Quantitative trait loci analysis of zinc efficiency and grain zinc concentration in wheat using whole genome average interval mapping

Abstract

Zinc (Zn) deficiency is a widespread problem which reduces yield and grain nutritive value in many cereal growing regions of the world. While there is considerable genetic variation in tolerance to Zn deficiency (also known as Zn efficiency), phenotypic selection is difficult and would benefit from the development of molecular markers. A doubled haploid population derived from a cross between the Zn inefficient genotype RAC875-2 and the moderately efficient genotype Cascades was screened in three experiments to identify QTL linked to growth under low Zn and with the concentrations of Zn and iron (Fe) in leaf tissue and in the grain. Two experiments were conducted under controlled conditions while the third examined the response to Zn in the field. QTL were identified using an improved method of analysis, whole genome average interval mapping. Shoot biomass and shoot Zn and Fe concentrations showed significant negative correlations, while there were significant genetic correlations between grain Zn and Fe concentrations. Shoot biomass, tissue and grain Zn concentrations were controlled by a number of genes, many with a minor effect. Depending on the traits and the site, the QTL accounted for 12–81% of the genetic variation. Most of the QTL linked to seedling growth under Zn deficiency and to Zn and Fe concentrations were associated with height genes with greater seedling biomass associated with lower Zn and Fe concentrations. Four QTL for grain Zn concentration and a single QTL for grain Fe concentration were also identified. A cluster of adjacent QTL related to the severity of symptoms of Zn deficiency, shoot Zn concentration and kernel weight was found on chromosome 4A and a cluster of QTL associated with shoot and grain Fe concentrations and kernel weight was found on chromosome 3D. These two regions appear promising areas for further work to develop markers for enhanced growth under low Zn and for Zn and Fe uptake. Although there was no significant difference between the parents, the grain Zn concentration ranged from 29 to 43 mg kg⁻¹ within the population and four QTL associated with grain Zn concentration were identified. These were located on chromosomes 3D, 4B, 6B and 7A and they described 92% of the genetic variation. Each QTL had a relatively small effect on grain Zn concentration but combining the four high Zn alleles increased the grain Zn by 23%. While this illustrates the potential for pyramiding genes to improve grain Zn, breeding for increased grain Zn concentration requires identification of individual QTL with large effects, which in turn requires construction and testing of new mapping populations in the future.

Appendix

Statistical models: baseline models without QTL

The mixed model forms the basis of the analysis and is given by

$${\mathbf{y}} = {\mathbf{X}}\tau + {\mathbf{Zu}} + {\mathbf{Z}}_l {\mathbf{g}} + {\mathbf{e}}$$

(1)

where X, Z and Z _l , and are known design matrices for the fixed effects, random effects and genetic effects respectively, τ is the vector of fixed effect parameters, u is a vector of random effects and e is a vector of residual random effects. These latter two effects are assumed independent, mean zero with covariance matrices G _u and R and respectively. The form of G _u and R will depend on the application.

We are specifically interested in the genetic line effects g. Two classes of analysis are required, firstly for the Zn scores and grain Zn and Fe concentrations, and secondly for the seedling traits. The two situations involve different models for g.

Zinc score

Since only the nil Zinc plants were scored, g represents a single set of genotypic line effects under the nil treatment, and it is assumed

$$g \sim N\left( {0,\sigma _g^2 {\text{I}}_{{\text{n}}_{\text{g}} } } \right)$$

(2)

where $\sigma _g^2$ is the genetic line variance and n _g is the number of lines. The base model fitted was

$${\text{ZincScore = Type + }}{\mathbf{Block}}{\text{ + }}{\mathbf{Variety}}{\text{ + }}{\mathbf{Error}}$$

where the bold terms are random effects. The term Type is a factor of three levels (DH, RAC875-2, Cascades) and hence distinguishes the DH lines from the parents. The Variety term represents the polygenic line effects.

It was assumed that the Error term was such that $e \sim N\left( {0,\sigma ^2 {\text{I}}_{\text{n}} } \right)$, so that R = σ ² I _n . Thus is the genetic variance associated with the doubled haploid lines, while σ ² is the residual or error variance.

Plant traits

Shoot dry matter, shoot Zn and Fe concentration were measured under both the Nil and the Zinc treatments, and in Experiments 1 and 2. The resulting four combinations will be considered a (structured) set of four environments. Thus we assume

$$g \sim N\left( {0,\sigma ^2 \left( {{\text{G}} \otimes {\text{I}}_{n_{\text{g}} } } \right)} \right)$$

(3)

where G is a 4 × 4 variance-covariance matrix that provides the genetic variances across lines for the trait grown under the two treatments in the two experiments (hence 4) and the genetic covariances of the trait between pairs of environments; G may be an unstructured (and hence fully parameterized) variance–covariance matrix, or it may take on another form. In the analysis of multi-environment trials, this matrix is taken to be a factor analytic (FA) structure (Smith et al. 2005). For the case of t environments, the FA model is given by

$${\mathbf{g}} = \left( { \wedge \otimes {\text{I}}_{n_g } } \right){\mathbf{f}} + \xi $$

where if there are n _f factors, f represents a vector of latent unobserved factors of size $n_f n_g \times 1$, $\wedge$ is t × n _f an matrix of factor loadings for each of the treatments and each factor, and ξ is a residual random vector for genetic variation not explained by the factors. To ensure identifiability, ${\mathbf{f}} \sim {\text{N}}{\left( {{\mathbf{0}}{\text{,}}{\mathbf{I}}_{{n_{f} n_{g} }} } \right)}$ and $\xi \sim N\left( {0,\Psi \otimes {\text{I}}_{n_g } } \right)$ where Ψ where is a diagonal matrix. These FA models provide a parsimonious structure in many applications (see Smith et al. 2005).

