Table 2 Predictors of species presence, models output for each species.

Predictors	E. aurinia			P. apollo			P. arion
Predictors	Est	SE	p value	Est	SE	p value	Est	SE	p value
Intercept	− 1.235	0.389	0.002	− 0.75	0.115	< 0.001	− 3.46	0.316	< 0.001
Temperature	50.975	8.471	< 0.001	30.993	3.184	< 0.001	17.707	6.32	0.005
Temperature²	− 28.998	13.167	0.028	− 20.806	3.977	< 0.001	− 25.506	9.977	0.011
sin(day of the season)	1.712	0.32	< 0.001	0.087	0.117	0.459	− 0.476	0.289	0.1
cos(day of the season)	− 0.862	0.346	0.013	− 1.313	0.158	< 0.001	− 0.955	0.298	0.001
Sex (Female as reference)	0.51	0.217	0.019	0.264	0.14	0.06	1.78	0.264	< 0.001
Temperature * sin(day of the season)	− 17.823	9.475	0.06	4.145	4.43	0.35	10.552	8.311	0.204
Temperature * sin(day of the season)	− 12.666	9.963	0.204	14.234	4.548	0.002	11.343	11.444	0.322
Temperature * cos(day of the season)	− 29.786	8.654	< 0.001	− 18.924	6.064	0.002	− 7.211	8.195	0.379
Temperature² * cos(day of the season)	10.518	13.325	0.43	− 17.666	7.416	0.017	− 12.95	11.243	0.249

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