Results
The selected monthly sightings over the 17-year observation period were merged into a single data set, reducing the number of sightings from 14,256 to 6,580. The total number of sightings and the subset of sightings used for the data analysis are shown in Figures 3a and 3b.
Figure 3 . Maps of the study areas in South-East Queensland, Australia showing: (a) point location of all incidental koala sightings recorded in KoalaBASE for the period January 1997 to December 2013 (n = 14,256); and (b) the subset of koala sightings (n = 6,580) using the data analysis to estimate koala density.
A line plot showing temporal pattern of the koala population by calendar time estimated from the spatio-temporal point process model using koala sightings (n = 6,580) is shown in Figure 4. The koala population was low for the period 1997 to 2000 without prominent peaks, then fluctuated with peaks from 2001 to 2008 (with biennial larger peaks), before reaching large seasonal peaks in 2009 and 2010, declining again to peaks similar to pre-2009 period, followed by another large peak in 2013.
Figure 4. Koala population by calendar time estimated from the spatio-temporal point process model using koala sightings (n = 6,580) recorded in South-East Queensland, 1997-2013.
Parameter estimates from a spatio-temporal point process model used to estimate koala population densities in South-East Queensland between 1997 and 2013 are shown in Figure 1. The coefficients of land lot density and mean temperature of the coldest month had positive coefficients, while the coefficients of the other covariates included in the model were negative (Table 1).
Table 1. Estimated parameters from a spatio-temporal point process model used to estimate koala population densities in South-East Queensland between 1997 and 2013.
The relative estimated koala population density in South-East Queensland, 1997-2013 is shown in Figure 5 ranging from 0 to 6 or above koalas per km2, with the spatial distribution of sightings remaining more or less the same. Based on the model presented in Equation 6, 𝜃 was > 0 and \(\varphi\) was small suggesting that koalas aggregate in large areas. The estimates are consistent with the observed sightings, with no koalas or very low koala density in the western part of the study area and increasing density towards the Eastern coast of South-East Queensland, with prominent pockets of high koala density in known areas with good koala habitat.
Figure 5. Estimated relative koala population density (koalas per km2) in South-East Queensland, 1997-2013. Estimates were derived from a spatio-temporal point process model using koala sightings data (n = 6,580).
The percentage of land area in South-East Queensland with varying koala sightings density (koalas per km2) for each year of the 1997-2013 period is shown in Table 2. The percentage of land areas with very low sightings densities (0-0.25 koalas per km2) remained similar throughout the study period representing in average (SD) 68.3% (0.06) of the total study area (Table 2). However, land areas with more koalas per km2 showed larger variations over the years, with koala mean (SD) densities of 0.25-0.5, 0.5-1, 1-2, 2-5 and > 5 koalas per km2 representing 16.8% (0.21), 13.8% (0.25), 0.7% (0.20), 0.3% (0.13), and 0.2% (0.1) of the study area in South-East Queensland, respectively.
Table 2. Percentage of land area in South-East Queensland, 1997-2013, with varying koala population density (koalas per km2). Estimates were derived from a spatio-temporal point process model using koala sightings data (n = 6,580).

Discussion

We present here the results of spatio-temporal point process model, where relative koala population density was estimated considering spatio-temporal detection bias, observed koala densities and potential clustering effects. As partial likelihood estimation was used, the intercept was not calculated and absolute koala sightings density could not be estimated. However, relative koala population density estimates were produced for each year of the 17-year observation period.
The density of the koala population in South-East Queensland varied throughout the study region due to the heterogeneous nature of koala habitat, with density estimates ranging from 0.005 to 8.9 koalas per km2. Limited information of koala densities exist in Australia, but Rhodes, Beyer, Preece and McAlpine (2015) estimated koala densities varying between 0.001 and 11.0 koalas per ha in coastal regions of South-East Queensland, with an average of 0.04 koalas per ha (or 4 koalas per km2). However, the model developed by Rhodes et al. (2015) utilized data collected through multiple systematic surveys, which were implemented in small areas and did not predict koala populations across large geographic areas due to uncertainties associated with extrapolations. In fact, extrapolating koala densities from statistical models for large geographical areas is questionable as koala habitat is not continuously distributed. To avoid this fallacy, densities should be predicted to strata of different habitat types (Dique, Preece, Thompson and Villiers 2004).
