Background

Animals are easier to detect at sites where they are abundant than at sites where they are rare.

This relationship can be exploited to estimate the average abundance of animals at a set of sites, rather than estimating the proportion of sites occupied. If n animals are present at a site and the probability of detecting each one is r, the probability of failing to detect all of them is

(1 - r)ⁿ

assuming that each detection is independent of the others, and that individual detection probability is the same for all animals. Hence the probability of detecting at least one animal at the site is

p = 1 - (1 - r)ⁿ

This value, p, is the probability of detecting the species at the site.

This idea is implemented in PRESENCE as the Royle/Nichols model.

An experiment with ants

Data collection

During the 'Tigers Forever' training course at Krau, 16-26 April 2007, Arjun Gopalaswamy and course participants investigated the relationship using ants on a lawn at the Institute of Biodiversity.

106 patches, each 3 x 3m, were marked out, covering almost the whole area of the lawn. Patches were searched for a particular species of large, black ant for 90 seconds by eight observers positioned around the patch, one at each corner and one at each side. Each observer noted independently whether they had detected ants, giving 8 detection occasions for analysis.

Participants worked in two teams, one team of eight surveying odd-numbered patches and the other the even-numbered patches.

The results are available here.

Preliminary data analysis in MS Excel®

1. Each participant calculated a 'naïve occupancy' estimate for the 53 patches which they had visited, assuming that ants were in fact absent from patches where he or she had not seen them.

Estimates ranged from 55% to nearly 80%, and high standard deviations for both odd- and even-numbered patches. (See the 'Single observer' tab of the spreadsheet.)

2. Observations for each patch were then pooled, and a new 'naïve occupancy' estimate calculated, this time assuming that ants were absent if all eight observers failed to detect them.

This of course resulted in a much higher estimate, with ants detected at 99 out of 106 patches, 93.4%. (See the 'Multiple observers' tab of the spreadsheet.)

3. A rough estimate of detection probability was made using only the 99 patches known to have ants. Of the 99 x 8 = 792 observations of these patches, ants were recorded 571 times; this gives a detection probability of 571/792 = 0.72.

On this basis the probability of ants actually being present at a patch but not detected by any of the 8 observers ('false absence') is (1 - 0.72)⁸ = 0.00003. So it is most unlikely that any of the remaining 7 patches harbor ants. This in turn means that our estimate of detection probability - based on a naïve estimate of occupancy - will only be slightly biased.

Data analysis using PRESENCE

The data for all 106 patches ('sites' in PRESENCE's terminology) and 8 observers ('occasions') were imported into PRESENCE.

A first analysis using the default model, psi(.) p(.), gave the same results as the manual analysis (estimate ± SE: occupancy = 93.4% ± 2.4, p = 0.72 ± 0.016).

The Royle/Nichols Heterogeneity Model turned out to be substantially better than the default model for these data (delta AIC = 147). The detection probability for an individual ant (r,  not p) was estimated as 0.42, with an estimated average of 2.94 ± 0.31 ants per patch, with a total population for all 106 patches estimated as 312 ± 32. (An average of about 3 ants per patch on the surface seemed reasonable to participants; there may have been many more underground.)

On this basis, PRESENCE estimated occupancy at 94.7% ± 1.6.

The output files from PRESENCE are here.

Conclusion

• Estimates of abundance can be made based on 'presence/absence' observations.
   
• The assumptions of the analysis - that all animals are equally detectable, and detections of animals are independent - will not be met in all cases.
   
• The method should work even if detections are based on sign rather than observations of animals. However, this needs to be tested in the field. Ullas Karanth, Arjun, and the WCS India Program are testing the method at their study sites in India.

For more information on this, see Royle & Nichols (2003) and pages 140-141 in MacKenzie et al (2006).