Maize is a major food crop in sub-saharan Africa (FAO,

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1 Published September, 01 RESEARCH Strateies to Subdivide a Taret Population of Environments: Results from the CIMMYT-Led Maize Hybrid Testin Prorams in Africa Vanessa S. Windhausen, Silke Waener, Cosmos Maorokosho, Dan Makumbi, Bindianavile Vivek, Hans-Peter Piepho, Albrecht E. Melchiner, and Gary N. Atlin* ABSTRACT To develop stable and hih-yieldin maize (Zea mays L.) hybrids for a diverse taret population of environments (TPE), breeders have to decide whether reater ains result from selection across the undivided TPE or within more homoeneous subreions. Currently, CIMMYT subdivides the TPE in eastern and southern Africa into climatic and eoraphic subreions. To study the extent of specific adaptation to these subreions and to determine whether selection within subreions results in reater ains than selection across the undivided TPE, yield data of 448 maize hybrids evaluated in 513 trials across 17 countries from 001 to 009 were used. The trials were rouped accordin to five subdivision systems into climate, altitude, eoraphic, country, and yield-level subreions. For the first four subdivision systems, enotype subreion interaction was low, suestin broad adaptation of maize hybrids across eastern and southern Africa. In contrast, enotype yieldlevel interactions and moderate enotypic correlations between low- and hih-yieldin subreions were observed. Therefore, hybrid means should be estimated by stratifyin the TPE considerin the yield-level effect as fixed and appropriately weihtin information from both subreions. This stratey was at least 10% better in terms of predicted ains than direct selection usin only data from the lowor hih-yieldin subreion and should facilitate the identification of hybrids that perform well in both subreions. V.S. Windhausen (formerly V.S. Weber), S. Waener, and A.E. Melchiner, Institute of Plant Breedin, Seed Science and Population Genetics, University of Hohenheim, Fruwirthstr. 1, Stuttart, Germany; C. Maorokosho, International Maize and Wheat Improvement Center (CIMMYT), P.O. Box MP163, Harare, Zimbabwe; D. Makumbi, CIMMYT, United Nations Avenue, Giiri PO Box 1041 Villae Market-0061, Nairobi, Kenya; B. Vivek, CIMMYT, C/o ICRISAT, Patancheru 5034, India; H.-P. Piepho, Institute of Crop Science, University of Hohenheim, Fruwirthstr. 3, Stuttart; G.N. Atlin, CIMMYT, Dep. of Plant Breedin and Genetics, Cornell University, 310 Bradfield Hall, Ithaca NY Received 4 Feb. 01. *Correspondin author (ary.atlin@atesfoundation.or). Abbreviations: BLUE, best linear unbiased estimation; H, broadsense heritability; OPV, open-pollinated variety; REML, restricted maximum likelihood; TPE, taret population of environments. Maize is a major food crop in sub-saharan Africa (FAO, 011a). It is rown in a wide rane of aroecoloies and plays an important role in the farmin systems and food security of the reion (Lanyintuo et al., 008). Yield levels in eastern and southern Africa are considerably lower than the world averae because maize crops are mostly rown under rain-fed conditions with little or no fertilizer or pesticide input and are often subject to abiotic and biotic stresses (Haussmann et al., 1998). Yields are also low because the adoption of hybrid maize seed is on averae only 35% in sub-saharan Africa (Lanyintuo et al., 008). The development of new, stable maize hybrids is an important way of increasin rain yield and food supply in Africa. To develop stable and hih-yieldin maize hybrids, breeders must decide whether reater ains can be obtained by dividin the Published in Crop Sci. 5: (01). doi: /cropsci Freely available online throuh the author-supported open-access option. Crop Science Society of America 5585 Guilford Rd., Madison, WI USA All rihts reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, includin photocopyin, recordin, or any information storae and retrieval system, without permission in writin from the publisher. Permission for printin and for reprintin the material contained herein has been obtained by the publisher. CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER

2 taret population of environments (TPE) to exploit specific adaptation or by selectin for broad adaptation (Atlin et al., 000a). Usually, hybrid testin prorams that serve a lare number of farmers across a wide area are more cost-effective than those selectin specifically adapted enotypes because the cost of breedin and product testin is spread across a larer market. Therefore, unnecessary subdivision of a hybrid testin proram should be avoided. Nevertheless, in a lare and heteroeneous TPE, enotypes may react differently to environmental variation resultin in enotypic rank chanes (Cooper et al., 1996; Lynch and Walsh, 1998; Frankham et al., 007). This enotype environment interaction complicates selection for broad adaptation (Basford and Cooper, 1998). If enotype environment interaction is lare within a TPE and associated with consistent subroupin of environments within the TPE, reater ains from selection may result by subdividin the breedin taret than by selectin for broad adaptation. The effect of subdividin a TPE was assessed by Atlin et al. (000b) for barley (Hordeum vulare L.) rowin reions in Canada. The authors showed that enotype subreion interactions were low and selection in any subreion was likely to result in response in other subreions. The subdivision of a TPE into less heteroeneous subreions will only increase