Assessing Regional Scale Weed Distributions, with an Australian Example Using Nassella Trichotoma

Assessing regional scale weed distributions, with an Australian example using Nassella trichotoma S W LAFFAN School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW, Australia Received 27 April 2005 Revised version accepted 4 October 2005 distinct from the main clusters, and 55 km2 that are Summary not clustered. There are 117 km2 of strongly clustered Knowledge of the spatial distribution of weed infesta- patch level cells, 3 km2 in distinct but weak clusters, and tions over regional scales is essential for effective none outside of a cluster area. Of the occasional plant management of source populations and to assess future level cells, 329 km2 are strongly clustered, 6.2 km2 are in threats. To this end, the distributions of Nassella distinct but weak clusters, and 19 km2 are not clustered. trichotoma across a study area in south-east New South These results provide a mechanism by which control Wales, Australia, were analysed using the geographically efforts can be prioritized. The analysis approach des- local Getis–Ord Gi* spatial hotspot clustering statistic. cribed in this paper provides a consistent, quantitative The clustering of N. trichotoma observations was ana- and repeatable approach to assess weed infestations lysed at three infestation levels: presence (at any across regional scales and can be applied to any weed density), patch level and the occasional plant level. species for which spatial distribution data are available. The results indicate that there are c. 578 km2 of cells Keywords: Nassella trichotoma, serrated tussock, spatial containing N. trichotoma in strongly clustered infesta- analysis, spatial clustering, weed management. tions, 11.2 km2 within weakly clustered infestations LAFFAN SW (2006) Assessing regional scale weed distributions, with an Australian example using Nassella trichotoma. Weed Research 46, 194–206. Introduction aid in further planning, or as inputs to spatio-temporal modelling approaches to explore the potential spread of The assessment of the spatial distribution of weed the infestations over time and conduct scenario analyses infestations over regional scales in a consistent, quan- of the effect of possible control measures. However, the titative and repeatable way is essential for effective methods commonly used to assess weed distributions management of source populations and for future threat have potentially significant limitations when applied at assessments. Spatial analyses of weed distributions the regional scale. provide a tool to assist managers to prioritize control A key issue for regional weed assessment is the scale options. This might be through identifying those infes- at which the problem is analysed. Most research into tations that are of a controllable extent and density now, the spatial analysis of weed distributions has focused those which will require longer-term control efforts, and on the field scale rather than the regional scale (for perhaps those that are beyond any current control example Zanin et al., 1998; Dieleman & Mortensen, methods. Such analyses could also be used to provide 1999; Colbach et al., 2000; Rew et al., 2001; Walter benchmark data against which the performance of et al., 2002; Ambrosio et al., 2004), with study areas subsequent control measures can be assessed. Depend- ranging from 190 m2 to 1.73 km2 (Rew & Cousens, ing on what managers are trying to achieve, the analysis 2001). While the analyses used by these researchers results could also be used in association with other were appropriate for field scale data, the spatial spatial data such as site accessibility, soil and climate to complexity caused by environmental and spatial con- Correspondence: S W Laffan, School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW 2052, Australia. Tel: (+61) 2 9385 8093; Fax: (+61) 2 9385 1558; E-mail: shawn.laff[email protected] Ó 2006 The Author Journal compilation Ó 2006 European Weed Research Society • Weed Research 2006 46, 194–206 Assessing regional scale weed distributions 195 trols means that their analyses cannot be directly Spatial analysis of weed distributions extended to the regional scale. A method is needed that can appropriately assess regional scale weed infesta- Maps of regional scale weed distributions (e.g. Fig. 2) tions in a robust manner and at an appropriate scale. It enable broad patterns to be discerned. However, while is this issue of the analysis method that is addressed in providing very useful information about the scale and this paper. extent of weed infestations, it is difficult to visually There are many candidate weed species with regional compare such infestations across a regional study area in distributions. The focus in this research is on Nassella the