Inferring habitat suitability and spread patterns from large-scale distributions of an exotic invasive pasture grass in north Australia

Authors


Correspondence author. E-mail: aaron.petty@cdu.edu.au

Summary

1. The understanding of large-scale patterns in expanding populations of alien invasive plants can be used to infer the environmental limiting factors, habitat heterogeneity and, ultimately, the range expansion potential of invasive plants.

2. We used multivariate analysis and a novel quantile regression technique accounting for spatial autocorrelation to compare and contrast factors influencing the abundance and distribution of the African grass Andropogon gayanus (gamba grass) at two large-scale invasion sites in the tropical savanna region of Australia. We collected data using aerial and ground surveys and tested for limiting factors using three landscape-scale indices related to soil quality, soil moisture and invasion history.

3. In one site, gamba grass was principally colonising drainage lines and riparian areas. Occupation of these areas was limited in proportion to the distance from the original gamba grass source. In the second site, gamba grass abundance was independent of distance from the original source and was well established in all vegetation communities, although abundance was also limited in higher elevation sites away from drainage lines.

4. Comparisons between these sites with different patterns of invasion enabled the estimation of both the invasion pathways and range expansion potential of gamba grass. Our results indicated that gamba grass spreads from riparian communities to invade upland sites and has the potential to invade 70% of north Australia’s upland savanna communities.

5. Aerial surveys comprehensively assessed patterns over a larger area than ground surveys and were much more economical.

6.Synthesis and applications. Large-scale surveys across multiple sites are critical to understanding the dynamics of recent alien species invasions where little is known about the pattern and potential range of spread. The application of quantile regression and aerial surveys shows promise as aerial surveys are efficient at capturing a large amount of data. The novel quantile regression technique we demonstrate here can account for both spatial autocorrelation and noisy ecological data from aerial surveys while returning robust results. We were thus able to demonstrate widespread colonisation of creek lines by gamba grass and recommend that management focuses on detection and eradication along drainage lines in addition to the present focus on transport corridors.

Introduction

Alien plant invasions pose a serious threat to ecosystems world-wide (Ehrenfeld 2010). Determining spread patterns, particularly the factors that limit or facilitate invasion, is challenging yet critical to the strategic and effective control of alien plants (D’Antonio et al. 2004). However, spread patterns vary significantly depending on the scale of the study (Collingham et al. 2000), the stage of invasion (Theoharides & Dukes 2007), and spatial and temporal variation in landscape structure (Melbourne et al. 2007). Fortunately, the concurrent development of statistical techniques and computing power is facilitating the development of tools that can both aid management decisions and test key hypotheses regarding the patterns of spread of invasive plants (e.g. Andrew & Ustin 2010).

One such statistical approach, quantile regression (QR), has had little application in the study of invasive species (but see Le Maitre, Thuiller & Schonegevel 2008), despite its increased use in modelling native species distributions. By measuring effect sizes across the distribution of the response variable, QR does not make any assumptions about variance and is robust to variation in the error distribution of the data. Quantile regression can provide more ecologically realistic models by describing the potential (or maximum) as well as the realised (or mean) patterns of species distribution (Vaz et al. 2008).

Quantile regression can be particularly useful in the study of alien plant invasions as in most instances invasive plants have yet to occupy all potential habitats in the landscape (Guisan & Thuiller 2005). Quantile regression provides robust effect estimates in situations where there may be multiple interacting limiting factors, some potentially unmeasured (Cade, Terrell & Schroeder 1999). For example, in the early stages of invasions, dispersal is a limiting factor that interacts strongly with other biotic and abiotic limiting factors (Pysek & Hulme 2005; Theoharides & Dukes 2007). Lower quantile estimates from QR can provide inferences on the potential range of suitable habitat (with the caveat that unoccupied habitat may be unoccupied owing to dispersal constraints), while upper quantile estimates can provide inferences on factors limiting the abundance of the invasive species.

This study uses QR as well as classical multivariate analysis to detect and predict the pathways and the range expansion potential of a highly invasive grass, Andropogon gayanus Kunth (hereafter referred to as ‘gamba grass’) in the northern Australian savannas (all species nomenclature used here follows Kerrigan & Albrecht 2007). We compare and contrast aerial and ground surveys from two sites located 20 km apart that are similar in soils, topography and distance to primary invasion sources, but have qualitatively different patterns of gamba grass invasion. We describe which factors limit the abundance of gamba grass at each site and spatial scale and how this informs our understanding of the pathways and the range expansion potential of gamba grass. We hypothesise that in the initial phases of spread, gamba grass abundance will be dependent upon its distance from the initial source. However, as gamba grass colonises the landscape, the relationship with distant propagule sources weakens and habitat characteristics are more important in determining abundance and distribution. We use our results to compare and contrast the efficacy of aerial and ground surveys in weed management and to inform land managers of optimal strategies for detecting and predicting the spread of invasive grasses across large regions.

