Book Of Why, Judea Pearl - Dependence of guinea pig weights on gestation period In the Book Of Why by Judea Pearl there is the mention of the dependence of weights of guinea pig pups on gestation period, as explored by Sewall Wright. The following is the causal diagram provided -

In the above diagram,
X = weight of pup in grams
P = Gestation period in days
Q = Utero growth rate
L = litter size
A and C = exogenous factors
We are interested in finding the impact of changing P on X in terms of grams/day, depicting the additional weight gain for each extra day of gestation.
The following are the path coefficients for each causal relation -
$L{\rightarrow}Q=l$
$L{\rightarrow}P=l'$
$Q{\rightarrow}X=q$
$P{\rightarrow}X=p$
Then the book says that, the influence of $P$ on $X$ can be found by $p+(l{\times}l'{\times}q)={\,}\text{rate of change of }X\text{ per day in grams/day}$.............$(i)$
My query is, what do the path coefficients denote exactly, in terms of their mathematical formulation? How are changes $\Delta P$ and $\Delta L$ related in terms of $l'$? Based on the definition of the coefficients, how is equation $(i)$ derived?

The coefficients are slopes in a data-generating (structural) model corresponding to a linear regression model. That is, $X := qQ + pP + u$, where $u$ corresponds to other (unobserved) factors (not included in the graph). This is the context of path analysis as described by Sewall Wright. See also Pearl's excellent paper "Linear Models: A Useful "Microscope" for Causal Analysis".
$(i)$ is derived using the rules of path analysis, which state that when variables are standardized to have a variance of 1, the relationship between two variables is equal to the sum of the open paths between them, where open paths are unique chains of arrows from one variable to the other that do not involve two arrows pointing at the same node (i.e., an unconditioned-upon collider). The two open paths from $P$ to $X$ are $P \rightarrow X$ and $ P \leftarrow L \rightarrow Q \rightarrow X$, and their magnitudes are $p$ and $l \times l' \times q$, respectively.
