Ecological Archives E096-072-A1

Ecological Archives E096-072-A1

Petr Pyšek, Ameur M. Manceur, Christina Alba, Kirsty F. McGregor, Jan Pergl, Kateřina Štajerová, Milan Chytrý, Jiří Danihelka, John Kartesz, Jitka Klimešová, Magdalena Lučanová,10 Lenka Moravcová, Misako Nishino, Jiří Sádlo, Jan Suda, Lubomír Tichý, and Ingolf Kühn. 2015. Naturalization of central European plants in North America: species traits, habitats, propagule pressure, residence time. Ecology 96:762–774. http://dx.doi.org/10.1890/14-1005.1

Appendix A. Parsimonious regression tree, magnitude of the coefficients, and the probability of significance for parsimonious models.

Fig. A1. Flowchart of the steps of statistical analysis. In white: steps which require quality control and are iterative (repeated until criteria met). Abbreviations: RMSR, root mean square residuals (a measure of model fit), PGIF: parsimony goodness of fit index (a measure of parsimony).

Fig. A2.Parsimonious regression tree to predict the number of North American regions invaded based on all traits (R² = 0.43). Average number of regions and, in brackets, the number of species in the group are shown for each terminal node.

FigA3

Fig. A3. Parsimonious regression tree to predict cultivation in the invaded range with all traits except cultivation in the native range, minimum residence time and regional frequency in the native range, expressed as the number of grid cells occupied by the species. Average cultivation index in the invaded range and the number of species in the group are shown for each terminal node.

FigA4

Fig. A4. Parsimonious regression tree to predict cultivation in the native range with all traits except cultivation in the invaded range, minimum residence time and regional frequency in the native range. Average cultivation index in the native range and the number of species in the group are shown for each terminal node.

FigA5

Fig. A5. Least parsimonious model which shows a path analysis with direct effects of biological traits on each driver of the invasion process: it fits the data best (RMSR = 0.06 ) but is not parsimonious (PGIF = 0.08); rather it is the most complex model. This model suggests that there are direct effects of the biological traits on each driver of invasion but several effects are rather negligible since the parameter estimates are small. (Note that the existence of an effect is accepted when the p value of the parameter estimate is less than 0.05). Also, in this model the biological traits explain a large part of variation in the number of North American regions invaded so that the size of the effect between the number of habitats and number of regions invaded is very small, and some of the parameter estimates show an unexpected negative sign (although the size of these effects is small and often not significant). This is symptomatic of an overfit model so Figs. 2, 3, and 4 in the main text result from a simplification of the path diagram shown here. Variables with nonsignificant effects are not framed.

Table A1. Magnitude of the coefficients and the probability of significance for the most parsimonious model presented in Fig. 1 in the main text. Since the variables are standardized, the estimate of the coefficient is also a measure of importance (large in absolute value means more important). Note: ~ signifies a regression path, whereas a ~~ signifies covariance.