Materials and methods

Study Sites

Field surveys were conducted approximately 80 km south of Darwin, Northern Territory, Australia (12º27′ S, 130º50′ E). The region is wet–dry tropical (Köppen class Aw) with a distinct wet season during the Austral summer months (November–March) that receives over 90% of the 1400 mm average annual rainfall. Soils are generally heavily laterised and range from clayey loams along alluvial margins to sandy, rocky soils on uplands.

Surveys were conducted at two sites located 30 km distant from each other (Fig. 1). One site, the Litchfield Site, was located in north-east Litchfield National Park. The second site, the Adelaide River Site, was located on an abandoned cattle property near the town of Adelaide River.

Figure 1.

 Map showing the location of ground survey study sites and gamba grass densities from the aerial surveys. ‘Gamba source’ indicates the original paddocks where gamba grass was planted in 1985 (J. and S. Whatley, pers. comm.).

Both study sites have similar soils and vegetation, and both are quite hilly with a network of intermittent streams in the valleys. Proximity to creek lines heavily influences vegetation, and stream order and slope determine the width of the transition zone from lowland, streamside vegetation to upland vegetation dominated by Eucalyptus miniata and E. tetrodonta (Petty & Douglas 2010). Generally, Melaleuca-dominated closed forest occupies a 10–20 m band adjacent to perennial streams and is often non-existent in smaller, intermittent streams.

Ecology and History of Gamba Grass in the Study Sites

Gamba grass is a perennial C4 grass that forms large tussocks in excess of 3m high and displaces the much shorter native herbaceous layer (Brooks, Setterfield & Douglas 2010). At the end of the wet season, gamba grass undergoes significant growth and soon grows above the native grass layer. In the early dry season, as much of the native vegetation begins to senesce with the receding rains, gamba grass remains green and forms a distinctive layer clearly visible on the landscape (Fig. 2).

Figure 2.

 In the early dry season, as native grasses begin to cure, gamba grass remains green and is easily recognisable from the air. This photo was taken in April from a helicopter in the Litchfield National Park study site. The linear features on the landscape marked by gamba grass are creeks.

We undertook a review of property surveys, weed control reports and internal reports to determine the history of Gamba grass spread particular to both of our study sites (Conservation Commission of the Northern Territory 1992; Barrow 1995; Griffiths et al. 1997; Baker & Price 2003). Additionally, we conducted an interview with two Northern Territory Bushfires Council employees who are local experts having lived in the region for over 30 years, monitoring the spread of gamba grass since the 1990s as part of their duties.

In our study region, gamba grass was first planted in 1985 in three smaller paddocks approximately 5 km east of the Litchfield study site and one larger paddock approximately 5 km east of the Adelaide River study site (Fig. 1). In both sites, gamba grass was rare to absent in the early 1990s. The 1992 Litchfield National Park plan of management mentions gamba grass ‘on several surrounding pastoral properties [to the east of the park]’ but does not state that it was in the park at that time (Conservation Commission of the Northern Territory 1992). However, Barrow (1995) reports gamba grass was present in 1994 inside the eastern boundary of Litchfield and had ‘spread westward, upstream along a creekline, away from a neighbouring station which has been planted with A. gayanus’ (p. 18). A 1997 biological survey of Litchfield National Park reports gamba grass along main roads and in a former cattle station on the north-western boundary (Griffiths et al. 1997). Local experts reported that there was no gamba grass at the Adelaide River site until 1990. It was reported as rare on the property in 1993, but by 2000 was ‘spreading everywhere’ (J. Whatley pers. comm.).

