Table 3.

Directions of the strongest selection on beak morphology during first 19 generations following population establishment in northwestern Montana, USA. Shown are eigenvalues (λ_i) and eigenvectors (m_i) of the M matrix from the canonical rotation of γ (table 2) and the direction of the strongest natural selection (a₁) estimated by the projection pursuit regression. Additional directions were not significantly different.

	generations
	5				6				7				8
	λi	BL	BD	BW	λi	BL	BD	BW	λi	BL	BD	BW	λi	BL	BD	BW
m1	0.06	−0.32	0.54	−0.16	0.05	−0.41	0.89	−0.17	0.06	0.86	−0.32	0.40	0.07	0.41	0.86	0.31
m2	0.01	0.67	0.31	−0.47	0.01	0.69	0.42	0.58	0.01	−0.09	0.67	0.73	−0.03	−0.73	0.32	0.65
m3	−0.03	0.12	0.41	0.31	−0.02	−0.59	−0.12	0.80	−0.02	0.51	0.66	−0.55	0.01	−0.12	0.31	0.21
a1	—	0.11	0.18	0.77	—	0.36	0.19	0.56	—	0.48	−0.14	0.58	—	0.39	0.01	0.59
	9				10				11				12
m1	0	0.53	0.67	0.52	0.02	0.54	0.15	0.83	0	0.53	0.02	0.85	0.02	0.92	0.39	−0.09
m2	−0.03	0.84	−0.29	−0.47	0	0.46	0.78	−0.44	−0.01	0.20	0.97	−0.15	0	0.13	−0.08	0.99
m3	−0.09	0.16	−0.68	0.71	−0.07	−0.71	0.61	0.36	−0.07	0.82	−0.25	−0.51	−0.03	−0.37	0.92	0.12
a1	—	0.24	0.04	0.35		0.52	0.82	0.11	—	0.39	0.23	0.87	—	0.53	0.21	0.42
	13				14				15				16
m1	0.02	0.08	0.84	−0.53	0.06	−0.65	0.05	0.76	0.03	−0.17	0.96	−0.21	0.07	0.60	0.27	0.75
m2	−0.01	0.36	0.46	0.81	0.01	0.28	0.94	0.19	0	−0.32	0.14	0.94	−0.01	0.75	0.65	0.14
m3	−0.03	0.93	−0.25	−0.26	−0.06	0.70	−0.33	0.63	−0.05	0.93	0.23	0.28	−0.06	−0.28	0.87	0.12
a1	—	0.63	0.11	−0.54	—	−0.15	0.03	−0.47	—	0.25	0.24	0.71	—	0.16	0.37	0.65
	17				18				overall
m1	0.01	0.52	0.01	0.84	0.01	0.79	0	−0.61	0.01	0.18	0.98	0.01
m2	−0.01	0.17	0.84	−0.14	0	0.22	0.27	0.94	0	0.69	−0.13	0.71
m3	−0.06	0.76	−0.24	−0.49	−0.02	0.27	0.74	−0.35	−0.01	−0.70	0.11	0.70
a1	—	0.49	0.07	0.67	—	0.54	−0.16	0.58	—	0.57	0.19	0.45

Bold a₁ values are significant at α < 0.05 and s.e. is determined by 500 bootstraps.