PBG 650 Advanced Plant Breeding

PBG 650 Advanced Plant Breeding Module 13: Breeding for Diverse Environments • Genotype x Environment Interactions

Genotype by environment interaction • Genotypes respond differently across a range of environments i.e., the relative performance of varieties depends on the environment • GXE, GEI, G by E, GE • Genotype by environment interactions are common for most quantitative traits of economic importance • Advanced breeding materials must be evaluated in multiple locations for more than one year • MET = multi-environment trials P = G + E + GE

Types of GEI • Interaction may be due to: • heterogeneity of genotypic variance across environments • imperfect correlation of genotypic performance across environments noncrossover crossover

The GEI challenge • Environmental effect is the greatest, but is irrelevant to selection (remember 70-20-10 rule, E: GE: G) • Many statistical approaches consider all of the phenotypic variation (i.e., means across environments), which may be misleading • Need analyses that will help you to characterize GEI • "GE Interaction is not merely a problem, it is also an opportunity" (Simmonds, 1991). Specific adaptations can make the difference between a good variety and a superb variety

The GEI challenge Some environmental variation is predictable • can be attributed to specific, characteristic features of the environment • e.g., soil type, soil fertility, plant density Some variation is unpredictable • e.g., rainfall, temperature, humidity

Questions a breeder may ask • How do I choose suitable environments for testing? • How do I allocate resources (number of testing sites vs replicates within sites)? • In general, increasing environments does more to reduce the standard error of genotype means than increasing replications

Conventional ANOVA • Ratios of Sums of Squares (SS) can be used to estimate the contribution of interactions to the total SS • Can also estimate variance components due to GXE

Mixed Models for analysis of MET • For evaluation of GEI among an elite group of cultivars, genotypes are often considered to be fixed effects and environments are random. The GEI component is random. One can obtain BLUP estimates of GEI effects. • For the purpose of estimating breeding values using BLUP, genotypes are considered to be random and environments are fixed effects. • Some statisticians believe that genotypes should always be random effects regardless of the stage of selection, provided that the objective is to select the best ones (Smith et al., 2005).

Strategies for coping with GXE • Broad adaptation - develop a variety that performs consistently well across a range of environments (high mean across environments) • this is equivalent to selection for multiple traits, which may reduce the rate of progress from selection • will not necessarily identify the best genotype for a specific environment • Specific adaptation - subdivide environments into groups so that there is little GEI within each group. Breed varieties that perform consistently well in each environment • you have to carry out multiple breeding programs, which means you have fewer resources for each, and hence reduced progress from selection • Evaluate a common set of breeding material across environments, but make specific recommendations for each environment

Stability • Static – performance of a genotype does not change under different environmental conditions (relevant for disease resistance) • Dynamic – genotype performance is affected by the environment, but its relative performance is consistent across environments

Ways that a variety can achieve stability • Genetic homeostasis – variety is heterogeneous and plants are adapted to slightly different environmental conditions • variety mixtures • open-pollinated varieties vs hybrids • Developmental homeostasis – individual genotype is able to adapt to a range of conditions • phenotypic plasticity • “reaction norms” – phenotypic variability among individuals with the same genotype

Regression of genotype on environmental index • Finlay and Wilkinson, 1963 • b=0 is a stable genotype (static or Type I) • Eberhart and Russel, 1966 • b=1 is stable, because genotypes with b~0 tend to have lower yields (dynamic or Type II) • stable genotypes have small deviations from regression (Type III) effect of ith genotype deviation from regression regression of ith genotype environmental index

Regression of genotype on environmental index

Stability analysis • Test for homogeneous slopes: F ~M2/M3 • Test that deviations from regression = 0: F ~M3/M4

Drawbacks of regression approach • Genotype means are not independent of site means • Genotype that has a consistent response to environmental factors, but is atypical of the genotypes in the trial, will have a high deviation from regression • Does not consider underlying causes for performance at each site • Sites with deficiencies and excesses of water, nutrients, etc. will be juxtaposed on the regression line, resulting in large deviations from regression • Heritabilities of bi and sd2 are low • Stability is a statistical, not a genetic concept

Other stability statistics • Ecovalence (Wricke, 1962) • Superiority measure of cultivars (Lin and Binns, 1988) • Wi is the ecovalence for the ith genotype across the j environments • Measures a genotype’s contribution to GEI • Mj is the maximum response in the jth location • n is the number of locations • Indicates how often a variety is close to being the best in the trial

Rank sum index • Utilizes Shukla’s ‘stability variance’ (Shukla, 1972) to represent the stability concept and the unadjusted mean across sites to represent mean performance • Genotypes are ranked for both parameters • The genotype with the highest mean yield receives a rank of one • the genotype with the smallest value for stability variance is ranked number one • Ranks are added together, and the genotype with the lowest score is considered to be the best