Aerial Surveys

Aerial surveys were conducted in May 2009 when gamba grass was clearly visible from a helicopter flying at 111 km h−1 (60 knots) and 91.4 m (300 ft) above-ground level along pre-determined transects spaced 400 m apart; this provided almost complete coverage of both study sites (Fig. 1). Observers were positioned on both sides of the helicopter and observed the ground from a horizontal projection of approximately 25 m from the point directly below the helicopter to an angle calibrated to equal a horizontal projection of 200 m from the point below the helicopter. An audible alarm sounded every 8 s to notify observers when the helicopter had travelled 250m. Observers would then record gamba grass cover over the resulting 175 × 250 m quadrat on a five-point scale (no gamba grass, <1% cover, 1–10% cover, 10–50% cover, >50% cover). These survey values were converted into a 250 m raster layer for analysis. Ground truthing was conducted in April 2010 (methods and results are provided in Appendix S1).

Vegetation and Soil Surveys

Ground surveys were undertaken in April 2009 (early dry season) before the onset of dry-season fires. Sampling was conducted in 150-m-wide belt transects established at right angles from perennial creek lines. The transects graded from riparian to upland savanna vegetation types, thus encompassing a gradient in soil moisture, soil type and canopy cover. Sampling inside each belt transect occurred at six locations 25, 75, 125, 225, 425 and 625 m from the bank edge. At each location, three plots, 25 m in radius with centres 50 m apart, were positioned parallel to the perennial creek line to cover the width of the belt transect at that location. The central plot was a more detailed survey (‘comprehensive plot’), while the two adjacent plots were less detailed ‘rapid plots’. Thus, there were in total 18 plots per transect, six of which were comprehensive and 12 rapid. In Litchfield National Park, 19 transects, comprising a total of 114 comprehensive and 228 rapid plots were surveyed. In the Adelaide River Site, five transects were surveyed. In the first transect of the Adelaide River Site, all plots at 25 m and 75 m from the bank edge were comprehensive plots, for a total of 34 comprehensive and 56 rapid plots.

At the centre point of each comprehensive plot, species and basal area of woody vegetation >1.5 m high and the basal area of standing dead trees was measured using a basal area wedge calibrated to 0.25 m2 ha−1. From the plot centre, the presence/absence of projected foliage cover was recorded for gamba grass at 2 m intervals along 26 m transects in each of the four cardinal compass directions. Each point was assessed using a Cajanus tube, and the resulting 52 scores for each layer were averaged across the plot.

In rapid plots, gamba grass cover was visually estimated over a 25-m radius plot and assigned a Braun–Blanquet cover score (Mueller-Dombois & Ellenberg 1974).

Soil colour and surface rockiness were estimated for both comprehensive and rapid plots. Additionally, soil texture, coarse fragment composition and ped structure were estimated in the comprehensive plots (full methods are provided in Appendix S2).

Distance to Source, Slope-Weighted Drainage Distance and Rockiness

Propagule pressure is a significant limiting factor in new plant invasions that is highly dependent on distance to seed source (Pysek & Hulme 2005). In our study, gamba grass was planted a similar distance to both sites at a similar time and in the same orientation, that is, to the east and upwind of the prevailing dry-season winds. We digitised the original location of the 1985 gamba grass plantings into a GIS and calculated the linear distance of all plots to these original plantings to indicate the distance of spread from the original invasion source.

Testing the hypothesis that established populations are more limited by habitat suitability variables than distance from source required a habitat suitability variable that was comprehensive across both study sites and data sets. Soil moisture is a significant abiotic limiting factor in gamba grass recruitment (Flores, Setterfield & Douglas 2005), and in the wet–dry tropics of Australia, it is highly dependent on topographic position. We developed an index of topographic position, the slope-weighted drainage distance (SWD), that reflected the distance to the water table and the level of retained moisture from the wet season. SWD was calculated from the distance to the nearest mapped drainage line weighted by slope (i.e. a shorter distance over a higher slope would have the same weighted distance as a longer distance over a lower slope). The index was developed from a 1:250 000 drainage map (Geoscience Australia 2010) and a 3-arcsecond digital elevation model (resolution approximately 90 m at the latitude of the study site; Shuttle Radar Topography Mission, http://www2.jpl.nasa.gov/srtm/) using the Spatial Analyst™ function ‘Cost Weighted’ in ESRI® ArcGIS™ 9.3 (ESRI, Redlands, California, USA). Distances to drainage lines were ln-transformed to normalise the distribution of values.

Additionally, we developed an indicator of rockiness based on principal components analysis of the soils data (described in Appendix S2). Because rockiness was not assessable from the air, only distance to source and SWD were used as predictive variables for the aerial data.

