*UdelaR, Facultad de Agronomía, Dept. Biometría, Estadística y Cómputo. Av. Garzón 780, 12900 Montevideo, Uruguay.*

*University of Wisconsin at Madison, Agronomy Dept. 1575 Linden Dr., 53705 Madison, USA.*

*Instituto Nacional de Investigación Agropecuaria (INIA), Estación Experimental La Estanzuela. Ruta 50 km 11, 70006 Colonia, Uruguay.*

*Instituto Nacional de Investigación Agropecuaria (INIA), Estación Experimental La Estanzuela. Ruta 50 km 11, 70006 Colonia, Uruguay.*

*DuPont Pioneer. Av. Fulvio S. Pagani 47, 2434 Córdoba, Argentina.*

*UdelaR, Facultad de Agronomía, Dept. Biometría, Estadística y Cómputo. Av. Garzón 780, 12900 Montevideo, Uruguay.*

*University of Wisconsin at Madison, Agronomy Dept. 1575 Linden Dr., 53705 Madison, USA.*

Modeling genotype by environment interaction (GEI) is one of the most challenging aspects of plant breeding programs. The use of efficient trial networks is an effective way to evaluate GEI to define selection strategies. Furthermore, the experimental design and the number of locations, replications, and years are crucial aspects of multi-environment trial (MET) network optimization. The objective of this study was to evaluate the efficiency and performance of a MET network of sunflower (

Sunflower (

Plant breeding programs require evaluation of new cultivars in experiments designed for a certain number of locations and years. This system has been defined as multi-environment trial (MET), where each environment refers to a particular combination of location and year (

An approach called Critical Percentage Difference (CPD) was proposed by

The GEI can also be studied through multiplicative models like additive main-effects and multiplicative (AMMI) and genotype plus genotype by environment interaction (GGE) that combine the variance analysis with principal components analysis, and can be represented graphically by biplots (

Characteristics such as grain yield and oil content in sunflower are complex and are determined by genetic, environmental and genotype by environment interactions (

To evaluate the efficiency of the current NENSU and to study the factors that limit the expression of sunflower yield potential in Uruguay, information of the NENSU during the 1991 to 2009 period was analyzed. The objectives of this study were: (i) to quantify and analyze the GEI in sunflower, (ii) to discuss the reliability of the current NENSU, (iii) to evaluate stability of the superior cultivars to each environment and (iv) to identify environmental and management factors with higher incidence in determining yield potential of sunflower.

The NENSU has official records of 324 cultivars that were evaluated over a period of 20 years (1991-2010). Each individual cultivar was evaluated between two to six years, but check cultivars were recurrently evaluated in a larger number of years. The NENSU is represented by two locations of evaluation, La Estanzuela (LE, latitude: 34°20'S, longitude: 57°41'W) and Young (YG, latitude: 32°42'S, longitude: 57°37'W) with two sowing dates in spring, early (1) and late (2).

The number of cultivars evaluated per year (diagonal) and the number of cultivars in common between years are shown in

An alpha-lattice (resolvable incomplete blocks) experimental design with three replications was used, according to the protocol of the National Seed Council (INASE), Uruguay (

Grain yield (kg/ha) corrected by moisture at 11% was recorded. The oil content (%) was determined by using a nuclear magnetic resonance spectrometry calibrated with a primary standard Soxhlet method (

The GRAS service of the National Institute of Agricultural Research of Uruguay (INIA) provided the meteorological information used for climatic characterization of the environments evaluated in the 2000's period. This information covers the period from 2003 to 2009, for both locations (LE and YG) and planting dates (1 and 2). The meteorological variables used were minimum, mean and maximum average temperatures and rainfall recorded daily. The phases evaluated were: pre-anthesis (from emergence to anthesis (R5.5)), anthesis (15 days ± R5.5) and post-anthesis (from the end of R5.5 to harvest). A singular value decomposition of the square Euclidean distance matrix of all environmental variables was used to create a biplot (

Spatial plot information (row and column position) for all replications, incomplete blocks and location in all 2000's period experiments were used to compare different experimental design efficiency through post-blocking. The three experimental designs most commonly used in cultivar evaluation were compared: randomized complete block design (RCBD), incomplete block design (IBD) and row-column design (RC). To determine the best fitting model, the AIC criterion was used. Comparisons were carried out for all environments in the 2000's period and implemented in PROC MIXED procedure of SAS (

where
_{i}
is the effect of the i-th cultivar, β
_{j}
is the effect of the j-th complete block or replication,
_{k(j)}
is the effect of the k-th incomplete block in j-th replication, α
_{k(j)}
is the effect of the k-th row in the j-th replication, d
_{l(j)}
is the effect of the l-th column in the t-th replication and ε
_{ij}
, ε
_{ijk}
and ε
_{ijkl}
are the experimental errors for each model with
_{k(j)}
~ N(0,s
^{2}
_{S}
), α
_{k(j)}
~ N(0,s
^{2}
_{R}
), d
_{l(j)}
~ N(0,s
^{2}
_{C}
) and ε
_{ij}
, ε
_{ijk}
and ε
_{ijkl}
~ N(0,s
^{2}
_{e}
).