Cluster analyses • Stratify environments into homogeneous groups so that there is no GEI within groups; maximize between group variation • Possible benefits • May suggest genetic relationships • May lead to better understanding of environmental factors influencing adaptation • Permits systematic approach for choosing testing sites • Disadvantage – location groupings are seldom consistent from one year to the next • Many choices of criteria exist for calculating distance beween sites (Euclidian distance, dissimilarity index) and assigning groups (e.g., average linkage or UPGMA)

Crossover interactions • GEI is only problematic for plant breeders when there are rank changes in performance of varieties in different environments (“crossover interactions”) • Tests for crossover interactions were presented by Baker (1988) • Shifted multiplicative model (Cornelius et al.,1992) • search for "separability" of crop cultivars based on GEI • identify clusters of genotypes in which crossover interactions are negligible • cluster environments so that the genotypes within each group show no crossover interactions • techniques have been further developed in recent years by Cornelius and Crossa

Principal component analysis (PCA) • With conventional multiple regression, coefficients can be misleading when the variables in the model are correlated. Values vary depending on the order that the variables appear in the model. • PCA is a multivariate approach that provides an alternative to conventional multiple regression analysis. PCA transforms the data into linear combinations of the original variables that are uncorrelated. • Useful for determining which agroclimatic or biotic factors can be used to discriminate among environments. • Drawback for PCA – interpretation is not as intuitive as with multiple regression or correlation analyses. Results do not bear any obvious relationship to environmental variables.

Additive Main Effects and Multiplicative Interaction Model (AMMI) • Method for analyzing GEI to identify patterns of interaction and reduce background noise • Combines conventional ANOVA with principal component analysis • May provide more reliable estimates of genotype performance than the mean across sites • Biplots help to visualize relationships among genotypes and environments; show both main and interaction effects • Enables you to identify target breeding environments and to choose representative testing sites in those environments • Enables you to select varieties with good adaptation to target breeding environments • Can be used to identify key agroclimatic factors, disease and insect pests, and physiological traits that determine adaptation to environments • A type of fixed effect, Linear-Bilinear Model Zobel et al., 1988; Gauch and Zobel, 1996

AMMI Model Yijl =  + Gi + Ej + (kikjk) + dij + eijl k = kth eigenvalue ik = principal component score for the ith genotype for the kth principal component axis jk = principal component score for the jth environment for the kth principal component axis dij = residual GXE not explained by model AMMI estimates for performance of genotype i in environment j E(Yijl) =  + Gi + Ej + (kikjk)

Benefits of AMMI • Based on a two-way matrix of genotypes x environments • Partitions treatment SS into model and residual • traditional approaches for controlling error partition the error SS into pure error and blocks. • both can be done • Gains in precision due to modeling using AMMI are often several times as large as those due to blocking • Can first run AMMI to get rid of noise and get clean estimates of variety means, and then apply classification procedures or other analyses that are not able to discriminate between patterns and noise

Biplots Shafi et al., 1998

Biplots http://www.uidaho.edu/ag/statprog/ammi/index.html

AMMI • General interpretation • genotypes that occur close to particular environments on the IPCA2 vs IPCA1 biplot show specific adaptation to those environments • a genotype that falls near the center of the biplot (small IPCA1 and IPCA2 values) may have broader adaptation • How many IPCAs (interaction principal component axes) are needed to adequately explain patterns in the data? • Rule of thumb - discard higher order IPCAs until total SS due to discarded IPCA's ~ SSE. • Usually need only the first 2 PC axes to adequately explain the data (IPCA1 and IPCA2). This model is referred to as AMMI2. • Approach is most useful when G x location effects are more important than G x year effects

GGE or SREG (Sites Regression) Model • Another fixed effect, linear-bilinear model that is similar to AMMI • Only the environmental effects are removed before PCA • The bilinear term includes both the main effects of genotype and GXE effects • Several recent papers compare AMMI and GGE (e.g. Gauchet al., 2008) • May be used to evaluate test environments (Yan and Holland, 2010) Yijl =  + Ej + (kikjk) + dij + eijl

Pattern Analysis Steps involved: • recommended pretreatment (transformation) – scale the data by removing environment main effects and adjust scale by dividing by the phenotypic standard deviation at each site. • use a classification procedure to identify environments which show similar discrimination among the genotypes. • use an ordination procedure (singular value decomposition) – similar to AMMI except that it uses transformed data • use biplots to show relationships between genotypes and environments Cooper and DeLacy, 1994