Multivariate Data Analysis

Plant community analysis of the comprehensive ground survey data was used to investigate the patterns of woody vegetation composition and gamba grass abundance and to investigate the potential range of suitable vegetation communities across northern Australia. A general additive model (GAM) of gamba grass abundance was fitted to a two-dimensional non-metric dimensional scaling (NMDS) ordination of woody vegetation basal area scores. Species basal area values were log5-transformed, and the Bray–Curtis dissimilarity index was used to calculate vegetation dissimilarity between plots. Because the vegetation of the region tends to be dominated by a few species, base-5 transformation was selected to weight the index towards rarer species to provide greater distinction between sites in ordination space (i.e. a fivefold increase in abundance equalled an increase by 1 in log5 space). Similar multivariate analyses were performed on the soils data and are detailed in Appendix S2.

Variables Used for Quantile Regression and Tests for Collinearity and Spatial Autocorrelation

We used quantile regression to compare and contrast the effect of invasion spread and habitat suitability on the patterns of abundance of gamba grass across four data sets (two survey methodologies applied to two study sites) using three variables: for invasion spread, (i) the distance from the original sources and, for habitat suitability, (ii) SWD and (iii) rockiness (for ground data only). For the ground survey data, both the comprehensive and rapid ground plots were combined to increase sample size.

Collinearity between descriptive variables was tested using the variance inflation factor (VIF) for ordinary least-squares regression (Fig. S1). SWD and rockiness had the highest collinearity (VIF = 1.93) and were positively correlated (r = 0.69). However, variable removal is only recommended for VIF > 5 (Montgomery & Peck 1992), and all variables were retained for quantile regression modelling of the ground survey data.

Semivariograms of the gamba grass abundance showed that most of the data sets were spatially autocorrelated at shorter distances (<600 m), while the Litchfield aerial data were spatially autocorrelated across much greater distances (<7000 m, Fig. S2).

Quantile Regression

Quantile regression was applied to each of the four grass data sets. One of the assumptions of quantile regression is that the response variable is smooth and continuous. This assumption is violated in this study for the aerial survey and rapid ground survey data as they were recorded in discrete cover categories. To overcome this limitation, we used the approach of Cade & Dong (2008), who transformed discrete data by randomly jittering the value across the intervals comprising the data.

All response variables were then logit-transformed to overcome the limitations of making linear predictions of percentage values (where linear models perform poorly for values near 0 and 100). Model predictions were fitted as linear on a logit scale and then back-transformed to per cent cover values for interpretation.

A third difficulty was to account for spatial autocorrelation in the data sets. To overcome this, we developed a novel method adapting semiparametric filtering as used in ordinary least-squares regression to quantile regression (Tiefelsdorf & Griffith 2007). Full details of jittering, logit transformation and spatial filtering are provided in Appendix S3.

For each data set, models were generated using combinations of all variables as well as the interaction between the habitat suitability variables and distance from source (Table 1). Each model was iterated 100 times to smooth the noise resulting from jittering discrete data (the Litchfield aerial models were iterated 10 times because of the large amount of computer time involved for the large data set). These models were run using the quantreg package in R, and confidence intervals were estimated using the rank score inversion test. To save computing time, quantiles were selected for estimation based on the distribution of the response variable within each data set (Table 1).

Table 1.   Models and the number of parameters used for each survey data set. Shown are the number of samples in each data set (N), the number of iterations of each model, the number of model parameters (including the intercept) and the median number of autocorrelation parameters selected across all iterations of the model. Brackets indicate the minimum and maximum number of autocorrelation parameters selected, respectively
Model parameters# Model parameters# Autocorrelation parameters
Litchfield Aerial Survey (N = 3415; iterations = 10; τ = 0.5, 0.6, 0.75, 0.8, 0.85, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98)
 Source + SWD + Source: SWD4139 [132, 148]
 Source + SWD3137.5 [134, 152]
 SWD2199.5 [191, 209]
 Source2144 [142, 152]
 Null1192 [187, 200]
Adelaide River Aerial Survey (N = 221; iterations = 100; τ = 0.25, 0.5, 0.6, 0.75, 0.8, 0.85, 0.9, 0.92, 0.94, 0.95, 0.96, 0.97, 0.98)
 Source + SWD + Source:SWD47 [5,9]
 Source + SWD38 [6,9]
 SWD27.5 [6,10]
 Source210 [8,12]
 Null19 [7,10]
Litchfield Ground Survey (N = 324; iterations = 100; τ = 0.6, 0.75, 0.8, 0.85, 0.9, 0.92, 0.94, 0.95, 0.96, 0.97, 0.98)
 Source + SWD + Rockiness + Source: SWD + Source: Rockiness618 [16,21]
 Source + SWD + Rockiness420 [16, 24]
 SWD + Rockiness320 [17,24]
 Source + Rockiness318.5 [16,23]
 SWD + Source322[19,26]
 Source223 [19,27]
 SWD223 [18,25]
 Rockiness223 [18,27]
 Null126 [22,29]
Adelaide River Ground Survey (N = 90; iterations = 100; τ = 0.1, 0.25, 0.5, 0.6, 0.75, 0.8, 0.85, 0.9, 0.92, 0.94, 0.95)
 Source + SWD + Rockiness + Source: SWD + Source: Rockiness62 [2,3]
 Source + SWD + Rockiness42 [1,4]
 SWD + Rockiness32 [1,4]
 Source + Rockiness36 [4,9]
 SWD + Source33 [2,4]
 Source24 [2,5]
 SWD22 [2,4]
 Rockiness25 [3,7]
 Null15 [3,8]