selection efficiency if (i) enotype subreion interactions are repeatable (Atlin et al., 001), (ii) enotypic correlations amon subreions are low (Presterl et al., 003), and (iii) the increase in within-subreion enotypic variance achieved by subdivision can counterbalance loss in precision of enotypic means associated with division of testin resources because dividin a lare TPE into smaller breedin tarets is unlikely to result in more resources for testin within each new subreion (Atlin et al., 000a, 001; Piepho and Möhrin, 005). The maize hybrid testin prorams of the International Maize and Wheat Improvement Center (CIMMYT) currently treat eastern and southern Africa as separate breedin tarets. Within these two major eoraphic subreions, five subreions are delineated on the basis of temperature, elevation, and rainfall; these climatic subdivisions are represented in both eastern and southern Africa (Bänzier et al., 004, 006). National hybrid testin prorams within eastern and southern Africa consider each country as a separate TPE. Consequently, different subdivision systems are used to cope with potential enotype subreion interactions. There is evidence that some of these divisions of the TPE may be unnecessary. For example CIMMYT has produced several inbred lines used in hybrids that are broadly adapted throuhout the Latin American and African subtropics (Braun et al., 010) as well as many hybrids and open-pollinated varieties (OPVs) that are used widely across most of eastern and southern Africa. Consequently, selection across the undivided TPE in eastern and southern Africa miht be more efficient than selection in several smaller subreions. The objectives of this study were therefore to determine whether selectin within climate, altitude, eoraphic, yield level, or country subreions was likely to increase rates of enetic ain. Data from more than 500 trials were used, coverin the years 001 to 009, from the advanced reional hybrid testin network coordinated by CIMMYT in eastern and southern Africa. To test the benefit of subdivision, we estimated enotypic, enotype subreion, and enotype environment interaction variances in the undivided TPE and enotypic correlations amon subreions. These parameter estimates were used to predict the efficiency of indirect selection across the undivided TPE relative to direct selection in each subreion. MATERIALS AND METHODS Genotypes and Experimental Desin The study is based on rain yield data of 448 elite maize hybrids collected in 17 countries in eastern and southern Africa. Between 001 and 009, 513 trials were conducted by national aricultural research prorams and private seed companies in collaboration with CIMMYT to identify elite hybrids for the reion. Each year, new hybrids were added to the trials and tested for up to 3 yr, with low-yieldin and disease-susceptible or otherwise undesirable hybrids discarded annually. Thus, there was no hybrid in common across all 9 yr. Within each 3-yr interval, the number of hybrids in common was between 1 and 13. The hybrids were classified accordin to their maturity into early- (n = 19) and late-flowerin maturity roups (n = 9). Early-maturin hybrids were evaluated in 75 trials and late-maturin hybrids in 38 trials. Trials were mainly conducted in the rainy season usin α-lattice desins with three replicates and two-row plots, with plot size ranin from 1.88 to 1.00 m. Trials included 4 to 65 hybrids and one to three local checks, with the number of entries bein constant in a iven year. Trials were rown with irriation in the dry season or under rain-fed conditions in the rainy season. Recommended quantities of fertilizers were applied. Weeds were controlled either by hand weedin or herbicide application, althouh weed control was imperfect in some trials. Ear yield was recorded in tonnes per hectare and adjusted to 10% moisture, and rain yield in tonnes per hectare was determined assumin 80% shellin percentae (Betrán et al., 003). Subdivision of the Taret Population of Environments Five different subdivision systems were used to stratify trials into less heteroeneous subreions to test for potential enotype subreion interactions in the undivided TPE (Table 1). The subdivisions were defined accordin to (i) climatic and elevation differences modified after Bänzier et al. (004, 006), with division of trials into five subreions denoted A throuh E, (ii) altitude patterns modified after Setimela et al. (005), in midaltitude and lowland subreions, (iii) mean rain yield, with trials rouped into low- (<3 t ha 1 trial mean yield) and hih-yieldin ( 3 t ha 1 trial mean yield) subreions modified after Weber et al. (01), (iv) eoraphic reions, in eastern (Ethiopia, Kenya, CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER 01

