The last survey for black rhinos using a block-survey design was conducted during 2008 and estimated that 627 (95% CI: 588–666) animals resided in Kruger [5]. We collated the number of black rhino’s poached every year from 2008 to 2012 (SANParks, unpublished data) and converted these to the average number of rhinos poached per day per year. An exponential model [12] fitted to this data predicted the expected daily poaching rate for 2013. Using the observed annual poaching rates, we subtracted these from randomly drawn values extracted from the statistical distributions of the population estimate [5], and allowed the population to increase annually at a rate of 6.75% (95% CI: 4.1–9.8%) [5]. We continued this annual process until we reached a prediction for 2013. By simulating such poaching and population growth effects iteratively (100000 repetitions) [13], we could define the statistical distribution (95% CI) of expected numbers of black rhinos in Kruger during 2013.
During 2012, SANParks conducted aerial distance sampling surveys of herbivores [14] during which observers noted white rhinos as well. The survey had an effective coverage of 6% of Kruger and estimated 10495 white rhino individuals (95% CI: 8500–12900) living in Kruger during 2012 [15]. We allowed annual rates of increases of population to vary between -9.6% and 9.0% predicted from the 2010 and 2012 estimates. We extracted values from the statistical white rhino estimate distribution during 2010 (10,621; 95% CI: 8,767–12,682; [6]), and used daily poaching predictions of white rhino from 2008 to 2012, together with management removal records (SANParks, unpublished data) to derive the expected white rhino population size for 2013. Again, using 100,000 iterative simulations [13], we could define the expected statistical distribution (95% CI) of white rhinos in Kruger during 2013.
Note that annual surveys typically take place during September, the hot dry season. We thus needed to calculate poaching incidence between two surveys. Our results for poaching detection suggest that most carcasses may be detected within three months of the poaching incident taking place (see below). Our collation of poaching data up to the end of 2013, three months after the last population survey, may thus accommodate carcass detection challenges when estimating poaching rates.
At the end of the dry season during 2013, we used block-based surveys [5] by intensely searching 878 blocks 3x3 km in size (41.5% coverage of Kruger) using a Eurocopter Squirrel helicopter. We distributed blocks randomly throughout Kruger National Park, with a slight bias towards the high-density areas south of the Sabie River. Our flights were at an altitude of 45 m above ground level at an average speed of 65 Knots. We divided each block into strips 400 m wide with a 200 m wide search area each side of the aircraft. We minimized double counting by systematically completing transects on a block. Two observers including the pilot on either side of the helicopter with one recorder noted rhinos encountered. Stratifying our samples into landscapes [11] and using Jolly’s estimator [18] allowed landscape-specific estimates and smaller confidence intervals for overall rhino estimates in Kruger.
As the accuracy (a measure of how close an estimate is to the real number of individuals in a population, [24]) of a population estimate comprises of precision (confidence intervals) and bias [25] of the survey methodology, we recognized three biases that could influence the accuracy of estimates. Availability bias [16, 17] estimates the proportion of animals not available to the survey observers, such as those rhinos standing under trees. We checked rhinos that were available, but not detected by sampling 56 white rhinos and 23 black rhinos in localities with varying tree cover [26]. For two black rhino and ten white rhino observations when an individual was already moving, we had the pilot hover and follow the rhino at the same height as our surveys for 10–15 minutes and noted the fraction of time during an observation that the rhino was visible. For cases where rhinos were sedentary (black rhino: n = 21; white rhino: n = 46) we completed a full circle with radius approximately 100 m at the same height as our surveys and again noted the fraction of time during an observation that the rhino was visible. We then calculated mean percentage time visible for 5% bins of woody cover and fitted an inverse sigmoid curve [27] to these estimates to define the relationship between availability bias and woody cover. We acknowledge, however, that numerous factors may influence the response of a rhino to a helicopter and hence availability bias.
To account for observers having different capabilities, we extracted previously published observer bias estimates [5]. By placing two observers on the same side of an aircraft and allowing independent recording of sightings, we previously [5] used Seber’s approach [28] to estimate that 3.8% of available rhinos to be seen will not be noted by either observer. Finally, we minimized detectability bias (individuals are present and available, but there is variation in detecting them, [14]) by our approach to intensely search blocks using flight paths 400 m apart (i.e. swath search widths on either side of the aircraft was 200 m). Distance-sampling approaches identified 200 m swath widths as minimally influenced by detectability [29]. Using Monte-Carlo simulations [13], we corrected population estimates for availability and observer bias through 100,000 iterations and define population estimates (median) and confidence intervals (2.5% and 97.5% percentiles) from the resultant statistical distribution.
