Transcript Across Location Analyses - Oregon State University

Combined Analysis of Experiments
 Basic Research
– Researcher makes hypothesis and conducts a
single experiment to test it
– The hypothesis is modified and another experiment
is conducted
– Combined analysis of experiments seldom required
– May provide greater precision (increased replication)
– Validates results from initial experiment
 Applied Research
– Recommendations to producers must be based on
multiple locations and seasons that represent target
environments (soil types, weather patterns)
Multilocational trials
 Often called MET = multi-environment trials
 How do treatment effects change in response to
differences in soil and weather throughout a region?
 Detect and quantify interactions of treatments and
locations and interactions of treatments and seasons in
recommendation domain
 Combined estimates are valid only if locations are
randomly chosen within target area
– Experiments often carried out on experiment stations
– Generally use sites that are most accessible or
convenient
– Can still analyze the data, but consider possible bias
due to restricted site selection when making
interpretations
Preliminary Analysis
 Complete ANOVA for each experiment
– Did we have good data from each site?
 Examine experimental errors from different locations for
heterogeneity
– Perform F Max test or Levene’s test for homogeneity of variance
– If homogeneous, we can combine results across sites
– If heterogeneous, may need to use transformation or break sites
into homogeneous groups and analyze separately
 Obtain preliminary estimate of interaction of treatment
with environment or season
– Will we be able to make general recommendations or should
they be specific for each site?
Treatments and locations are random
Source
df
SS
MS
Location
Blocks in Loc.
Treatment
Loc. X Treatment
Pooled Error
l-1
l(r-1)
t-1
(l-1)(t-1)
l(r-1)(t-1)
SSL
SSB(L)
SST
SSLT
SSE
M1
M2
M3
M4
M5
Expected MS
2e  r2TL  tR2 (L)  rtL2
2e  tR2 (L)
2e  r2TL  rl2T
 2e  r2TL
 2e
F for Locations = (M1+M5)/(M2+M4)
Satterthwaite’s approximate df
N1’ = (M1+M5)2/[(M12/(l-1))+M52/(l)(r-1)(t-1)]
N2’ = (M2+M4)2/[(M22/(l-1))+M42/(l)(r-1)(t-1)]
F for Treatments = M3/M4
F for Loc. x Treatments = M4/M5
Treatments are fixed, Locations are fixed
Fixed Locations
• constitute the entire population of environments
OR
• represent specific environmental conditions (rainfall, elevation, etc.)
Source
df
SS
MS
Expected MS
Location
Blocks in Loc.
Treatment
Loc. X Treatment
Pooled Error
l-1
l(r-1)
t-1
(l-1)(t-1)
l(r-1)(t-1)
SSL
SSB(L)
SST
SSLT
SSE
M1
M2
M3
M4
M5
2e  tR2 (L)  rtL2
F for Locations = M1/M2
F for Treatments = M3/M5
F for Loc. x Treatments = M4/M5
2e  tR2 (L)
2e  rl2T
2e  r2TL
 2e
Treatments are fixed, Locations are random
Source
df
SS
MS
Expected MS
Location
Blocks in Loc.
Treatment
Loc. X Treatment
Pooled Error
l-1
l(r-1)
t-1
(l-1)(t-1)
l(r-1)(t-1)
SSL
SSB(L)
SST
SSLT
SSE
M1
M2
M3
M4
M5
2e  tR2 (L)  rtL2
F for Locations = M1/M2
F for Treatments = M3/M4
F for Loc. x Treatments = M4/M5
2e  tR2 (L)
2e  r2TL  rl2T
 2e  r2TL
 2e
SAS Expected Mean Squares
PROC GLM;
Class Location Rep Variety;
Model Yield = Location Rep(Location) Variety Location*Variety;
Random Location Rep(Location) Location*Variety/Test;
Source
Type III Expected Mean Square
Location
Var(Error) + 3 Var(Location*Variety) +
7 Var(Rep(Location)) + 21 Var(Location)
Dependent Variable: Yield
Source
Location
Error
DF
Type III SS
Mean Square
F Value
Pr > F
0.20
0.6745
1
0.505125
0.505125
5.8098
15.027788
2.586644
Error: MS(Rep(Location)) + MS(Location*Variety) - MS(Error)
Treatments are fixed, Years are random
Source
df
SS
MS
Expected MS
Years
Blocks in Years
Treatment
Years X Treatment
Pooled Error
l-1
l(r-1)
t-1
(l-1)(t-1)
l(r-1)(t-1)
SSY
SSB(Y)
SST
SSYT
SSE
M1
M2
M3
M4
M5
2e  tR2 (Y)  rt2Y
2e  tR2 (Y)
2e  r2TY  ry2T
F for Years = M1/M2
F for Treatments = M3/M4
F for Years x Treatments = M4/M5
2e  r2TY
 2e
Locations and Years in the same trial
 Can analyze as a factorial
Source
df
Years
y-1
Locations
l-1
Years x Locations
(y-1)(l-1)
Block(Years x Locations)
yl(r-1)
 Can determine the magnitude of the interactions
between genotypes and environments (G x Y, G x L,
G x Y x L)
 For a simpler interpretation, can consider all year and
location combinations as “sites” and use one of the
models appropriate for multilocational trials
Preliminary ANOVA
Assumptions for this example:
- locations and blocks are random
- Treatments are fixed
Source
Total
Location
Blocks in Loc.
Treatment
Loc. X Treatment
Pooled Error
df
lrt-1
l-1
l(r-1)
t-1
(l-1)(t-1)
l(r-1)(t-1)
SS
SSTot
SSL
SSB(L)
SST
SSLT
SSE
MS
F
M1
M2
M3
M4
M5
M1/M2
M3/M4
M4/M5
If interactions of Loc. X Treatment are significant, must be cautious
in interpreting main effects combined across all locations
Genotype by Environment Interactions (GEI)
 When the relative performance of varieties differs
from one location or year to another…
– how do you make selections?
– how do you make recommendations to farmers?
No rank changes,
but interaction
A
B
Response
No interaction
A
B
Environments
Rank changes and
interaction
B
A
Genotype x Environment Interactions (GEI)
 How much does GEI contribute to variation
among varieties or breeding lines?
P = G + E + GE
P is phenotype of an individual
G is genotype
E is environment
GE is the interaction
DeLacey et al., 1990 – summary of results from
many crops and locations
70-20-10 rule
E: GE: G
20% of the observed variation among
genotypes is due to interaction of
genotype and environment
Stability
 Many approaches for examining GEI have
been suggested since the 1960’s
 Characterization of GEI is closely related to the
concept of stability. “Stability” has been
interpreted in different ways.
– Static – performance of a genotype does not
change under different environmental conditions
(relevant for disease resistance, quality factors)
– Dynamic – genotype performance is affected by the
environment, but its relative performance is
consistent across environments. It responds to
environmental factors in a predictable way.
Measures of stability
 CV of individual genotypes across locations
 Regression of genotypes on environmental index
– Eberhart and Russell, 1966
 Ecovalence
– Wricke, 1962
 Superiority measure of cultivars
– Lin and Binns, 1988
 Many others…
Analysis of GEI – other approaches
 Rank sum index (nonparametric approach)
 Cluster analysis
 Factor analysis
 Principal component analysis
 AMMI
 Pattern analysis
 Analysis of crossovers
 Partial Least Squares Regression
 Factorial Regression