3 Table 1. Mean and standard deviation of maize rain yield (t ha 1 ) and testin effort in five different subdivision systems of the taret population of environments in eastern and southern Africa from 001 to 009. Subdivision Typical environment Early maturity roup Late maturity roup Number of Number of Countries Trials Grain yield Countries Trials Grain yield t ha 1 t ha 1 Climate A: Mid altitude, humid, and warm ± ±.61 B: Mid altitude, humid, and hot ± ±.34 C: Mid altitude and dry ± ±.40 D: Lowland, tropical, and humid ± ± 1.66 E: Lowland, tropical, and dry ± ± 1.8 Altitude Mid altitude ± ±.71 Lowland ± ± 1.79 Yield level Low-yieldin subreion, <3 t ha ± ± 0.88 Hih-yieldin subreion, 3 t ha ± ±.01 Georaphic Eastern Africa ± ±.49 reion Southern Africa ± ±.79 Country Anola ± ±.41 Malawi ± ± 1.49 Mozambique ± ± 1.55 Tanzania ± ±.09 Zambia ± ±.80 Zimbabwe ± ± 3.40 Eastern Africa: Ethiopia, Kenya, Tanzania, Uanda, Sudan. Southern Africa: Anola, Botswana, Democratic Republic of Cono, Lesotho, Malawi, Mozambique, Namibia, Nieria, South Africa, Swaziland, Zambia, Zimbabwe. Tanzania, Uanda, and Sudan) and southern Africa (Anola, Botswana, Democratic Republic of Cono, Lesotho, Malawi, Mozambique, Namibia, Nieria, South Africa, Swaziland, Zambia, and Zimbabwe), and (v) political country borders, in Anola, Malawi, Mozambique, Tanzania, Zambia, and Zimbabwe. Country and eoraphic subreions were contiuous areas whereas climate, yield level, and altitude subreions were noncontiuous areas. The information permittin climate and altitude subdivision was available only for those locations that were used reularly for hybrid evaluation. The whole data set was included in the yieldlevel and eoraphic subdivision. For the country subdivision, six countries, each with a maize production area >900,000 ha in 009, were selected accordin to FAO (011b) for inclusion in the analysis. Between 006 and 009 there were no trials in Anola. It should be noted that the yield-level subdivision differs in a fundamental way from the others in that trials cannot be allocated to low- and hihyieldin subreions in advance (i.e., for optimally manaed, rain-fed trials, we cannot predict with certainty which trials will yield more or less than 3 t ha 1 in advance of plantin). In contrast, trials could be allocated to the other subdivision systems before plantin, meanin that enotype subreion interaction variance in those could be exploited by breedin for specific adaptation. Statistical Analysis Estimation of Mean Grain Yield in Individual Trials Mean rain yield and repeatability were estimated for individual trials usin an α-lattice analysis of variance, treatin all effects as random. Estimates of mean rain yield per trial were used to stratify trials into low- and hih-yieldin subreions as described above. Trial repeatability was based on entry means over three replicates in a sinle trial. All 513 trials included in the current study had a repeatability of rain yield >0.15. General Description of Analyses Variance components, broad-sense heritability (H) (Eq. []), enotypic correlations amon subreions (Eq. [3]), and selection efficiency across the undivided TPE and each subreion (Eq. [6]) were estimated for plot data usin the restricted maximum likelihood (REML) method. The estimation was conducted within seven overlappin 3-yr intervals from 001 to 009 because there was no hybrid in common across the 9 yr and to reflect the 3-yr testin cycle of hybrid evaluation. Local checks were excluded as they were not in common across trials. Arithmetic means and standard deviations of the seven 3-yr intervals were calculated for all parameter estimates to ive an overall measure across 9 yr (001 to 009). Variance Components and Broad-Sense Heritability For the analyses within the five subdivision systems, years were nested within subreions, followin Atlin et al. (000b), because it is unlikely that a common year effect across an area as lare as eastern and southern Africa exists. We tried to fit a model with trials nested within year location combinations, but this led to sinularities durin REML iterations. Therefore, each year location trial combination was defined as a sinle environment. Environments were considered to be nested within years followin Patterson (1997) and, consequently, a nested model instead of a factorial model was applied: Y ijklmn = μ + s i + y(s) j(i) + e(ys) k( ji) + r(eys) l(kji) + b(reys) m(lkji) + n + ni + y(s) nj(i) + e(ys) nk( ji) + ijklmn, [1] in which μ is the overall mean, s i the effect of subreion i, y(s) j(i) the effect of the year j nested within subreion i, e(ys) k(ji) the effect of the environment k nested within year j and subreion i, r(eys) l(kji) CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER

4 the effect of replicate l nested within environment k, year j, and subreion i, b(reys) m(lkji) the effect of block m nested within replicate l, environment k, year j, and subreion i, n the effect of enotype n, ni the interactions between enotype n and subreion i, y(s) the interaction of enotype n and year j nested within subreion i, e(ys) nk(ji) nj(i) the interactions of enotype n and environment k nested within year j and subreion i, and ijklmn the residual associated with a sinle plot. The subreion main effect was rearded as fixed to allow inferences to be made about specific subreions of the undivided TPE. All other effects were considered as random. It should be noted that when the purpose of hybrid testin is to predict future performance in farmers fields, individual environments are best treated as random samples from the TPE. For estimatin H of rain yield across the undivided TPE and in each subreion, variance components were calculated applyin Eq. [1], but excludin the subreion effect and combinin the year and location effects representin individual trials, to facilitate converence of REML estimates of hybrid effects. Broad-sense heritability was estimated accordin to Hallauer et al. (010) across e environments and r replicates as follows: H = σ / σ + ( σ e / e) + ( σ / er), [] in which σ, σ e, and σ are enotypic, enotype environment, and residual variance components, respectively. Estimation of H based on Eq. [] assumes balanced data whereas in the current data set enotypes were tested in α-lattice