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RESEARCH ARTICLE

Spatio-temporal trends in the abundance of grey kangaroos in Victoria, Australia

Michael P. Scroggie https://orcid.org/0000-0001-9441-6565 A * , Paul D. Moloney A and David S. L. Ramsey https://orcid.org/0000-0002-4839-1245 A
+ Author Affiliations
- Author Affiliations

A Arthur Rylah Institute for Environmental Research, Department of Energy, Environment and Climate Action, 123 Brown Street, Heidelberg, Vic 3084, Australia.


Handling Editor: Shannon Dundas

Wildlife Research 52, WR23133 https://doi.org/10.1071/WR23133
Submitted: 10 October 2023  Accepted: 19 November 2024  Published: 24 January 2025

© 2025 The Author(s) (or their employer(s)). Published by CSIRO Publishing

Abstract

Context

Aerial distance sampling surveys are a widely used approach for estimating the abundance of wildlife populations, including kangaroos and other macropods. When analysing such data, design-based estimates of abundance extrapolate density from the sampled region to the broader area. In contrast, model-based approaches that use relationships between population density and habitat variables can deliver greater precision and ecological insight into population estimates.

Aims

This study aimed to evaluate recent spatio-temporal trends in the abundance of grey kangaroos (Macropus giganteus and M. fuliginosus) in Victoria, Australia using both design-based and model-based distance sampling.

Methods

Aerial surveys were conducted in seven management zones spread across the non-forested parts of Victoria on four occasions between 2017 and 2022. Distance sampling data were analysed to obtain design-based and model-based estimates of population size and relative precision across the entire study area, and for each management zone for each of the four surveys.

Key results

Model-based and design-based estimates of abundance proved to be broadly comparable, but with mostly higher precision for the model-based estimates at both statewide and management zone scales. The model-based approach revealed relationships between transect-level abundance and land-use type, normalised difference vegetation index (NDVI), annual rainfall and the amount of ecotonal habitat in the vicinity of the transects. Between 2017 and 2022 (a period coinciding with a prolonged La Niña event), the total abundance of grey kangaroos increased by approximately 87% (based on the model-based inferences) despite an ongoing harvesting program.

Conclusions

In addition to improved precision, model based estimation revealed relationships between habitat variables and transect-level abundance, allowing prediction of abundance at small scales.

Implications

The improved precision of model-based estimates of abundance will provide greater confidence in kangaroo management decisions such as setting of statewide harvest quotas. Model-based estimates at smaller spatial scales will similarly support localised management decisions.

Keywords: abundance, aerial survey, density-surface model, distance sampling, harvest management, macropod, model-based inference, spatio-temporal model.

Introduction

Grey kangaroos (Macropus giganteus and M. fuliginosus) are widespread herbivorous marsupials that occur across much of the Australian mainland and in Tasmania. As a consequence of a long history of both commercial exploitation (for meat and skins) and non-commercial culling to address conflict with livestock grazing and cropping land uses, monitoring of populations using aerial transect surveys has been applied in all mainland Australian states to provide periodic assessments of abundance, and to allow the setting of ecologically sustainable culling quotas. In Victoria, the modern history of commercial harvesting of kangaroos is shorter than in other mainland states, where regulated commercial harvesting of both grey kangaroo species, along with other macropod species, has been practiced for decades. Prior to 2014, kangaroo culling in Victoria was only permitted under the Authority to Control Wildlife (ATCW) provisions of the Wildlife Act 1975. Since 2014, limited commercial harvest of both grey kangaroo species has been permitted in Victoria, initially under the Kangaroo Pet Food Trial (KPFT, DELWP 2018), then from 2019 under the Kangaroo Harvest Management Plan (DELWP 2020). To support decision making regarding appropriate quotas, a program of regular aerial surveys of the state was initiated in 2017, with the resulting estimates of abundance being used to determine culling quotas in each of seven geographically defined harvest zones, in proportion to their estimated total abundances (Scroggie and Ramsey 2019).

Estimation of kangaroo abundance using aerial surveys has a long history (Lunney et al. 2018; Finch et al. 2021), with the issue of imperfect detection (i.e. undercounting) being of central importance. Methods for accounting for imperfect detection have included the use of simple correction factors (Pople et al. 1998) which are used to correct raw counts of kangaroos observed on strip transects. As an alternative to correction factors, distance sampling (Buckland et al. 1993; Pople et al. 2007; Fewster and Pople 2008) has provided a more rigorous and flexible means of obtaining accurate estimates of kangaroo abundance. Both conventional distance sampling (CDS) using single observers, and mark–recapture distance sampling (MRDS) with pairs of independent observers, have been employed in recent years to assess macropod abundances in the various Australian jurisdictions, including in Victoria (Fewster and Pople 2008; Moloney et al. 2017, 2018a; Finch et al. 2021).

Typically, estimation of kangaroo abundances using distance sampling methods has relied on design-based inference (DBI) where the total numbers of kangaroos in defined geographic strata are inferred by extrapolating from estimates of density (corrected for non-detection using distance sampling) obtained from a set of randomly or systematically selected transects. Variation in density amongst the transects is further used to infer the uncertainty in the total population estimate for each stratum using finite sampling theory (Buckland et al. 1993; Thompson 2012). This approach is statistically robust, makes minimal assumptions and has been found to provide estimates of abundance for kangaroos that are of sufficient precision for management purposes (Pople 2008). However, the design-based approaches has several disadvantages. Firstly, it does not provide estimation of population densities at spatial scales smaller than the stratum. Secondly, design-based approaches require random or at least representative sampling of survey location. Thirdly, design-based approaches give limited insight into ecological or management drivers of spatial and temporal fluctuations in abundance.

As an alternative to design-based inference, model-based analysis of distance sampling data (Miller et al. 2013; Buckland et al. 2015, 2016) has the advantage that densities are related to covariates using regression models such as generalised linear models (GLM, McCullagh and Nelder 1989) or generalised additive models (Tibshirani and Hastie 1990). This approach allows estimates of population densities to be informed by the observed relationships between density and a set of covariates. Well-constructed model-based estimates of population abundance can often have lower uncertainty, as unlike design-based estimates of uncertainty, they benefit from the extra information conveyed by the relationships between density and the covariates to explain variation among sample locations (Miller et al. 2013). Furthermore, the estimated relationships between density and the covariates can provide ecological insight into the processes governing abundance and allow predictions at unobserved locations. Model-based approaches are also applicable where site selection is not random or representative. For these reasons, model-based approaches to the analysis and interpretation of distance sampling data are being increasingly adopted by researchers and wildlife managers (Camp et al. 2020; Carvalho et al. 2022; Hinton et al. 2022).

