Prevalence of monarch (Danaus plexippus) and queen (Danaus gilippus) butterflies in West Texas during the fall of 2018

Table 4 Summary of candidate models

Candidate model	Fixed effects of candidate models	Df	AIC_c	Δi	W_i	E_i
Model 1	Julian day	7	187.56	0	0.768	1
Model 2	Julian day + Plot area	9	190.58	3.01	0.170	5
Model 3	Julian day + Area size	9	194.24	6.68	0.027	28
Model 4	Julian day + Ramet density	9	194.39	6.83	0.025	30
Model 5	Julian day + Ramet density + Plot area	11	197.31	9.75	0.006	131
Model 6	Julian day + Area size + Plot area	11	198.57	11.01	0.003	246
Model 7	Julian day + Ramet density + Area size	11	201.78	14.22	0.001	1222
Model 8	Julian day + Ramet density + Area size + Plot area	13	206.80	19.24	0	15,035
Model 9	Area size	5	220.49	32.92	0	>10⁶
Model 10	Plot area	5	221.03	33.47	0	>10⁶
Model 11	Area size + Plot area	9	225.76	38.20	0	>10⁷
Model 12	Ramet density + Area size + Plot area	7	226.80	39.24	0	>10⁷
Model 13	Ramet density	5	227.07	39.51	0	>10⁷
Model 14	Ramet density + Area size	7	233.97	46.41	0	>10⁹
Model 15	Ramet density + Plot area	7	234.87	47.31	0	>10⁹

The set of candidate models used in the model selection procedure to predict monarch egg density (eggs/milkweed ramet). All candidate models are generalized additive mixed models with site (Fisher 1–3 and Stonewall 1–3) as the random intercept. Our predictor variables were Julian day, plot area, area size, and ramet density (ramets/m²). We considered all possible combinations of these predictor variables. Smoothers were applied to Julian day (at the county level), plot size, and ramet density. The results are based on a negative binomial distribution because of overdispersion. Results presented include the degrees of freedom (df), corrected AIC (AIC_c), the AIC_c difference between the best model and all other models (Δi), Akaike weights (w_i), and the evidence ratio (E_i). The results are ranked by AIC_c, from the best to the worst model

ISSN: 1472-6785