desins involvin incomplete blocks. The ad hoc estimation is justified if the block variance is smaller than σ (Comstock and Moll, 1963) and σ / er is small relative to σ and σ /e (Holland et al., 003). e Genotype Means There are four alternative approaches that can be used to predict enotype means in a tareted subreion: (i) direct selection based on local means estimated usin only data from the tareted subreion, (ii) indirect selection based on local means estimated usin only the data from the complementary subreion, (iii) indirect selection usin all data to estimate a lobal mean, inorin subdivision, and (iv) index selection based on local means estimated usin all data and treatin the subreion main effect as fixed. In the latter approach, different weihts are iven to the tareted subreion and its neihbors, dependin on the similarity between subreions and the number of trials per subreion (Piepho and Möhrin, 005). Based on best linear unbiased estimation (BLUE), hybrid means were derived usin all data but inorin subdivision (approach 3) and by usin only the data from the tareted subreion (approach 1). Those estimates were used for estimatin enotypic correlations and relative efficiencies of indirect selection. Equation [1] was applied treatin all effects as random, except the enotype effect, excludin the subreion effect and combinin the year and location effects as described above. Genotypic Correlations and Relative Efficiency of Indirect and Index Selection Under the assumed mixed model, enotype effects within subreions have a compound symmetry variance covariance structure, in which enotypic variances are the same in each subreion, and enotypic covariances and correlations are the same for each pair of subreions. Based on a compound symmetry variance covariance structure, the enotypic correlation amon pairs of subreions as well as between the undivided TPE and subreion s and s can be estimated by usin the approach of Cooper and DeLacy (1994): r (ss ) = r p(ss ) /(H s H s ) 1/, [3] in which r p(ss ) is the phenotypic correlation coefficient between hybrid means estimated by usin only the data from subreion s or s and H is the broad-sense heritability in subreion s and s. The enotypic correlations between the undivided TPE t and subreions s and s can be estimated similarly. Estimates of enotypic correlation exceedin 1 are presented but were restricted to 1 when estimatin response to indirect selection. Selection ain (R) was predicted for direct (approach 1) and indirect selection (approaches and 3; Falconer and Mackay, 1996) usin the results of the variance component analysis with an assumed selection intensity of i = 1.755: R = ihσ. [4] Gain from index selection (approach 4) was predicted for subreions s and s with an assumed selection intensity of i = followin Wricke and Weber (1986). Response to selection in both subreions (s and s ), defined as R = (R s, R s ), can be expressed as R = ib G/(b Pb) 1/. [5] Smith (1936) and Hazel (1943) showed that the unknown index weihts (b) can be derived by multiplyin the inverse of the phenotypic variance covariance matrix (P), the enotypic variance covariance matrix (G), and the economic weihts of each trait. The economic weiht of the tareted reion was 1 and of the complementary subreion 0 to optimize recommendations for farmers in each subreion. The efficiency of indirect selection in subreion s relative to direct selection in the tareted subreion s can be expressed as CR s,s /DR s = r (ss ) (H s /H s ) 1/, [6] in which CR s,s is the predicted correlated response in subreion s to selection in subreion s and DR s is the predicted direct response to selection in subreion s. The efficiency of indirect selection in the undivided TPE t, inorin subdivision, relative to direct selection in subreion s and s can be estimated accordinly. Further, we calculated the predicted ratio between index selection and direct selection response. Estimates >1 indicate that indirect or index selection is predicted to be more efficient than direct selection. The compound symmetry variance covariance structure mentioned before assumes a very simplistic model. The assumption of variance homoeneity was rejected by performin a likelihood-ratio test. Optimally, variance components and enotypic correlations should therefore have been estimated by usin an unstructured variance covariance structure for the subreion effect appearin in every nested effect or by a low-rank approximation thereof usin a factor-analytic model (Piepho, 1997). This was not possible, however, because the hih number of parameters and the very unbalanced nature of the data sets led to sinularities and/or converence problems. Consequently, a compound symmetry variance covariance CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER 01