In this paper we report the results of an analysis of a five-year aerial monitoring program for grey kangaroos in Victoria Australia. Using distance sampling data collected during 2017, 2018, 2020 and 2022 we examine spatial and temporal variability in kangaroo abundance and their relationships to a suite of environmental predictors. Using model-based inferences we report trends in abundance at various spatial scales during the monitoring period. We also compare regional and statewide estimates of abundance and precision to estimates previously obtained using a design-based approach (Moloney et al. 2017, 2018a, 2021, 2023).

Methods

Survey design and data collection

The survey was conducted in the state of Victoria, located in the southeast of the Australian mainland. A stratified random sample of 25 km aerial transects was established in each of seven geographically defined kangaroo harvest zones (Fig. 1). The harvest zones were formed by aggregating groups of local government areas with similar climate, vegetation and landforms. Some transects were shorter than the nominal length of 25 km to address safety and logistic requirements, or because they abutted state borders or excluded heavily forested habitat. Only broadly open habitats such as grasslands, pastures, crops, shrublands, woodlands and mallee type vegetation were included in the sampling design, with heavily timbered forest habitats excluded from the surveys and associated abundance estimates as kangaroos cannot be reliably detected from the air in such habitats. Heavily urbanised areas were also excluded from the surveys as kangaroos are rare in such habitats, and air safety regulations prohibit low-level helicopter flights over urban areas. The total area of habitat considered in the surveys was 163,250 km2, which represents approximately 72% of the total land area of Victoria. Full details of the survey design are given in Scroggie et al. (2017) and Moloney et al. (2018b).

Fig. 1.

Map of Victoria showing the boundaries of the seven survey zones with the transects surveyed in each of the 4 years overlaid (horizontal lines). Areas shaded green were available for inclusion in the survey design. Areas shaded beige were unsuitable for aerial surveys due to dense forest habitat or high levels of urbanisation.


WR23133_F1.gif

Commencing in 2017, aerial surveys were flown along the transects using a helicopter (Bell LongRanger) flying at an altitude of 200 feet (~60 m) and speed of 50 knots (~93 km/h). Surveys were always conducted in the three hours after sunrise or before sunset, with the helicopter always flying away from the sun to reduce the impact of glare. Two observers (one each side of the helicopter) counted groups of grey kangaroos (both species) in distinct distance bands (0, 20, 40, 70, 100 and 150 m) either side of the transect line, with boundaries between the distance bands being discerned with aid of graduated distance bars that were fixed to the aircraft. Animals at distances beyond 150 m from the transect were disregarded. Observations were recorded (including geolocation using GPS) with the aid of a datalogger (see Lethbridge et al. 2019). While all macropod species were counted, only eastern and western grey kangaroos are considered in this manuscript. Consideration was given to using paired observers on both sides of the aircraft to collect double-count data suitable for analysis in a mark–recapture distance sampling (MRDS) framework. Such an approach relaxes the assumption that detection of animals at zero distance is perfect and reduces the negative bias that occurs when this assumption is violated. MRDS has been utilised elsewhere in Australia for aerial kangaroo surveys (Finch et al. 2021). Ultimately, it was decided that a single observer approach would be adopted which entails accepting a degree of negative bias in the population estimates. We considered that this negative bias in the estimation of abundance, while unquantified, will provide an additional guard against overharvesting by making the harvest quotas more conservative.

In 2017, 79 transects totalling 1638 km were surveyed. From 2018 onwards, additional transects were added bringing the total number of transects to approximately 150 with around 3000 km of survey effort during the 2018, 2020 and 2022 surveys (Table 1). The same transects were usually repeated in each survey. In a small number of cases where a transect could not be surveyed in a given year due to accessibility or aircraft safety considerations, another nearby transect (located within the same kangaroo harvest zone) was substituted and included in the year’s total survey effort. Surveys were always conducted during September and October.

Table 1.Summary statistics for aerial survey effort and encounter rates for grey kangaroos in the study area.

YearNumber of transectsTotal survey effort (km)Mean group sizeNumber of grey kangaroosGrey kangaroos per transect km
20177916383.6419631.20
201814529874.1838661.29
202015031074.2555461.78
202214730584.0554401.78
Average13026984.0942041.51

Estimation of detection probabilities using distance sampling

We fitted a series of standard detection functions to the binned data using multi-covariate distance sampling (MCDS) in package Distance in R (Miller et al. 2019). Half-normal, Hazard-rate, and Uniform key functions with cosine, polynomial and Hermite adjustment terms (Buckland et al. 1993) were fitted using conventional distance sampling (CDS). As kangaroos were detected in groups of one or more individuals, hazard rate and half-normal models with group size as a covariate influencing the detection probability were also considered. Similarly, as the observers differed between years, we considered models where the parameters of the detection function differed between years. We also considered models with effects of observer identity, habitat (open or wooded, recorded by the observers for each kangaroo observation) and time of day (morning or afternoon) as covariates. Model selection was on the basis of Akaike’s Information Criterion (AIC, Burnham and Anderson 2002). Suitability of fit of the preferred detection function was assessed using a Chi-squared test on the binned detection data.

Spatial modelling of abundance using density surface models

We modelled the spatial variation in the density of kangaroos across the state using a spatio-temporal density surface model (DSM, Miller et al. 2013; Buckland et al. 2016; Camp et al. 2020). The 25 km long transects were first divided into segments of approximately 5 km length. The DSM related the abundance on each segment to a series of environmental covariates using a generalised additive model (GAM). Generalised additive models extend ordinary generalised linear models (GLM, McCullagh and Nelder 1989) to allow the relationships between the outcome (abundance) and the covariates to be described by flexible, non-linear spline terms, with the degree of smoothness of the splines estimated from the data.

Segment-level offset terms were included in the DSM that allowed for the varying lengths of the segments (not all segments were exactly 5 km in length), and for imperfect detection of kangaroos out to the maximum detection distance of 150 m. This latter component of the offset term was calculated using the detection function modelled in Distance (Buckland et al. 1993, see above). The DSM thus represents a ‘two-stage’ approach to the modelling of distance-sampling data (Buckland et al. 2015), where the detection component of the model is first fitted to the distance data, and the resulting estimates of detection probability are incorporated into the offset term of the GAM to correct for imperfect detection and varying survey effort.

