Reciprocal recurrent genomic selection: an attractive tool to leverage hybrid wheat breeding

Abstract

Key message

Using a two-part breeding strategy based on a population improvement and a product development component can leverage hybrid wheat breeding.

Abstract

Despite the technological advance of methods to facilitate hybrid breeding in self-pollinating crops, line breeding is still the dominating breeding strategy. This is likely due to a higher long-term selection gain in line compared to hybrid breeding. In this respect, recent studies on two-part strategies splitting the breeding program into a population improvement and a product development component could mark a trend reversal. Here, an overview of experimental and simulation-based studies exploring the possibilities to integrate genome-wide prediction into recurrent selection is given. Furthermore, possibilities to make use of recurrent selection for inter-population improvement are discussed. Current findings of simulation studies and quantitative genetic considerations suggest that long-term selection gain of hybrid breeding can be increased by implementing a two-part selection strategy based on reciprocal recurrent genomic selection. This would strengthen the competitiveness of hybrid versus line breeding facilitating to develop outstanding hybrid varieties also for self-pollinating plants such as wheat.

Appendix

In reciprocal recurrent genomic selection, the aim is to develop complementary heterotic groups yielding high hybrid performance. The degree of dominance, i.e., k = d/a with d referring to the dominance and a to the additive effects, at each single locus plays a crucial role to select for complementarity. In order to exploit successfully the dominance effects in hybrid breeding, selection directions have to be chosen carefully. For positive overdominance, the favorable allele should be fixed in one heterotic group but eliminated in the other. In contrast, in the presence of negative or partial dominance, heterozygous genotypes are disadvantageous compared to the homozygous genotypes. Therefore, the aim should be to fix the favorable allele in both heterotic groups so that the hybrid offspring is homozygous at the locus of interest.

Schnell (1965) introduced a concept of breeding value for hybrid populations. Let us denote the favorable allele B and the unfavorable allele B. Assume a male (m) and female heterotic group (f). Following Schnell (1965), the breeding values of genotypes that are homozygous for the favorable allele (BB) are defined for the male and the female heterotic group as:

$$\left\{ {\begin{array}{*{20}l} {F_{\text{BB}} = 2q_{\text{f}} \alpha_{\text{m}} } \hfill \\ {M_{\text{BB}} = 2q_{\text{m}} \alpha_{\text{f}} } \hfill \\ \end{array} } \right.\quad {\text{with}}\quad \left\{ {\begin{array}{*{20}l} {\alpha_{\text{m}} = a + d\left( {q_{\text{m}} - p_{\text{m}} } \right)} \hfill \\ {\alpha_{\text{f}} = a + d\left( {q_{\text{f}} - p_{\text{f}} } \right)} \hfill \\ \end{array} } \right..$$

F_BB and M_BB refer to the breeding values for the genotypes in the female and the male heterotic group, respectively, carrying the favorable allele. The frequency of the favorable allele B is denoted as p, and the frequency of the unfavorable allele b is denoted as q. The subscripts m and f identify allele frequencies of the male and female heterotic group, respectively. The question arises whether the concept of Schnell (1965) is suited for long-term reciprocal recurrent genomic selection. In the following, we studied the direction of selection for different k in dependency on the allele frequencies in the two heterotic groups. We assume that the initial allele frequencies q_f and q_m are nonzero, i.e., the favorable allele has not been fixed in either of the two heterotic groups. We further assume that k ≠ 0, otherwise the breeding value is purely contributed by a, and the favorable allele will be fixed through selection in both heterotic groups just like in line breeding.

Situation A

0 < k ≤ 1.

Suppose F_BB < 0, then we have α_m < 0, which is equivalent to $p_{\text{m}} > \frac{k + 1}{2k}$. But, $\frac{k + 1}{2k} \ge 1$ since 0 < k ≤ 1. This implies $p_{\text{m}} > 1$, which is impossible. The same arguments hold true when supposing $M_{\text{BB}} < 0$. Thus, F_BB and $M_{\text{BB}}$ will always be positive. So in this situation the selection will eventually fix the favorable allele in both heterotic groups, which is desirable.