5 Table. Mean and standard deviation of variance components of maize rain yield in five different subdivision systems of the undivided taret population of environments from 001 to 009 based on a compound symmetry variance covariance structure. Early maturity roup (n = 19) Late maturity roup (n = 9) σ σ σ σ y( s) e( ys) σ σ σ σ σ y( s) e( ys) σ Climate 0.18 ± ± ± ± ± ± ± ± ± ± 0.03 Altitude 0.15 ± ± ± ± ± ± ± ± ± ± 0.03 Yield level 0.09 ± ± ± ± ± ± ± ± ± ± 0.03 Georaphic reion 0.19 ± ± ± ± ± ± ± ± ± ± 0.03 Country 0.1 ± ± ± ± ± ± ± ± ± ± 0.05 Variance components includin enotypic (σ ), enotype subreion (σ ), enotype year (σ y( s ) ), enotype environment ( σ e( ys) ), and residual variance ( σ ). structure was applied. Furthermore, applyin power transformations did not result in variance homoeneity between sub reions. All analyses were performed usin the R software version.1. (R Development Core Team, 011). For estimation of variance components and hybrid means the ASREML software packae version 3 was used (Butler et al., 009). RESULTS Estimates of Variance Components and Broad-Sense Heritability Mean rain yields over the 9 yr for early- and late-maturin hybrids were 4.5 and 5.0 t ha 1, respectively. From 001 to 009, σ was about twice as lare for the climate, altitude, eoraphic, and country subdivision (0.15 to 0.3; Table ) as for the yield-level subdivision (0.09 to 0.1) in both maturity roups. The lower σ in the yield-level subdivision tended to be associated with a hiher enotype subreion variance component ( σ ) (0.05 to 0.07) whereas σ was close to 0 for the other subdivision systems. This indicated that only the yield-level subdivision explained a lare proportion of enotype environment interactions. For all subdivision systems, the enotype year variance component ( σ ) was relatively small (0.0 y( s ) to 0.08) whereas the enotype environment variance component ( σ e( ys )) was the second larest variance component (0.3 to 0.33). Because σ e( ys ) and σ were considerably larer than σ and σ, the variance of hybrid y( s ) means was more influenced by local field conditions and trial-to-trial variation than by differences in hybrid rankin amon locations, subreions, and years. Genotypic Correlations and Relative Efficiency of Indirect and Index Selection Genotypic correlations and relative efficiency of indirect and index selection relative to direct selection were estimated based on BLUEs solely for the yield-level subdivision because low σ in the other subdivision systems indicated that enotypic correlations between subreions are hih and subdivision of the TPE will not increase selection ain. The predicted selection ain due to direct selection in subreion s (approach 1) was compared with that of indirect selection in the complementary subreion s (approach ), the undivided TPE t (approach 3), and index selection (approach 4). The enotypic variance in the low-yieldin subreion was only 10% of that in the hih-yieldin subreion (Table 3). This difference was primarily caused by the lower absolute value of rain yield in the low- relative to the hihyieldin subreion. In the undivided TPE, H of rain yield was 0.97 for both maturity roups. In the hih-yieldin subreion, H was nearly as hih as in the undivided TPE whereas it raned from 0.74 to 0.81 in the low-yieldin subreion. Even when H was estimated assumin equal testin effort, it was larer in the hih- than in the lowyieldin subreion, primarily because of lower enotypic variance in the latter subreion (data not shown) relative to other sources of variation affectin hybrid means. Genotypic correlations between low- and hihyieldin subreions (r (ss ) ) were on averae 0.81 for the early maturity roup and 0.69 for the late maturity roup. Therefore, enotypic performance in one subreion explained a maximum of 66% of the performance in the complementary subreion. Furthermore, this indicated that enotypic rank chanes occurred between them and that only a few hybrids had a ood performance in both. In the 3-yr intervals between 003 and 006 the predicted relative efficiency of indirect selection in the hih-yieldin subreion for performance in the lowyield subreion was >1. Averaed over all 3-yr sets, indirect selection in one subreion s for performance in the complementary subreion s was predicted to be less efficient ( ; Table 3) than direct selection. This was also the case when estimates of H were predicted for testin in 50 environments (data not shown). Genotypic correlations between hybrid means estimated usin only data from the low-yieldin subreion and means estimated by usin all available trials but inorin subdivision (r (st) ) were between 0.76 and 0.87 (Table 3). In the 3-yr intervals between 003 and 007, the predicted relative efficiency of indirect selection in the undivided TPE for the performance in the low-yield subreion was >1 for the early maturity roup because H in the low-yieldin subreion was small relative to that in the undivided TPE. In all other 3-yr intervals, direct selection was predicted to be more efficient. Averaed CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER

6 Table 3. Mean and standard deviation of the efficiency of indirect relative to direct selection. Three different approaches were applied to predict performance in the low- (LYS) and hih-yieldin subreion (HYS) based on the enotypic variance (σ ), broad-sense heritability (H), and enotypic correlation (r ). Parameters σ H r (ss ) r (st) in s (approach ) Indirect selection Efficiency of Indirect selection in t (approach 3) Index selection (approach 4) Early maturity roup LYS 0.0 ± ± ± ± ± ± ± 0.15 HYS 0.35 ± ± ± ± ± ± 0.05 Late maturity roup LYS 0.04 ± ± ± ± ± ± ± 0.05 HYS 0.36 ± ± ± ± ± ± 0.05 s, tareted subreion; s, complementary subreion; t, all data comprisin tareted and complementary subreions. The economic weiht of the tareted reion was 1 and of the complementary subreion 0 to make optimal recommendations for farmers in each subreion. across all 3-yr intervals, the efficiency of indirect selection in the undivided TPE for performance in the low-yieldin subreion was predicted to be between 0.83 and 1.01 for both maturity roups (Table 3). Indirect selection in the undivided TPE was predicted to be as efficient as direct