects from Golden Glow at C0; D0 = contribution of dominance effects from Golden Glow at C0; ALI = linear function of changes in allelic frequencies influencing additive effects in subpopulation I; DLI = linear function of changes in allelic frequencies influencing dominance effects in subpopulation I; DQ I = quadratic function of changes in allelic frequencies influencing dominance effects for subpopulation I; HQ = quadratic function of the changes in allelic frequencies and dominance effects for the cross of subpopulation I and subpopulation J.

The estimates of A0, AL, D0, DL, DQ, and HQ were obtained by the ordinary least squares method using SAS PROC GLM. A reduced model, obtained by the elimination of the parameters that did not meet the 0.05 significance level, was derived from the full model for each trait. Parameters were included hierarchically in the model, so that the addition of dominance effects would require the presence of the corresponding additive effects, and quadratic terms could only be included once linear terms were present. Thus the order of inclusion would be: A0, ALs, D0, DLs, DQs, and HQs.

Response to Selection, Inbreeding, and Heterosis
Selection response cycle^–1 was expressed by the linear regression coefficient relating performance to cycle. The observations regressed were the overall means of each cycle.

For each trait, heterosis (%) in the interpopulation crosses was estimated as the ratio of least square means:

that is, the mean of the population cross divided by the average of the means of the parental populations (which are subscripted as "rm" because they are considered random-mated populations).

Inbreeding (%) for any population was calculated as:

that is, the mean of the S₁ bulk divided by the mean of the parental populations (in this case the reference population is qualified by the "rm" subscript because we may estimate the inbreeding of a population cross, in which case the reference population is the random mated offspring of the hybrid).

We also used generation means estimates (GMEs) to calculate analogous parameters on the basis of the GMA, in which case the least-square estimates of means of observed populations were replaced by GMEs of observed, or hypothetical, populations:

where GME_i is the GMA estimate of the ith population mean.

Molecular Marker Data
For the molecular marker analysis, we used 82, 103, 126, and 126 plants from GGC0, GG(MP)C21, GG(A)C5, and GG(B)C5, respectively. We also included in the analysis 19 S₁ families from each GG(A)C5 and GG(B)C5 that were selected for the synthesis of cycle 6 [one of the 20 selected S₁ families was lost for both GG(A)C5 and GG(B)C5]. These two sets were designated GG(A)C5SEL and GG(B)C5SEL. The DNA was extracted from a bulk of freeze-dried tissue from at least 15 plants from each selected S₁ family. A CTAB DNA extraction protocol was used (Kidwell and Osborn, 1992). Both AFLP and SSR electrophoretic separations were done on polyacrylamide sequencing gels. Twenty-seven SSR loci were scored on these individuals. We multiplexed primers before PCR in 8 pools. Pools 1 through 8 contained primers of loci [phi036 (bin 3.03), phi127 (2.07), bngl589 (4.11), phi093 (4.08)]; [phi091 (7.03), bngl210 (10.03), phi119 (8.02), bngl439 (1.03)]; [phi099 (3.02), bngl615 (1.07)]; [bngl469 (2.02), bngl147 (1.02), dupssr034 (4.07), bngl125 (2.02)]; [phi064 (1.11), bngl240 (8.06), phi116 (7.06), bngl162 (8.05)]; [phi074 (4.04), bngl426 (6.01), phi045 (7.06), bngl128 (9.07)]; [dupssr023 (3.06), phi112 (7.01)]; and [dupssr014 (8.09), phi123 (6.07), phi069 (7.05)], respectively. The PCR reactions were performed in 96-well microtiter plates with a PTC-100 Thermal Cycler (MJ Research, Watertown, MA). After 10 min at 95°C, a "touchdown" profile was followed (Mellersch and Samson, 1993). It began with 1 min at 94°C, 1 min at 65°C, 2 min at 72°C. This cycle was repeated with a reduction in 0.5°C of the annealing temperature at each cycle until 55°C was reached, and then followed by 20 more cycles with the annealing temperature held at 55°C. The reactions were then maintained at 4°C. The 10-µL reaction contained 40 ng of template DNA, 17 ng of each primer (independent of the number of primers in the pool), 0.7 unit of AmpliTaq Gold (Applied Biosystems, Foster City, CA), 1x reaction buffer (10 mM Tris-HCl, pH 8.3, 50 mM KCl), 1.5 mM MgCl₂, 100 mM each dNTPs, 67 nCi of [–³³P]dATP (Amersham Pharmacia Biotech, Piscataway, NJ), 1 mg/mL of nonacetylated BSA, and distilled deionized water.