Situation B

$k > 1$

There are four possible combinations of positive and negative F_BB and M_BB:

Situation B1

F_BB < 0 and M_BB < 0

This means $p_{\text{m}} > \frac{k + 1}{2k}$, and $p_{\text{f}} > \frac{k + 1}{2k}$. Since F_BB < 0, the selection will aim to decrease the frequency of genotypes that are homozygous for the allele of interest, and thus decrease p_f. In parallel, as M_BB < 0, the selection will aim to decrease p_m. Thus, in both heterotic groups the frequencies of the allele of interest will be decreased until one of them goes below the threshold $\frac{k + 1}{2k}$. Then, it changes to Situation B2 or B3, depending on the allele frequency p of which heterotic groups decrease below the threshold first.

• (i) Situation B2, F_BB < 0 and M_BB > 0

  This means $p_{\text{m}} > \frac{k + 1}{2k}$, and $p_{\text{f}} < \frac{k + 1}{2k}$. Since F_BB < 0, the selection will aim to decrease the frequency of genotypes that are homozygous for the allele of interest, and thus decrease p_f. Because $p_{\text{f}} < \frac{k + 1}{2k}$, a decrease in $p_{\text{f}}$ will not change the sign of M_BB. Thus, we still have M_BB > 0, implying that the selection in the male group will further increase p_m. As $p_{\text{m}} > \frac{k + 1}{2k}$, the sign of F_BB will also stay negative. Hence, M_BB will always favor genotypes carrying two alleles of interest, while F_BB will constantly discriminate against these very genotypes. This process finally leads to $p_{\text{m}} = 1,$ and p_f = 0. This is a desirable constellation that allows to produce hybrid offspring that is heterozygous for the allele of interest.

• (ii) Situation B3, F_BB > 0 and M_BB < 0

  This means $p_{\text{m}} < \frac{k + 1}{2k}$, and $p_{\text{f}} > \frac{k + 1}{2k}$. Since F_BB > 0, the selection will increase the frequency of genotypes that are homozygous for the allele of interest. Because $p_{\text{f}} > \frac{k + 1}{2k}$, the breeding value of these very genotypes will stay negative in the male heterotic group. Then, the selection in the male group will further decrease p_m, implying that F_BB will stay positive. Eventually, this process leads to $p_{\text{f}} = 1,$ and p_m = 0. This is a desirable constellation that allows to produce hybrid offspring that is heterozygous for the allele of interest.

• (iii) Situation B4, F_BB > 0 and M_BB > 0

  This means $p_{\text{m}} < \frac{k + 1}{2k}$, and $p_{\text{f}} < \frac{k + 1}{2k}$. Since F_BB > 0 and M_BB > 0, the selection will aim to increase the frequency of genotypes that are homozygous for the allele of interest in both heterotic groups. As soon as the frequency of these very genotypes goes above the threshold of $\frac{k + 1}{2k}$ in one heterotic group, the sign of the breeding value in the opposite heterotic group will change the sign, and thus, the selection direction will be reversed here, leading back to Situation B2 or Situation B3 and the allele of interest will be fixed in one heterotic group and eliminated in the other. Finally, both heterotic groups are in a complementary genetical constitution.

Situation C

− 1 ≤ k < 0

Suppose F_BB < 0, which is equivalent to $p_{\text{m}} < \frac{k + 1}{2k}$. Since − 1 ≤ k < 0, we have $\frac{k + 1}{2k} \le 0$. This implies $p_{\text{m}} < 0$, which is impossible. The same arguments hold true if we suppose $M_{\text{BB}} < 0$. Thus, F_BB and M_BB will always be positive. So as in Situation A, the selection will eventually fix the favorable allele in both heterotic groups.