selection in the hih-yieldin subreion when restrictin the enotypic correlation to 1. Estimates of enotypic correlations between the undivided TPE and the hihyieldin subreion slihtly exceeded 1 (i) whether they were derived from Eq. [3], (ii) if the enetic covariance between the undivided TPE and the hih-yieldin subreion was estimated directly by subtractin the environmental covariance from the phenotypic covariance (Falconer and Mackay, 1996), (iii) when H was predicted for n = 50 environments, or (iv) estimated on the basis of the enotypic variance and the variance of best linear unbiased predictions (Holland et al., 003; Piepho and Möhrin, 007; data not shown). The ratio of the response to index selection and direct selection in the low-yieldin subreion was predicted to be between 1.10 and 1.31, assumin that the economic weiht of the tareted reion was 1 and of the complementary subreion 0 (Table 3). Consequently, selection based on all available data usin a model considerin the yield-level effect as fixed and the enotype yield-level effect as random would be at least 10% better than direct selection usin only data from the low- or hih-yieldin subreion. DISCUSSION Variance Components of Maize Grain Yield in Eastern and Southern Africa Genotypic variance is a prerequisite for improvement of maize hybrids. Some hybrid testin prorams try to increase enotypic variance by subdividin a TPE into several less heteroeneous subreions, in effect convertin enotype subreion interaction variance into enotypic variance. Optimal subreion delineation, in breedin terms, should maximize enetic ains for the testin resources available (Atlin et al., 000a). The International Maize and Wheat Improvement Center currently divides its hybrid testin prorams into eastern and southern African subreions. If a TPE is subdivided, it is implicitly assumed that sinificant enotype subreion interaction exists, a hypothesis that should be verified. Examination of variance components can provide initial information about the manitude and practical importance of enotype subreion interactions. Variance components of maize rain yield were estimated for five different subdivision systems, assumin homoeneous variances. For the climate, altitude, eoraphic, and country subdivisions, σ was small relative to σ in both maturity roups. This indicated that there was little specific adaptation to the respective subreions and that simultaneous selection for a wide rane of environments is possible and may be cost-effective. Even thouh locations were rouped accordin to their similarity in earlier studies usin cluster analysis and eoraphic information system data (Bänzier et al., 004, 006), enotype subreion interaction variance based on these roupin was small, indicatin that the patterns of enotype environment interaction on which the subdivisions were based included substantial noise, and do not recur. These results clearly show that adaptation of elite maize hybrids across eastern and southern Africa is very broad, a findin that is in accordance with commercial maize breedin practice in the reion; several OPVs and hybrids are used from the Limpopo reion of northern South Africa to the mid-elevation reions of Ethiopia. Hence, for maximizin enetic ains, treatin climate, altitude, eoraphic, and country subreions as separate TPEs is not useful if databased roupin tend not to recur and no reion-specific farmin practices or locally important quality traits must be considered. Subdividin the TPE accordin to locations (i.e., Harare and Nairobi) would also not be appropriate as the testin effort in the resultin subreions would be very low and this subdivision system probably accounts for very little or no enotype subreion interaction variance. Furthermore, the yields at a certain location vary from year to year, which means that trials may be cateorized as low yieldin in one and as hih yieldin in another year. This CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER 01

7 also may imply low correlation amon those trials, even thouh they are conducted at the same location. Predicted ains obtainable via selection for specific adaptation to different aroecoloies miht have been slihtly underestimated because (i) enotypes were already selected for wide adaptation in previous breedin staes and (ii) information permittin subdivision was only available for those locations that were reularly used for hybrid evaluation. However, the consistent adoption of the best CIMMYT and commercial hybrids across subreions in eastern and southern Africa is stron support for the overall findin of little local or specific adaptation. Reportin hybrid means separately for each subreion, in addition to the undivided TPE, can provide confidence in the rane of adaptation of the selected hybrids. In the yield-level subdivision σ was relatively lare (~60% of σ for both maturity roups). Because of the fact that σ was nearly as hih as σ, it is likely that some hybrids do not perform well under both low- and hihyield subreions and that their performance in each must be considered in makin selection decisions. The underlyin environmental factors reducin yields in the low-yieldin subreion may be multifold, includin various combinations of abiotic and biotic stresses (Weber et al., 01). It may be of interest to research the relative importance of each of those stresses. Nevertheless, it should be noted that maize yields in farmers fields are usually not decreased by one particular stress at a certain plant rowth stae but rather