The Akaike’s information criteria (AIC) for quantiles, with correction for small sample sizes (AICc(τ), Hurvich & Tsai 1990), were used to assess model performance across selected quantiles. As with AICc used in normal least-squares regression, AICc(τ) provides a relative measure of how well a particular model is supported by the data. For quantile regression, relative support amongst models is calculated by ΔAICc(τ), the difference in AICc(τ) between the model and the null model at that quantile,τ, (ΔAICc(τ)model = AICc(τ)null - AICc(τ)model). Lower AIC values indicate greater support, so the higher the ΔAICc(τ), the better supported the model. A negative ΔAICc(τ) indicates less support than the null model.

All parameters, including effect sizes, confidence intervals and AICc(τ) values, were averaged across all iterations for analysis. The means and standard deviation of the effect sizes and confidence intervals across iterations for the aerial data are provided in Appendix S3.

Results

Similarity Between Sites

Soil composition was highly similar across both sites. Of the four soil groups classified in this study (Fig. S9), only two were unique to Litchfield and these comprised a small minority (11 out of 114 comprehensive plots). The Adelaide River and Litchfield plots in the two main soil groups were indistinguishable in ordination space (Fig. S10).

Woody species recorded across both sites were less similar (Fig. S11). However, the composition of dominant species in both plots was similar and was typical of lowland savanna species in the region (Eucalyptus miniata woodland with grassland understorey; E. tectifica, Corymbia latifolia woodland with Sorghum grassland understorey and E. tintinnans low woodland with Sorghum grassland understorey; Wilson et al. 1990), except for three Litchfield plots, which were typical of sandstone vegetation (i.e. Acacia woodland with Triodia grassland understorey).

Accuracy of the Aerial Survey

Agreement between ground and aerial data using the quadratic weighted kappa statistic was 0.66 (95% confidence between 0.38 and 0.93). Omission rates from the aerial surveys were high (65%); however, the majority of these (88%) were from very small populations (ground assessed at <1% cover) that were difficult to see from the air (Table S4 & Fig. S12). The error of commission was 3%.

Patterns of Gamba Grass Abundance

Gamba grass cover was generally higher in the Adelaide River Site than in Litchfield (Fig. 3). Gamba grass declined in cover with increasing distance from perennial creeks in the Litchfield site, but was more evenly distributed along transects in the Adelaide River site.

Figure 3.

 A comparison of gamba grass cover from combined comprehensive and rapid plots at both study sites. Box-and-whisker plots show the combined data for each site (‘All’), and then the data arranged by their distance from the main perennial stream. The circles indicate outliers. Letters join transect locations that are statistically similar (P ≥ 0.05 after Holm adjustment for multiple comparisons) using the two-sided Mann–Whitney test. Total sample sizes are shown for each site–samples were equally distributed across the six distances.

A similar pattern was found both amongst the four soil types resolved from clustering. Gamba grass was associated with clayey soils in Litchfield but was common across soil types in the Adelaide River site (Fig. S13).

Gamba grass was also more common amongst vegetation associated with moister, poor draining areas in Litchfield but was abundant across vegetation communities in the Adelaide River Site (Fig. S10).

Quantile Regression

Gamba grass also showed two distinct patterns of abundance between the Litchfield and Adelaide River study sites in the QR models. Gamba grass abundance was best explained by distance to source and the slope-weighted drainage distance (SWD) for the Litchfield site, but by SWD alone for the Adelaide River site (Fig. 4).