Yield variance components were estimated using a random effect model with information from each experiment for the 1990´s and 2000´s periods. The model used was:

where μ is the overall mean, Y
_{i}
is the main effect of the i-th year, L
_{j}
is the main effect of the j-th environment, YL
_{ij}
is the year and location interaction effect, G
_{k}
is the effect of the k-th cultivar, YG
_{ik}
is the year and cultivar interaction effect, LG
_{jk}
is the location and cultivar interaction effect, YLG
_{ijk}
is the year, location and cultivar interaction effect, β
_{l(ij)}
is the effect of the l-th complete block or replication within the ij-th environment,
_{m(ijl)}
is the effect of the m-th incomplete block within the ij-th environment and l-th replication, and ε
_{ijklm}
is the residual error. All variance components were estimated by restricted maximum likelihood (REML), using PROC MIXED of SAS (

The CPD for the NENSU was calculated by evaluating the effects of the number of years, locations and replications, where a lower value of CPD indicates greater efficiency to detect differences between means (

where z
_{(α)}
is the value to which the standard normal variable (Z) should be exceeded with α probability, μ is the yield overall mean and V is half of the variance of the difference between means of cultivars and was calculated as follows:

where n
_{Y}
, n
_{L}
, n
_{B}
and n
_{I}
, are the number of years, locations, incomplete blocks and replications, respectively.

The correlation between environments in years was studied through biplots (

where, Y
_{ij}
is the standardized mean yield of the i-th cultivar in the j-th environment, μ is the overall mean, β
_{j}
is the effect of the j-th environment, λ
_{m}
inertia or variance explained (eigenvalue) by the m-th axis,
_{mi}
and d
_{mj}
are the projections of the cultivars and the environments in the m-th axis and p
_{ij}
is the residual. These analyses were performed to study the GEI in grain yield on all cultivars and the 11 environments selected in the 2000's period. Multiplicative models for these analyses were implemented using SAS (

PLS regression method relates matrices X and Y through a multivariate linear model (

Finlay-Wilkinson regressions were used to analyze stability of cultivars through different environments of evaluation (

The grain yield and oil content yield means of the eleven cultivars evaluated in this period were 2260 and 1031 kg/ha, respectively (

The efficiency of the experimental designs used in MET's was evaluated for all environments during the 2000's period (

In the 1990's period the largest proportion of the variability was attributed to the location effect (29.0%), followed by the location by year interaction (16.9%) (

Increasing the number of locations from one to two decreased the CPD more than 3%, while incorporating a third location decreased the CPD 1.5% (

The first two principal components of the grain yield of the GGE biplot accounted 61.3% of the total variability for grain yield (

Of the total variability, 80% was retained in the first two principal components for agronomic characteristics (

Cultivars have shown differences in terms of grain yield stability (

The estimation of variance components is an efficient tool to quantify the relative magnitude of the genotype, genotype by environment interaction effects and to predict response to selection (

The evaluation of the NENSU efficiency in terms of the selection of superior cultivars using CPD indicates the relevance of the analysis of number of years, locations and replications to optimize MET networks. This result is consistent with other studies that have used the CPD to evaluate METs network efficiency (

The RCBD had the worst model fit for all environments (

While the study of the GEI has great relevance in the process of genetic improvement, there is a growing interest in understanding more deeply which are the environmental and management factors affecting the determination of yield potential of different cultivars. In this sense, statistical tools have been developed such as Factorial Regression and PLS regression (

In the current context of climate change, constant increases in global temperatures have been reported (

Another climatic factor analyzed in this work was the accumulated rainfall for different environments and cultivars during the vegetative and grain filling phases.

The yield of a cultivar is explained by environmental factors, genetic factors and the presence of significant interactions between cultivar and environmental factors. One alternative to study this phenomenon is to evaluate the stability or phenotypic plasticity of the cultivars (

Our study was able to identify environmental and management factors that directly affect the NENSU in terms of network and experimental design efficiency. Early planting dates are more beneficial for sunflower performance in our conditions. No differences among locations were found in terms of ranking of cultivars for each sowing date. The adoption of any of these management practices could be contributing to the reduction of the gap existing between research trials and farmers yield performances, making it a more competitive and attractive crop.

The optimization of current MET network in the context of increments in the number of cultivars evaluated should focus on increasing the number of locations and/or sowing dates, using at least three replications and two years of evaluation. The use of incomplete block design shows acceptable performance in terms of efficiency. However, the use of spatial information of experimental units could contribute to improve network efficiency by the use of model analysis that includes such information in many situations. The three defined mega-environments were most affected by differences in sowing dates than by geographical differences. In this sense, the use of early sowing dates is preferred because they escape to periods of high temperature stress in relevant phases that determine the performance as the pre-anthesis period and increase the total growing cycle period. It is expected that the available methodological contributions like those applied in this study, be also increasingly applied on plant breeding programs and on the networks of cultivar evaluation to contribute positively in increasing the yield potential and decreasing the gap with the farmer yields.