For AFLP, we proceeded according to manufacturer's instructions (Life Technologies, Rockville, MD), with the following differences: 0.25x reactions were used for the restriction, digestion, ligation and preamplification steps, and selective amplifications were adjusted to a 10-µL final reaction volume. The labeling was done through phosphorylation of the 5' end of the EcoRI primers with [–³³P]dATP and T4 kinase. We used six AFLP primer pairs: (E-AGC, M-CAC); (E-AGC, M-CAG); (E-AGG, M-CAA); (E-AGG, M-CAC); (E-AGG, M-CTA); and (E-AGG, M-CTC). We scored, as presence–absence, 27, 32, 38, 20, 37, and 31 bands for each of these primer pairs respectively. We assumed that each band corresponded to a single dominant genetic locus.

Both SSRs and AFLP amplifications were terminated by adding 10 µL of formamide buffer [0.1% (v/v) xylene cyanol FF, 0.1% (v/v) bromophenol blue, and 10 mM EDTA, 98% (v/v) deionized formamide] to each reaction and denaturing at 90°C for 3 min. A 38- x 50-cm Sequi-Gen sequencing Cell (Bio-Rad, Hercules, CA) was used for vertical polyacrylamide electrophoresis (0.4 mm thick; 6% of 19:1 acrylamide:bis-acrylamide, 7.5 M urea; 1x TBE, 0.05%TEMED, 0.052% ammonium persulfate). A 97-well sharktooth comb was used to load the samples (3 µL well^–1) and a 30- to 300-bp molecular ladder was used as a size indicator (Life Technologies). The gels were run for 2 h at constant power (85W) then vacuum dried between a sheet of blotting paper and a sheet of cellophane. A Biomax M_r (Kodak) film was exposed to the gel for 1 to 3 d, before development.

AFLP gels were scored visually, some twice (blind) to estimate the scoring error rate (below 0.5%). AFLP loci were scored as dominant (presence or absence of the band). All SSRs gels were scored twice, and SSR loci were scored as codominant. Loading errors and pollen contamination of the selfed progenies where detected by data scanning tools programmed in Visual Basic for Excel (not shown). Such errors amounted to less than 1% of the data, and the suspected outliers were removed from the data set.

Analysis of Population Structure
SSR and AFLP data were analyzed separately. The population parameters estimated were the effective number of alleles (or reciprocal of homozygosity), expected heterozygosity within populations (i.e., expected heterozygosity under random mating), expected heterozygosity between populations [equivalent to gene diversity (Nei, 1973)], and the fixation index (i.e., change in expected heterozygosity relative to GGC0). These analyses were done using Popgene software (Yeh and Boyle, 1997). We also estimated the effective population size, Ne, of these populations relative to GGC0 by re-arranging equation 3.13.3 from Crow and Kimura (1970):

Where H₀ is the heterozygosity at Cycle 0, and H_t is the heterozygosity at Cycle t.

	RESULTS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Realized Gains
RRS initiated with the single source population, Golden Glow, worked well (Table 1, 2). Selection response for grain yield, as measured by the linear regression coefficient, for the GG(A) x GG(B) population crosses, was 5.3 g plant^–1 cycle^–1 (4% cycle^–1), which was equivalent to gains observed from successful RRS programs in maize using diverse populations (Coors, 1999). The yield increase was accompanied by a decrease in grain moisture (–0.5% cycle^–1), an increase in prolificacy (0.03 ears cycle^–1), and a decrease in root lodging (–5.2% cycle^–1). There were significant responses to selection for most traits in most subpopulations, with notable exceptions being grain yield for GG(A) and GG(B) per se, where the realized gains were not significant. The realized gains in the selfed populations were generally no larger than those in the populations per se.

