Genomic regions involved in response to grain yield selection at high and low nitrogen fertilization in maize

Abstract

In order to validate the role of genomic regions involved in nitrogen use efficiency and detected in a population of recombinant inbred lines (RIL), we have applied from the same population a recurrent selection for adaptation to low N-input (N0) and to high N-input (N1). Variation of allele frequency at neutral marker during the two cycles of recurrent selection may provide information about markers linked to QTLs. Significant temporal variation of allele frequency was investigated using the test of Waples, which tests the hypothesis of genetic drift versus selection. Most genomic regions (12/19) responding to selection were detected for selection at high N-input and only two were common to selection at high and low N-inputs. This was consistent with the greater grain yield response to selection observed for the population selected under high N-input compared with the population selected under low N-input, when they were evaluated at high N-fertilization. In contrast, when they were evaluated at low N-input both types of selection gave similar yield. As was expected, in the first cycle we observed selection of markers linked to grain yield QTLs. In the course of the second cycle three situations were observed: the confirmation of most regions already selected in C1 including all C1 regions overlapping with grain yield QTLs; the non-confirmation of some C1 regions (2/9); and the identification of new genomic zones (10/17). The detected marker–QTL associations revealed the consistency of the involvement of some traits, such as root architecture and glutamine synthetase activity, which would be of major importance for grain yield setting whatever the nitrogen fertilization.

Appendix: Derivation of var(p x −p y )

In what follows, p _x represents the frequency of allele from F2 parent in population x (with x=0, 1 or 2). As we can write var(p _x −p _y ) = var p _x  + var p _y  − 2 cov(p _x p _y ), we have to then derive var p _x and cov(p _x p _y ).

Derivation of the variance of marker frequencies assuming only genetic drift

Our experiment corresponds to a sampling in three steps:

• From an infinite RIL population where p=0.5, 99 RIL have been drawn leading to the population C0 with a frequency p ₀ , and var p ₀=p(1−p)/N ₀, with p=0.5 and N ₀ the number of RIL in C0.

• From C0 to C1: N₁ RIL have been selected (already genotyped), leading to p ₁|p ₀ (p ₁ conditional to p ₀), and var p ₁|p ₀=p(1−p ₀)/N ₁.

• From C1 to C2: N₂ non-inbred individuals (2N₂ genes) were selected and genotyped, leading to p ₂ |p ₁ and var p ₂(p ₁=p ₁(1−p ₁)/2N ₂.

To derive var p ₁ and var p ₂, we used the relationship var Y = E[var(Y|X)] + var[E(Y|X)], which means that the total variance is equal to the sum of intraclass variance and interclass variance. Then

$$ \text{var} p_{n} = E[\text{var} (p_{n} |p_{{n - 1}} )] + \text{var} [E(p_{n} |p_{{n - 1}} )]; $$

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with $E(p_{n} |p_{{n - 1}} ) = p_{{n - 1}}$ then

$$ \text{var} p_{n} = E[\text{var} (p_{n} |p_{{n - 1}} )] + \text{var} p_{{n - 1}} . $$

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Furthermore,

$$ E{\left[ {\text{var} {\left( {p_{n} |p_{{n - 1}} } \right)}} \right]} = E{\left[ {\frac{{p_{{n - 1}} (1 - p_{{n - 1}} )}} {{\theta N_{n} }}} \right]}, $$

N _n being the number of sampled plants to develop generation n, and θ=1 in C0 and C1, and θ=2 in C2, with

$$ E[p_{{n - 1}} (1 - p_{{n - 1}} )] = E(p_{{n - 1}} ) - E(p^{2}_{{n - 1}} ) = p - (\text{var} p_{{n - 1}} + p^{2} ), $$

results in

$$ E{\left[ {\text{var} {\left( {p_{1} |p_{0} } \right)}} \right]}{\text{ }} = {\text{ }}\frac{{p(1 - p)}} {{N_{1} }} - \frac{{\text{var} p_{0} }} {{N_{1} }} = p{\left( {1 - p} \right)}\frac{1} {{N_{1} }}{\left( {1 - \frac{1} {{N_{0} }}} \right)}, $$

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with

$$ \text{var} p_{1} = p(1 - p){\left[ {1 - {\left( {1 - \frac{1} {{N_{0} }}} \right)}{\left( {1 - \frac{1} {{N_{1} }}} \right)}} \right]} $$

and

$$ \text{var} p_{2} = p(1 - p){\left[ {1 - {\left( {1 - \frac{1} {{N_{0} }}} \right)}{\left( {1 - \frac{1} {{N_{1} }}} \right)}{\left( {1 - \frac{1} {{2N_{2} }}} \right)}} \right]}. $$

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More generally

$$ \text{var} p_{n} = p(1 - p){\left[ {1 - {\prod\limits_{i = 0}^{i = n} {{\left( {1 - \frac{1} {{\theta N_{i} }}} \right)}} }} \right]}, $$

which is indeed the Fisher–Wright formula when θN _i =2N.

According to expression 4 the variance in gene frequency at a generation m can also be written as the sum of all sampling variances from generation 0:

$$ \begin{aligned}{} \text{var} p_{1} {\text{ }} & = E{\left( {\text{var} p_{1} |p_{0} } \right)} + \text{var} p_{0} , \\ \text{var} p_{2} {\text{ }} & = E{\left( {\text{var} p_{2} |p_{1} } \right)} + \text{var} p_{1} = E{\left( {\text{var} p_{2} |p_{1} } \right)} + E(\text{var} p_{1} |p_{0} ) + \text{var} p_{0} , \\ \end{aligned} $$

and more generally

$$ \text{var} p_{m} = {\sum\limits_{i = 1}^{i = m} {E(\text{var} p_{i} |} }p_{{i - 1}} ) + \text{var} p_{0} . $$

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Derivation of cov p ₁ p ₂, cov p ₀ p ₁, cov p ₀ p ₂

At a generation n deriving from an ancestor generation m, it is possible to write

$$ p_{n} = p_{m} + \varepsilon , $$

where ε is a random deviation due to sampling process from m to n, resulting in

$$ \text{cov} p_{m} p_{n} = \text{var} p_{m} . $$

Thus, cov p ₁ p ₀ = var p ₀, cov p ₂ p ₀ = var p ₀ and cov p ₂ p ₁ = var p ₁.