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Table 1.  Properties of vegetation in the north and south units of Theodore Roosevelt National Park, North Dakota, USA.
Vegetation Type	North Unit		South Unit		Transects
	Undisturbed	Disturbed	Undisturbed	Disturbed	Total	Alien (%)
Used in model selection
Chrysothamnus nauseosus/Agropyron smithii	29	7	55	18	109	53
Artemisia tridentata/Atriplex confertiflora	26	9	51	9	95	59
Populus deltoides/Juniperus scopulorum	18	3	11	1	33	91
Artemisia cana	22	7	45	15	89	94
Symphoricarpos occidentalis/Prunus virginiana	32	4	50	16	102	98
Andropogon scoparius	31	5	56	16	108	68
Andropogon scoparius/Juniperus horizontalis	23	10	57	3	3	63
Stipa comata/Bouteloua gracilis	24	6	32	10	72	75
Juniperus scoparius/Oryzopsis micrantha	26	10	52	11	99	88
Agropyron smithii/Stipa viridula	31	4	58	15	108	95
Agropyron smithii/Stipa comata	32	3	45	15	95	96
Not used in model selection
Achenbach Hills complex	5	1	0	0	6	83
Populus tremuloides	0	0	3	0	3	100
Symphoricarpos occidentalis	10	5	3	0	18	94
Artemisia tridentata/Bouteloua gracilis	0	0	23	1	24	83
Grassed sand floodplain	19	2	0	0	21	71
Marsh	6	3	0	0	9	67
Petrified Forest complex	0	0	1	2	3	100
Populus tremuloides/Betula occidentalis	4	5	0	0	9	89
River bottom	9	0	17	3	29	100
Rolling scoria complex	0	0	33	12	45	95
Steep scoria complex	0	0	29	10	39	95
Salix spp.	15	3	0	0	18	100
Notes: Alien transects are those with at least one alien plant. "Disturbed" refers to those transects that were within 100 m of a road, trail, seeded field, campground, or picnic area. The vegetation types that were not used in the analysis were excluded because they lacked representation in one of the park units and/or in one disturbance category.

Number and frequency of alien species. — The number and frequency of alien plant species depended on the interaction among all three variables: vegetation type, disturbance, and park unit (Table 2). In each case, vegetation type as a main effect had the least difference in AIC score from the best model (Table 2), which indicated that this variable had the largest effect on the number and frequency of alien plants.

Table 2.  Variables included in the three best models of vegetation structure, as determined by Akaike's Information Criterion (AIC).
Response variable	Sample size (no. transects)	Best model (difference in AIC score from third)	Second-best model (difference in AIC score from third)	Third-best model (difference in AIC score from fourth)	Difference in AIC score from best for each main effect
					V	U	D
Total number of alien species	1003	V × U × D (32)	V × U (18)	V, U, D (4)	69	258	265
Mean frequency of alien species	796	V × U × D (74)	V × D (1)	V × U (30)	108	217	219
Salsola iberica	27	V (3)	V, D (1)	V, U (3)	0	44	43
Tragopogon dubius	242	V (2)	V, U (1)	V, D (1)	0	83	83
Bromus japonicus	204	V, U (1)	V × U (1)	V, U, D (10)	12	108	121
Melilotus officinalis	434	V, U or V, U, D (5)	V × U (1)	V or V, D or V × U × D (1)	6	22	27
Taraxacum officinale	225	V, U, or V × U (3)	V or V, U, D (2)	V, D (5)	3	74	78
Camelina microcarpa	68	V × U (14)	V × U × D (5)	V, U or V, U, D (14)	33	85	98
Cirsium arvense	39	V × U (15)	V × U × D (15)	V, U (2)	32	72	80
Euphorbia esula	112	V × U (18)	V × U × D (37)	V, U (2)	98	112	148
Poa pratensis	377	V × U (7)	V (1)	V, U (1)	7	172	172
Descurainia sophia	37	D, U or D × U (1)	D (1)	U (8)	13	2	1
Convolvulus arvensis	34	D (2)	D × U (1)	U (1)	4	3	0
Poa compressa	25	U (1)	D (3)	U, D (1)	10	0	1
Lactuca serriola	17	U (2)	D (1)	U, D (3)	26	0	2
Chenopodium album	59	D (1)	U (3)	U, D (1)	14	1	0
Alyssum desertorum	13	D or U, D (1)	U or D × U (21)	V, U, D (2)	24	1	0
Agropyron cristatum	25	U or D (2)	U, D (2)	U × D (7)	11	0	0
Bromus inermis	144	V, D or V × D (1)	V, U, D (7)	V (1)	8	46	38
Notes: Numbers in parentheses report the difference between the AIC score for that model and for the next-best model. The final three columns indicate the difference in AIC score between models containing each main effect alone and the best model. The magnitude of the AIC score is dependent on sample size, so scores can only be compared among models for a given response variable. The difference in AIC scores between models reflects uncertainty in model selection, with relatively small difference indicating greater uncertainty. V = native vegetation type, U = park unit, D = anthropogenic disturbance. Variables separated by "×" or commas indicate interaction between main effects of main effect without interaction, respectively.

The number of species per transect varied more among than within vegetation types (Fig. 1a). For the most part, the interactions reflected the magnitude rather than direction of differences in numbers of alien species. The number of alien species on disturbed transects either did not differ from, or was greater than, the number on undisturbed transects, regardless of vegetation type or park unit. However, in Agropyron smithii/Stipa viridula and Populus deltoides/Juniperus scopulorum vegetation types, disturbed transects in the north unit had far more alien species than did undisturbed transects. This was true for A. smithii/S. viridula but not for P. deltoides/J. scopulorum vegetation in the south unit, where both disturbed and undisturbed transects had very high numbers of alien species. With a single exception (in A. smithii/S. viridula vegetation), the number of alien species per transect in the south unit was the same as or greater than the number in the north unit in each vegetation type.

