# Using the Formozov–Malyshev–Pereleshin formula to convert mammal spoor counts into density estimates for long-term community-level monitoring

> Every September, community trackers in Namibia’s Salambala Conservancy walk 215 km of transects counting spoor. Using a Russian formula that divides track counts by how far each species travels in a day, researchers turned seven years of these counts into density estimates for 10 mammals, more species than the conservancy’s sighting surveys could manage. The catch: the formula needs every spoor crossing recorded, and good day ranges, which trackers trailing animals could help provide.

Summary by Kersey Lawrence, Original Wisdom. Updated 9 November 2026. Page: https://www.originalwisdom.com/tracking-literature/2019-ahlswede-fabiano-formozov-malyshev-pereleshin-formula/

## Citation and access

- **Authors:** Steve Ahlswede, Ezequiel Chimbioputo Fabiano, Derek Keeping and Klaus Birkhofer
- **Year published:** 2019
- **Journal or source:** African Journal of Ecology
- **Full citation:** Ahlswede, S., Fabiano, E. C., Keeping, D. and Birkhofer, K. 2019. Using the Formozov–Malyshev–Pereleshin formula to convert mammal spoor counts into density estimates for long-term community-level monitoring. African Journal of Ecology 57(2): 177–189.
- **DOI:** 10.1111/aje.12587
- **Access status:** Publisher link only
- **Where to find it:** https://doi.org/10.1111/aje.12587

## Tags

- **Species:** Mammals > African buffalo; Mammals > African elephant; Mammals > Blue wildebeest; Mammals > Common duiker; Mammals > Eland; Mammals > Giraffe; Mammals > Greater kudu; Mammals > Impala; Mammals > Jackal; Mammals > Leopard; Mammals > Plains zebra; Mammals > Reedbuck; Mammals > Roan antelope; Mammals > Spotted hyena; Mammals > Steenbok; Mammals > Warthog; Mammals > Waterbuck
- **Region:** Africa > Namibia
- **Tracking:** Spoor age estimation; Track counts; Tracking; Tracks; Tracks and signs identification
- **Behaviour and ecology:** Behaviour; Daily travel distance
- **Methods and technology:** Body mass–day range scaling; Bootstrapping; Distance sampling; Formozov–Malyshev–Pereleshin (FMP) formula; Global Positioning System (GPS) collars; Linear regression; Population estimation; Simulation
- **Data type:** Existing data
- **Observer qualification:** Reported but not validated
- **Discipline:** Population trends; Wildlife tracking
- **Year published:** 2019

