Effects of selection criteria on yield stability in chickpea (Cicer arietinum L.)

Summary Selection in the F₃ generation for seed yield, fruiting branches/plant, effective pods/plant, and seed index (100-seed weight) was carried out in two chickpea crosses. Sixty F₅ lines (15 lines/selection criterion) along with check variety were evaluated for seed yield in three distinct environments. The effects of selection criteria on yield stability was examined using linear regression approach and genotype-grouping technique. There were no differences between selection criteria for linear yield responses of F₅ lines to different environments. Within all four selection criteria the lines showed similar linear responses. The non-linear component was relatively higher for lines selected for effective pods and seed index than lines selected for yield and fruiting branches. On the basis of mean yield and coefficient of variation across environments, the seed index was the least effective selection criterion for developing high yielding and stable lines. When the results of stability parameters and genotype-grouping technique were considered together, selection for yield and fruiting branches was highly effective for isolating stable and high yielding lines.     

Genotype X environment interaction and simultaneous selection for high yield and stability in soybeans (Glycine max (L.) Merr.)

Eighteen genotypes of soybean were grown in five locations in Nigeria. The heritability estimates for seed yield were generally low, ranging from 22.6% to 45.3%. Joint regression analysis indicated the presence of genotype x environment, although a large proportion was non-linear. The genotypes responded differently to environments, highlighting the possibility of breeding for specific environments. The correlation of regression coefficients with mean yield indicated that high yielding genotypes were responsive to changing environments. The simultaneous selection parameters Pi, S³ and rank-sums gave somewhat similar results but Pi produced higher yielding genotypes than others. The correlation between Pi and rank-sum indicated that either of the techniques could be employed during selection.     

Efficient strategies to assess yield stability in winter wheat

Key message

Selecting contrasting environments allows decreasing phenotyping intensity but still maintaining high accuracy to assess yield stability.

Abstract

Improving yield stability of wheat varieties is important to cope with enhanced abiotic stresses caused by climate change. The objective of our study was to (1) develop and implement an improved heritability estimate to examine the required scale of phenotyping for assessing yield stability in wheat, (2) compare yield performance and yield stability of wheat hybrids and inbred lines, (3) investigate the association of agronomic traits with yield stability, and (4) explore the possibility of selecting subsets of environments allowing to portray large proportion of the variation of yield stability. Our study is based on phenotypic data from five series of official winter wheat registration trials in Germany each including 119–132 genotypes evaluated in up to 50 environments. Our findings suggested that phenotyping in at least 40 environments is required to reliably estimate yield stability to guarantee heritability estimates above 0.7. Contrasting the yield stability of hybrids versus lines revealed no significant differences. Absence of stable associations between yield stability and further agronomic traits suggested low potential of indirect selection to improve yield stability. Selecting posteriori contrasting environments based on the genotype-by-environment interaction effects allowed decreasing phenotyping intensity, but still maintaining high accuracy to assess yield stability. The huge potential of the developed strategy to select contrasting and informative environments has to be validated as a next step in an a priori scenario based on genotype-by-location interaction effects.

     

Genetic properties of four types of stability parameter

Summary The genetic properties of four types of stability parameter for individual genotypes were investigated using a set of diallel cross data (28 genotypes x four locations x 3 years). The specific parameters studied were: the variance of a genotype across environments (T1); the genotype x environment (GE) interaction effect for a genotype, squared and summed across all environments (T2); the residual mean square (MS) of deviations from the regression of a genotype on an environmental index (T3); and years within locations MS for a genotype, averaged over all locations (T4). Each stability statistic was fitted to the additive model, based on the assumption that if the stability parameter is heritable, stability of F₁ is most likely to be the average stability of its parents. The results showed that T1 and T4 were additive, but T2 and T3 were not. A study of the consistency of stability rankings between two seeding rates over the same set of environments showed a similar pattern. It appears that stability parameters of types 1 and 4 are heritable, and thus useful for selection, while those of types 2 and 3 are nonheritable, and thus not useful.Contribution No. R-029     

Environmental stability and heritability estimates for grain yield and test weight in triticale

