Table 2 Factors impacting the rate of male incursions in ursine colobus monkeys, as well as the propensity of adult males and adult females to participate aggressively in these incursions.

Model and Fixed Effects	b Estimate	SE	χ²	p	− 95% CI	+ 95% CI
Male incursion rate
(Intercept)	− 3.72	0.18	–	–	–	–
Rainfall	− 0.02	0.11	0.04	0.840	-0.23	0.19
Population size	0.14	0.11	–	–	–	–
Food availability in home range	− 0.31	0.16	5.20	0.023	-0.64	-0.04
Number adult females	− 0.22	0.13	3.46	0.063	-0.56	0.01
Single male vs multi-male	− 0.83	0.29	–	–	–	–
Population size * SM vs MM	− 0.65	0.22	7.73	0.005	− 1.08	− 0.21
Male aggression in male incursions
(Intercept)	2.90	1.75	–	–	–	–
Rainfall	− 0.61	0.35	3.08	0.079	− 1.33	0.07
Population size	− 0.77	0.57	1.87	0.171	− 2.00	0.32
Food availability in home range	1.43	0.65	5.98	0.014	0.26	2.86
Number adult females	2.14	1.01	5.92	0.015	0.37	4.45
Single male vs multi-male	− 2.11	1.56	1.82	0.178	− 5.45	1.03
Female aggression in male incursions
(Intercept)	− 1.73	0.35	–	–	–	–
Rainfall	− 0.07	0.33	0.05	0.824	− 0.74	0.57
Population size	1.63	0.57	10.32	0.001	0.60	2.84
Food availability in home range	0.44	0.45	0.95	0.331	− 0.47	1.32
Number adult females	0.11	0.67	0.03	0.873	− 1.22	1.43
Single male versus multi-male	1.51	0.83	3.47	0.062	− 0.08	3.32

The male incursion rate model explained a third of the variation in male incursion rates (R²_GLMM(C) = 0.29), and performed significantly better than the null model, which contained only the offset, intercept, and random effect (likelihood ratio test: N = 146, χ² = 27.35, p < 0.001). The models examining male (likelihood ratio test: N = 146, χ² = 19.73, p = 0.001; R²_GLMM(C) = 0.79) and female participation in male incursions (likelihood ratio test: N = 146, χ² = 30.77, p < 0.001; R²_GLMM(C) = 0.40) both performed significantly better than the null models (i.e., models with intercept, number of encounters as a weighted term, and random effects only). Significant predictors are presented in bold and trends are italicized.

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