poultry breeding

1. Genotype x Environment
Interactions
Analyses of Multiple Location Trials

2. Why do researchers conduct
multiple experiments?
Effects of factors under study vary from
location to location or from year to year.
To obtain an unbias estimate.
Interest in determining the effect of
factors over time.
To investigate genotype (or treatment) x
environment interactions.

3. What are Genotype x
Environment Interactions?
Differential response of genotypes to
varying environmental conditions.
Delight for statisticians who love to
investigate them.
The biggest nightmare for plant
breeders (and some other agricultural
researchers) who try to avoid them like
the plague.

4. What causes Genotype x
Environment interactions?

5. B
A
Yield
Locations
No interaction

6. B
A
Yield
Locations
B
A
Yield
Locations
No interaction
Cross-over
interaction

7. B
A
Yield
Locations
B
A
Yield
Locations
B
A
Yield
Locations
No interaction
Scalar interaction
Cross-over
interaction

8. Examples of Multiple Experiments
Plant breeder grows advanced breeding
selections at multiple locations to determine
those with general or specific adaptability
ability.
A pathologist is interested in tracking the
development of disease in a crop and records
disease at different time intervals.
Forage agronomist is interested in forage
harvest at different stages of development
over time.

9. Types of Environment
Researcher controlled environments,
where the researcher manipulates the
environment. For example, variable
nitrogen.
Semi-controlled environments, where
there is an opportunity to predict
conditions from year to year. For
example, soil type.
Uncontrolled environments, where there
is little chance of predicting environment.

10. Why?
• To investigate relationships between
genotypes and different environmental
(and other) changes.
• To identify genotypes which perform well
over a wide range of environments.
General adaptability.
• To identify genotypes which perform well
in particular environments. Specific
adaptability.

11. How many environments do I need?
Where should
they be?

12. Number of Environments
Availability of planting material.
Diversity of environmental conditions.
Magnitude of error variances and
genetic variances in any one year or
location.
Availability of suitable cooperators
Cost of each trial ($’s and time).

13. Location of Environments
 Variability of environment
throughout the target region.
Proximity to research base.
 Availability of good cooperators.
 $$$’s.

14. Analyses of Multiple
Experiments

15. Points to Consider before Analyses
Normality.
Homoscalestisity
(homogeneity) of error
variance.
Additive.
Randomness.

16. Points to Consider before Analyses
Normality.
Homoscalestisity
(homogeneity) of error
variance.
Additive.
Randomness.

17. Bartlett Test
(same degrees of freedom)
M = df{nLn(S) - Ln2}
Where, S = 2/n
2
n-1 = M/C
C = 1 + (n+1)/3ndf
n = number of variances, df is the df
of each variance

18. Bartlett Test
(same degrees of freedom)
df 2
Ln(2
)
5 178 5.148
5 60 4.094
5 98 4.585
5 68 4.202
Total 404 18.081
S = 101.0; Ln(S) = 4.614

19. Bartlett Test
(same degrees of freedom)
df 2
Ln(2
)
5 178 5.148
5 60 4.094
5 98 4.585
5 68 4.202
Total 404 18.081
S = 100.0; Ln(S) = 4.614
M = (5)[(4)(4.614)-18.081] = 1.880, 3df
C = 1 + (5)/[(3)(4)(5)] = 1.083

20. Bartlett Test
(same degrees of freedom)
df 2
Ln(2
)
5 178 5.148
5 60 4.094
5 98 4.585
5 68 4.202
Total 404 18.081
S = 100.0; Ln(S) = 4.614
M = (5)[(4)(4.614)-18.081] = 1.880, 3df
C = 1 + (5)/[(3)(4)(5)] = 1.083
2
3df = 1.880/1.083 = 1.74 ns

21. Bartlett Test
(different degrees of freedom)
M = ( df)nLn(S) - dfLn2
Where, S = [df.2]/(df)
2
n-1 = M/C
C = 1+{(1)/[3(n-1)]}.[(1/df)-1/ (df)]
n = number of variances