Construction and selection of a preferred GAM proceeded in three stages. Firstly, we considered a series of models with alternative space-time smoothing bases of varying complexity:

  1. A bivariate latitude-longitude smooth with abundance constant in time.

  2. A bivariate latitude-longitude smooth with a separate spline term describing a spatially invariant temporal trend in abundance.

  3. A bivariate latitude-longitude smooth with categorical terms for the effect of each survey year (2017, 2018, 2020, 2022) on abundance.

  4. Separate, bivariate latitude-longitude smooths for each survey year.

  5. A trivariate (latitude, longitude, time) spatial and temporal smoothing model. This approach allowed temporal trends in abundance to vary spatially.

The spatial (latitude/longitude) trends were represented using Duchon splines (Duchon 1977; Miller and Wood 2014), with thin-plate splines (Wood 2003) used for the temporal trends. Variants of these five basic space-time models for abundance were considered with Poisson, Negative Binomial and Tweedie error distributions, with selection of a preferred spatio-temporal smoothing scheme and error distribution made on the basis of Akaike’s Information Criterion (AIC, Burnham and Anderson 2002).

After selecting the best space-time smoothing model, we then attempted to improve the model by including additional habitat covariates. Spline terms (thin-plate splines, Wood 2003) for the habitat variables (which were mapped as grids at a 5 km resolution) were selected for inclusion in the model due to their likely importance as drivers of kangaroo abundance. The habitat variables included were:

  1. The proportions of crop, open (grassland and pasture), woody and urban habitat within each 5 km grid cell. The 5 km resolution data were compiled by computing the proportional cover of each of these habitat types within the 5 km grid cells from 25 m resolution land cover data for the state (White et al. 2020). These land cover classes are relevant to understanding of habitat use by grey kangaroos given that they readily utilise the food resources provided by pasture and crops, while also utilising woody vegetation for shade and refuge (Arnold et al. 1989; Cairns et al. 1991; Coulson 1993; Roberts et al. 2016).

  2. We also considered the effect of ecotonal habitats around the edges of woody vegetation by computing the amount of such edge habitat in each 5 km grid cell by applying a Sobel filter (Fortin et al. 2000) to the original 25 m resolution woody vegetation data. We hypothesised that this variable would describe the availability of transitional habitat between woodland and the open areas typically favoured for foraging (Coulson 1993).

  3. Broad climatic and vegetation gradation across the state was described using grids of mean annual rainfall, and from images representing the mean normalised difference vegetation index, which is an ecologically informative measure of vegetation greenness (normalised difference vegetation index, NDVI; Pettorelli et al. 2011). NDVI data were obtained from the MODIS satellite observing program (Didan 2015) and from Google Earth Engine (Gorelick et al. 2017). The NDVI images were for the month of September in each year, which coincides with the timing of the aerial surveys. Annual rainfall was included in the model given that relationships between rainfall and kangaroo density have been widely documented (Short et al. 1983; Caughley et al. 1987; Cairns et al. 1991).

Separate smooth terms (thin-plate splines) for each of these covariates were added to the preferred spatio-temporal smoothing model. Uninfluential covariate effects were progressively removed until no further improvement in AIC was evident. Where the effective degrees of freedom for a covariate effect was equal to one, the spline term was replaced with a linear term.

Finally, the preferred model, as selected by AIC, was used to predict spatial and temporal variation in the abundance of grey kangaroos across the study area (exclusive of the habitats not considered in the survey design), and to estimate total (statewide) and regional (kangaroo harvest zone) population totals (N^) for each year of survey. Uncertainties attributable to both the detection function and the GAM were propagated into the abundance estimates using the approaches described by Miller et al. (2013) and Bravington et al. (2021). Uncertainty in abundance and density estimates was expressed using 95% confidence intervals and coefficients of variation.

To assess overall changes in estimated kangaroo density, mean annual rates of population change λi¯ were estimated for each grid cell (i) using the equation:

(1)λi¯=( D ^i,2022 D ^i,2017 )1/5

where Di,y^ are the estimated densities of grey kangaroos in each of the 5 km × 5 km grid cells across the state in years y = 2017 and y = 2022 respectively.

Results

Survey results

Annual survey effort varied between 1638 km and 3058 km of transect, with a substantial increase in effort after the first year of survey (2017). The numbers of grey kangaroos observed during the aerial surveys varied between 1963 and 5546 per year. Accounting for the varying survey effort between years, the number of kangaroos per kilometre of transect varied between 1.20 and 1.78, with a tendency towards increased encounter rates over time (Table 1).

Distance sampling analysis

There was negligible model selection uncertainty (model selection weight w = 0.999 for the best supported model). The selected model was a hazard rate function which included effects of kangaroo group size and year (categorical) as covariates (Supplementary Table S1).

The fitted detection functions for each year of the survey are given in Fig. 2, with the raw data as histograms for comparison with the fitted curves. A chi-squared test did not reveal any significant evidence of lack of fit (χ2 = 20.0, d.f. = 16, P = 0.220), and visual comparison of the fitted curves and raw data shows a close concordance between the data and the fitted detection model. Overall detection probability (mean P^) varied from year to year, with the 2022 survey recording a somewhat lower probability of detection than the other three survey years (Fig. 2). This difference might be attributed to the use of different observers during the 2022 surveys, although observer identity had been confounded with survey year, so it was not possible to definitively test this hypothesis.

Fig. 2.

Fitted detection functions (hazard rate) for each survey year with histograms showing the number of detections in each bin superimposed. Estimates of the proportion of detected kangaroos (P^) present between 0 and 150 m from the transect line are annotated onto each plot.


WR23133_F2.gif

Density surface modelling

Initial modelling of spatio-temporal variation in the abundance of grey kangaroos focussed on selection of appropriate space-time smoothing function and error distribution for the generalised additive models. The results of this initial exploration of alternative models are presented in Table 2. There was strong support for the use of a negative binomial error distribution, with the top four models using this choice. The best supported smoothing model was a trivariate smooth on latitude, longitude and time. This smoothing model was very strongly supported over other highly ranked models, with a difference of more than 13 AIC units between the best and second-best supported models (Table 2). Accordingly, the model with a trivariate space-time smooth was used as a basis for further exploration of the effects of habitat covariates on the abundance of grey kangaroos.

Table 2.Comparison of the top 10 spatio-temporal density surface smoothing models for grey kangaroo abundance in Victoria.