Actual koala numbers are very difficult to estimate. In 2010, the Department of Environmental Heritage and Protection (DEHP) predicted that the Queensland koala’s population was between 157,000 and 177,000 animals, while the Threatened Species Scientific Committee of Australia estimated Queensland’s koala population to be approximately 167,000 animals in 2010, representing as 43% decline from 1990 (Rhodes, Beyer, Preece and McAlpine 2015). Another study estimated Queensland’s koala population to be about 79,300 in 2012 (Adams-Hosking, et al. 2016). Using expert elicitation methods the koala population for the whole of Australia was approximated to be 329,000 individuals (ranging from 144,000 to 605,000) (Adams-Hosking, McBride, Baxter, Burgman, de Villiers, Kavanagh, Lawler, Lunney, Melzer, Menkhorst, Molsher, Moore, Phalen, Rhodes, Todd, Whisson, McAlpine and Richardson 2016).
The results of the statistical model presented here provide estimates of yearly koala population densities, which are informed and therefore strongly influenced by observed sightings. Our model results showed increased koala population densities in some years, which might simply represent a higher observed fraction of koalas from the true koala population. We could also show strong clustering of koalas in locations in and around the Moreton Bay and Redland areas which is similar to the high density areas identified by Rhodes, Beyer, Preece and McAlpine (2015) using systematic field survey data. However, our model did identify low densities of koalas in the western part of South-East Queensland whereas Rhodes et al. (2015) predicted higher densities there, although this was probably due to the uncertainty associated with the model estimates for this region.
Importantly, we were able to estimate koala population density over time and space while incorporating a range of covariates expected to be associated with observed sighting densities or spatio-temporal detection bias. For example, distance to primary roads was considered to be covariate predominately influencing spatio-temporal bias, while foliage protective cover was influencing an observer’s ability to sight a koala and therefore impacting on observed sighting density. However, the contribution of covariates to the two different components of the model cannot be quantified as these components were included as additive factors on a log-scale in the model. Considering that covariates with a negative sign, would decrease estimated koala population density, our model indicated that larger distance to primary roads, denser foliage, higher altitude, but also increases precipitation would result in less sightings being reported. In contrast, increased lot density and warmer temperatures in the colder months were associated with increases population densities.
Uncertainties in estimated koala densities can be further reduced if additional data are collected at the time of each sighting event. This data could then be used in the modelling approaches to estimate and remove the effect of the bias on population density estimates. In our study, no observer-related variables were collected at the time when koalas were sighted. It has been shown that the probability of detection of a koala by an observer varies with previous experience of detecting koalas: an experienced observer can have a detection rate of around 70%, while an inexperienced observer might have a detection rate of only 30% (Corcoran, et al. 2019). As a result, many koalas may go undetected simply because of the lack of observer experience. The situation is somewhat different in systematically conducted field surveys by trained individuals where detection probabilities are estimated (Rhodes, Beyer, Preece and McAlpine 2015). Thus, incidental sightings reported by members of the public represent a biased sample of the koala population at any given time, but the collection of data on experience of observers at the time of the sighting, could provide value information to address this bias.
Koala sightings vary between seasons of the year. Such seasonal variations might be due to more frequent dispersal of koalas during breeding periods, but also due to better visibility of animals and better weather conditions that are more favorable for people to go outdoors and spot koalas. Interestingly, the results of our model indicated that clustering of koalas is not prominently different between the mating (theta1 = 2.0056) and non-mating seasons of koalas (theta2 = 2.029). This might be explained by koalas being solitary animals and although they travel over larger distances in the breeding season, their greater mobility might not necessary be associated with clustering of animals.
We included an average home range of koalas in our model, as we did not have detailed koala home range information for different parts of our study area. We realize that koala home ranges are not uniform and even within the Redland Local Government Area, koala home ranges of koalas vary between 0.05 and 0.55 km2 (de Oliveira, Murray, de Villiers and Baxter 2014). The precisions of koala densities could be improved, if home ranges appropriate for each habitat types are included in the model.
It has been predicted that drier and warmer climatic conditions have an undesirable impact on koala habitat and thereby negatively impacting koala populations (Adams-Hosking, et al. 2011). Unfortunately, our study was constrained by the non-availability of temporally varying covariates. As a result, the temporal effect of covariates, such as the impact of temperature changes over time on koala densities, could not be quantified.
Overall, while acknowledging the limitations associated sightings data collected by members of the public, we developed a statistical model that addressed the spatio-temporal bias associated with observed koala sightings and provided long-term relative koala density estimates for one of the largest koala populations of Australia over a 17-year period. In future research, the model proposed here could be used for systematic survey data and ultimately for combining (spatially restricted, but more precise) koala survey data with koala sightings data, that is incidental and often biased by nature, but often collected over large geographical areas.