consistent, repeatable and objective manner required trichotoma (serrated tussock) (Nees) Arech, for which to prioritize control efforts. Such an approach is possible there is a spatially extensive data set of aerial observa- using spatial statistics, for which some general consid- tions across the Snowy River, Cooma Monaro and erations and approaches are now described. Bombala Shires (local government areas) in New South The analysis of spatial data may be broadly categor- Wales (NSW), Australia (Figs 1 and 2). ized into the spatially implicit and the spatially explicit The objective of this study is therefore to identify the (Mackey & Laffan, 2002). Spatially implicit analyses main hotspots of N. trichotoma infestations across the take no account of the spatial relationships among the study region, although the approach is applicable to any data, in ignorance of Tobler’s (1970) First Law of weed species. Knowledge of these distributions will Geography ÔThat everything is related to everything else; enable managers to identify and prioritize their control but that near things are more related than those far options, and serve as an indication of the possible source apartÕ. Spatially explicit analyses account for this, and of future expansions of the infestations. The analyses are quantifying the extent to which geographical phenom- described following a consideration of the general ena fulfil Tobler’s law is one objective of such analyses. principles of spatial analysis of weed distributions and There are two main approaches for the spatially the characteristics of N. trichotoma. explicit analysis of spatial data. These are the spatially NSW 0 100 200 300 400 500 Kilometres NSW Cooma-Monaro Snowy River 0250 500 1000 1500 2000 Kilometres Bombala 0255075100 Kilometres Fig. 1 The study area is located in south-east NSW, Australia. Ó 2006 The Author Journal compilation Ó 2006 European Weed Research Society • Weed Research 2006 46, 194–206 196 S W Laffan Fig. 2 The distribution of N. trichotoma infestations across the study area. Ó 2006 The Author Journal compilation Ó 2006 European Weed Research Society • Weed Research 2006 46, 194–206 Assessing regional scale weed distributions 197 global and the spatially local. Both are normally the spatial relationship is of weed infestations, or if it is implemented using a moving window to define the of the absence of weed infestations: neighbourhood of sample locations used in the analysis, 1 Xnd for which any window shape may be used, provided it is cðdÞ¼ fgZðx ÞZðx Þ 2 ð1Þ 2n i iþd a reasonable representation of the process driving the d i¼1 distribution (Laffan, 2002). A circular shape is most where d is the lag distance for which the statistic is to be often used because normally there is no certainty about calculated, n is the number of neighbours of location i which driving process applies where. d at distance d. Z(x ) is the value at location i, Z(x )is The difference between global and local approaches is i i+d the value at the neighbouring location at distance d. in how the results are reported. Global approaches As noted above, many local statistics are adaptations summarize the spatial relationships in the data as a of global statistics, although this need not always be the single figure or graph. However, this represents the case. Of the many possible approaches (e.g. Anselin, system as an average process and can conceal important 1995; Whelan et al., 2001), the Getis–Ord G * hotspot local variations. It is also subject to the effects of spatial i cluster statistic is of most use here (Getis & Ord, 1992, non-stationarity and inconsistent anisotropy (directional 1996; Ord & Getis, 1995). The G * statistic measures the effects), particularly where distributions are not in i degree of spatial clustering of a local sample and how spatial equilibrium. Geographically local analyses are different it is from the expected value (Eqn 2). It is often adaptations of global statistics, and result in a calculated as the sum of the differences between values geographic surface of results. This means that local in the local sample and the mean, and is standardized as variations may be elucidated and that the analyses are a z-score with a mean of zero and a standard deviation less susceptible to the effects of spatial non-stationarity. of 1: The latter factor is particularly important when one P considers that spatial non-stationarity is to be expected w ðdÞx À W ÃxÃ Ã j ijqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij i Gi ðdÞ¼ ð2Þ at regional scales. Local analyses require a more nSÃ W Ã2 Ã ð 1iÞ i consistent density of data than do global statistics but, s nÀ1 where such data are available, they usually produce better results than global analyses because they can cope where i is the centre

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