## Detailed keywords

- **Species:** Studied (density estimates from spoor): African elephant (Loxodonta africana), blue wildebeest (Connochaetes taurinus), common duiker (Sylvicapra grimmia), common impala (Aepyceros melampus), eland (Taurotragus oryx), giraffe (Giraffa camelopardalis), greater kudu (Tragelaphus strepsiceros), plains zebra (Equus quagga), spotted hyena (Crocuta crocuta) and warthog (Phacochoerus africanus). Spoor recorded but too rarely for density estimates: African buffalo (Syncerus caffer), jackal, steenbok, leopard (Panthera pardus), reedbuck, roan and waterbuck (Kobus ellipsiprymnus); the paper gives no scientific names for jackal, steenbok, reedbuck and roan. Also listed as living in the conservancy: African lion (Panthera leo). Day range data for 22 species of the order Artiodactyla (from Carbone et al. 2005) were used to build the body mass to day range relationship.
- **Location and habitat:** Salambala Conservancy (930 km²), north-eastern Namibia, a communal conservancy across the Chobe River from Chobe National Park, Botswana; animals move freely between the two. Floodplains with lush grass, and dry sandy areas with open woodland of mopane (Colophospermum mopane), teak (Baikiaea plurijuga), false mopane (Guibourtia coleosperma), silver terminalia (Terminalia sericea), wild seringa (Burkea africana), Combretum and Acacia. Mostly deep sand with some loamy clay to clay. Tropical climate, rain December to March, about 620 mm a year.
- **Topics:** spoor transect counts; converting track counts to density; the Formozov–Malyshev–Pereleshin (FMP) formula; day range (mean daily travel distance); allometric scaling of day range with body mass; community-based natural resource management (CBNRM) and communal conservancies; community game guards and community monitoring; population trends; comparison with distance sampling; undercounting caused by the survey protocol (spoor counted once per individual, spoor of sighted animals ignored); gregarious species; rainfall and day range; recommendation to trail animals to measure day ranges.
- **Statistics or models:** FMP formula, D = (π/2)(x/SM), where x is the number of spoor crossings, S the transect length and M the day range; bootstrapping (5,000 resamples) for confidence intervals (R package boot); least-squares linear regression of log day range on log body mass; empirical day ranges from Global Positioning System (GPS) collar data of 21 African buffalo and five plains zebra (Euclidean distance between fixes) and from the literature; generalised additive models (GAM, R package mgcv) of density against year and rainfall; an informal test of trend using overlap of 85% confidence intervals (Buckland et al. 1992); simulation adding all direct sightings to the spoor data; precision compared as confidence interval length as a percentage of the mean. Inconsistencies in the paper: (1) the abstract says six species were stable or increasing and four declining; the Results say three declining (eland, elephant, warthog) and seven stable or increasing (zebra among them); the Discussion says five increasing and four declining (zebra among them), and later “six of the 10 species populations are stable” and “the 10 stable species”. (2) The Results text says the GAM explained 75% or more of the variation for eland and less than 30% for kudu, but Table 3 gives 68% for eland and 63% for kudu. (3) The text says nine day ranges were estimated allometrically; Table 1 lists eight. (4) The Results give densities as “(100 per km2)”; the tables show this means per 100 km². (5) Table 3 gives an eland confidence interval for 2010, but its footnote says the eland series begins in 2012 (Table 2 shows no eland spoor in 2010 and 2011).
- **Data type:** Existing data: the conservancy’s annual dry-season (September) spoor surveys, 2010 to 2016, collected largely by community members; the authors took part in the 2016 survey. Distance sampling estimates from the Namibian Association of CBNRM Support Organizations (NACSO), published GPS collar data, and day ranges from the literature.

## Synopsis

### 1. What they did

Namibia’s communal conservancies must count their wildlife every year, and spoor (track) counts are a routine and efficient way for communities to do it. On their own, spoor counts are an index, not a density. The Formozov–Malyshev–Pereleshin (FMP) formula, used for decades in Russia, converts spoor counts into density using each species’ day range: how far an animal travels in a day. The more an animal moves, the more tracks one animal leaves, so the formula divides by day range. Accurate day ranges are often missing, so the authors tested whether estimates from body size could fill the gap.

- Spoor surveys. In Salambala Conservancy, north-eastern Namibia, teams of three or four surveyors walked 16 transects (215 km in all) over 2 days each September from 2010 to 2016, starting at 6:30 a.m. They recorded the location, species and number of spoor for all hoofed mammals and large carnivores, counting only spoor judged to be from different individuals and made within the last 24 hours. Spoor of animals they saw were left out, because sightings went to a separate distance sampling count.

- Day ranges. For African buffalo and plains zebra they calculated day ranges from Global Positioning System (GPS) collar data; for elephant, giraffe and spotted hyena they used published values. For the other species, they predicted day range from body mass, using the known relationship across 22 hoofed species.

- Density and trends. They combined spoor counts and day ranges in the FMP formula, used bootstrapping to get confidence intervals, and fitted generalised additive models (GAM) with rainfall to look for trends from 2010 to 2016.

- Checks. They simulated what would happen if all sighted animals had also been counted as spoor, and compared their densities with the conservancy’s distance sampling estimates.

### 2. What they found

Densities

- Seventeen mammal species were recorded over the seven years. Densities could be estimated for 10; the other seven (buffalo, jackal, steenbok, leopard, reedbuck, roan and waterbuck) had very few spoor or appeared in only a few years.

- The highest average densities (per 100 km²) were common impala (34.5), blue wildebeest (23.8), common duiker (16.1) and greater kudu (15.2). The lowest were eland (5.4), giraffe (3.9) and spotted hyena (0.2).

Trends

- No trend was statistically significant: the confidence intervals for 2010 and 2016 overlapped for every species.

- The paper describes the trends differently in different places (see the detailed keywords). In the Discussion, five species tended to increase (blue wildebeest, impala, duiker, giraffe and kudu) and four to decrease (eland, elephant, zebra and warthog).

- Adding all sightings as spoor gave similar trends; only zebra and blue wildebeest differed.

