Table 1.

Best candidate models from the multi-model procedure explaining growth rate of the overwintering population in Mexico, growth rate of the adult population in North America, and of egg density per host plant in North America. Models are ranked according to their second-order Akaike’s information criterion (AICc). Only models with ΔAICc < 7 are shown. Log-likelihood (logLik), R² (or marginal pseudo-R² for lme) and model weights are also reported. In all analyses, we removed two years for which the population was affected by severe winter storms in Mexico (2002 and 2004). df indicated the number of estimated parameters calculated as the number of fixed effect coefficients + number of variance parameters.

Rank	Fixed effects	Random effects	ΔAICc	df	logLik	R2	Model weight
Overwintering population in Mexico (Model 3: linear model)
1st	N t-1 + Time	—	0	4	−17.892	0.3677	0.502
2nd	N t-1 + Time + N t-1 x Time	—	1.38	5	−16.833	0.4283	0.252
3rd	N t-1	—	2.40	3	−20.635	0.1789	0.151
4th	—	—	3.79	2	−22.705	0	0.075
5th	Time	—	6.51	3	−22.693	0.0011	0.019
Adult population in North America (Model 4: linear mixed-effects model)
1st	Density t-1	Site	0	4	−101.39	0.5035	0.592
2nd	Density t-1 + Time	Site	1.56	5	−101.05	0.5072	0.272
3rd	Density t-1 + Time + Density t-1 x Time	Site	2.94	6	−100.60	0.5121	0.136
Egg density per host plant in North America (Model 5: linear mixed-effects model)
1st	Egg t-1	Site	0	4	−95.599	0.4190	0.680
2nd	Egg t-1 + Time	Site	2.11	5	−95.486	0.4177	0.237
3rd	Egg t-1 + Time + Egg t-1 x Time	Site	4.20	6	−95.324	0.4165	0.083