Spatial smoothError distributionEffective degrees of freedomΔAICPercentage of deviance explained (%)
s(long, lat, time)Negative binomial44.6022.7
s(long, lat) + s(time)Negative binomial22.713.0520.1
s(long, lat) + factor(time)Negative binomial24.716.4820.1
s(long, lat)Negative binomial21.823.7419.5
s(long, lat, time)Tweedie47.665.6530.2
(long, lat) + s(time)Tweedie25.583.4327.9
s(long, lat) + factor(time)Tweedie27.586.6627.9
s(long, lat,by = factor(time))Negative binomial50.7101.3518.6
s(long, lat)Tweedie24.9102.5627.1
s(long, lat,by = factor(time))Tweedie63.8210.2425.8

Models are ranked by AIC (lower is better).

ΔAIC, Akaike’s Information Criterion with the value for the best supported model subtracted.

The final model incorporating habitat covariates had a large improvement in AIC (ΔAIC = 153.2) and an increase in the proportion of deviance explained by the model from 22.7% to 29.7%.

The proportion of urban land cover was found to have no influence and was removed from the model. Estimated partial response curves for each of the included habitat covariates are given in Fig. 3. At very high proportional covers of crop, open or woody habitats, abundances of kangaroos were reduced, while abundances were generally higher where the amount of woody edge ecotonal habitat was at intermediate to high levels. Mean annual rainfall had a strong positive influence on kangaroo abundance, with expected abundances rapidly increasing once rainfall exceeded 400 mm per year and plateauing at rainfalls greater than approximately 700 mm. Abundances were highest at low to medium NDVI, although this effect was relatively uncertain (Fig. 3).

Fig. 3.

Partial effects of the habitat covariates on log-abundance of grey kangaroos. Spline terms are thin-plate regression splines (TPRS).


WR23133_F3.gif

After accounting for the habitat covariate effects, the space-time smoothing term in the model remained strongly influential (Table 3). Maps of the predicted spatio-temporal effect for each of four survey years are given in Fig. 4. It is apparent that across all four years, a large area of central and western Victoria, and parts of the extreme east of the state, had kangaroo abundances that were larger than can be explained by the effects of the habitat covariate effects alone. Similarly, parts of the far north and west, south Gippsland and the northeast of the state, had consistently lower kangaroo abundances than could be explained by the habitat covariates alone. This spatio-temporal effect increased in central and western Victoria over the 5-year duration of the study (Fig. 4).

Table 3.Effective degrees of freedom (e.d.f.), Chi-squared and P-values for each of the smooth terms included in the final (second stage) density surface model for grey kangaroo abundance in Victoria.

Terme.d.f.Chi-squareP
s(long, lat, time)24.47148.7<0.001
s(crop)3.1349.15<0.001
s(open)2.5628.85<0.001
s(woody)1.6410.6<0.001
s(wood edge)2.3926.5<0.001
s(rainfall)1.8912.9<0.001
s(NDVI)1.818.50.003
Fig. 4.

Space-time smoothing effect from the preferred density surface model for abundance of grey kangaroos in Victoria. This quantity represents the effect of space and time on the log-density of kangaroos after the effects of the additional habitat covariate terms in the model (Fig. 3, Table 4) are accounted for. Areas shaded blue have higher densities of kangaroos (and the opposite is true for red-shaded areas) than would be expected based purely on the effects of the habitat covariates (Fig. 3).


WR23133_F4.gif

Estimates of abundance

Predicted densities of grey kangaroos across the state for the 4 years of survey are given in Fig. 5 along with associated maps of the coefficients of variation for these predictions. Predicted densities were highest in Central Victoria, with densities in excess of 30 kangaroos per square kilometre being expected for much of this area during the entire period of the study. Conversely, predicted densities were mostly low in the pastoral and cropping country in the northwest and northeast of the state, with densities of less than one kangaroo per square kilometre applicable to much of these areas (Fig. 5). Uncertainty (expressed as the coefficient of variation) in the estimated densities was highest in the far northwest part of the state and across much of Gippsland. Conversely, there was little uncertainty in density estimates in Central Victoria, or across much of the pastoral and cropping areas of northern and western Victoria (Fig. 5).

Fig. 5.

Predictions of density (kangaroos per square kilometre) and uncertainty (coefficient of variation, CV) across the study area. Overlaid red lines delimit the harvest zones.


WR23133_F5.gif

The predicted cell-wise abundances derived from the density surface model were used to infer the total grey kangaroo population in the study area for each of 4 years in which aerial surveys were conducted (Table 4). Uncertainty in the estimates (expressed as 95% confidence intervals and coefficients of variation) was calculated using the function dsm_var_gam from the dsm R package (Miller et al. 2020), which allows for propagation of the uncertainty in both the detection model and the density-habitat model into the estimates of abundance derived from the density surface model (see Bravington et al. 2021). The total abundance increased over the course of the study from 1.27 million kangaroos in 2017 to a high of 2.39 million kangaroos in 2022. Coefficients of variation for all four of these estimates were small (<0.15) indicating a high degree of confidence in the estimates. These statewide estimates can be compared with the design-based estimates provided by Moloney et al. (2017, 2018a, 2021, 2023). For two out of four surveys, the model-based estimates were more precise, with narrower confidence intervals (Table 4). The actual estimates of the total population size were broadly comparable, although three out of four model-based estimates of abundance were slightly smaller than the comparable design-based estimates.

Table 4.Model-based and design-based estimates of the abundance of grey kangaroos (in millions) within the survey area for the 4 years in which aerial surveys were conducted.

YearEstimate95% CICVMethodSource
20171.280.97, 1.680.14Model-based (DSM)This study
20181.481.15, 1.900.13Model-based (DSM)This study
20201.831.40, 2.380.13Model-based (DSM)This study
20222.391.79, 3.190.15Model-based (DSM)This study
20171.440.98, 2.130.19Design-basedMoloney et al. (2017)
20181.421.05, 1.940.16Design-basedMoloney et al. (2018b)
20201.941.51, 2.490.13Design-basedMoloney et al. (2021)
20222.421.91, 3.050.12Design-basedMoloney et al. (2023)

CI, 95% confidence interval; CV, coefficient of variation.

The spatio-temporal model was also used to infer the abundances in each of the seven kangaroo harvest zones for each year of the study. These estimates were compared with the design-based estimates provided by Moloney et al. (2017, 2018a, 2021, 2023) (Fig. 6). For the majority of the seven harvest zones, the model-based estimates of abundance had narrower confidence intervals leading to generally similar conclusions regarding trends in abundance. The improvements in precision that followed from the model-based approach were most apparent in the Lower Wimmera, Upper Wimmera, North East and Otway harvest zones. Conversely, the precision of the model-based estimates of abundance for Gippsland and the Mallee were somewhat higher than the design-based equivalents reported by Moloney et al. (2017, 2018a, 2021, 2023).

