Table 1.

Derivation of population dynamical stability properties. Point estimates for population parameters [r_i, K_i] (in log-normal scale), equilibrium densities in number of breeding pairs [N_i*] and eigenvalues [λ_i] for the three study plots with statistical support for interspecific interactions (α_ij). All systems are feasible [all N_i* > 0] and locally stable (all |λ_i| < 1), such that populations will return to equilibrium following a small perturbation. Plot B shows a shift in relative abundances of the two species across the temperature threshold (θ), but no change in feasibility or local stability conditions. We created 1000 bootstrap samples and estimated the parameters for the corresponding model in each sample. By definition, the system is locally stable when (α_ii · α_jj > α_ij · α_ji). In our case, (α_ii · α_jj = 1) and (1 > α_ij · α_ji). Models formulations are summarized in electronic supplementary material, table S1.

location	speciesi	ri	Ki	αij	Ni*	λi	significance of 1 > αij · αji	interpretation
Plot HP	GT	3.77	5.11	0.51	43.27	0.83	p < 0.001	stable coexistence
	BT	2.24	5.84	0.84	14.22	0.05
Plot B	GT (TempSpring < θ)	5.20	4.70	0.25	47.45	−0.51	p < 0.001	stable coexistence
	BT (TempSpring < θ)	6.20	6.21	0.74	28.98	0.40
	GT (TempSpring ≥ θ)	5.20	4.70	0.25	41.49	0.75	p < 0.001	stable coexistence (tending towards unstable; see text)
	BT (TempSpring ≥ θ)	4.65	9.51	1.51	49.49	−0.34
Marley Wood	GT	2.16	4.55	0.25	35.76	0.85	p < 0.001	stable coexistence
	BT	1.59	7.05	0.90	45.64	0.45
Liesbos	GT	3.29	3.81	0.06	36.94	0.14	p < 0.001	stable coexistence
	BT	2.00	2.32	−0.21	21.59	0.14