this ppt gives you basics of path coefficient only. for for further studies go through books of quantitative genetics.....

1. PATH COEFFICIENT
by,
Kanaka
K.K.
IVRI

2. Introduction
 Given by professor Sewall Wright
in1934.
 “ Path coefficient is a measure of the
direct effect of a causing factor in
causing the variation in the dependent
variable’’

3. PATH DIAGRAM
Y
X
Z
X
Z
For UNCORRELATED factors For CORRELATED factors
rxz
Y

4. Mathematically,
“Ratio of standard deviation of the
effect(dependent variable) due to a
given cause to the total standard
deviation of the effect’’
Ex:
Y
X
Z
Py
x
Py
z
yz/Pyz
y/



 xPyx

5. Characteristics of
PathcoefficientA. Between P.C. and Correlation
coefficient:
 Both are absolute no. without units.
 Ranges: C.C.-1 to +1
P.C. may greater than unity
are may undergo beyond negative
unity.
 C.C does not explains direction,
P.C. explains direction.

6. B. Path coefficient and Regression
coefficient
 Both explains directions.
 Regression coefficient having
physical units.

7. C. Path coefficient and standardized
regression coefficient.
 P.C. is same as SRC.
 By Standardizing the each variables
we can get P.C. from regression
.coefficient

8.    
A
P
P
PP
A
AA
ndardisatiosafter
PPAA
PA
P
A
b
b
b
b
AP
AP
Ap
AP



.
,tan_
)1.......(






AAP 2
 Since
P AP
P
A
PA
A
PA
AP
.
2









9. Analysis of quantitative traits
1. Complete determination of a variable
determined by independent or
correlated causes
2. Total correlation between two
variables with two or more common
independent or correlated causes

10. 1.1complete determination of a
variable by independent
causes Ex. Correlation between breeding
value and phenotypic value
P=A+R
AP
P
A
PA
A
PA
PA
PA
RPRAPAAR
P
Cov
rtkw
CovCovCovhere
.
2
2
,
2
.,..
,0,









11. 1
,
..
..
2
..
2



RPAP
APAP
APAP
dd
dPso
dr
Where dPA means degree of
variation in P that can be
determined by breeding value

12. 1.2 complete determination of a
variable by correlated causes
 Ex. Half sib mating
X=A+B
arbr
similarlybra
r
rCovABce
rAB
CovABCovAA
BAbecauseX
BAACovCovAX
r
ABXB
AB
X
B
AB
X
A
BAAB
XA
BA
XA
A
XAXA
XA
XA








..........
,sin........
.....
))((
2












13. The coefficient of determination of X by
correlated causes A and B are;
12
1
2
2
22
.
2.
2
2
2
2
2
2





AB
ABXXBXA
AB
X
BAAB
ABX
X
B
XB
X
A
XA
abrba
ddd
abr
r
d
bd
ad







14. For more than two correlated
causing factors,
213121
2...........22........1 2222
nn XXXXXX rrrncba 
a
b
c
n

15. Extension theorem
 Determining effect of distant cause on variable.
 Ex:- P=G+E where G= A+D
P
G
E
A
D
g
e
a
d
P
D
PD
P
A
GP
AG
GAPGPA
P
similarlyPPP







 ,.............

16. 2.Theory of correlation of two
variables
2.1 Single common cause affecting two
variables
ex:- half sibs
X
Y
B
C
A
Y
B
X
B
XY bbr




.'. 

17. 2.2 Two common independent causes
ex:- full sibs X
Y
B
C
b’
b
c’
c'' ccbbrXY 

18. 2.3 two common correlated causes
X
Y
B
C
b
b’
c
c’
rBC
BCBCXY rcbrbcccbbr '''' 

19. Applications of path
coeffcient
 Helps in solving complex inbreeding
problems
 To study non additive gene effects
 Sex linked inheritance
 Polysomic inheritance

20.  Environmental influence on traits
 linkage
 Theory of evaluation
 Analysis of quantitative traits

21. THANK YOU,