Hexaploid triticale has many advantages over both parental species for both grain and forage production in certain environments. Additional information on environmental stability and heritability would be desirable to develop appropriate selection strategies in the production of superior widely-adapted cultivars. The grain yield of 22 diverse genotypes grown at four ecologically-distinct geographical locations [Quincy, FL, USA (approximate geographical coordinates (AGC) = 30 degreesN 84 degreesW, approximate elevation (AE) = 58 m), Plains, GA, USA (AGC = 32 degreesN 84 degreesW, AE = 76 m), Bozeman, MT USA (AGC = 45 degreesN 111 degreesW, AE = 1458 m), and Aberdeen, ID, USA (AGC = 42 degreesN 112 degreesW, AE = 1360 m)] was measured in two years with winter and spring planting dates only at Bozeman and Aberdeen. Test weight (grain weight in a given volume) was determined for two years at Bozeman and Aberdeen at both planting dates and one year at Quincy. Stability analyses indicated that significant (P < 0.01) variation in means, regression coefficients, and deviation mean squares of the genotypes were present for both characters. Realized heritability (h2) estimates were as follows: grain yield ranged from -0.02 to 0.80 with a mean of 0.57; test weight ranged from 0.63 to 1.05 with a mean of 0.93. The results indicated that substantial genetic variation is present and selection for widely-adapted cultivars would be effective for both characters especially test weight.     

The area under the function: an index for selecting desirable genotypes

The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (D _i). Thus, D _i is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. D _i is equal to the mean of the i ^th genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large D _i. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of D _i was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of D _i 's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on D _i .     

Heritability estimates in contrasting environments as influenced by the adaptation level of barley germ plasm

Low heritability estimates in marginal or stress environments have often been used as one of the main justification for conducting selection work in environments with optimum or near‐optimum conditions for plant growth and grain yield. In this study, we have examined the relationships between grain yield and broad‐sense heritability in four groups of recombinant inbred lines (RILs) obtained from four barley crosses derived from parents differing in adaptation to stress. The RILs and the parents were grown in 13 combinations of years and locations (environments) in Syria and Jordan. Grain yields ranged from about 30 kg ha^?1 to nearly 4000 kg ha^?1 and genotype × environment interactions explained about half of the total variance for environmentally standardised data. Broad‐sense heritability in the individual year–location combinations varied from 0 to 0.68 and both the simple correlation and the rank correlation coefficients between grain yield and heritability were not significant. Genotype × years within individual locations, which measures the repeatability of a location in discriminating between genotypes, was also independent from the yield level, confirming that low‐yielding locations can be reliable selection environments. Also, there was no relationship between the type of cross and the magnitude of heritability in the various environments, but, as expected, the magnitude of heritability was significantly associated with the genetic distance between the parents. It is concluded that, holding all other factors affecting response to selection constant, concerns about the magnitude of heritability at low‐yielding locations are not justified and should not prevent them from being used as selection sites.     

Efficiency of physiological trait-based and empirical selection approaches for drought tolerance in groundnut

Drought is the major abiotic constraint affecting groundnut productivity and quality worldwide. Most breeding programmes in groundnut follow an empirical approach to drought resistance breeding, largely based on kernel yield and traits of local adaptation, resulting in slow progress. Recent advances in the use of easily measurable surrogates for complex physiological traits associated with drought tolerance encouraged breeders to integrate these in their selection schemes. However, there has been no direct comparison of the relative efficiency of a physiological trait‐based selection approach (Tr) vis‐à‐vis an empirical approach (E) to ascertain the benefits of the former. The genetic material used in the present study originated from three common crosses and one institute‐specific cross from four collaborating institutes in India (total seven crosses). Each institute contributed six genotypes and each followed both the Tr and E selection approaches in each cross. The field trial of all selections, consisting of 192 genotypes (96 each Tr and E selections), was grown in 2000/2001 in a 4 × 48 alpha design in 12 season × location environments in India. The selection efficiency of Tr relative to E, RE_Tr, was estimated using the genetic concept of response to selection. Based on all the 12 environments, the two selection methods performed more or less similarly (RE_Tr= 1.045). When the 12 environments were grouped into rainy season and post‐rainy season, the relative response to selection in Tr method was higher in the rainy than in the post‐rainy season (RE_Tr= 1.220 vs 0.657) due to a higher genetic variance, lower G × E, and high h². When the 12 environments were classified into four clusters based on plant extractable soil‐water availability, the selection method Tr was superior to E in three of the four clusters (RE_Tr= 1.495, 0.612, 1.308, and 1.144) due to an increase in genetic variance and h² under Tr in clustered environments. Although the crosses exhibited significant differences for kernel yield, the two methods of selection did not interact significantly with crosses. Both methods contributed more or less equally to the 10 highest‐yielding selections (six for E and four for Tr). The six E selections had a higher kernel yield, higher transpiration (T), and nearly equal transpiration efficiency (TE) and harvest index (HI) relative to four Tr selections. The yield advantage in E selections came largely from greater T, which would likely not be an advantage in water‐deficient environments. From the results of these multi‐environment studies, it is evident that Tr method did not show a consistent superiority over E method of drought resistance breeding in producing a higher kernel yield in groundnut. Nonetheless, the integration of physiological traits (or their surrogates) in the selection scheme would be advantageous in selecting genotypes which are more efficient water utilisers or partitioners of photosynthates into economic yield. New biotechnological tools are being explored to increase efficiency of physiological trait‐based drought resistance breeding in groundnut.     

