Simplified large African carnivore density estimators from track indices

1. What they did

Counting tracks is a cost-effective way to estimate how many large carnivores live in an area. The number of tracks found per 100 km is turned into a density (animals per 100 km²) with a formula fitted to places where the true density is known. A formula used in several recent studies for sandy soils (Funston et al. 2010) includes an intercept: it does not pass through zero, so at very low track counts (below 0.4 tracks per 100 km) it gives impossible, negative numbers of animals.

The authors asked whether a simpler line forced through zero (no tracks when no carnivores are present) fits the same data better. They:

• Reanalysed the existing data. They repeated the original regressions with intercept and added regressions through the origin, for six models: lion on sand; all carnivores on sand; a “General Carnivores on Sand” model that also included brown hyaena data and Stander’s (1998) leopard data; lion on clay; lion and cheetah on clay; and a low-density model for sandy soils (below 1 animal per 100 km²).
• Compared the models. They used a set of published statistical criteria, the standard error of estimate, the mean square residual and the corrected Akaike Information Criterion (AICc). They also fitted a curved (logarithmic) line to the low-density data to test whether the relationship stops being straight near zero.
• Tested the general model against one independent lion population of known size.
• Compared population estimates from three formulas for a hypothetical 10,000 km² area, using track densities from published studies.

2. What they found

Which line fits best

• All six models through the origin were statistically significant. Of the models with an intercept, Lion on Clay and Low Density on Sand were not.
• In every model with an intercept, the intercept could not be told apart from zero.
• In every case the line through the origin fitted better (smaller errors), and AICc gave none of the intercept models substantial support.
• Adding the brown hyaena and leopard data did not change the slope for carnivores on sand (3.26). This slope is very close to the one Stander (1998) found for a small sample of lion and wild dog data (3.28).
• The curved line for low densities was not significant (P = 0.056).

Independent test

In a 629 km² area with 18 lions (2.86 lions per 100 km²), the team surveyed 294 km and found 13 lion track incidences made by 22 individuals. The general model estimated 2.2 lions per 100 km² (95% confidence interval 1.0 to 3.4), about 78% of the true density, with the true density inside the interval.

Comparing estimates

• The general model through the origin gave leopard estimates that were 58% of those from Stander’s leopard model.
• The difference between the new general model and the older intercept model was largest at low densities: 43.5% at 0.88 tracks per 100 km, falling below 10% at about 3.1 tracks per 100 km.
• The low-density model gave estimates about 80% of those from the general model.
• Survey effort climbs steeply at low densities. To find the recommended minimum of 19 track incidences, Table 7 shows about 2,159 km of survey at 0.88 tracks per 100 km and 4,750 km at 0.4 tracks per 100 km (the text gives 2,273 km and 5,000 km).

3. What they concluded

• A line through the origin is justified over the usual line with an intercept for all the models tested.
• One general formula can be used across species and study areas on sandy soils: observed track density = 3.26 × carnivore density. It never gives negative estimates, and it is valid down to about 0.27 carnivores per 100 km² (0.88 tracks per 100 km).
• Below that, estimates are questionable, partly because the relationship may not be straight near zero, but they may still be the best data available to guide conservation. Estimates and trends from low-density populations should be read with caution.
• Substrate matters: sandy and clay soils need different models.
• The models rest mostly on lion data. More data are needed for other species, especially at low densities, and more independent data are needed to validate the models.
• Studies using track surveys should publish a full data summary, so densities can be recalculated as new calibrations become available.
• Track surveys are cost effective and cover large areas, but at low densities there is a trade-off between data quality and survey effort. The right survey method depends on the objectives, resources, expertise, area size and expected densities.

4. How tracking was or was not used

The paper is built on track counts: the number of carnivore track incidences found per 100 km of survey, compared with known densities. Most of the track data come from earlier surveys (Funston et al. 2010; Stander 1998); the paper refers readers to Funston et al. (2010) for the survey protocol. The authors also ran one new track survey of a lion population of known size, recording 13 lion track incidences made by 22 individuals over 294 km.

5. Tracker or observer certification

Not reported. The paper does not say who identified and counted the tracks in the new lion survey or in the earlier datasets. This matters because the formulas assume tracks were found and identified reliably.

6. Other technologies, skills or innovations

• A simple, single formula (track density = 3.26 × carnivore density) that field teams can apply on sandy soils without needing an intercept.
• Table 7 converts track densities into the survey distance needed for 19 track incidences, which helps plan survey effort.

7. Implications for conservation (from the paper)

• The range, population size and trend of large carnivores are used to assess their status and plan conservation, from the whole range of a species down to national plans.
• The older intercept model can badly misjudge numbers at low densities (or give negative numbers), which is exactly where many threatened populations are.
• Surveys at low densities need very long distances to collect enough tracks, so planners must weigh data quality against effort.