Situation D

k < − 1

There are four possible combinations of positive and negative F_BB and M_BB:

Situation D1

F_BB < 0 and M_BB < 0

This means $p_{\text{m}} < \frac{k + 1}{2k}$, and $p_{\text{f}} < \frac{k + 1}{2k}$. Since F_BB < 0, the selection will aim to decrease the frequency p_f of the favorable allele B. In parallel, as M_BB < 0, the selection will aim to decrease p_m. Both, p_m and p_f will eventually reach zero. This is problematic because the favorable allele will be eliminated, while the unfavorable allele will be fixed in both heterotic groups.

Situation D2

F_BB < 0 and M_BB > 0

This means $p_{\text{m}} < \frac{k + 1}{2k}$, and $p_{\text{f}} > \frac{k + 1}{2k}$. Since F_BB < 0, the selection will aim to decrease the frequency of the genotypes carrying the favorable allele in the female heterotic pool, and thus decrease p_f. Here, the selection intensity heavily influences how the selection directions behave. When $p_{\text{f}} \gg \frac{k + 1}{2k}$, and low selection intensity is applied, a small decrease in p_f will not change the sign of M_BB. This leads to an increase in p_m and eventually F_BB will change the sign, which leads to Situation D4. If the selection intensity is large enough, then $p_{\text{f}} < \frac{k + 1}{2k}$. As a consequence, M_BB will change the sign, e.g., M_BB < 0, which leads back to Situation D1.

Situation D3

F_BB > 0 and M_BB < 0

This means $p_{\text{m}} > \frac{k + 1}{2k}$, and $p_{\text{f}} < \frac{k + 1}{2k}$. Since F_BB < 0, the selection will aim to increase the frequency of the genotype carrying the favorable allele in the female heterotic pool, and thus increase p_f. If $p_{\text{f}} \approx \frac{k + 1}{2k}$, the increase in p_f can eventually lead to $p_{\text{f}} > \frac{k + 1}{2k}$ and finally to a positive breeding value of genotypes carrying favorable allele in the male heterotic group, e.g., M_BB > 0. This will lead to Situation D4. If $p_{\text{f}} \ll \frac{k + 1}{2k}$, a small increase in p_f may not change the sign of M_BB. As long as M_BB is smaller than zero, p_m will be decreased. If selection intensity in the male heterotic pool is higher enough, then p_m decrease below the threshold before M_BB change its sign, F_BB will change to negative, which leads back to Situation D1.

Situation D4

F_BB > 0 and M_BB > 0

This means $p_{\text{m}} > \frac{k + 1}{2k}$, and $p_{\text{f}} > \frac{k + 1}{2k}$. Since F_BB > 0 and M_BB > 0, the selection will aim to increase the frequency of the genotype carrying the favorable allele in both populations, until p_m = 1 and p_f = 1. This is the ideal constitution of heterotic groups in the presence of negative overdominance as it leads to hybrids that are homozygous for the beneficial allele.

As a final remark, note that in the above discussion we have assumed that the selection is first applied to the female group and then to the male group. Assuming the opposite (that the selection is first applied to males and then to females) will lead to similar results. However, if the selection is applied simultaneously to both groups, the conclusions are slightly different. More precisely, in Situation B1 and B4, there is an additional case that p_m and p_f could simultaneously change from above to below the threshold $\frac{k + 1}{2k}$ and back and forth. Similarly, in Situations D2 and D3, there is an additional case that the frequencies change from $p_{\text{m}} > \frac{k + 1}{2k}$, $p_{\text{f}} < \frac{k + 1}{2k}$ to $p_{\text{m}} < \frac{k + 1}{2k}$, $p_{\text{f}} > \frac{k + 1}{2k}$ and back and forth. These additional cases are undesirable as the selection goal will be either delayed, or even can never be achieved.