22. Bartlett Test
(different degrees of freedom)
df 2
Ln(2
) 1/df
9 0.909 -0.095 0.111
7 0.497 -0.699 0.1429
9 0.076 -2.577 0.1111
7
5
0.103
0.146
-2.273
-1.942
0.1429
0.2000
37 0.7080
S = [df.2]/(df) = 13.79/37 = 0.3727
(df)Ln(S) = (37)(-0.9870) = -36.519

23. Bartlett Test
(different degrees of freedom)
df 2
Ln(2
) 1/df
9 0.909 -0.095 0.111
7 0.497 -0.699 0.1429
9 0.076 -2.577 0.1111
7
5
0.103
0.146
-2.273
-1.942
0.1429
0.2000
37 0.7080
M = (df)Ln(S) - dfLn 2 = -36.519 -(54.472) = 17.96
C = 1+[1/(3)(4)](0.7080 - 0.0270) = 1.057

24. Bartlett Test
(different degrees of freedom)
S = [df.2]/(df) = 13.79/37 = 0.3727
(df)Ln(S) = (37)(=0.9870) = -36.519
M = (df)Ln(S) - dfLn 2 = -36.519 -(54.472) = 17.96
C = 1+[1/(3)(4)](0.7080 - 0.0270) = 1.057
2
3df = 17.96/1.057 = 16.99 **, 3df

25. Heterogeneity of Error Variance
0
10
20
30
40
50
60
70
80
Mosc Gene Tens Gran Pend Colf Kalt Mocc Boze
Seed
Yield

26. Significant Bartlett Test
“What can I do where there is
significant heterogeneity of error
variances?”
Transform the raw data:
Often  ~ 
cw Binomial Distribution
where  = np and  = npq
Transform to square roots

27. Heterogeneity of Error Variance
0
2
4
6
8
10
Mosc Gene Tens Gran Pend Colf Kalt Mocc Boze
SQRT[Seed
Yield]

28. Significant Bartlett Test
“What else can I do where there is
significant heterogeneity of error
variances?”
Transform the raw data:
Homogeneity of error variance can always
be achieved by transforming each site’s data
to the Standardized Normal Distribution
[xi-]/

29. Significant Bartlett Test
“What can I do where there is
significant heterogeneity of error
variances?”
Transform the raw data
Use non-parametric statistics

30. Analyses of Variance

31. Model ~ Multiple sites
Yijk =  + gi + ej + geij + Eijk
i gi = j ej = ij geij
Environments and Replicate blocks are usually
considered to be Random effects. Genotypes are
usually considered to be Fixed effects.

32. Analysis of Variance over sites
Source d.f. EMSq
Sites (s)
Rep w Sites (r)
Genotypes (g)
Geno x Site
Replicate error

33. Source d.f. EMSq
Sites (s) s-1
Rep w Sites (r) s(1-r)
Genotypes (g) g-1
Geno x Site (g-1)(s-1)
Replicate error s(r-1)(g-1)
Analysis of Variance over sites

34. Source d.f. EMSq
Sites (s) s-1 2
e + g2
rws + rg2
s
Rep w Sites (r) s(1-r) 2
e + g2
rws
Genotypes (g) g-1 2
e + r2
gs+ rs2
g
Geno x Site (g-1)(s-1) 2
e + r2
gs
Replicate error s(r-1)(g-1) 2
e
Analysis of Variance over sites

35. Yijkl = +gi+sj+yk+gsij+gyik+syjk+gsyijk+Eijkl
igi=jsj=kyk= 0
ijgsij=ikgyik=jksyij = 0
ijkgsyijk = 0
Models ~ Years and sites

36. Analysis of Variance
Source d.f. EMSq
Years (y) y-1 2
e+gy2
rwswy+rg2
swy+rgs2
y
Sites w Years (s) y(s-1) 2
e + g2
rwswy + rg2
swy
Rep w Sites w year (r) ys(1-r) 2
e + g2
rwswy
Genotypes (g) g-1 2
e + r2
gswy + rs2
gy + rl2
g
Geno x year (y-1)(g-1) 2
e + r2
gswy + rs2
gy
Geno x Site w Year y(g-1)(s-1) 2
e + r2
gswy
Replicate error ys(r-1)(g-1) 2
e