Genetic variability,character association and path analysis of oil yield and its component characters in Cymbopogon sp.

Seeking an opportunity for genetic improvement in aromatic grasses lead to an explorative study on the aspects of genetic variability, character association and path analysis between essential oil yield/plot and its contributing traits in twenty five genotypes of Cymbopogon sp. collected from different agro-climatic zones of India, grown in RBD with three replicates. Highly significant differences between genotypes were recorded for the traits that were brought under study. High genotypic and phenotypic coefficients of variation coupled with high heritability and moderate to high genetic advance over mean were recorded in geraniol content, citral content and geranyl acetate content indicating predominance of additive gene effects controlling these traits. Correlation and path analysis revealed that oil content, herb yield/plot and geranyl acetate content are overriding traits among all other growth and yield parameters, therefore more emphasis should be laid upon them while designing selection indices for improvement of essential oil yield.     

Divergent selection for dinitrogen fixation and yield in soybean

Summary Nitrogen fixation is generally considered to be a major parameter of productivity in soybean (Glycine max). The aim of the investigations reported here was to analyse the genetic behaviour of this trait in view of its possible use as an indirect criterion of selection for productivity. Divergent selection for nitrogen fixation rate was carried out on F₂ populations obtained from crosses between high-yielding cultivars that are well adapted to French climatic conditions. The genetic component of nitrogen fixation and yield was isolated through the analysis of (1) the nitrogen fixation potentials of the genotypes under controlled conditions and (2) the field yields under favourable conditions. Divergent selection resulted in two groups of genotypes whose nitrogen fixation abilities are significantly different. The F₆ filial progeny obtained by single seed descent from the two groups displayed significantly different abilities for nitrogen fixation and for field productivity. The gain achieved for the nitrogen fixation activity with respect to the mean value of the parents ranged from 20% to 33% for the positive selection, depending on the crosses. The occurrence of positive and significant correlations between the level of nitrogen fixation activity in F₂ plants and N₂ fixation or yield in the F₆ generation corroborates the relatively high heritability of this trait and suggests its possible use as an indirect selection criterion for yield.     

Genetic parameters for growth, wood density and pulp yield in Eucalyptus globulus

Genetic variation and co-variation among the key pulpwood selection traits for Eucalyptus globulus were estimated for a range of sites in Portugal, with the aim of improving genetic parameters used to predict breeding values and correlated response to selection. The trials comprised clonally replicated full-sib families (eight trials) and unrelated clones (17 trials), and exhibited varying levels of pedigree connectivity. The traits studied were stem diameter at breast height, Pilodyn penetration (an indirect measure of wood basic density) and near infrared reflectance predicted pulp yield. Univariate and multivariate linear mixed models were fitted within and across sites, and estimates of additive genetic, total genetic, environmental and phenotypic variances and covariances were obtained. All traits studied exhibited significant levels of additive genetic variation. The average estimated within-site narrow-sense heritability was 0.19 ± 0.03 for diameter and 0.29 ± 0.03 for Pilodyn penetration, and the pooled estimate for predicted pulp yield was 0.42 ± 0.14. When they could be tested, dominance and epistatic effects were generally not statistically significant, although broad-sense heritability estimates were slightly higher than narrow-sense heritability estimates. Averaged across trials, positive additive (0.64 ± 0.08), total genetic (0.58 ± 0.04), environmental (0.38 ± 0.03) and phenotypic (0.43 ± 0.02) correlation estimates were consistently obtained between diameter and Pilodyn penetration. This data argues for at least some form of pleiotropic relationship between these two traits and that selection for fast growth will adversely affect wood density in this population. Estimates of the across-site genetic correlations for diameter and Pilodyn penetration were high, indicating that the genotype by environment interaction is low across the range of sites tested. This result supports the use of single aggregated selection criteria for growth and wood density across planting environments in Portugal, as opposed to having to select for performance in different environments.     