by a combination of different stresses occurrin at the same or at different plant rowth staes. As such, selection of enotypes in low- and hih-yieldin environments may be optimal to serve farmers needs. The second larest variance component of rain yield was σ e( ys ), resultin from random chanes in the relative performance of enotypes from environment to environment and year to year, which is consistent with results of other studies (Cooper et al., 1999; Atlin et al., 000a; Setimela et al., 005). The contribution of σ e( ys ) and σ to the variance of entry means could be decreased with increasin testin effort plus ood field technique and trial desins. Unlike σ e( ys ) and σ, σ was low, as also y( s ) reported for rain yield of maize in India (Atlin et al., 011) and rice (Oryza sativa L.) in Thailand (Cooper et al., 1999). However, σ could have been imprecisely estimated y( s ) because it was based on a maximum of 13 common hybrids. To estimate σ and breedin proress across time with y( s ) more accuracy, it would be worthwhile to use lon-term checks that are retained in the trials across many years. Efficiency of Direct Selection Versus Indirect and Index Selection Applyin classical results from selection theory (Falconer and Mackay, 1996) to the problem considered here, relative efficiency of indirect selection compared with direct selection depends on H of rain yield in and enotypic correlation between the selection environments. Examination of Eq. [6] shows that indirect selection will be more efficient than direct selection if H in the indirect selection environment is hiher than that in the direct selection environment and if enotypic correlation between both selection environments is hih (Atlin et al., 000a). Broad-sense heritability is proportional to testin effort. Often, a decrease of H is observed with decreasin environmental mean yield (Bänzier et al., 1997; Mandal et al., 010; Weber et al., 01). In the current study, H of rain yield was considerably larer in the undivided TPE and in the hih-yieldin subreion than in the low-yieldin subreion based on the actual testin effort (Table 3) and on hypothetical testin in 50 environments (data not shown). Therefore, even if the number of low-yieldin trials is equal to the number of trials in the undivided TPE or in the hih-yieldin subreion, precision of the correspondin hybrid means will be lower. Genotypic correlations between the low- and hihyieldin subreions were moderate (Table 3). This indicated that substantial enotypic rank chanes between the two subreions occurred. Therefore, selection based on means estimated across the undivided TPE may fail to achieve the oal of CIMMYT to select maize hybrids that are both hih yieldin and optimal for farmers in low-yieldin, stress-prone environments. Furthermore, the product of the enotypic correlation and H in the hih-yieldin subreion was smaller than H in the lowyieldin subreion. Consequently, direct selection in the low-yieldin subreion was predicted to be more efficient than indirect selection in the hih-yieldin subreion and vice versa (Table 3). These results indicate that hybrid means should be reported separately for the low- and hih-yieldin subreions to identify those that perform well in each, which is in accordance with the results of Mandal et al. (010) and Venuprasad et al. (008). Specific adaptation to either low- or hih-yieldin subreions may have been more important than for the other subdivision systems because yield differences between subreions were much larer for this subdivision system, and mean yield difference has been neatively associated with enotypic correlation in performance across environments (Bänzier et al., 1997). Furthermore, it was reported that early-maturin hybrids performed better in low-yieldin trials whereas late-maturin hybrids performed better in hih-yieldin trials because they needed more water and N to complete their life cycle (Diallo, 1996; Weber et al., 01). Therefore, different physioloical mechanisms and enes responsible for hih relative rain yield in low- and hih-yieldin production environments miht lead to the relatively low enotypic correlation between them. In the current study, a small portion of the improved performance of certain hybrids in low-yieldin environments appeared to be the result CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER

8 of early flowerin. In both the early and late maturity roups the hihest yieldin hybrids in the low-yieldin environments flowered on averae between 1.4 and 1.6 d earlier than the hihest yieldin hybrids in the hihyieldin environments (data not shown). When subdividin the TPE accordin to yield levels, the effect of reduced testin effort in the resultin subreions has to be taken into account. The testin effort in the low-yieldin subreion was reduced by about 70% relative to that in the undivided TPE whereas it was reduced by about 30% in the hih-yieldin subreion. The relative proportion of low-yieldin environments in these reional trials miht have been lower than in the TPE because trials were rown with recommended quantities of fertilizers and weed control whereas maize hybrids are mostly rown with little or no fertilizer or pesticide input on-farm in the TPE. Furthermore, identifyin enotypes adapted to lowyieldin and drouht-prone production environments from rain-fed testin only is difficult because the number of low-yieldin trials per year is difficult to predict and the stress resultin in low yields is uncontrolled. For these reasons, the