Fig. 6.

Predictions of total abundance and abundance for each harvest zone. The model-based estimates are derived from the model presented in this report, the design-based estimates are taken from the reports by Moloney et al. (2017, 2018b, 2021, 2023).


WR23133_F6.gif

The estimated mean annual rate of change in the density of kangaroos for the period 2017–2022 is presented in Fig. 7. Across most of the state, the grey kangaroo population was found to have increased during the study period. Across the entire state, the mean annual rate of increase was 11.0% per year, with annual rates of over 15% estimated for some parts of central and western Victoria. Declines in abundance were only inferred for the small parts of the far northwest of the state and Gippsland, with these representing only a very small proportion of the state’s total area of grey kangaroo habitat (Fig. 7).

Fig. 7.

Predicted mean annual rate of change (λ) in the density of grey kangaroos for the period 2017–2022. Populations in areas shaded red (and delimited by the red contour line) are predicted to have undergone a decline in abundance during the monitoring period. A value of λ = 1 implies a population that has neither increased nor decreased.


WR23133_F7.gif

Discussion

This study represents the first occasion on which model-based distance sampling approaches have been applied to large-scale kangaroo surveys. As design-based methods have long predominated for assessment and monitoring of kangaroo populations for management purposes. The results presented here will be of considerable interest to wildlife managers seeking to obtain more precise estimates of kangaroo abundance and its temporal trends at a variety of spatial scales.

In employing conventional distance sampling techniques, it is acknowledged that the resulting population estimates contain some negative bias due to the assumption that detection on the transect line is perfect, which was almost certainly violated to some degree. As previously mentioned, some negative bias in the overall population estimates provides an additional guard against overharvesting by making the harvest quotas more conservative. Other potential sources of bias experienced during aerial surveys include availability bias, where animals may be present on the transect, but obscured and hence unavailable for detection. This sort of bias is more frequently encountered during aerial surveys of marine mammals, that spend periods of time submerged and hence, are unavailable to be observed (e.g. Brown et al. 2023)

Our results have demonstrated that the model-based approach can lead to improved precision of population estimates, both at a statewide and regional scale. The generally lower precision of design-based estimates of abundance was due primarily to high spatial variation in abundance among transects (i.e. sampling variation). In contrast, model-based estimates of variance are derived from the uncertainties in parameter estimates of the generating model and hence, variation due to the sampling design does not influence model-based estimates of variance. Some studies consider model-based estimation to be more efficient than design-based estimation, especially with smaller sample size (Brus and de Gruijter 1997; Dorazio 1999). However, model-based estimates of population parameters can be biased if the model is misspecified or is used to predict abundance at locations where values of covariates are outside the range of values used to estimate the model (Ramsey et al. 2019). The similarity of the design-based and model-based estimates of kangaroo abundance in this study are a direct result of the probabilistic and spatially representative sampling design employed and hence, gives us some confidence that the estimated model is a reasonable approximation to the true data generating process. Due to its relatively greater efficiency and ability to predict kangaroo abundance over arbitrary spatial scales, the model-based approach used here is considered superior to the design-based approach as it yields precise estimates of abundance at arbitrary spatial scales, not only at the scale of the survey strata. Hence, we recommend this estimation procedure be adopted when undertaking analyses of any future aerial surveys for kangaroos in Victoria. Calculation of design-based estimates can continue in parallel with the model-based approach to provide a point of comparison that is based on fewer statistical and ecological assumptions, and to provide a check on the model-based estimates.

As well as providing abundance estimates with improved precision, the model-based approach also provides insight into the habitat preferences of grey kangaroos. The results suggest that kangaroo densities are influenced by average productivity, for which average rainfall is a proxy (Fig. 3). The partial effects of rainfall on log-density of kangaroos point to a three-fold increase in expected density when rainfall increases from 200 mm to 800 mm. This finding is not unexpected based on previous work on the determinants of distribution of kangaroo populations elsewhere in Australia, which has demonstrated that grey kangaroo abundances are higher in areas of relatively high rainfall, especially in the absence of dingo predation (Short et al. 1983; Caughley et al. 1987; Cairns et al. 1991).

We also noted a strong effect of the amount of ecotonal habitats around the edges of woody vegetation. While previous data from grey kangaroos are lacking, studies of other macropods have noted their dependence on wooded areas as shelter from extremes of heat (Roberts et al. 2016), and potentially as refuge from predators (McAlpine et al. 1999). While the association of grey kangaroos with open grassland and agricultural habitats is well known, our model established that there were negative associations between kangaroo density and large proportional cover of these habitat types (Fig. 3). Together with the finding of an association with ecotonal wood edge habitats, these results collectively point to a dependence of kangaroos on landscapes with a combination of open habitat and habitats with ecotonal and woody areas which provide both foraging opportunities and shelter, at least at the spatial scale (5 km grid cells) used in our model.

There are several aspects of the model-based approach that would benefit from further refinement, and which may yet yield more accurate and precise estimates of abundance. Firstly, it is apparent that the habitat covariates considered in our model, while strongly influential, do not adequately explain the pattern of spatio-temporal variability in grey kangaroo abundance. A large proportion of this variability was still found to be better explained by the space-time smoothing function, which identified several regions of the state with higher or lower abundances than would be explained by the habitat covariates alone. While use of space-time smoothing function solves the problem of obtaining reasonable estimates of kangaroo density across the state, in and of itself it gives little insight into the ecological drivers of abundance. Hence, the space-time smooth acts as a proxy for additional ecological and/or anthropogenic drivers of population dynamics that if identified, could lead to improvement in the performance and interpretability of the spatio-temporal model. Overall, the proportion of total variation explained by the model (~29%) was moderate, meaning that there is considerable room for future improvement. Future work should focus on identifying additional habitat covariates and/or improved model structures that allow better explanation of variation in grey kangaroo abundance.