Figure 4.

 Differences in the Akaike information criteria by quantile [ΔAICc(τ)] are shown for each model and data set. Higher ΔAICc(τ) values indicate a better supported model (generally, ΔAICc(τ) >7 indicates good support). SWD is the slope-weighted drainage distance, ‘Source’ is the distance to the nearest paddock where gamba grass was planted in 1985 and ‘Rockiness’ is the derived rockiness index (Appendix S2). An ‘X’ indicates the additive effects of each term plus the interactions between the terms.

The best-selected models and effect sizes were consistent between ground and aerial surveys; however, the patterns were not as strong for the ground data, where effect sizes were not significantly different from zero even for the best-selected models (probably due to a combination of smaller sample sizes, weakened effect sizes from jittering in general and sampling over a more limited range). Here, we present and discuss results from the aerial data; however, those interested in exploring our statistical methods further can find full results for all methods as well as a comparison between our methods and other quantile regression approaches available in the (Appendix S3).

SWD was an important variable for all data sets, indicating that proximity to creek lines is important for the establishment of gamba grass. Interestingly, the effect strength of SWD decreased for higher quantiles of gamba grass (Figs 5 and 6), which suggests that as gamba grass becomes more established proximity to creek lines is less of a limiting factor. However, for the Litchfield data, abundance appears much more strongly limited by distance from source than SWD (Fig. 5). Moreover, the interaction between SWD and distance to source causes the effect of SWD to decrease with distance to source in the Litchfield model.

Figure 5.

 (a) Predicted gamba grass abundance based on the best-selected model for Litchfield aerial data: the interaction between SWD and distance from source. (b) Marginal fit of distance from source vs. abundance (displayed as the first of 10 jittered data sets) at SWD = 0. (c) Marginal fit of SWD vs. abundance (displayed as the first of 10 jittered data sets) at distance from source = 0. All percentage cover values shown are back-transformed from predictions made on the logit scale. (d) – (f) Averaged effect sizes of model terms by quantile. Averaged 5% and 95% confidence intervals are shown in grey.

Figure 6.

 (a) Fit of gamba grass abundance (shown is the first of 100 jittered data sets) by SWD, the best-selected model for the Adelaide River aerial data. Per cent cover values shown are back-transformed from predictions made on the logit scale. (b) Averaged effect size of SWD by quantile. Averaged 5% and 95% confidence intervals are shown in grey.

Discussion

Patterns of Gamba Grass Invasion

The quantile regression (QR) method we detail here was highly effective in detecting different patterns of invasion for the two study sites. Our results indicate that while habitat suitability is limiting abundance in both the Adelaide River and Litchfield sites, dispersal is a more significant limiting factor in the Litchfield site. Further, in the Litchfield site, there was a slight increase in the rate of decline with distance to source for higher quantiles, consistent with the observations of other invasive populations in that small-density satellites are more likely to be further from the invasion source than high-density patches (Lonsdale 1993). By contrast, in the Adelaide River site, gamba grass abundance was independent of the distance from the original source. Gamba grass had expanded to colonise all or nearly all suitable habitats, and its abundance was limited only by topographic position, with little effect even of topographic position at higher quantiles (Fig. 6b).

Hypotheses concerning why there were such stark differences in invasion patterns between the two sites were not tested in this study. However, it is unlikely that the differences in pattern between the two sites were because of the environmental factors or to physical distance from source populations as these factors were similar between the sites. We propose that gamba grass is more established within the Adelaide River site because of a combination of the greater size of the initial source population (Fig. 1), and increased propagule dispersal within the Adelaide River site facilitated by traffic along a major highway immediately to the west of the site, as well as active cattle stations surrounding the site. By contrast, the Litchfield site is in a more remote area and with only one secondary road (albeit heavily used in the tourist season), and hence is less subject to dispersal from anthropogenic factors.

Gamba Grass Ecosystem Impacts and Future Management

The rapid speed with which gamba grass has spread from the initial source paddocks to its present distribution across both sites (Fig. 1) suggests ‘explosive’ rates of spread commensurate with highly invasive plants elsewhere (Andrew & Ustin 2010) and is cause for grave concern given the significant ecological impact of gamba grass (Rossiter et al. 2003; Setterfield et al. 2005, 2010; Brooks, Setterfield & Douglas 2010). Given the level of gamba grass colonisation already present in Litchfield National Park (Fig. 1), and gamba grass’s demonstrated capacity to invade a range of savanna habitats, we can expect rapid and significant ecosystem decline in one of Australia’s iconic national parks if gamba grass is not controlled and contained. Moreover, without significant and widespread management intervention, gamba grass will continue to spread across the tropical savanna region of Australia.

