TABLE A1.

Top‐ranked models two‐species co‐occurrence models for canid candidate sets estimating occupancy ($\mathrm{\Psi }$) of focal species B (${\mathrm{\Psi }}^{\mathrm{B}}$) when the occupancy state of interacting species A (${\mathrm{\Psi }}^{\mathrm{A}}$) is present (${\mathrm{\Psi }}^{\mathrm{BA}}$) or absent (${\mathrm{\Psi }}^{\mathrm{Ba}}$), and detection ($p$) independent or conditional ($r$) on occupancy or detection. Results for models within 10 ΔAICc of the top model are presented models including uninformative parameters are not shown). Co‐occurrence was considered independent when probability of occupancy for focal species B was constrained to be the same regardless of the occupancy state of interacting species B (${\mathrm{\Psi }}^{\mathrm{A}}\ne {\mathrm{\Psi }}^{\mathrm{BA}}={\mathrm{\Psi }}^{\mathrm{Ba}}$), and conditional if occupancy of species B was dependent of occupancy state of species A (${\mathrm{\Psi }}^{\mathrm{A}}\ne {\mathrm{\Psi }}^{\mathrm{BA}}\ne {\mathrm{\Psi }}^{\mathrm{Ba}}$). Detection of species B was modeled as independent of occupancy or detection of species A ($p^{\mathrm{A}}\ne p^{\mathrm{B}}=r^{\mathrm{BA}}=r^{\mathrm{Ba}}$), conditional on the occupancy of species A ($p^{\mathrm{A}}\ne p^{\mathrm{B}}\ne r^{\mathrm{BA}}=r^{\mathrm{Ba}}$), conditional on the detection of species A ($p^{\mathrm{A}}\ne r^{\mathrm{A}}\ne p^{\mathrm{B}}=r^{\mathrm{BA}}\ne r^{\mathrm{Ba}}$), or conditional on the status and detection of species A ($p^{\mathrm{A}}\ne r^{\mathrm{A}}\ne p^{\mathrm{B}}\ne r^{\mathrm{BA}}\ne r^{\mathrm{Ba}}$)

Species A – Species B	Co‐occurrence submodel	Occupancy covariates	Conditional detection submodel	Detection covariates	ΔAICc	wgt a	K b	neg2ll c
Red fox – gray fox	Independent	Distance to structure + differential species response	Independent	None	0	0.65	6	1120.25
	Independent	% forest + differential species response	Independent	None	2.67	0.17	6	1122.92
	Independent	Distance to structure + differential species response	Conditional on occupancy and detection	None	3.38	0.12	9	1117.36
	Independent	% forest + species interaction term	Conditional on occupancy and detection	None	6.22	0.03	9	1120.19
	Independent	Distance to structure	Independent	None	7.31	0.02	5	1129.63
	Independent	Structures/ha	Independent	None	9.14	0.01	5	1131.46
	Independent	% forest	Independent	None	9.26	0.01	5	1131.58
	Independent	None	Independent	None	9.59	0.01	4	1133.97
Coyote – gray fox	Independent	% forest cover	Independent	Mean temperature	0	0.92	6	2046.75
	Independent	None	Independent	Mean temperature	6.37	0.04	5	2055.18
	Independent	Distance to structure	Independent	Mean temperature	8.25	0.01	6	2055
	Independent	Structures/ha	Independent	Mean temperature	8.37	0.01	6	2055.11
	Independent	% forest + differential species response	Independent	None	9.53	0.01	6	2056.28
	Independent	% forest	Independent	None	9.6	0.01	5	2058.41
Dog – gray fox	Conditional	Distance to structure + differential species response	Conditional on occupancy	None	0	0.44	8	1819.23
	Conditional	Distance to structure + differential species response	Conditional on occupancy and detection	Previous gray fox detection	2.71	0.11	11	1815.59
	Conditional	% forest + differential species response	Conditional on occupancy	Previous gray fox detection	2.73	0.11	9	1819.85
	Conditional	% forest + differential species response	Conditional on occupancy and detection	Previous gray fox detection	2.78	0.1	11	1815.66
	Conditional	Distance to structure + differential species response	Conditional on occupancy and detection	None	2.8	0.1	10	1817.81
	Conditional	% forest + differential species response	Conditional on occupancy and detection	None	3.15	0.09	10	1818.16
	Conditional	% forest + differential species response	Conditional on occupancy	None	3.86	0.06	8	1823.09
	Independent	Distance to structure + differential species response	Conditional on dog occupancy	None	7.19	0.01	7	1828.51
	Conditional	Distance to structure + differential species response	Independent	None	8.52	0.01	7	1829.85
	Independent	Distance to structure + differential species response	Independent	None	9.24	0	6	1832.64
Coyote – red fox	Independent	Distance to structure + differential species response	Independent	None	0	0.9	6	1922.02
	Independent	Distance to structure + differential species response	Conditional on occupancy and detection	None	4.65	0.09	9	1920.39
	Independent	Distance to structure	Independent	None	8.89	0.01	5	1932.98
	Independent	Structures/ha	Independent	None	9.96	0.01	5	1934.04
Domestic dog – red fox	Independent	Distance to structure	Conditional on occupancy	Year	0	0.39	8	1666.35
	Independent	Distance to structure + differential species response	Conditional on occupancy and detection	Year	0.15	0.36	11	1660.15
	Independent	Distance to structure	Conditional on occupancy and detection	Year	1.43	0.19	10	1663.55
	Independent	Distance to structure	independent	Year	3.75	0.06	7	1672.19
Domestic dog – coyote	Independent	Distance to structure + differential species response	Conditional on detection	Mean temperature	0	0.58	8	2623.81
	Independent	Distance to structure + differential species response	Conditional on detection	None	2.11	0.2	7	2628.01
	Independent	Distance to structure + differential species response	Conditional on occupancy and detection	Mean temperature	3.78	0.09	10	2623.37
	Independent	Distance to structure + differential species response	Independent	Mean temperature	4.72	0.05	7	2630.62
	Independent	Distance to structure + differential species response	Conditional on occupancy and detection	None	5.74	0.03	9	2627.44
	Independent	Distance to structure + differential species response	Independent	None	6.43	0.02	6	2634.41
	Independent	Distance to structure + differential species response	Conditional on occupancy	None	7.63	0.01	7	2633.53
	Conditional	Distance to structure + differential species response	Conditional on detection	Mean temperature	9.84	0	8	2633.65

^a Akaike model weight, recalculated following removal of models with uninformative parameters.

^b Number of parameters.

^c 2 × negative log‐likelihood.