330 
GENETICS: S. WRIGHT 
Proc. N. a. S, 
The squared path coefficients and the expressions for joint determination 
measure the portion of the mean square deviation of the effect due to the 
causes singly and jointly, respectively. 
The correlation between two variables can be shown to equal the sum 
of the products of the chains of path coefficients along all of the paths 
by which they are connected. In figure 6 
rxY = hh' + cc' + hTBcc' + cfBch'- (2) 
The path coefficients in a system of causes and effects can be calculated, 
if a sufficient number of simultaneous equations can be made, expressing 
the known correlations in terms of the unknown path coefficients as in 
the last equation (2), and expressing complete determination of the effects 
by their causes as in equation (1). 
The correlation between characteristics of parent and offspring are 
represented in figure 5 as tracing back to a single cause, the genetic consti- 
tution of the parent. Litter mates on the other hand are correlated for 
three reasons, the genetic constitutions of the sire and dam, respectively, 
and the common environment. In the absence of assortative mating, these 
causes are not correlated with each other. In such a system, the path 
coefficients are merely coefficients of correlation. 
That the square of the coefficient of correlation measures the degree of 
determination of one variable by another in such cases may be seen from 
Pearson's fomula for the standard deviation of one variable {X) when an- 
other {A) is constant. 
= 1-4^ (4) 
The expression 1 — a(^1/<^1 is obviously the portion of the mean square 
deviation of X which is directly due to A if the latter is a cause of varia- 
tion in X. In the present case the degree to which pattern is determined 
by the three independent factors, heredity (//), tangible environment {E) 
and irregularity in development {D) are measured by /0H7 f'^aE ^nd Tod, 
Using the letters of figure 5 for the correlations, we have 
+ e"" + = I from (1). (5) 
The correlation between parent and offspring is the product of the 
correlations along the single chain of factors by which they are connected. 
rpo = hbah = abh^ (6) 
The correlation between litter mates is the sum of the products of the 
correlations along the three connecting paths, 
ToQi = habbah + habbah -\- ee = 2a^b%^ + e^. (7) 
In a sense, the genetic constitution of the fertilized egg is simply the 
sum of the constitutions of the egg and sperm. The latter are independent 