Day ranges from body size

- Day ranges predicted from body mass varied much less than real GPS data. For buffalo, the GPS day ranges varied more than twice as much (standard deviation 3.73 km against 1.57 km). This made the density estimates look more precise than they really were.

Spoor counts compared with distance sampling

- The two methods mostly agreed, with the largest differences for impala, zebra and warthog.

- Precision was similar: distance sampling was more precise in 15 of 29 comparisons, FMP in 13, with one tie. Distance sampling needed three years of sightings pooled together for each estimate.

- FMP densities were lower than distance sampling in 25 of 29 comparisons.

- FMP gave estimates for 10 species; distance sampling for eight, and for only two of them across the whole 2010 to 2016 period.

Undercounting

- The survey rules ask trackers to record each animal’s spoor only once and to ignore spoor of animals they saw. The FMP formula needs every crossing of a transect counted. For zebra alone, up to 10,174 spoor may have gone unrecorded over the seven years.

### 3. What they concluded

- Applied to routine community spoor counts, the FMP formula can give density estimates for more species than the conservancy’s distance surveys, including elusive species and those at low density.

- Densities were probably underestimated, because of the recording rules, and day ranges from body size or from GPS fixes an hour or more apart add error. The study also assumed day ranges stayed the same every year, although rainfall varied.

- The authors recommend recording all spoor, whatever the individual and whether or not the animal was also seen, and measuring day ranges over several years, for example by local experienced trackers trailing animals. They also recommend double sampling with line transects run at the same time.

- With these changes, the FMP method could be an invaluable tool for monitoring many species together.

### 4. How tracking was or was not used

The whole study rests on spoor counts. Surveyors on foot identified the species of each spoor crossing the transect, judged whether spoor were made within the last 24 hours, and judged whether spoor came from different individuals, discarding duplicates. No trailing was done in this study, but the authors note that in many places where the FMP can be used, trackers can follow trails with handheld GPS units to measure day ranges, and they recommend local experienced trackers trailing animals to fill this gap.

### 5. Tracker or observer certification

Reported but not validated. Surveyors were Ministry of Environment and Tourism (MET) rangers, local community game guards and trained community members; the paper says the community game guards “were all expert trackers”. No certification or test of their skill is reported. The authors cite Stander et al. (1997) to say indigenous trackers have proven highly accurate under different conditions, but that study did not test these surveyors. Many of the same community members took part across the seven years.

### 6. Other technologies, skills or innovations

- Allometric scaling: predicting a species’ day range from its body mass, with bootstrapped regression to carry the uncertainty into the density estimates.

- GPS collar data (four fixes a day for buffalo, one an hour for zebra) to measure day ranges. The authors note that fixes an hour or more apart miss fine-scale movement and underestimate day range, which inflates density.

- Generalised additive models to smooth year-to-year ups and downs when looking for trends.

### 7. Implications for conservation (from the paper)

- Communities already collect spoor data routinely; turning them into densities and trends makes them more useful for decisions such as hunting quotas.

- Distance sampling estimates pooled over three years can hide sudden changes and would need three times the current effort for robust yearly estimates.

- Possible declines in eland, elephant, warthog and zebra deserve attention. The authors suggest causes: eland were reintroduced in 2012 and are sensitive to disturbance and hunted for meat; warthog may be killed in retaliation for crop damage or poached; elephants are declining across Africa, with poaching a possible driver in Namibia; and zebra declines may be linked to rainfall.

### 8. Implications for tracking (Original Wisdom's observations)

_These are Original Wisdom's observations, not the authors'._

- The study shows how a recording rule can shape the results: counting each animal’s spoor only once, and ignoring spoor of animals seen, suits an index but not the FMP formula, which needs every crossing.

- The FMP formula depends on knowing how far animals travel each day. Trailing by skilled trackers is one of the methods the authors point to for measuring this, which gives tracking a second role in the same monitoring.

## Cite this summary

Lawrence, K. 2026. Summary of: Using the Formozov–Malyshev–Pereleshin formula to convert mammal spoor counts into density estimates for long-term community-level monitoring (Ahlswede and Fabiano et al., 2019). Original Wisdom, Tracking Literature. https://www.originalwisdom.com/tracking-literature/2019-ahlswede-fabiano-formozov-malyshev-pereleshin-formula/