CIMMYT breedin pipeline relies heavily on manaed stress screens conducted under drouht and low-n conditions to enerate low-yield environments via the application of stress timin and levels that are thouht to be representative of those occurrin in farmers fields (Bänzier et al., 000; Weber et al., 01). Indirect selection based on all data but inorin subdivision accordin to yield levels was in most cases less efficient than direct selection based on means estimated by usin only the data from the tareted subreion (Table 3). The disadvantae of estimatin hybrid means inorin subdivision is that, effectively, much reater weiht is iven to hih- than to low-yieldin subreions. This may explain why crop varieties bred primarily under hihyieldin conditions sometimes failed to have an impact in low-yieldin production environments (Atlin and Frey, 1990; Ceccarelli et al., 199; Simmonds, 1991; Atlin et al., 001). Index selection was enerally more efficient than direct selection in low- or hih-yieldin subreions (approach 4 in Table 3). Especially for the low-yieldin subreion, predicted ains from indirect selection were hihest when stratifyin the TPE considerin the yieldlevel effect as fixed, thereby usin information from both subreions, appropriately weihted, in estimatin hybrid effects within each. It follows from the theory of mixed models that this approach minimized prediction error and maximized ain from selection (Piepho and Möhrin, 005; Table 3). Therefore, the application of this approach is optimal to estimate enotype means for low- and hihyieldin subreions, which is in areement with the results of Przystalski et al. (008) for oranic and nonoranic production environments. Selection Stratey for Hybrids Adapted to Both Low- and Hih-Yieldin Environments Precision of hybrid mean estimates and response to selection can be maximized by stratifyin the TPE into subreions, usin all available information, and weihtin the subreions based on their relevance to the tareted subreion (Piepho and Möhrin, 005). The extent to which the information from neihborin subreions is exploited depends on H in the neihborin subreions and on the enotypic correlation to the subreion of interest. Estimatin hybrid means based on Eq. [1] considerin the yield-level effect as fixed and the enotype yield-level effect as random (approach 4) constitutes an advance over usin information from only one subreion (approach 1 and ) and inorin subdivision and enotypic correlation between subreions (approach 3). Approach 4 is rarely used in the analysis of cultivar trial data (for an exception, see Przystalski et al. [008]) but is expected to always result in selection response that equals or exceeds the response from direct selection. The flexible subdivision of the eastern and southern African TPE into yield levels miht be optimal to exploit specific adaption but also to identify hybrids that are broadly adapted to both the low- and hih-yieldin subreions. This is an important oal for CIMMYT maize hybrid testin prorams, which serve both resource-poor farmers in hihly unfavorable areas as well as small farmers in more productive reions who invest substantially in inputs. CONCLUSIONS The existence of enotype environment interactions in the undivided TPE may indicate that subdivision is necessary. However, it is not always true that small differences between environments require specifically adapted hybrids or that selection response can be increased by dividin the TPE. Whether to select across the undivided TPE or separately in several subreions has to be validated for each hybrid testin proram individually. The current study showed that maize hybrids are very broadly adapted to different aroecoloies across eastern and southern Africa and that the subdivision of the broad TPE into climate, altitude, eoraphic, and country subreions was identifyin little or no specific adaptation within the early- and late-maturin hybrid roups used in this study. In contrast, means need to be estimated for the low- and hih-yieldin subreions separately to identify hybrids adapted to both subreions because enotype subreion interaction variances were lare relative to enotypic variance and enotypic correlations between subreions were relatively low, indicatin that enotypic rank chanes between low- and hih-yieldin subreions occurred. As a consequence, the CIMMYT maize hybrid testin prorams will now report hybrid means separately for low- and hih-yieldin subreions, estimatin these CROP SCIENCE, VOL. 5, SEPTEMBER OCTOBER 01

9 means usin all available data. The yield-level effect will be considered as fixed and correlation between subreions as correlated random enotype effects nested within subreions. With this stratey, it is possible to identify hybrids that perform well in both low- and hih-yieldin subreions, and that will therefore efficiently serve African smallholders in a broad rane of environments. Acknowledments We thank all collaborators involved in conductin the trials and C. Ayala for the construction of the data base used in this study. Furthermore, we thank H. F. Utz and T. Schra for their help durin the statistical analysis. This study was supported in part by the Rockefeller Foundation, the Bill and Melinda Gates Foundation, and the BMZ research project. Two anonymous referees are also thanked for very helpful comments and suestions. References Atlin, G.N., R.J. Baker, K.B. McRae, and X. Lu. 000a. Selection response in subdivided taret reions. 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