The same issue may also apply to the inferred temporal trends in the model, which is not based on any ecological or population process embedded in the model, but instead relies on smoothing of the observed trends in abundance in the vicinity of the monitoring transects. Future refinements to the model might allow inference regarding the temporal, as well as spatial drivers of changes in abundance. For example, it is possible to create a model which includes the influences of temporally varying resource availability on remote-sensed estimates of grassy vegetation greenness, productivity or biomass (e.g. Reeves et al. 2006; Creech et al. 2016; Johnson et al. 2018) and climatic conditions on the rate of change in abundance. Similarly, it may be possible to integrate data on local culling pressure on the populations (disaggregated to small spatial scales), and the process of density dependence into the temporal component of the model. Such approaches have been previously applied to uncover the ecological basis of population changes from large-scale distance sampling surveys of marine mammal populations (Nadeem et al. 2016; Boyd et al. 2018). But in principle, these methods would work equally well for kangaroos. Such approaches are however likely to require more temporal replication in the surveys (perhaps a minimum of 10 years of monitoring) before they become viable as an alternative to the current approach of statistical smoothing of the temporal trends in abundance.

The model-based approach also provides other advantages over previous design-based approaches. In particular, the model allows us to make inferences about predicted total abundance for arbitrary points in space and time, rather than computing single estimates of average abundance that are assumed to apply across an entire stratum. These inferences rely on interpolation in ecological and geographic space to predict abundance at unobserved times and places, which provides a powerful means of using the model for predictive purposes, which could be helpful for answering management questions at spatial scales smaller than the harvest zone. However, some caution is warranted, particularly when making inference to small geographic scales, where there is scope for actual densities of kangaroos on the ground to diverge significantly from the predictions – such predictions should be treated as tentative, and the risks of reliance on them for making management decisions need to be carefully considered. Ideally, such small scale predictions should be tested using an independent data set to determine the true precision and accuracy of the model’s predictions at a given spatial scale. The gold-standard for management decisions at small geographic scales remains one of direct assessment of abundance within areas of management interest.

Both the design-based and model-based inferences regarding temporal trends in the state’s grey kangaroo population reveal that the population has increased markedly since monitoring commenced in 2017. The model-based and design-based approaches to interpretation of the data suggest population increases of 67% and 86% respectively, over the 5 year period. This equates to mean annual rates of increase of 10.0% and 13.3%. This result is notable because the monitoring period coincides with programs of both commercial harvesting and regulated culling which have typically permitted annual harvest rates of approximately 10% of the design-based population estimate (Scroggie and Ramsey 2019; Ramsey and Scroggie 2020). Clearly, the kangaroo populations have proven resilient to the level of culling that has been applied, as abundances at both harvest zone and statewide levels have consistently increased over the monitoring period despite this level of culling.

In interpreting this apparent resilience of the populations to the regulated culling program, it is important to note that much of the monitoring period has coincided with a relatively benign climatic conditions in southeastern Australia, including a prolonged La Niña event which has lasted from late 2020 until late 2022 (Bureau of Meteorology 2023). A period of less favourable, hot and dry conditions would likely cause a decline in kangaroo abundance. Experience with macropod populations elsewhere in Australia points to strong declines during periods of prolonged drought (Caughley et al. 1984; Bayliss 1985; Bayliss and Choquenot 2002). The currently adopted approach of setting quotas as a proportion of the current population size provides a mechanism for limiting the impacts of culling when the population declines, as does the current policy of undertaking comprehensive aerial surveys of the population every 2 years.

It is also notable that the apparent annual rate of increase in the population varied in space, with lower (and indeed negative) rates of increase predicted in parts of the semi-arid northwest of the state. Given that this area includes much of the Victorian geographic range of the western grey kangaroo (M. fuliginosus), continued caution in harvest quota setting in this part of the state is warranted, both because of this species’ limited geographic range and population size in Victoria, and because more variable, semi-arid climatic conditions likely entail more variable rates of increase for kangaroo populations (Jonzén et al. 2010). Such variability may render populations less resilient to high harvesting rates, and may require more conservative approaches to the setting of harvest quotas (Engen et al. 1997).

Supplementary material

Supplementary material is available online.

Data availability

Data for this paper are available from the the Zenodo data repository https://doi.org/10.5281/zenodo.14642559.

Conflicts of interest

The authors declare that they have no conflicts of interest.

Declaration of funding

The research described in this paper was funded by the Victorian Government Department of Energy, Environment and Climate Action.

Acknowledgements

This work was funded by the Department of Energy, Environment and Climate Action. We thank Adam Lee, Jim Thomson and Lindy Lumsden for helpful comments on the manuscript and Justin Cally for helpful discussions regarding statistical modelling. Aerial survey data were collected by EcoKnowledge Pty Ltd. We thank Mark Lethbridge in particular for his work in coordinating the acquisition and collation of the aerial survey data.

References

Arnold GW, Steven DE, Weeldenburg JR (1989) The use of surrounding farmland by western gray kangaroos living in a remnant of wandoo woodland and their impact on crop production. Wildlife Research 16, 85-93.
| Crossref | Google Scholar |

Bayliss P (1985) The population dynamics of Red and Western Grey Kangaroos in arid New South Wales, Australia. I. Population trends and rainfall. Journal of Animal Ecology 54, 111-125.
| Crossref | Google Scholar |

Bayliss P, Choquenot D (2002) The numerical response: rate of increase and food limitation in herbivores and predators. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 357, 1233-1248.
| Crossref | Google Scholar | PubMed |

Boyd C, Barlow J, Becker EA, Forney KA, Gerrodette T, Moore JE, Punt AE (2018) Estimation of population size and trends for highly mobile species with dynamic spatial distributions. Diversity and Distributions 24, 1-12.
| Crossref | Google Scholar |

Bravington MV, Miller DL, Hedley SL (2021) Variance propagation for density surface models. Journal of Agricultural, Biological and Environmental Statistics 26, 306-323.
| Crossref | Google Scholar |

Brown AM, Allen SJ, Kelly N, Hodgson AJ (2023) Using unoccupied aerial vehicles to estimate availability and group size error for aerial surveys of coastal dolphins. Remote Sensing in Ecology and Conservation 9, 340-353.
| Crossref | Google Scholar |

Brus DJ, de Gruijter JJ (1997) Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with discussion). Geoderma 80, 1-44.
| Crossref | Google Scholar |

Buckland ST, Anderson DR, Burnham KP, Laake JL (1993) ‘Distance sampling: estimating abundance of biological populations.’ (Springer: New York, NY, USA)

Buckland ST, Rexstad EA, Marques TA, Oedekoven CS (2015) Model-based distance sampling: two-stage models. In ‘Distance sampling: methods and applications’. Methods in Statistical Ecology. (Eds ST Buckland, EA Rexstad, TA Marques, CS Oedekoven) pp. 127–140. (Springer International Publishing: Cham, Switzerland) 10.1007/978-3-319-19219-2_7