Generation Means Analysis
The additive effects in the original population (A0) were significantly different from zero for all traits (Table 3). Except for number of ears plant^–1, the dominance effects in the original population (D0) differed significantly from zero for all other traits. For yield plant^–1, D0 was much greater than A0, and, in fact, A0 was negative. The strong inbreeding depression for yield upon selfing accounts for this observation. For grain moisture, ears plant^–1, and root lodging, D0 was substantially smaller than A0. Additive linear effects (AL) were significant for all traits with the exception of ears plant^–1 for GG(A) and GG(B). For number of ears plant^–1, only the linear effects of changes in the allele frequencies of genes with additive effects (AL) in the MP populations were significant. For grain yield and root lodging, the gains can be attributed mainly to changes in allelic frequencies of genes with additive effects. For moisture, both dominance and additive effects played a role in the response to selection.

Inbreeding estimates for grain yield averaged 0.44 to 0.50 for GG(A) and GG(B), and GG(B) had slightly greater inbreeding depression than GG(A) (Table 4). Inbreeding depression for grain yield tended to decrease over cycles of RRS selection based on GMA estimates for GG(A) and GG(B), perhaps reflecting the contribution that inbreeding, caused by the intervening generation(s) of selfing in each cycle, may have had on reducing the frequency of deleterious recessive alleles in these populations. There was little, if any, inbreeding depression for grain moisture or prolificacy. As expected, inbreeding increased root lodging in GG(A) and GG(B), but there was no obvious pattern over cycles. Inbreeding depression estimates in GG(MP)C21 appeared similar or smaller than the average inbreeding depression for GG(A) and GG(B) for all traits (data not provided).

Analysis of Population Structure
The effective number of SSR alleles ranged from 3.54 in GGC0 to 2.64 in GG(B)C5SEL. For AFLP markers, the range was from 1.56 in GGC0 to 1.46 in GG(B)C5SEL (Table 5). The reduction in the average effective number of SSR alleles in relation to GGC0 was of 6% for GG(MP)C21, 15% for GG(A)C5, 22% for GG(B)C5, 20% for GG(A)C5SEL, and 25% for GG(B)5SEL. For the AFLP markers these losses ranged from 0.6% for GG(MP)C21 to 6.4% for GG(B)C5SEL. Thus both marker systems consistently show that the loss of alleles has been much slower in GG(MP). This is in agreement with the estimated effective population sizes (Table 5), which are of magnitudes that are somewhat comparable to the number of selected individuals or families in each cycle, according to what we know from the selection history of the three populations. Therefore, the fixation index for each population, which corresponds to the loss of within-population heterozygosity (Table 5), most likely reflects the expected inbreeding due to random genetic drift rather than selection and fixation of genes linked to the marker loci used in this study. The overall genetic diversity of the GG(A)C5SEL and GG(B)SEL subpopulations, i.e., the expected heterozygosity if the two populations were intermated, was only slightly lower than that present originally in GGC0 (0.62 versus 0.67, respectively, on the basis of SSR data).

	DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The GG(A) and GG(B) subpopulations diverged genetically during RRS. Nei's genetic distance between GG(A) and GG(B) (using SSR markers) changed from 0 to 0.271 after six cycles of RRS. This compares with the change from 0.21 to 0.66, measured with RFLP loci, over 12 cycles of RRS between BSSS and BSCB1 (Labate et al., 1997). Gene diversity within GG(A) and GG(B) decreased (fixation index increased), while total gene diversity over both GG(A) and GG(B) did not change appreciably from that of the original Golden Glow.

The GG(MP) subpopulation supports the notion that much of the genetic divergence seen in the RRS subpopulations may be due to genetic drift. GG(MP) diverged more slowly from GGC0 due to a much larger effective population size. Despite the greater number of selection cycles and the high selection intensity, at cycle 21, GG(MP) remained genetically similar to GGC0 (distance of 0.073) even though it experienced extensive morphological change (de Leon and Coors, 2002). Gene diversity within GG(MP) has not changed from that of Golden Glow.