		Estimate	Std. err	Z value	P(>\|z\|)
Regressions
Number of regions in North America~	Number of habitats	7.539	0.845	8.921	0.000
	Minimum residence time	9.894	0.795	12.439	0.000
Minimum residence time~	Cultivation in invaded range	0.525	0.051	10.401	0.000
Cultivation in invaded range~	Cultivation in native range	1.274	0.177	7.186	0.000
Cultivation in native range ~	Regional frequency	0.290	0.047	6.237	0.000
Regional frequency~	Number of habitats	0.918	0.043	21.568	0.000
Number of habitats~	Stress-tolerant life strategy	-0.479	0.088	-5.445	0.000
	Seed bank persistence	0.510	0.041	12.359	0.000
	Specific leaf area	0.050	0.049	1.022	0.307
	Leaf dry matter content	0.041	0.042	0.974	0.330
	Flowering period	0.153	0.040	3.814	0.000
	Clonality	0.084	0.021	3.968	0.000
	Height	0.073	0.037	1.943	0.052
	Propagule size	0.150	0.034	4.433	0.000
Covariances
Stress-tolerant life strategy ~~	Seed bank persistence	0.014	0.023	0.606	0.545
	Specific leaf area	0.039	0.022	1.808	0.071
	Leaf dry matter content	-0.106	0.023	-4.646	0.000
	Flowering period	0.004	0.024	0.145	0.885
	Clonality	0.203	0.042	4.864	0.000
	Height	-0.149	0.027	-5.611	0.000
	Propagule size	-0.123	0.026	-4.816	0.000
Seed bank persistence ~~	Specific leaf area	0.034	0.048	0.693	0.488
	Leaf dry matter content	-0.003	0.047	-0.064	0.949
	Flowering period	0.301	0.047	6.466	0.000
	Clonality	0.270	0.085	3.184	0.001
	Height	-0.166	0.054	-3.072	0.002
	Propagule size	-0.305	0.065	-4.662	0.000
Specific leaf area ~~	Leaf dry matter content	-0.302	0.049	-6.164	0.000
	Flowering period	0.179	0.047	3.818	0.000
	Clonality	-0.027	0.092	-0.298	0.766
	Height	-0.116	0.045	-2.594	0.009
	Propagule size	-0.072	0.046	-1.558	0.119
Leaf dry matter content~~	Flowering period	-0.244	0.046	-5.312	0.000
	Clonality	0.029	0.089	0.331	0.741
	Height	0.260	0.054	4.798	0.000
	Propagule size	0.071	0.047	1.508	0.131
Flowering period ~~	Clonality	-0.017	0.097	-0.175	0.861
	Height	-0.274	0.055	-5.004	0.000
	Propagule size	-0.209	0.055	-3.833	0.000
Clonality~~	Height	-0.147	0.090	-1.639	0.101
	Propagule size	-0.068	0.081	-0.839	0.401
Height ~~	Propagule size	0.393	0.141	2.78	0.005

Table A2. Magnitude of the coefficients and the probability of significance for the highly parsimonious model with improved fit represented in Fig. 2 in the main text. Since the variables are standardized the estimate of the coefficient is also a measure of importance (large in absolute value means more important). Note: ~ signifies a regression path, whereas a ~~ signifies covariance.

		Estimate	Std. err	Z value	P(>\|z\|)
Regressions
Number of regions in North America~	Number of habitats	8.471	0.864	9.800	0.000
	Minimum residence time	9.887	0.830	11.907	0.000
Minimum residence time~	Cultivation in invaded range	0.479	0.050	9.654	0.000
Cultivation in invaded range~	Cultivation in native range	0.838	0.078	10.740	0.000
Cultivation in native range ~	Stress-tolerant life strategy	-0.250	0.097	-2.582	0.010
	Specific leaf area	-0.067	0.037	-1.799	0.072
	Height	0.148	0.044	3.383	0.001
	Propagule size	0.134	0.051	2.613	0.009
	Regional frequency	0.314	0.044	7.147	0.000
Regional frequency ~	Number of habitats	0.905	0.042	21.597	0.000
Number of habitats ~	Stress-tolerant life strategy	-0.372	0.082	-4.521	0.000
	Seed bank persistence	0.517	0.040	12.842	0.000
	Flowering period	0.182	0.040	4.535	0.000
	Clonality	0.081	0.020	3.966	0.000
	Height	0.069	0.037	1.882	0.060
	Propagule size	0.122	0.035	3.464	0.001
Covariances
Stress-tolerant life strategy ~~	Specific leaf area	0.034	0.021	1.603	0.109
	Height	-0.151	0.027	-5.691	0.000
	Propagule size	-0.124	0.026	-4.859	0.000
	Seed bank persistence	0.014	0.023	0.590	0.555
	Flowering period	0.005	0.024	0.195	0.845
	Clonality	0.197	0.042	4.693	0.000
Specific leaf area ~~	Height	-0.112	0.045	-2.483	0.013
	Propagule size	-0.063	0.046	-1.367	0.172
	Seed bank persistence	0.070	0.054	1.290	0.197
	Flowering period	0.191	0.047	4.091	0.000
	Clonality	-0.015	0.091	-0.166	0.868
Height ~~	Propagule size	0.384	0.141	2.733	0.006
	Seed bank persistence	-0.166	0.055	-3.007	0.003
	Flowering period	-0.275	0.056	-4.925	0.000
	Clonality	-0.129	0.092	-1.401	0.161
Propagule size ~~	Seed bank persistence	-0.309	0.067	-4.620	0.000
	Flowering period	-0.213	0.055	-3.865	0.000
	Clonality	-0.055	0.081	-0.680	0.496
Seed bank persistence ~~	Flowering period	0.295	0.047	6.305	0.000
	Clonality	0.271	0.085	3.199	0.001
Flowering period ~~	Clonality	-0.020	0.097	-0.209	0.834

