## Abstract

###
**Key message**

**Commercial heterosis for grain yield is present in hybrid wheat but long-term competiveness of hybrid versus line breeding depends on the development of heterotic groups to improve hybrid prediction.**

### Abstract

Detailed knowledge of the amount of heterosis and quantitative genetic parameters are of paramount importance to assess the potential of hybrid breeding. Our objectives were to (1) examine the extent of midparent, better-parent and commercial heterosis in a vast population of 1,604 wheat (*Triticum aestivum* L.) hybrids and their parental elite inbred lines and (2) discuss the consequences of relevant quantitative parameters for the design of hybrid wheat breeding programs. Fifteen male lines were crossed in a factorial mating design with 120 female lines, resulting in 1,604 of the 1,800 potential single-cross hybrid combinations. The hybrids, their parents, and ten commercial wheat varieties were evaluated in multi-location field experiments for grain yield, plant height, heading time and susceptibility to frost, lodging, septoria tritici blotch, yellow rust, leaf rust, and powdery mildew at up to five locations. We observed that hybrids were superior to the mean of their parents for grain yield (10.7 %) and susceptibility to frost (−7.2 %), leaf rust (−8.4 %) and septoria tritici blotch (−9.3 %). Moreover, 69 hybrids significantly (*P* < 0.05) outyielded the best commercial inbred line variety underlining the potential of hybrid wheat breeding. The estimated quantitative genetic parameters suggest that the establishment of reciprocal recurrent selection programs is pivotal for a successful long-term hybrid wheat breeding.

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## Acknowledgments

M. Gowda, J. Mühleisen and Y. Zhao were supported by BMBF within the HYWHEAT project (Grant ID: FKZ0315945D).

### Conflict of interest

The authors declare that they have no conflict of interest.

## Author information

## Additional information

C. F. H. Longin and M. Gowda contributed equally to this work.

Communicated by P. Langridge.

## Electronic supplementary material

Below is the link to the electronic supplementary material.

## Appendix

### Appendix

Assume two unrelated base populations *π*1 (females) and *π*2 (males) with two alleles, no epistasis, no linkage and equilibrium within and among loci in the base populations. For hybrid breeding, the total genetic variance is then defined after Schnell (1965, 1982) as \(\sigma_{\text{G}}^{2} ({\text{hybrid}}) = \varphi^{\prime}\sigma_{{GCA^{\prime}}}^{2} + \varphi^{\prime\prime}\sigma_{{GCA^{\prime\prime}}}^{2} + \varphi^{\prime}\varphi^{\prime\prime}\sigma_{\text{SCA}}^{2}\), where \(\varphi^{\prime} = 1/2\left( {1 + F_{\pi 1} } \right)\) and \(\varphi^{\prime\prime} = 1/2\left( {1 + F_{\pi 2} } \right)\) refer to the probability that testcross lines received alleles identical by descent from *π*1 and *π*2, and *F* is the inbreeding coefficient of the respective population. Regarding the reciprocal recurrent selection of GCA, each heterotic group is tested with few elite testers from the opposite pool, e.g., numerous female parental lines with few male lines. Thus, for *φ″*, we need to consider the number of tester lines. Imagine the homozygous lines J and K, which will be combined in a single-cross tester. Consequently, *φ″* = 1/2 + 1/2*f*
_{
jk
}, where *f*
_{
jk
} refers to the coefficient of coancestry among lines J and K. For three lines J, K, and L assuming theoretically an equal contribution of gametes to the tester, we get *φ″* = 1/3 + 2/9(*f*
_{
jk
} + *f*
_{
jl
} + *f*
_{
lk
}) and for arbitrary numbers of *n* lines, \(\varphi^{\prime\prime} = \frac{1}{n} + \frac{2}{{n^{2} }}\mathop \sum \nolimits_{j = 1}^{n - 1} \mathop \sum \nolimits_{k > 1}^{n} f_{jk}\). The value *n* represents the product of the number of testers multiplied by the number of tester lines (gametes) used to build up each tester, e.g., *n* = 4 for either using four inbred testers or two single-cross testers. The efficiency of type and number of tester lines with different relatedness [*f*
_{
jk
} = 0 (○), 0.25 (Δ) and 0.5 (×)] on the reduction of SCA is then determined relative to the use of one inbred tester as \({\text{Eff}} = 100 - \left[ {{{100 \times \left( {\varphi^{\prime}\varphi^{\prime\prime}\sigma_{\text{SCA}}^{2} + \varphi^{\prime}\varphi^{\prime\prime}\sigma_{{{\text{SCA}} \times {\text{E}}}}^{2} } \right)} \mathord{\left/ {\vphantom {{100 \times \left( {\varphi^{\prime}\varphi^{\prime\prime}\sigma_{\text{SCA}}^{2} + \varphi^{\prime}\varphi^{\prime\prime}\sigma_{{{\text{SCA}} \times {\text{E}}}}^{2} } \right)} {\left( {\varphi^{\prime}\sigma_{\text{SCA}}^{2} + \varphi^{\prime}\sigma_{{{\text{SCA}} \times {\text{E}}}}^{2} } \right)}}} \right. \kern-0pt} {\left( {\varphi^{\prime}\sigma_{\text{SCA}}^{2} + \varphi^{\prime}\sigma_{{{\text{SCA}} \times {\text{E}}}}^{2} } \right)}}} \right] = 100 - 100 \times \varphi^{\prime\prime}.\)

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Longin, C.F.H., Gowda, M., Mühleisen, J. *et al.* Hybrid wheat: quantitative genetic parameters and consequences for the design of breeding programs.
*Theor Appl Genet* **126, **2791–2801 (2013). https://doi.org/10.1007/s00122-013-2172-z

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### Keywords

- Powdery Mildew
- Leaf Rust
- Specific Combine Ability
- Hybrid Performance
- Yellow Rust