The fact that the genetic distance between GG(A)C5SEL and GG(B)C5SEL is greater than that between either population and GGC0 is not sufficient evidence to indicate that selection for GG(A) x GG(B) hybrid performance directly increased genetic distance between the subpopulations. Subpopulations represented by GG(A)C5SEL and GG(B)C5SEL have been apart from each other for twice as many generations (with small effective population size) as either of them have been from GGC0. In addition, we examined the SSR-derived genetic distance between GG(A)C5 and GG(B)C5 progeny pairs used to generate hybrids during cycle 5 of the RRS program, and we found no significant correlation between grain yield and genetic distance (data not shown). The relatively high fixation index in GG(A) and GG(B), and the potential for significant inbreeding by genetic drift, may help explain the absence of significant yield gain in the populations per se, when we would expect a gain resulting from the accumulation of alleles with a favorable additive effect.

Reciprocal recurrent selection within a single germplasm pool should be effective. Initially, RRS would act similarly to full-sib intrapopulation selection, which has been proven successful in many studies (Coors, 1999). Initially, selection response would be due to genes with additive effects. However, after the two subpopulations begin to diverge (most likely through genetic drift), then dominance can contribute to the population-cross response (Comstock et al., 1949). On the basis of this study, it appears that the GG(A) x GG(B) RRS program has not yet progressed to this latter stage, and the per se performance of the individual subpopulations has been reduced because of genetic drift.

	APPENDIX

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Generation Means Analysis—Definitions and Derivations
We assumed no interaction between loci, thus effects at individual loci add across the genome. We define the equations for a single locus with n alleles as follows:

Parameters for population 1:

Parameters for population 2:

The generation means model was developed for a cross (c), the random-mating of a cross (rm), and the selfing (s) of a cross, between cycle j of Population 1 and cycle k of Population 2.

The phenotype of an individual with genotype ii' at a locus is given by:

Observe that Y_ii' is an ordered genotype (the first subscript referring to Population 1 and the second subscript referring to Population 2 in a cross, and from the male and the female gamete respectively in a random-mating and in a selfing).

We can build all the generation mean equations as a linear function of the following parameters:

A01 = µ + 2p_ia_i = contributions of additive effects for POP1 at the initial cycle ;

A02 = µ + 2q_i'a_i' = contributions of additive effects for POP2 at the initial cycle ;

AL1 = _ia_i = linear function of changes in allelic frequencies influencing additive effects in POP1;

AL2 = _i'a_i' = linear function of changes in allelic frequencies influencing additive effects in POP2;

D01 = p_ip_i'd_ii' = contributions of dominance effects for POP1 at the initial cycle ;

D02 = q_iq_i'd_ii' = contributions of dominance effects for POP2 at the initial cycle ;

DL1 = p_ii'd_ii' = linear function of changes in allelic frequencies influencing dominance effects for POP1;

DL2 = q_ii'd_ii' = linear function of changes in allelic frequencies influencing dominance effects for POP2;

DQ1 = _ii'd_ii' = quadratic function of changes in allelic frequencies influencing dominance effects for POP1;

DQ2 = _ii'd_ii' = quadratic function of changes in allelic frequencies influencing dominance effects for POP2;

H012 = p_iq_i'd_ii' = average heterosis in the cross of POP1 and POP2 at C0;

HQ12 = _ii'd_ii' = quadratic function of the changes in allelic frequencies and dominance effects for the cross of POP1 and POP2;

HL1/2 = _iq_i'd_ii' = linear function of changes in allelic frequencies in POP1 influencing heterosis in relation to original allele frequencies in POP2;

HL2/1 = p_ii'd_ii' = linear function of changes in allelic frequencies in POP2 influencing heterosis in relation to original allele frequencies in POP1.

The general GM equations are:

These equations become simpler in some special cases, such as when population 1 and 2 are the same (at the same or different cycles). Another simplification that applies for our situation is that cycle zero is the same for all populations. In this case we have:

	ACKNOWLEDGMENTS

 
The authors are grateful to Dustin T. Eilert and Patrick J. Flannery for assistance with all aspects of the field experiments. We also greatly appreciate the support provided by the USDA-NRICGP grant #9701693.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
This research has been funded in part by USDA-NRICGP grant #9701693.