Buckland ST, Oedekoven CS, Borchers DL (2016) Model-based distance sampling. Journal of Agricultural, Biological, and Environmental Statistics 21, 58-75.
| Crossref | Google Scholar |

Bureau of Meteorology (2023) Climate Driver Update archive. Available at http://www.bom.gov.au/climate/enso/wrap-up/archive/20230314.archive.shtml [accessed 25 July 2023]

Burnham KP, Anderson DR (2002) ‘Model selection and multimodel inference: a practical information-theoretic approach.’ 2nd edn. (Springer: New York, NY, USA)

Cairns SC, Pople AR, Grigg GC (1991) Density distributions and habitat associations of red kangaroos, Macropus rufus, and western grey kangaroos, M. fuliginosus. Wildlife Research 18, 377-401.
| Crossref | Google Scholar |

Camp RJ, Miller DL, Thomas L, Buckland ST, Kendall SJ (2020) Using density surface models to estimate spatio-temporal changes in population densities and trend. Ecography 43, 1079-1089.
| Crossref | Google Scholar |

Carvalho JS, Stewart FA, Marques TA, Bonnin N, Pintea L, Chitayat A, Ingram R, Moore RJ, Piel AK (2022) Spatio-temporal changes in chimpanzee density and abundance in the Greater Mahale Ecosystem, Tanzania. Ecological Applications 32, e2715.
| Crossref | Google Scholar | PubMed |

Caughley J, Bayliss P, Giles J (1984) Trends in kangaroo numbers in western New South Wales and their relation to rainfall. Wildlife Research 11, 415-422.
| Crossref | Google Scholar |

Caughley G, Short J, Grigg GC, Nix H (1987) Kangaroos and climate: an analysis of distribution. Journal of Animal Ecology 56, 751-761.
| Crossref | Google Scholar |

Coulson G (1993) Use of heterogeneous habitat by the western grey kangaroo, Macropus fuliginosus. Wildlife Research 20, 137.
| Crossref | Google Scholar |

Creech TG, Epps CW, Monello RJ, Wehausen JD (2016) Predicting diet quality and genetic diversity of a desert-adapted ungulate with NDVI. Journal of Arid Environments 127, 160-170.
| Crossref | Google Scholar |

DELWP (2018) Kangaroo pet food trial evaluation report. Department of Environment, Land, Water and Planning, East Melbourne, Vic, Australia. Available at https://www.wildlife.vic.gov.au/__data/assets/pdf_file/0019/412723/KPFT-Evaluation-Report_Dec_2018a.pdf [accessed 26 August 2019]

DELWP (2020) Victorian kangaroo harvest management plan 2021–2023. Department of Environment, Land, Water and Planning, East Melbourne, Vic, Australia. Available at https://www.wildlife.vic.gov.au/__data/assets/pdf_file/0022/505624/Victorian_Kangaroo_Harvest_Management_Plan_2021-2023.pdf [accessed 12 June 2020]

Didan K (2015) MOD13A2 MODIS/Terra Vegetation Indices 16-Day L3 Global 1km SIN Grid V006. USGS.

Dorazio RM (1999) Design-based and model-based inference in surveys of freshwater mollusks. Journal of the North American Benthological Society 18, 118-131.
| Crossref | Google Scholar |

Duchon J (1977) Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In ‘Constructive theory of functions of several variables’. Lecture Notes in Mathematics. (Eds W Schempp, K Zeller) pp. 85–100. (Springer: Berlin, Heidelberg, Germany) 10.1007/BFb0086566

Engen S, Lande R, Sæther B-E (1997) Harvesting strategies for fluctuating populations based on uncertain population estimates. Journal of Theoretical Biology 186, 201-212.
| Crossref | Google Scholar |

Fewster RM, Pople AR (2008) A comparison of mark–recapture distance-sampling methods applied to aerial surveys of eastern grey kangaroos. Wildlife Research 35, 320-330.
| Crossref | Google Scholar |

Finch N, Pople A, McLeod SR, Wallace G (2021) Advances in aerial survey methods for macropods in New South Wales and Queensland. Ecological Management & Restoration 22, 99-105.
| Crossref | Google Scholar |

Fortin M-J, Olson RJ, Ferson S, Iverson L, Hunsaker C, Edwards G, Levine D, Butera K, Klemas V (2000) Issues related to the detection of boundaries. Landscape Ecology 15, 453-466.
| Crossref | Google Scholar |

Gorelick N, Hancher M, Dixon M, Ilyushchenko S, Thau D, Moore R (2017) Google Earth Engine: planetary-scale geospatial analysis for everyone. Remote Sensing of Environment 202, 18-27.
| Crossref | Google Scholar |

Hinton JW, Wheat RE, Schuette P, Hurst JE, Kramer DW, Stickles JH, Frair JL (2022) Challenges and opportunities for estimating abundance of a low-density moose population. The Journal of Wildlife Management 86, e22213.
| Crossref | Google Scholar |

Johnson HE, Gustine DD, Golden TS, Adams LG, Parrett LS, Lenart EA, Barboza PS (2018) NDVI exhibits mixed success in predicting spatiotemporal variation in caribou summer forage quality and quantity. Ecosphere 9, e02461.
| Crossref | Google Scholar |

Jonzén N, Pople T, Knape J, Sköld M (2010) Stochastic demography and population dynamics in the red kangaroo Macropus rufus. Journal of Animal Ecology 79, 109 116.
| Crossref | Google Scholar | PubMed |

Lethbridge M, Stead M, Wells C (2019) Estimating kangaroo density by aerial survey: a comparison of thermal cameras with human observers. Wildlife Research 46, 639 648.
| Crossref | Google Scholar |

Lunney D, Purcell B, McLeod S, Grigg G, Pople T, Wolter S (2018) Four decades of research and monitoring the populations of kangaroos in New South Wales: one of the best long-term datasets in Australia. Australian Zoologist 39, 784-800.
| Crossref | Google Scholar |

McAlpine CA, Grigg GC, Mott JJ, Sharma P (1999) Influence of landscape structure on kangaroo abundance in a disturbed semi-arid woodland of Queensland. The Rangeland Journal 21, 104-134.
| Crossref | Google Scholar |

McCullagh P, Nelder JA (1989) ‘Generalized linear models.’ 2nd edn. (Chapman & Hall: London, UK)

Miller DL, Wood SN (2014) Finite area smoothing with generalized distance splines. Environmental and Ecological Statistics 21, 715-731.
| Crossref | Google Scholar |