There was less variation in frequency of alien species on occupied transects than there was in number of alien species (Fig. 1b). Frequency was, in fact, only very weakly related to number of species (r = 0.07, P = 0.046). Differences between frequencies of alien plants on disturbed and undisturbed transects in general were small, as were differences between the north and south units. Interaction among the three variables was primarily evident in Juniperus scopulorum/Oryzopsis micrantha, where disturbed transects had higher frequencies of aliens in both north and south units, and in Symphoricarpos occidentalis/Prunus virginiana vegetation, where disturbed transects had higher frequencies only in the north unit. Again, it was the magnitude rather than the direction of differences in frequency that resulted in the interaction: alien species were never more frequent on undisturbed compared with disturbed transects and in only one vegetation type were they more frequent in the north than in the south unit.

Presence of individual alien species on transects. — AIC identified, either as a main effect or as an interaction, vegetation type as a variable in the best model for 10 species, park unit for 12 species, and disturbance for seven species (Table 2). For the seven species best described by either park unit or disturbance, AIC scores differed little between models containing either variable. This suggests considerable uncertainty in model selection between these two variables. In general, vegetation type was unlikely to be included in models for those species that occurred infrequently. Vegetation type more closely approximated the best model (and therefore had the largest effect in the model) for seven species, park unit and disturbance for six; the remainder were either well defined by interactions present in the best model (e.g., Cirsium arvense, Camelina microcarpa, and Euphorbia esula), or showed little difference among any of the models (e.g., Convolvulus arvensis) (Table 2).

For two species, Tragopogon dubius and Salsola iberica, the best model included only vegetation type (Table 2). Tragopogon dubius was most likely to occur in grasslands dominated by cool-season grasses with little or no shrub or tree canopy (Fig. 2a). Salsola iberica occurred most often on transects in the Chrysothamnus nauseosus/Agropyron smithii vegetation type, which is primarily composed of bare ground, and was never recorded in vegetation types dominated by sod-forming grasses (Fig. 2a).

The best models for Bromus japonicus and Melilotus officinalis included vegetation type and park unit as main effects (Table 2). In each case, vegetation type had a larger effect than park unit as indicated by the smaller difference in AIC score between the main effect of vegetation type and the best model. Both species tended to be more commonly encountered in the south unit, but relative occurrence among vegetation types was similar in both units (Fig. 3a, b). The best models for Camelina microcarpa, Cirsium arvense, Euphorbia esula, and Poa pratensis included the interaction between vegetation type and park unit (Table 2). The AIC score was the same with and without this interaction term for Taraxacum officinale, and vegetation type alone had nearly as high a score as the two-term model (Table 2). Taraxacum officinale occurred on either the same or greater proportion of transects in the north than in the south unit in each vegetation type (Fig. 3c). Camelina microcarpa, Cirsium arvense, and Euphorbia esula frequencies were strongly defined by the interaction; main effects alone had relatively large differences in AIC scores from the best model. Camelina microcarpa was very uncommon in the north unit, but occurred there in the two vegetation types in which it was most common in the south unit (Fig. 3d). Cirsium arvense was unusual in that it was more commonly encountered in the north than the south unit, and occurred in the south unit in vegetation types different from where it occurred in the north (Fig. 3e). Euphorbia esula varied substantially among vegetation types in the south unit, and although present on two transects in the north unit, was absent from the 11 vegetation types in this analysis (Fig. 3f). Poa pratensis was more frequently encountered in the south unit than the north in Populus deltoides/Juniperus scopulorum vegetation, but was more common in the north unit in Agropyron smithii/Stipa viridula and Symphoricarpos occidentalis/Prunus virginiana vegetation (Fig. 3g).

Fig. 3  Proportions of transects on which alien species were found in 11 vegetation types, by park unit. Vegetation type and park unit were main effects in models for Bromus japonicus, Melilotus officinalis, and Taraxacum officinale; for Camelina microcarpa, Cirsium arvense, Euphorbia esula, and Poa pratensis, models also included the interaction between vegetation type and park unit. Shown are least-squares means with 1SE.

The best models for Lactuca serriola, Poa compressa, Agropyron cristatum, Alyssum desertorum, Chenopodium album, and Convolvulus arvensis included either park unit or disturbance as main effects, although AIC did not distinguish well between the two variables (Table 2). All of these species occurred relatively infrequently in the vegetation types under consideration. Agropyron cristatum and L. serriola tended to be more common in the south unit, P. compressa in the north unit (Fig. 4). Where significantly different, each species was more commonly encountered on disturbed than on undisturbed transects (Fig. 4). Descurainia sophia was the only species for which the interaction between disturbance and park unit defined the best model (Table 2). This species was far more common on disturbed than undisturbed transects in the south unit, but did not differ by disturbance in the north unit, where it was substantially less abundant (Fig. 4). The best model for Bromus inermis included the interaction between vegetation type and disturbance, the only species for which this was the case (Table 2). However, the model containing all three main effects (but no interaction) differed from the best model by only one unit (Table 2). Bromus inermis was always more commonly encountered on disturbed transects, especially in the Agropyron/Stipa communities (Fig. 5).

Fig. 4  Proportion of transects occupied by species for which the best model contained park unit and/or disturbance. AIC did not differentiate these two variables well, so both effects are depicted. Shown are least-squares means with 1 SE.

Fig. 5  Proportion of transects occupied by Bromus inermis, for which the best model contained the interaction between vegetation type and disturbance. Shown are least-squares means with 1 SE.