Dry matter was multiplied by 100 to improve the scale for both estimation and reporting. However, there was clear variance heterogeneity for this and the other traits and the analysis was conducted on the log-scale. For the three plant traits (seedling biomass, shoot Zn and Fe concentrations), the base model fitted was:

$$\log \left( {{\text{trait}}} \right) = {\text{Type}}{\text{.Env + }}{\mathbf{at}}\left( {{\mathbf{Site}}} \right).{\mathbf{Block}} + {\mathbf{Env}}.{\mathbf{Variety}} + {\mathbf{Error}}$$

where Site represents the two experiments (Adelaide and Adana), Env is a factor of four levels, being a 2 × 2 factorial structure of level of Zinc (Nil, Zinc) by experiment (Adelaide, Adana) and Block reflects the randomized complete block design. The term Env.Variety allows for the interaction of genetic effects with the environment, and the latter is determined by the treatment by experiment combinations. The term at(Site).Block allows for separate block effects at each Site.

The Error term allowed for differing residual variances for each experiment by treatment combination; thus four residual variances were estimated.

Grain traits

Kernel weight, Zn and Fe concentration were measured on grain from the Zn-treated plants in Experiment 3 (the field trial). The model for g as given by (2) is again appropriate. The base model fitted for kernel weight was

$${\text{kwt = Type + }}{\mathbf{Block}} + {\mathbf{Column}} + {\mathbf{Variety}} + {\mathbf{Error}}$$

where Block reflects the design of the field trial, and the random Column effect allows for between column variation in the field. The Error term allowed for spatial variation in the field as indexed by the row and column position of the plots (see Gilmour et al. 2006).

For grain Zn concentration, the base model fitted is given symbolically as

$${\text{zc = Type + }}{\mathbf{Block}} + {\mathbf{Variety}} + {\mathbf{Error}}$$

where terms are very similar to the kernel weight model. For grain Fe concentration, the base model fitted was:

$${\text{fe = Type + lin}}\left( {{\text{Column}}} \right) + {\mathbf{Block}} + {\mathbf{spl}}\left( {{\mathbf{Column}}} \right) + {\mathbf{Variety}} + {\mathbf{Error}}$$

where additional terms were required to account for smooth spatial field dependence across rows that was evident in the analysis.

Statistical Models for QTL analysis

Zinc score and grain traits

The approach used for QTL analysis is based on Verbyla et al. (2007) who provide an approach that uses the full linkage map simultaneously in a staged analysis. A working model is used in which all intervals are assumed to possibly contain a QTL. The vector of the sizes of QTL effects for all intervals is denoted by a and is assumed to be a random effect with mean zero and variance$\left( {\sigma _a^2 } \right)$. If this variance is significant, an outlier detection technique is used to sequentially select putative QTL. At each selection step, the putative QTL interval is moved to the fixed effects part of the model and selection ceases when the between interval variation$\left( {\sigma _a^2 } \right)$ is no longer statistically significant.

The initial mixed model that is used for the QTL analysis is given by

$${\mathbf{y}} = {\mathbf{X\tau }} + {\mathbf{Zu}} + {\mathbf{M}}_{E} a + Z_{l} {\mathbf{g}} + {\mathbf{e}}$$

where the matrix M _E consists of pseudo-markers that relate to intervals on the linkage map (see Verbyla et al. 2007 for details). An important summary of the contribution of the selected QTL is the percentage of genetic variance explained by the QTL. An overall measure is given by

$$\% \operatorname{var} = \frac{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\sigma } ^{2}_{{g,b}} - \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\sigma } ^{2}_{{g,q}} }}{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\sigma } ^{2}_{{g,b}} }} \times 100$$

where $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\sigma } ^{2}_{{g,b}}$ is the estimated polygenic genetic variance for the baseline model (that is, without marker effects) and $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\sigma } ^{2}_{{g,b}}$ is the equivalent estimated polygenic genetic variance after finding the QTL. This quantity is reported in the results for each analysis.

Plant traits

A common approach for QTL analysis was used for plant traits and is based on the whole genome approach of Verbyla et al. (2007) in the case of multi-environment and multi-trait data (based on work in preparation by Verbyla and Cullis). A FA model (Smith et al. 2005) is used to allow detection of QTL that affect the trait in multiple environments or under multiple treatments or both. The initial mixed model for QTL analysis in this case is given by

$${\mathbf{y}} = {\mathbf{X\tau }} + {\mathbf{Zu}} + \left( { \wedge _a \otimes {\mathbf{M}}_E } \right){\mathbf{f}}_a + \left( {{\mathbf{I}} \otimes {\mathbf{M}}_E } \right)\xi _a + {\mathbf{Z}}_{\operatorname{l} {\mathbf{g}}} + {\mathbf{e}}$$

where the term$\left( { \wedge _a \otimes {\mathbf{M}}_E } \right){\mathbf{f}}_a$ allows for a common QTL effect across the 4 environments but with differential association in terms of size of effect, and$\left( {{\mathbf{I}} \otimes {\mathbf{M}}_E } \right)\xi _a$ allows for environment specific QTL effects. The selection of QTL proceeds by choosing common effects until that term is no longer statistically significant. Subsequently, environment specific QTL are selected using the second term. Once this term is no longer statistically significant, the selection process is concluded.

Note that there are four polygenic “traits”, and hence four polygenic variances. Thus the calculations given in equation (3) can be conducted for each of the polygenic variances as given by the diagonal elements of G. Not only can the percentage of genetic variance be given for the combination of location and treatment, the variances and the correlations between the four combinations can be reported both before QTL and after QTL analysis thereby allowing the assessment of the impact of the QTL selected. Thus in the analysis of the plant traits the estimated G before and after QTL analysis is presented and discussed.