Table 3 Global engineering and dispersal model results

	Diversiflorum	Centrale	Eragrostis	Scaevola
Engineering Model
Fire season: winter	3.02 ** [1.48, 6.15]	0.87 [0.39, 1.93]	0.37 *** [0.28, 0.49]	1.59 * [1.04, 2.44]
Fire Frequency	0.69 [0.17, 2.74]	4.06 ** [1.48, 11.16]	1.04 [0.69, 1.56]	0.80 [0.38, 1.67]
TSF diversity	3.08 *** [1.75, 5.45]	1.50 [0.69, 3.29]	0.56 *** [0.42, 0.74]	1.46 [0.91, 2.35]
TSFdiv × Fire freq	0.58 [0.18, 1.83]	0.47 [0.16, 1.38]	1.57 [0.94, 2.61]	1.43 [0.58, 3.56]
Season × Fire freq	1.47 [0.33, 6.57]	2.61 [0.79, 8.62]	2.73 *** [1.56, 4.77]	0.93 [0.35, 2.48]
R² Fixed effects	11.44%	12.07%	7.19%	1.98%
R² Fixed + Random	41.12%	56.94%	30.52%	40.17%
Dispersal Model
Site distance	0.27 *** [0.15, 0.49]	0.38 * [0.16, 0.91]	0.69 * [0.49, 0.98]	3.49 *** [1.94, 6.29]
Land use	17.01 *** [6.50, 44.50]	1.20 [0.36, 4.02]	0.77 [0.50, 1.17]	0.46 [0.20, 1.07]
Major site	0.08 * [0.01, 0.58]	1.04 [0.06, 18.04]	1.80 * [1.05, 3.07]	0.19 * [0.05, 0.71]
H₂O Perm	3.84 * [1.04, 14.24]	1.34 [0.22, 8.27]	0.40 * [0.19, 0.87]	0.09 ** [0.02, 0.43]
Land use × H₂O Perm	2836.02 *** [314.78, 25551.36]	0.03 * [0.00, 1.00]	1.84 [0.58, 5.89]	0.21 [0.03, 1.54]
Site dist × Land Use	0.01 *** [0.00, 0.09]	0.62 [0.04, 8.69]	0.08 *** [0.03, 0.20]	12.67 ** [2.30, 69.84]
R² Fixed effects	44.88%	14.88%	8.75%	19.05%
R² Fixed + Random	55.50%	68.10%	43.54%	68.79%

Model covariates (GLM, binomial, n = 10 random effect levels, n = 2924 observations) as the standardized odds ratio for the best presence models (±95% CI in square brackets). The odds ratios reported here give the relative change in the likelihood of presence for a two-standard deviation increase in the predictor variable. Odds ratios higher than 1 indicate the predictor variable increases the odds of presence; those less than 1 indicate a negative relationship (the predictor variable decreases the likelihood of presence). Interaction (crossed) terms in the model are represented by “X”. Caution must be used in interpreting the coefficients from interaction terms. R² terms are reported as Nakagawa’s R² and are suggestive of the proportion of variation explained by the fixed terms, vs the fixed terms plus the random effect of Transect. Predicted values for some variables are shown in Fig. 2. Asterisks indicate significant p values (* = <0.05, ** = <0.01, *** = <0.001).

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