Table 2.

Test of conditional independence implied by the path diagram (figure 1). ((X; Y)|{Z} means that variables X and Y are independent conditional of variable Z (i.e. if Z is held constant, variation in X does not imply variation in Y). The associated mixed model used to test the independence claims are Y ∼ Z + X + 1|Year, where Year represents a random effect. The variable whose partial regression includes zero is X1 for all claims. Variables: X1 (CORTf), X2 (Arrival date), X3 (Body condition), X4 (Laying date), X5 (Hatching success) and X6 (Survival of an avian cholera outbreak).)

d-sep claim of independence	mixed model	partial regression slope (s.e.)	null probability	(distribution)
(X1,X4)|{X2,X3}	X4 ∼ X1 + X2 + X3 + (1|Year)	0.072 (0.176)	0.68	(normal)
(X1,X5)|{X4}	X5 ∼ X4 + X1 + (1|Year)	−0.046 (0.090)	0.61	(binomial)
(X2,X5)|{X1,X4}	X5 ∼ X4 + X1 + X2 + (1|Year)	0.014 (0.096)	0.89	(binomial)
(X1,X6)|{X4}	X6 ∼ X4 + X1 + (1|Year)	0.014 (0.039)	0.71	(binomial)
(X2,X6)|{X1,X4}	X6 ∼ X4 + X1 + X2 + (1|Year)	−0.074 (0.069)	0.28	(binomial)
(X3,X6)|{X1,X4}	X6 ∼ X4 + X1 + X3 + (1|Year)	0.010 (0.039)	0.79	(binomial)
(X4,X6)|{X5}	X6 ∼ X4 + X5 + (1|Year)	0.057 (0.046)	0.21	(binomial)