Miller DL, Burt ML, Rexstad EA, Thomas L (2013) Spatial models for distance sampling data: recent developments and future directions. Methods in Ecology and Evolution 4, 1001-1010.
| Crossref | Google Scholar |

Miller DL, Rexstad E, Thomas L, Marshall L, Laake JL (2019) Distance sampling in R. Journal of Statistical Software 89, 1-28.
| Crossref | Google Scholar |

Miller DL, Rexstad E, Burt L, Bravington MV, Hedley S (2020) dsm: density surface modelling of distance sampling data. Available at https://CRAN.R-project.org/package=dsm

Moloney PD, Ramsey DSL, Scroggie MP (2017) A state-wide aerial survey of kangaroos in Victoria. Arthur Rylah Institute for Environment Research Technical Report Series No. 268. Arthur Rylah Institute for Environmental Research, Heidelberg. Available at https://www.ari.vic.gov.au/__data/assets/pdf_file/0007/122011/ARI-Technical-Report-286-A-state-wide-aerial-survey-of-kangaroos-in-Victoria.pdf [accessed 26 August 2019]

Moloney PD, Ramsey DSL, Scroggie MP (2018a) State-wide abundance of kangaroos in Victoria: results from the 2018 aerial survey. Arthur Rylah Institute for Environment Research Technical Report Series No. 296. Arthur Rylah Institute for Environmental Research, Heidelberg. Available at https://www.wildlife.vic.gov.au/__data/assets/pdf_file/0030/415596/Statewide_kangaroo_report_2018_FINAL.pdf [accessed 26 August 2019]

Moloney P, Scroggie M, Ramsey D (2018b) Revisiting the Victorian kangaroo aerial survey design. Unpublished Client Report. Arthur Rylah Institute for Environmental Research, Heidelberg. Available at https://www.wildlife.vic.gov.au/__data/assets/pdf_file/0020/442622/Kangaroo-Aerial-Survey-Redesign-2018-FINAL.pdf

Moloney PD, Ramsey DSL, Scroggie MP (2021) State-wide abundance of kangaroos in Victoria: results from the 2020 aerial survey. Arthur Rylah Institute for Environment Research Technical Report Series No. 324. Arthur Rylah Institute for Environmental Research, Heidelberg.

Moloney PD, Ramsey DSL, Scroggie MP (2023) State-wide abundance of kangaroos in Victoria: results from the 2022 aerial survey. Arthur Rylah Institute for Environment Research Technical Report Series No. 356. Arthur Rylah Institute for Environmental Research, Heidelberg.

Nadeem K, Moore JE, Zhang Y, Chipman H (2016) Integrating population dynamics models and distance sampling data: a spatial hierarchical state-space approach. Ecology 97, 1735-1745.
| Crossref | Google Scholar | PubMed |

Pettorelli N, Ryan S, Mueller T, Bunnefeld N, Jędrzejewska B, Lima M, Kausrud K (2011) The Normalized Difference Vegetation Index (NDVI): unforeseen successes in animal ecology. Climate Research 46, 15-27.
| Crossref | Google Scholar |

Pople AR (2008) Frequency and precision of aerial surveys for kangaroo management. Wildlife Research 35, 340-348.
| Crossref | Google Scholar |

Pople AR, Cairns SC, Clancy TF, Grigg GC, Beard LA, Southwell CJ (1998) An assessment of the accuracy of kangaroo surveys using fixed-wing aircraft. Wildlife Research 25, 315-326.
| Crossref | Google Scholar |

Pople AR, Phinn SR, Menke N, Grigg GC, Possingham HP, McAlpine CA (2007) Spatial patterns of kangaroo density across the South Australian pastoral zone over 26 years: aggregation during drought and suggestions of long distance movement. Journal of Applied Ecology 44, 1068-1079.
| Crossref | Google Scholar |

Ramsey DSL, Scroggie MP (2020) Kangaroo harvest quotas for Victoria, 2021. Arthur Rylah Institute for Environment Research Technical Report Series No. 323. Arthur Rylah Institute for Environmental Research, Heidelberg.

Ramsey DSL, Forsyth DM, Wright E, McKay M, Westbrooke I (2019) Using propensity scores for causal inference in ecology: options, considerations, and a case study. Methods in Ecology and Evolution 10, 320-331.
| Crossref | Google Scholar |

Reeves MC, Zhao M, Running SW (2006) Applying improved estimates of MODIS productivity to characterize grassland vegetation dynamics. Rangeland Ecology & Management 59, 1-10.
| Crossref | Google Scholar |

Roberts JA, Coulson G, Munn AJ, Kearney MR (2016) A continent-wide analysis of the shade requirements of red and western grey kangaroos. Temperature 3, 340-353.
| Crossref | Google Scholar |

Scroggie MP, Ramsey DSL (2019) Kangaroo harvest quotas for Victoria, 2020. Arthur Rylah Institute for Environment Research Technical Report Series No. 308. Arthur Rylah Institute for Environmental Research, Heidelberg. Available at https://www.ari.vic.gov.au/__data/assets/pdf_file/0019/453502/ARI-Technical-Report-308-Kangaroo-harvest-quotas-Victoria-2020.pdf [accessed 21 April 2020]

Scroggie MP, Moloney PD, Ramsey DSL (2017) Design of an aerial survey to estimate the abundance of kangaroos in Victoria. Arthur Rylah Institute for Environment Research Technical Report Series No. 280. Arthur Rylah Institute for Environmental Research, Heidelberg. Available at https://www.ari.vic.gov.au/__data/assets/pdf_file/0032/80789/ARI-Technical-Report-280-Design-of-an-aerial-survey-for-abundance-of-kangaroos-in-Victoria.pdf [accessed 26 August 2019]

Short J, Caughley G, Grice D, Brown B (1983) The distribution and abundance of kangaroos in relation to environment in Western Australia. Wildlife Research 10, 435-451.
| Crossref | Google Scholar |

Thompson SK (2012) ‘Sampling.’ (John Wiley & Sons: Hoboken, NJ, USA)

Tibshirani R, Hastie T (1990) ‘Generalized additive models.’ (Chapman and Hall: London. UK)

White M, Griffioen P, Newell G (2020) Multi-temporal land cover and native vegetation extent for Victoria. Arthur Rylah Institute for Environment Research Technical Report Series No. 311.

Wood SN (2003) Thin plate regression splines. Journal of the Royal Statistical Society Series B: Statistical Methodology 65, 95-114.
| Crossref | Google Scholar |