Table 1. Relationships between the magnitude of population fluctuations (response variable) and a number of ecological, demographic, life-history and genetic parameters of European breeding bird species according to phylogenetic generalized least square regression models.

Parameter	Including population trend				Also including abundance
	Estimate (SE)	t	N	λ	Estimate (SE)	t	N	λ
Dichromatism	-0.020 (0.015)	-1.35	231	0.530
Coloniality	0.063 (0.017)	3.70***	231	0.356	0.053 (0.015)	3.62***	227	0.000
Water habitat	0.049 (0.011)	4.34***	231	0.473	0.023 (0.010)	2.20*	227	0.402
Urbanisation	-0.053 (0.013)	-3.91***	231	0.694	-0.001 (0.013)	-0.07	227	0.000
Body mass	0.006 (0.015)	0.38	229	0.588
Clutch size	0.041 (0.045)	0.91	229	0.531
Annual fecundity	-0.012 (0.044)	-0.29	228	0.517
Abundance	-0.064 (0.006)	-10.35***	227	0.000
Density a	-0.074 (0.008)	-8.81***	227	0.416
W. Palearctic range	-0.003 (0.005)	-0.60	227	0.550
Total range	0.009 (0.003)	3.00**	227	0.407	0.011 (0.002)	4.53***	227	0.000
No. subspecies b	-0.045 (0.019)	-2.40*	227	0.336	-0.012 (0.016)	-0.77	227	0.352
Migration	-0.004 (0.003)	-1.35	205	0.470
Parasitism	-0.007 (0.003)	-2.42*	189	0.469	0.002 (0.003)	0.76	187	0.000
Relative brain mass c	0.046 (0.063)	0.72	187	0.459
Distance to mainland	-0.022 (0.014)	-1.62	153	0.658
Survival rate	-0.012 (0.008)	-1.54	143	0.529
Flight initiation dist.	0.017 (0.029)	0.58	140	0.656
Heterogeneity distrib.	0.108 (0.037)	2.95**	139	0.692	-0.038 (0.040)	-0.95	138	0.556
First arrival date	-0.040 (0.025)	-1.57	139	0.305
Mean arrival date	0.028 (0.034)	0.82	96	0.160
Nest predation	-0.003 (0.006)	-0.54	85	0.182
Sparrowhawk d	0.012 (0.011)	1.08	82	0.595
Goshawk d	0.009 (0.012)	0.77	76	0.000
Natal dispersal	0.072 (0.020)	3.62***	69	0.000	0.008 (0.021)	0.39	69	0.488
Cat d	0.009 (0.017)	0.56	55	0.000
Band-sharing coef.	0.027 (0.083)	0.33	49	0.764
Alleles	-0.087 (0.062)	-1.40	40	0.000
Polymorphic loci	-0.208 (0.102)	-2.03*	39	0.000	-0.134 (0.095)	-1.41	39	0.000
Inbreeding coef.	0.001 (0.130)	0.01	35	0.000

Species population trend was included in all models. Phylogenetic relations among species and the number of populations used to estimate population fluctuations in each species were controlled in all analyses (see Statistical analysis for details). Lambda parameter (λ), the optimum degree of phylogenetic dependence, is shown for each model. When the relationship between population fluctuations and another parameter had a P-value less than 0.10, the test was repeated including also abundance in the model (second column). Abundance was always statistically significant (|estimate| ≥ 0.044, |t| ≥ 2.96, P ≤ 0.0055) in models of the second column.

* P < 0.05,

** P < 0.01,

*** P < 0.001.

^a Abundance and Western Palearctic breeding range were included in the model.

^b Total breeding range was also included in the model.

^c Brain mass controlled for body mass (residuals after regressing log₁₀-transformed brain mass on log₁₀-transformed body mass while controlling for phylogenetic relations among species).

^d Body mass and (body mass)² were also included in the model because predators usually have an optimal prey size.