The primary aim of this study was to employ a range a geostatistical tools to analyse long-term spatial patterns and variations in kangaroo distribution as a basis for improving the spatial scale of kangaroo management in the South Australian pastoral zone. Kriging allowed a detailed exploratory analysis of spatial pattern within the point data set. In combination with the ability to assess or map the likely error in the kriged surfaces, this interpolation technique was inherently suited to exploring and mapping spatial patterns in wildlife survey data and, perhaps, modifying survey design to improve the accuracy and precision of estimates. Thus, high density areas and areas with large error could be surveyed with increased sampling intensity and, conversely, sampling could be reduced in areas of uniformly low density.
Conversion of point-based samples from long-term, frequent, systematic surveys to a spatially extensive map of population density enables recurrent patterns in the distribution of animals to be clearly identified. The results show that the broad pattern of distribution of both red and western grey kangaroos in the SAPZ was relatively stable over the study period. High densities of red kangaroos were recorded consistently in the north-east of the SAPZ, an area with a mosaic of soil and vegetation types, but dominated in general by low bluebush shrublands and calcareous soils and where sheep are grazed at a relatively high density (Cairns, Pople & Grigg 1991). Western greys are restricted to the less arid parts of the study area and densities were consistently high in the south-west. This area is also heterogeneous in terms of soil, landform and vegetation, with many areas of woodland interspersed with grassland and open shrubland (Cairns, Pople & Grigg 1991). There is temporal variation in this pattern for both species, particularly where they occur at relatively low density (Fig. 5). This probably reflects the vagaries of marginal habitat, despite the inflation of the CV by more frequent zero observations. Whether these areas with highly fluctuating densities experience high rates of local extinction and recolonization, or are driven just by local population dynamics, or whether the high coefficient of variation is due to the interaction of low density and sampling design, is unclear from these data.
From year-to-year there were also substantial shifts in kangaroo distribution, which cannot be explained by birth and death alone. Even an unstable age distribution and biased sex ratio, possible in or after drought, can result in an annual exponential rate of increase < 0·69 in the population size (Bayliss 1985; Pople 1996). This rate is well short of the increases identified here for large areas of the SAPZ. Cairns, Pople & Grigg (1991) reported a shift in the distribution of red kangaroos during the 1982–3 drought. This was due largely to spatial variation in the onset of drought, which was delayed in the west of the pastoral zone, and resulted in spatially uneven declines in density. Uneven changes in density resulting in changes in distribution can be particularly marked during declines because of the convex shape of the numerical response of kangaroos (Davis, Pech & Catchpole 2002). What became apparent with a re-analysis of these data and over a longer time period was that distribution shifts were also associated with increases in regional density.
Long distance movements of > 100 km have been recorded for individual red kangaroos from tagging and radio telemetry (Bailey 1971; Bailey & Best 1992). However, these have been considered exceptions in a generally sedentary population where individuals move within home ranges of variable size (McCullough & McCullough 2000). Adult red kangaroos have been recorded ranging more widely during drought (Norbury, Norbury & Oliver 1994), and movements of up to 30 km have been reported for red kangaroos in response to patchy rainfall during prolonged dry spells, resulting in geographical shifts of the population (Newsome 1971; Denny 1980; Priddel 1987; Croft 1991).
The data presented here lends support to the hypothesis that large-scale movements occur to areas of potentially higher quality food supply. However, Priddel, Wellard & Shepherd (1988) and Bayliss (1985) considered red kangaroo movement had little influence on their dynamics at a scale of 440 km2. However, the results of this study provide evidence for the existence of long-distance movement, and that populations are not closed at this scale or even at smaller scales. This apparent discrepancy from previous studies may be due to a number of factors including: the relatively short time-frame and small spatial scale of many radio-tracking and tagging studies, site-specific factors such as fences and lakes which influence movement, low recapture rates of some population classes in tagging studies and a bias towards selection of adult animals in radio tracking studies.
The exceptional fit of these data to Taylor's power law is not surprising, given its fit to a broad range of taxa (Taylor, Woiwod & Perry 1978; Taylor & Woiwod 1982). A slope of between 1 and 2 has also been found for most species. We do not offer an explanation for this scaling relationship; rather, we highlight its ability to detect increased aggregation of red kangaroos during dry times, supporting fine-scale observations. What is interesting was that increased aggregation was detected here at the scale of a 2-km2 survey segment. This suggests that seasonal movements can be detected with broad-scale aerial survey and that the more extensive NDVI data may be able to predict movement and the resulting changes in spatial distribution of kangaroos.
These seasonally variable distribution patterns have important implications for management. Annual harvest quotas are based on surveys conducted at least 6 months prior to the actual harvest, by which time the geographical variation in kangaroo density may have altered. Spatial allocation of quotas needs to account for seasonal shifts in the spatial dispersion of kangaroos and the results here suggest this may be possible. Harvest rate appears to be influenced by spatial dispersion of kangaroos with increased harvests when animals are aggregated (Kirkpatrick & Amos 1985). Rainfall or NDVI could be used to predict downturns in harvest offtake, although the direct link between harvest rate and rainfall or NDVI needs to be quantified for the SAPZ, western New South Wales and Queensland.
appropriate scale of management and analysis
A semi-variogram range of 13–97 km indicates that spatial autocorrelation needs to be accommodated in spatial modelling with data collected within these distances. The correlation structure can be incorporated directly into the model (Guisan & Zimmerman 2000; Keitt et al. 2002) or data can be pooled into larger units that are less likely to be autocorrelated (Buckland & Elston 1993).
Appropriate geographical stratification of regional-scale data has been considered critical for monitoring population trends in declining populations (Villard & Maurer 1996). Similarly, it will be important for other management fields such as regulating harvests. For both species, broadly matches average density, which tends to cluster and differ in value for each SCB, providing support for this level of current kangaroo management in South Australia. Management activities such as harvest regimes, survey frequency and enforcement could be tailored to the new strata identified here. At present these activities, including the proportion of the population that is offered as a harvest quota, are undertaken uniformly or applied across SCBs within the SAPZ (SADEH 2002). However, harvest rate and variability differs among as well as within these SCBs (Jonzen et al. 2005), suggesting that management would be more efficient if it varied its activities accordingly (Pople, Cairns & Menke 2003; Pople 2004). The lack of clustering in the local semi-variogram range suggests that there is no need to use population management units other than the present management SCBs.
In South Australia, kangaroo harvest quotas are allocated to individual properties. More widely within Australia, permits for culling are given to individual properties. Ideally, this requires fine-scale estimates of density, relative or absolute, to divide a regional quota among constituent properties, or to assess requests for culling permits by a property manager. An obvious method for estimating density on an individual property is ground survey, but these are just not feasible on such a broad scale as the SAPZ (Caughley & Grigg 1981). This study highlights how kriging can overcome the imprecision and bias associated with low sampling intensities when estimating density on a fine scale. The marked differences between interpolated densities and averaged segment densities within properties highlights the gains that can accrue by taking the approach we have described in this paper.