Integration of genomic information into sport horse breeding programs for optimization of accuracy of selection

Reliable selection criteria are required for young riding horses to increase genetic gain by increasing accuracy of selection and decreasing generation intervals. In this study, selection strategies incorporating genomic breeding values (GEBVs) were evaluated. Relevant stages of selection in sport horse breeding programs were analyzed by applying selection index theory. Results in terms of accuracies of indices (r_TI) and relative selection response indicated that information on single nucleotide polymorphism (SNP) genotypes considerably increases the accuracy of breeding values estimated for young horses without own or progeny performance. In a first scenario, the correlation between the breeding value estimated from the SNP genotype and the true breeding value (= accuracy of GEBV) was fixed to a relatively low value of r_mg = 0.5. For a low heritability trait (h² = 0.15), and an index for a young horse based only on information from both parents, additional genomic information doubles r_TI from 0.27 to 0.54. Including the conventional information source ‘own performance’ into the before mentioned index, additional SNP information increases r_TI by 40%. Thus, particularly with regard to traits of low heritability, genomic information can provide a tool for well-founded selection decisions early in life. In a further approach, different sources of breeding values (e.g. GEBV and estimated breeding values (EBVs) from different countries) were combined into an overall index when altering accuracies of EBVs and correlations between traits. In summary, we showed that genomic selection strategies have the potential to contribute to a substantial reduction in generation intervals in horse breeding programs.     

QTL for yield in bioenergy Populus: identifying G×E interactions from growth at three contrasting sites

Populus is a genus of fast growing trees that may be suitable as a bioenergy crop grown in short rotation, but understanding the genetic nature of yield and genotype interactions with the environment is critical in developing new high-yield genotypes for wide-scale planting. In the present study, 210 genotypes from an F₂ population (Family 331; POP1) derived from a cross between Populus trichocarpa 93-968 and P. deltoides ILL-129 were grown in southern UK, central France and northern Italy. The performance of POP1, based upon first- and second-year main stem traits and biomass production, improved from northern to southern Europe. Trees at the Italian site produced the highest mean biomass ranging from 0.77 to 18.06 oven-dried tonnes (ODT) ha⁻¹ year⁻¹, and the UK site produced the lowest mean biomass ranging from 0.18 to 10.31 ODT ha⁻¹ year⁻¹. Significant genotype × environment interactions were seen despite heritability values across sites being moderate to high. Using a pseudo-testcross analysis, 37 quantitative trait loci (QTL) were identified for the maternal parent and 45 for the paternal parent for eight stem and biomass traits across the three sites. High genetic correlations between traits suggested that collocating QTL could be inferred as a single pleiotropic QTL, reducing the number of unique QTL to 23 and 24 for the maternal and paternal parent, respectively. Additive genetic effects were seen to differ significantly for eight QTL on the maternal map and 20 on the paternal map across sites. An additive main effects and multiplicative interaction analysis was carried out to obtain stability parameters for each trait. These parameters were mapped as QTL, and collocation to trait QTL was accessed. Two of the eight stability QTL collocate to trait QTL on the maternal map, and 8 of the 20 stability QTL collocate to trait QTL on the paternal map, suggesting that a regulatory gene model is prevalent over an allele sensitivity model for stem trait stability across these environments.     