Table A3. Magnitude of the coefficients and the probability of significance for the most parsimonious model including additional feedbacks between the regional frequency in the native range and cultivation in the native range, and a direct link between cultivation in the invaded range and the number of North American regions invaded (represented in Fig. 3 in the main text). Since the variables are standardized the estimate of the coefficient is also a measure of importance (large in absolute value means more important). Note: ~ signifies a regression path, whereas a ~~ signifies covariance.

		Estimate	Std.err	Z value	P(>\|z\|)
Regressions
Number of regions in North America~	Number of habitats	8.032	0.906	8.869	0.000
	Minimum residence time	7.988	0.850	9.397	0.000
	Cultivation in invaded range	2.465	0.969	2.544	0.011
Minimum residence time~	Cultivation in invaded range	0.454	0.052	8.699	0.000
Cultivation in invaded range~	Cultivation in native range	0.759	0.066	11.425	0.000
Cultivation in native range ~	Stress-tolerant life strategy	-0.290	0.100	-2.884	0.004
	Specific leaf area	-0.063	0.038	-1.656	0.098
	Height	0.166	0.045	3.654	0.000
	Propagule size	0.111	0.049	2.275	0.023
	Regional frequency	0.253	0.051	4.911	0.000
Regional frequency ~	Number of habitats	0.864	0.041	20.872	0.000
	Cultivation in native range	0.164	0.051	3.209	0.001
Number of habitats~	Stress-tolerant life strategy	-0.334	0.082	-4.074	0.000
	Seed bank persistence	0.518	0.040	12.98	0.000
	Flowering period	0.185	0.040	4.610	0.000
	Clonality	0.081	0.020	3.949	0.000
	Height	0.055	0.037	1.472	0.141
	Propagule size	0.108	0.033	3.296	0.001
Covariances
Stress-tolerant life strategy ~~	sla	0.035	0.021	1.617	0.106
	Height	-0.152	0.027	-5.724	0.000
	Propagule size	-0.125	0.026	-4.891	0.000
	Seed bank persistence	0.011	0.023	0.466	0.641
	Flowering period	0.004	0.024	0.157	0.875
	Clonality	0.193	0.042	4.590	0.000
Specific leaf area ~~	Height	-0.113	0.045	-2.517	0.012
	Propagule size	-0.065	0.046	-1.401	0.161
	Seed bank persistence	0.070	0.054	1.297	0.195
	Flowering period	0.191	0.047	4.095	0.000
	Clonality	-0.016	0.091	-0.175	0.861
Height ~~	Propagule size	0.407	0.142	2.871	0.004
	Seed bank persistence	-0.157	0.055	-2.833	0.005
	Flowering period	-0.273	0.056	-4.860	0.000
	Clonality	-0.120	0.092	-1.298	0.194
Propagule size ~~	Seed bank persistence	-0.300	0.067	-4.499	0.000
	Flowering period	-0.211	0.055	-3.835	0.000
	Clonality	-0.054	0.081	-0.659	0.510
Seed bank persistence ~~	Flowering period	0.294	0.047	6.295	0.000
	Clonality	0.272	0.085	3.201	0.001
Flowering period ~~	Clonality	-0.021	0.097	-0.212	0.832

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