. 1999 Sep 14;96(19):10735–10740. doi: 10.1073/pnas.96.19.10735

Table 1.

Analysis of exogenous and endogenous components in Phytobia population dynamics

Component	Dependent variable	Host stand	Step	Independent variables added	F_model	df_model	df_error	SS	MSE	r²	F_improvement
Exogenous	Abundance	Peikkola	1	StndAge, StndAge², StndAge³	610.93^***	3	1321	1302.45	0.711	0.58	610.93^***
			2	Species	495.59^***	4	1320	1345.36	0.679	0.60	63.22^***
			3	Tree (Species)	90.45^***	27	1297	1463.78	0.599	0.65	8.59^**
			4	Species × StndAge, Species × StndAge²	88.45^***	29	1295	1489.31	0.581	0.66	21.98^***
			5	Tree × StndAge, Tree × StndAge²	56.37^***	75	1249	1730.08	0.409	0.77	12.79^***
	Abundance	Valtatie	1	StndAge, StndAge²	287.19^***	2	1227	550.84	0.959	0.32	287.19^***
			2	Species	192.31^***	3	1226	552.82	0.958	0.32	2.06
			3	Tree (Species)	47.15^***	31	1198	949.40	0.650	0.55	21.81^***
			4	Species × StndAge, Species × StndAge²	45.94^***	33	1196	965.68	0.637	0.56	12.77^***
			5	Tree × StndAge, Tree × StndAge²	22.44^***	89	1140	1099.77	0.551	0.64	4.35^*
Endogenous	Growth rate	Peikkola	6	N_t−1	31.22^***	1	49	0.2374	0.00760	0.39	31.22^***
			7	N_t−2	19.40^***	2	48	0.2727	0.00703	0.45	5.02^*
	Growth rate	Valtatie	6	N_t−1	12.51^**	1	37	0.0427	0.00342	0.25	12.51^**
			7	N_t−2	6.82^**	2	36	0.0465	0.00341	0.28	1.10

Exogenous component: development of general linear model quantifying the exogenous effects of host plant factors on the abundance of Phytobia [population density = ln (Phytobia + 1)]. The explanatory factors are: stand age (StndAge), birch species (Species), and tree individuals within birch species (Tree). With each step in the model development, we conducted an F-test (F_improvement) to evaluate whether the new model allowed a significant reduction in variance compared to the model that included all other factors (F_model = F statistic for full model at each step). Endogenous component: stepwise development of linear response surface models testing for effects of population density in year t − 1 (N_t−1) and t − 2 (N_t−2) on population growth rate [r_t = ln (N_t/N_t−1)] calculated from residuals of the general linear model steps (1–5). F-tests are approximate and were used primarily as a guide for model development (7, 24). Significance levels are indicated by asterisks: ∗∗∗, P < 0.001; ∗∗, P < 0.01; and ∗, P < 0.05.