Received for publication July 1, 2003.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 

• Comstock, R.E., H.F. Robinson, and P.H. Harvey. 1949. A breeding procedure designed to make maximum use of both general and specific combining ability. J. Am. Soc. Agron. 41:360–367.
• Coors, J.G. 1999. Selection methodology and heterosis. In J.G. Coors et al. (ed.) The genetics and exploitation of heterosis in crops: Proceedings of an International CIMMYT symposium. ASA, CSSA, SSSA. Madison, WI.
• de Leon, N., and J.G. Coors. 2002. Twenty-four cycles of mass selection for prolificacy in the Golden Glow maize population. Crop Sci. 42:325–333.[Abstract/Free Full Text]
• Hallauer, A.R. 1985. Compendium of recurrent selection methods and their applications. Crit. Rev. Plant Sci. 3:1–33.
• Keratinijakal, J.F., and K.R. Lamkey. 1993a. Responses to reciprocal recurrent selection in BSS and BSCB1 maize populations. Crop Sci. 33:73–77.[Abstract/Free Full Text]
• Keratinijakal, J.F., and K.R. Lamkey. 1993b. Genetic effects associated with reciprocal recurrent selection in BSS and BSCB1 maize populations. Crop Sci. 33:78–82.[Abstract/Free Full Text]
• Kidwell, K.K., and T.C. Osborn. 1992. Simple plant DNA isolation procedures. p. 1–13. In J. Beckman and T.C. Osborn (ed.) Plant genomes: Methods for genetic and physical mapping. Kluwer Academics Publishers Group AH, Dordrecht, the Netherlands.
• Labate, J.A., K.R. Lamkey, K.R., Lee, M. and W.L. Woodman. 1997. Molecular genetic diversity after reciprocal recurrent selection in BSSS and BSCB1 maize populations. Crop Sci. 37:416–423.[Abstract/Free Full Text]
• Labate, J.A., Lamkey, M. Lee, and W.L. Woodman. 1999. Temporal changes in allele frequencies in two reciprocally selected maize populations. Theor. Appl. Genet. 99:1166–1178.
• Maita, R., and J.G. Coors. 1996. Twenty cycles of biparental mass selection for prolificacy in the open-pollinated maize population Golden Glow. Crop Sci. 36:1527–1532.[Abstract/Free Full Text]
• Mellersch, C., and J. Sampson. 1993. Simplifying detection of microsatellite length polymorphism. Biotechniques 15:582–584.[Web of Science][Medline]
• Moore, R.A., and H.W. Albertz. 1924. Pedigreed crops pay. Wisc. Agric. Exp. Stn. Circ. 170.
• Nei, M. 1973. Analysis of gene diversity in subdivided populations. Proc. Natl. Acad. Sci. USA 70:3321–3323.[Abstract/Free Full Text]
• Penny, L.H., and S.A. Eberhart. 1971. Twenty years of reciprocal recurrent selection with two synthetic varieties of maize (Zea mays L.). Crop Sci. 11:900–903.[Abstract/Free Full Text]
• SAS Institute. 2001. SAS user's guide. Version 8. SAS Inst., Cary, NC.
• Schnicker, B.J., and K.R. Lamkey. 1993. Interpopulation genetic variance after reciprocal recurrent selection in BSSS and BSCB1 maize populations. Crop Sci. 33:90–95.
• Smith, O.S. 1979. A model for evaluating progress from recurrent selection. Crop Sci. 19:223–226.[Abstract/Free Full Text]
• Tracy, W.F., M.A. Chandler, and J.G. Coors. 2003. Historical and biological bases of the concept of heterotic groups. In Agronomy abstracts. ASA, Madison, WI.
• Yeh, F.C., and T.J.B. Boyle. 1997. Population genetic analysis of co-dominant and dominant markers and quantitative traits. Belgian J. Bot. 129:157.

Related articles in Crop Science:

THIS ISSUE IN CROP SCIENCE

Crop Science 2004 44: 1507-1510. [Full Text]  

This Article Abstract Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Related articles in Crop Science Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Butruille, D. V. Articles by Coors, J. G. Search for Related Content PubMed Articles by Butruille, D. V. Articles by Coors, J. G. Agricola Articles by Butruille, D. V. Articles by Coors, J. G. Related Collections Germplasm Enhancement Maize Crop Genetics