Animal Density and Track Counts: Understanding the Nature of Observations Based on Animal Movements

1. What they did

The Formozov–Malyshev–Pereleshin (FMP) formula turns track counts into population density using only the number of track crossings, the transect length and the animals' average day range. People often doubt it because animals do not move in straight lines. The authors tested whether the shape of an animal's travel path (its tortuosity) affects the formula, at three levels of increasing realism.

• Virtual animals: they simulated populations on a computer across a wide range of densities, day ranges (0.3 to 30 km) and tortuosity levels, from straight lines to paths with 50 random turns. Each scenario was surveyed with randomly placed 10 km transects, repeated 1200 times. Animals could move freely in and out of the area, so there were no edge effects.
• Real travel paths in a simulation: trackers followed the tracks of 17 gemsbok and 6 steenbok over 24 hours, recording each path with GPS loggers taking a fix every second. Steenbok defend small territories, so they were back-tracked: after rain had wiped out old tracks, an animal was sighted 24 hours later and its tracks followed back to where they became marked by raindrops. Gemsbok were sighted one morning and forward-tracked from horseback from the same point the next morning. These real paths were then scattered at random in the simulation and surveyed 500 times.
• Real populations: the tracks on one 10 km transect were wiped clean each morning with a steel beam dragged behind a vehicle. The next morning, two observers on seats at the front of the vehicle counted every track crossing, over six consecutive 24-hour periods. No attempt was made to leave out repeat crossings by the same animal. The resulting FMP estimates were compared with independent estimates from distance sampling along three parallel 10 km line transects.

2. What they found

Path shape does not change track counts

• In the simulations, doubling density doubled the crossings per kilometre, and so did doubling day range.
• With density and day range held constant, the average number of crossings stayed the same whether animals moved in straight lines or wandered in tight random walks.
• FMP estimates came within 2% of the true simulated densities in every scenario.

Path shape does change detectability

• More winding paths meant fewer individual animals were detected. With the most winding paths, transects counted fewer than 30% of the individuals counted when the same animals moved in straight lines.
• Each animal that was detected crossed more times, so the total number of crossings stayed the same.

Precision

• Shorter, more winding paths produced more variable counts, and so less precise estimates.
• At 250 km of survey effort, 95% confidence intervals ranged from 97–102% of true density in the best case to 54–154% in the worst.

Gemsbok and steenbok

• The two species travelled similar daily distances: gemsbok 5.65 km and steenbok 4.20 km on average.
• Their paths were very different. Gemsbok moved more directly (tortuosity 4.22), while territorial steenbok wandered much more (10.86).
• At equal densities, 3.3 times more individual gemsbok than steenbok were detected per transect. A detected gemsbok crossed a transect 2.2 times on average; a detected steenbok crossed 5.4 times.
• Even so, FMP estimates for both species came within 5% of the true value. For example, at a true density of 2 per km², gemsbok were estimated at 1.97 and steenbok at 2.03 per km².

Field comparison

• Gemsbok crossed the track transect 8.59 times and steenbok 9.58 times per kilometre per 24 hours.
• FMP estimates: gemsbok 2.39 per km² (95% confidence interval 1.57–3.23); steenbok 3.33 per km² (2.71–4.17).
• Distance sampling (74 gemsbok and 66 steenbok sightings): gemsbok 2.57 per km² (1.43–4.62); steenbok 3.7 per km² (2.47–5.55).
• The two methods matched closely, and the track-based estimates were more precise. Track counts gave close to 100 observations per transect, while some line transects recorded no sightings of either species.

Occupancy

• In one simulation (100 animals in the study area), single transects detected gemsbok presence 51% of the time but steenbok presence only 18.2% of the time. So presence-absence data from tracks can be biased by differences in how animals move.

3. What they concluded

• The formula held up: their attempts to disprove the FMP formula found "no flaw in the simple equation". The number of crossings depends only on how many animals there are and how far they walk; the shape of their paths is irrelevant.
• Count every crossing: re-counting the same animal is not a problem. It is "in fact desirable" to count every re-crossing within the 24 hours. Counting each individual only once makes the result depend on path shape.
• Three assumptions: the formula should apply to any land animal with readily visible tracks if (1) animal movements are not influenced by the transect, (2) every animal that crosses is detected and identified correctly, and (3) every crossing is counted, regardless of which individual made it.
• Roads and trails: many carnivores use roads and trails, so transects placed along them (as in many large carnivore spoor surveys) would presumably give biased estimates. Transects placed at random relative to animal movements are needed.
• Track indices: using track counts as an index of abundance quietly assumes that day range, and for once-per-individual counts also path shape, stays the same between places, times and species. That may not hold.
• Occupancy: because all tracks have to be looked at anyway, counting every crossing takes little extra effort, and presence-absence data can be pulled out later. In many cases the FMP formula may be simpler than occupancy modelling for monitoring abundance from tracks.
• Main limitation: getting accurate day ranges. Even coarse estimates can be useful for species that cannot be counted any other way.
• Survey effort: larger surveys are needed for populations with lower density, clumped distribution, larger groups, shorter daily movements and more winding paths.

4. How tracking was or was not used

• Track counts: an expert local tracker and the first author identified and counted every gemsbok and steenbok track crossing on a pre-cleared transect, including repeat crossings by the same animal.
• Trailing: daily travel paths were traced by following tracks. Steenbok were back-tracked on foot from a sighting to the point where rain had reset the track record; gemsbok were forward-tracked from horseback until the animal was seen again or fled.
• Distance sampling: when animals fled before a distance could be measured, a tracker walked to where they had stood so it could be measured with a laser rangefinder.
• The authors note that detecting individuals reliably from tracks is much harder, and possible perhaps only for a few species and with exceptional trackers or detailed measurements.

5. Tracker or observer certification

• Reported but not validated. Track counts were made by "one expert local tracker" and the first author. The trailing was made possible by "the skilled horsemen trackers of Zutshwa". No certification or test of their skill is reported.
• The authors expect almost all tracks to be seen in the Kalahari, where tracks are easily visible and can be checked by more than one expert. They add that tracking skill surely varies widely around the world and that tracker proficiency "should be addressed more often".

6. Other technologies, skills or innovations

• Track drag: a heavy steel beam dragged behind the vehicle wiped out old tracks, so each count covered exactly 24 hours.
• GPS loggers: fixes every second gave fine, detailed tracings of each animal's daily path.
• Rain as a reset: rainfall that wiped out old tracks let trackers back-track steenbok over a known 24-hour period without disturbing them.
• Computer simulation: this separated the effect of path shape from day range and density, something that cannot be done in the field because it is usually impossible to know for certain whether tracks belong to the same or different animals.

7. Implications for conservation (from the paper)

• Many land mammals are nocturnal or hard to see, so indirect observations such as tracks are often the only realistic way to count them. Conservation practitioners would benefit from understanding how track counts relate to true abundance.
• The FMP formula has been used in Russia for decades. The authors argue that practitioners around the world can benefit from it.
• Track surveys detect animals over a much larger area than direct sightings can. In this study, 95% of gemsbok and steenbok sightings were within 355 m and 120 m of the line, while track counts captured animals that had travelled from far beyond that distance.
• Because day range can change with density, food and season, how often it needs to be reassessed matters when monitoring populations, whether with track counts or camera trap rates.