Partial Least Squares Regression (PLS) • AMMI model only considers one response variable • PLS is a type of bilinear model that can utilize information about environmental factors (covariables) • rainfall, temperature, and soil type • PLS can accommodate additional genotypic data • disease reaction • molecular marker scores • Analysis indicates which environmental factors or genotypic traits can be used to predict GEI for grain yield

Factorial Regression (FR) • A fixed effect, linear model • Can incorporate additional genotypic and environmental covariables into the model • Similar to stepwise multiple regression, where additional variables are added to the model in sequence until sufficient variability due to GEI can be explained • FR is easier to interpret than PLS, but may give misleading results when there are correlations among the explanatory variables in the model

Linear-Bilinear Mixed Models • Have become widely accepted for analysis of GEI • Lead to Factor Analytic form of the genetic variance-covariance for environments • Has desirable statistical properties • When genotypes are random, coancestries can be accommodated in the model Burgueño, J.; Crossa, J.; Cornelius, P.L.; Yang, R.-C. 2008. Using factor analytic models for joining environments and genotypes without crossover genotype × environment interaction. Crop Sci. 48:1291-1305.

Nonlinear models for GEI analysis • Assumptions for linear models • homoscedasticity (errors homogeneous = common variance) • normal distribution of residuals • errors are independent (e.g. no relationship between mean and variance) • Generalized linear models can be used when assumptions are not met • SAS PROC GENMOD, PROC NLMIXED, PROC GLIMMIX • Nonparametric approaches • Smoothing spline genotype analysis

Agroecological zones • The Geographic Information System (GIS) can be used to define regions with similar ecologies for crop production • Gauch and Zobel (1997) described methodologies for defining mega-environments and regions of cultivar adaptation using actual yield data from multi-locational trials • Further work is needed to integrate information from GIS with actual performance data to help define target breeding environments

Crop models • Crop simulation models calculate or predict crop yield as a function of: • Weather conditions • Soil conditions • Crop management scenarios • Genetic coefficients • Potential production determined by • Solar radiation and temperature as input • Simulate growth and development • Plant carbon balance (photosynthesis, respiration, partitioning) • More sophisticated models may also consider yield reductions due to: • limited water • limited nitrogen and other nutrients • insects, diseases, and weeds From a presentation by Gerrit Hoogenboom, 2002

Peanut Varieties in Thailand • Development Coefficients (Photothermal days): • Time between emergence and flowering (16.4 - 25.0 d) • Seed filling Duration (22.0 - 44.0 d) • Time required for final pod load (13.0 - 30.0 d) • Growth Coefficients: • Maximum leaf photosynthetic rate(1.04 - 1.40 mg CO2 m-2 s-1 ) • Maximum partitioning to seed + shell (0.58-0.95) • Maximum weight per seed (0.39-1.18 g) From a presentation by Gerrit Hoogenboom, 2002

Peanut Varieties in Thailand Simulated and observed above ground biomass for entry no. 9

GEI - Conclusions • Many techniques available • An active area of research • Need to synthesize information • performance data and stability analyses • understanding of crop physiology, crop models • disease and pest incidence • molecular genetics • agroclimatology, GIS

References Crossa, J. 2012. From genotype × environment interaction to gene × environment interaction. Current Genomics 13: 225-244. Gauch, H.G., H.-P. Piepho, and P. Annicchiarico. 2008. Statistical analysis of yield trials by AMMI and GGE: further considerations. Crop Sci. 48: 866-889 Hussein, M.A, Bjornstad, A., and A.H. Aastveit. 2000. SASG X ESTAB: A SAS program for computing genotype x environment stability statistics. Agron. J. 92: 454–459. Agron. J. 92:454–459. Kang, M.S., M.G. Balzarini, and J.L.L. Guerra. 2004. Genotype-by-environment interaction. In (A.M. Saxton ed.) Genetic Analysis of Complex Traits Using SAS. Cary, NC: SAS Institute Inc. Peipho, H.P., and J. Mohring. 2005. Best Linear unbiased prediction of cultivar effects for subdivided target regions. Crop Sci. 45: 1151-1159. Smith, A.B., B.R. Cullis, and R. Thompson. 2005. The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches. Journal of Agricultural Science 143: 449-462. Yan, W., and J.B. Holland. 2010. A heritability-adjusted GGE biplot for test environment evaluation. Euphytica 171: 355-369. Yang, R.-C., J. Crossa, P.L. Cornelius, and J. Burgueño. 2009. Biplot analysis of genotype x environment interaction: proceed with caution. Crop Sci. 49: 1564-1576.

PBG 650 Advanced Plant Breeding