The genetics of phenotypic plasticity. VI. Theoretical predictions for directional selection

We explore the effects of linear and quadratic reaction norms on heritability and directional selection. Genetic variation for reaction norm parameters can alter the heritability of traits; the magnitude of the heritability depends upon both the environment and the correlation among the parameters. Genetic variation for reaction norm parameters can alter the response to directional selection. Selection on a trait in one environment can shift both the mean of the trait measured across environments and the plasticity of the trait; the signs and magnitudes of these responses depend on the correlations among the parameters of the reaction norm. Our model is consistent with the results of ten experiments for selection on a trait in a single environment. In all experiments, selection towards the overall mean of the population always resulted in a relatively lower plasticity than selection away from the overall mean. Our model was able to predict the results of two experiments for selection on a trait index calculated over more than one environment. Predictions were good for the direct response to selection but poorer for the correlated response to selection. Our results indicate the need for more data on the effects of environment on genetic parameters, especially correlations among reaction norm parameters.     

Selection,structure and the heritability of behaviour

Characters which are closely linked to fitness often have low heritabilities (V_A/V_P). Low heritabilities could be because of low additive genetic variation (V_A), that had been depleted by directional selection. Alternatively, low heritabilities may be caused by large residual variation (V_R=V_P – V_A) compounded at a disproportionately higher rate than V_A across integrated characters. Both hypotheses assume that each component of quantitative variation has an independent effect on heritability. However, V_A and V_R may also covary, in which case differences in heritability cannot be fully explained by the independent effects of elimination‐selection or compounded residual variation. We compared the central tendency of published behavioural heritabilities (mean=0.31, median=0.23) with morphological and life history data collected by 26 ). Average behavioural heritability was not significantly different from average life history heritability, but both were smaller than average morphological heritability. We cross‐classified behavioural traits to test whether variation in heritability was related to selection (dominance, domestic/wild) or variance compounding (integration level). There was a significant three‐way interaction between indices of selection and variance compounding, related to the absence of either effect at the highest integration level. At lower integration levels, high dominance variance indicated effects of selection. It was also indicated by the low CV_A of domestic species. At the same time CV_R increased disproportionately faster than CV_A across integration levels, demonstrating variance compounding. However, neither CV_R nor CV_A had a predominant effect on heritability. The partial regression coefficients of CV_R and CV_A on heritability were similar and a path analysis indicated that their (positive) correlation was also necessary to explain variation in heritability. These results suggest that relationships between additive genetic and residual components of quantitative genetic variation can constrain their independent direct effects on behavioural heritability.     

Utilization of leaf temperature for the selection of leaf gas-exchange traits to induce heat resistance in sunflower (Helianthus annuus L.)

Heat stress is a major production constraint of sunflower worldwide. Therefore, various populations (parental, F₁, F₂, F₃, and plant progenies) of sunflower were screened for leaf gas-exchange traits with the objectives to formulate selection criteria of heat resistance and development of heat-resistant lines. Initial screening and F₂ seeds exposed to heat stress (45°C) resulted in the development of an adapted F₂ population that showed leaf gas-exchange and morphological traits better than the unadapted population. Correlation coefficients of traits were partitioned into direct and indirect effects via a path analysis technique to determine the cause of their relationship with a basic parameter such as a reproductive head mass (HM). Path analysis showed a positive direct effect of leaf temperature (T_leaf) (0.32) on HM and also an indirect effect (0.77) of the transpiration rate (E) on HM. Moreover, T_leaf showed high heritability estimates. T_leaf was used to select superior plants within the F₂ population. This selection brought about an improvement in the net photosynthetic rate (P _N) and E as it was indicated from progeny performance and realized heritability. Progenies selected on the basis of T_leaf also showed an increase in achene yield and heat resistance over unselected F₃ progenies and a commercial hybrid.     

Heritability and expected selection response for yield traits in blanched asparagus

Despite the continuous breeding that has been conducted with asparagus (Asparagus officinalis L.) since the beginning of the last century, there is little information on parameters for predicting direct and indirect selection response. Yield traits for blanched asparagus production were studied along a two-year period in a half-sib family population planted in Zavalla, Argentina. Half-sib family mean heritability values were low for total yield and marketable spear number (0.31 and 0.35), intermediate for marketable yield and total spear number (0.55 and 0.64), and relatively high for spear diameter and spear weight (0.75 and 0.74). An average increase in marketable yield of 15.9% is expected after each cycle of selection of the top 5% of the families. Total yield failed to express significant genetic correlations with any of the yield components; meanwhile marketable yield showed highly significant relations with market spear number (0.96) and spear weight (0.89). Indirect selection response over yield components (CRx) failed to be advantageous over direct selection (Rx), since the ratio CRx/Rx was always equal or below unity.     