Our results show that any regions in proximity to substantial cultivated areas of gamba grass are at significant risk of invasion. This risk is particularly acute for two major conservation reserves 100 km east and south of our study areas, respectively, that are at present mostly clear of gamba grass: (i) Kakadu National Park lies 10 km from Moline mine, where gamba grass was planted to stabilise tailings in the mid-1990s and is also known to be spreading along creek lines towards Kakadu (S. Setterfield, unpublished data) and (ii) Fish River conservation reserve is adjacent to a large cattle property where some of the largest known paddocks of gamba grass were planted in the early 2000s. Gamba grass is now spreading towards Fish River (S. Setterfield, unpublished data), and the situation is in many ways analogous to our study sites 20 years ago.

Given the strong pattern of spread along riparian areas in early stages of invasion, land managers should include riparian areas as places of high significance for mapping, controlling and containing gamba grass. Current management of potential spread has focussed on transport and service corridors (e.g. telecommunication access roads, Northern Territory Government 2010); however, riparian areas may be more significant as a spread pathway because riparian areas cover a vastly greater proportion of the Northern Territory landscape (Douglas, Townsend & Lake 2003).

Use of Aerial Surveys for Modelling Invasive Species Spread

Our study concurs with others that aerial surveys coupled with available GIS data can be a highly effective and efficient method for rapidly studying widespread exotic plant invasions (van Klinken et al. 2007; Puckey, Brock & Yates 2007). The total cost (in 2009 AUD) for aerial surveys for both sites was $13 670, including costs to ground truth the surveys. By contrast, the ground surveys cost $32 187 for both sites. The ground studies provided insights into the range of occupied vegetation communities and validated the similarity between the two sites in terms of soils and vegetation. However, our inferences from quantile regression regarding the process of invasion were much stronger using the more complete aerial survey data.

We suggest that where the target species is distinctly spotted from aircraft, as is the case for gamba grass, aerial surveys are the most effective way of determining pathways of spread and the key factors limiting spread. The high omission rate in aerial surveys is an important caveat for using this method to detect small infestations; however, our results show that aerial surveys still maintain significant advantages in comprehensiveness, efficiency and the ability to detect large-scale patterns and processes in biological invasions.

Synthesis and Applications

Aerial surveys and quantile regression can be a highly effective means of comparing and contrasting across different study sites when predicting invasion pathways. This is particularly important in the early stages of invasion when the pathways and range expansion potential are unclear. In our study, aerial surveys were the most economical means of comparing across these sites and generated a large amount of data that demonstrated qualitatively different patterns of invasion.

The quantile regression technique we demonstrate here can account for spatial autocorrelation inherent in comprehensive aerial surveys and is robust in detecting and predicting patterns of biological invasions for non-ideal data sets such as the categorical data generated from aerial surveys. As a result of the application of this technique, we were able to demonstrate the widespread colonisation of creek lines by gamba grass, and we recommend that management focuses on detection and eradication along drainage lines in addition to the present focus on roadways.

It would be interesting to test whether the pattern shown here holds for invasive populations in general, where the absolute effect size correlated with distance from a known invasion source increases with increasing quantiles, while the absolute effect size correlated with habitat suitability decreases with increasing quantiles. If this is the case, the use of aerial surveys followed by quantile regression analysis can be used as a relatively rapid and inexpensive means of inferring the stage of invasion of exotic species, particularly in cases of recent invasions where the alien species has not expanded across its potential range.

Acknowledgements

This project was funded by the research grants from the Commonwealth Environmental Research Fund Significant Project scheme, Land and Water Australia and the Australian Weed Research Centre. We thank the Litchfield National Park rangers and Bushfires Northern Territory who facilitated access to our field sites and provided information on invasion history. We thank Brian Cade for his guidance on statistical analysis and three anonymous referees for their contributions that greatly improved the manuscript. We would particularly like to thank our field team for their hard work: Alistair Danger, Susanne Casanova, Adrian Hendry, Ranid May, Claire Haysom and Nicola Golding.

Ancillary