Genome-wide association study for agronomic and physiological traits in spring wheat evaluated in a range of heat prone environments

Key message

We identified 27 stable loci associated with agronomic traits in spring wheat using genome-wide association analysis, some of which confirmed previously reported studies. GWAS peaks identified in regions where no QTL for grain yield per se has been mapped to date, provide new opportunities for gene discovery and creation of new cultivars with desirable alleles for improving yield and yield stability in wheat.

Abstract

We undertook large-scale genetic analysis to determine marker-trait associations (MTAs) underlying agronomic and physiological performance in spring wheat using genome-wide association studies (GWAS). Field trials were conducted at seven sites in three countries (Sudan, Egypt, and Syria) over 2–3 years in each country. Twenty-five agronomic and physiological traits were measured on 188 wheat genotypes. After correcting for population structure and relatedness, a total of 245 MTAs distributed over 66 loci were associated with agronomic traits in individual and mean performance across environments respectively; some of which confirmed previously reported loci. Of these, 27 loci were significantly associated with days to heading, thousand kernel weight, grain yield, spike length, and leaf rolling for mean performance across environments. Despite strong QTL by environment interactions, eight of the loci on chromosomes 1A, 1D, 5A, 5D, 6B, 7A, and 7B had pleiotropic effects on days to heading and yield components (TKW, SM^?2, and SNS). The winter-type alleles at the homoeologous VRN1 loci significantly increased days to heading and grain yield in optimal environments, but decreased grain yield in heat prone environments. Top 20 high-yielding genotypes, ranked by additive main effects and multiplicative interaction (AMMI), had low kinship relationship and possessed 4–5 favorable alleles for GY MTAs except two genotypes, Shadi-4 and Qafzah-11/Bashiq-1–2. This indicated different yield stability mechanisms due to potentially favorable rare alleles that are uncharacterized. Our results will enable wheat breeders to effectively introgress several desirable alleles into locally adapted germplasm in developing wheat varieties with high yield stability and enhanced heat tolerance.

     

Quantitative analysis of correlations among flower traits in Gerbera hybrida,Compositae

Summary A Mean Correlation Response (MCR) model was developed to estimate the relative effectiveness of direct selection when other traits also respond to the selection. A measure of the relative effects of mean correlated response and direct response (R) and a measure of the relative efficiency of direct selection (IE) were applied to a genetic correlation matrix of 38 traits. These were measurements of inflorescence, receptacle and involucre, scape, disk florets, ray florets, and trans florets in the Davis population of Gerbera hybrida, Compositae. Generally, traits with high heritability had high direct and mean correlated response; these were often traits measuring disk and trans florets. Traits with low heritability had low direct and mean correlated response; these were often traits measuring the inflorescence. Traits of the inflorescence had the lowest efficiency of direct to mean correlated response.     

Efficiency of indirect selection at selection equilibrium

Summary Efficiency of indirect selection compared with that of direct selection to increase the mean value of some trait has been usually studied by considering a single generation of indirect and direct responses to selection only. However, under continued selection, genetic variances and covariances, and therefore expected genetic responses, change each generation due to linkage disequilibrium. With directional and truncation selection, genetic parameters asymptote to limiting values after several generations. The efficiency of indirect selection is examined in this limiting situation. The ratio of correlated response to direct response for the trait to improve in the limit is compared with the ratio after the first generation of selection. For all initial parameter values for which indirect selection is more efficient than direct selection, relative efficiency of indirect selection is smaller in the limit than in the first generation. For some parameter values, indirect selection is more efficient than direct selection in the first generation, but less efficient in the limit. Expressions for minimum values of the initial genetic correlation and heritability of the alternative trait required for indirect selection to be preferred in the limit are derived. These values are higher when limiting responses are used instead of single generation responses. The loss in relative efficiency of indirect selection from changes in genetic parameters due to selection should be taken into account when applications of indirect selection are considered.