On Indices of Population Abundance

A discussion with Murray Efford last week stimulated me to raise again this issue of using indices to measure population changes. One could argue that this issue has already been fully aired by Anderson (2003) and Engemann (2003) and I discussed it briefly in a blog about 2 years ago. The general agreement appears to be that mark-recapture estimation of population size is highly desirable if the capture procedure is clearly understood in relation to the assumption of the model of estimation. McKelvey and Pearson (2001) made this point with some elegant simulations. The best procedure then, if one wishes to replace mark-recapture methods with some index of abundance (track counts, songs, fecal pellets, etc.), is to calibrate the index with absolute abundance information of some type and show that the index and absolute abundance are very highly correlated. This calibration is difficult because there are few natural populations on which we know absolute abundance with high accuracy. We are left hanging with no clear path forward, particularly for monitoring programs that have little time or money to do extensive counting of any one species.

McKelvey and Pearson (2001) laid out a good guide for the use of indices in small mammal trapping, and showed that for many sampling programs the use of the number of unique individuals caught in a sampling session was a good index of population abundance, even though it is negatively biased. The key variable in all these discussions of mark-recapture models is the probability of capture of an individual animal living on the trapping area per session. Many years ago Leslie et al. (1953) considered this issue and the practical result was the recommendation that all subsequent work with small rodents should aim for a maximum probability of capture of individuals. The simplest way to do this was with highly efficient traps and large numbers of traps (single catch traps) so that there was always an excess of traps available for the population being censused. Krebs and Boonstra (1984) presented an analysis of trappability for several Microtus populations in which these recommendations were typically followed (Longworth traps in excess), and they found that the average per session detection probability ranged from about 0.6 to 0.9 for the four Microtus species studied. In all these studies live traps were present year round in the field, locked open when not in use, so the traps became part of the local environment for the voles. Clean live traps were much less likely to catch Microtus townsendii than dirty traps soiled with urine and feces (Boonstra and Krebs 1976). It is clear that minor behavioural quirks of the species under study may have significant effects on the capture data obtained. Individual heterogeneity in the probability of capture is a major problem in all mark-recapture work. But in the end natural history is as important as statistics.

There are at least two take home messages that can come from all these considerations. First, there are many statistical decisions that have to be made before population size can be estimated from mark-recapture data or any kind of quadrat based data. Second, there is also much biological information that must be well known before starting out with some kind of sampling design. Detectability may vary greatly with observers, with types of traps used, and observer skills so that again the devil is in the details. A third take home message given to me by someone who must remain nameless is that mark-recapture is hopeless as an ecological method because even after much work, the elusive population size that one wishes to know is lost in a pile of assumptions. But we cannot accept such a negative view without trying very hard to overcome the problems of sampling and estimation.

One way out of the box we find ourselves in (if we want to estimate population size) is to use an index of abundance and recognize its limitations. We cannot use quantitative population modelling on indices but we may find that indices are the best we can do for now. In particular, monitoring with little money must rely on indices of many populations of both plants and animals. Some data are better than no data for the management of populations and communities.

For the present time spatially explicit capture-recapture (SECR) methods of population estimation have provided a most useful approach to estimating density (Efford et al. 2009, 2013) and much future work will be needed to tell us how useful this relatively new approach is for accurately estimating population density (Broekhuis and Gopalaswamy 2016).

And a final reminder that even if you study community or ecosystem ecology, you must rely on getting measures of abundance for many quantitative models of system performance. So methods that provide accuracy for population sizes are just as essential for the vast array of ecological studies.

Anderson, D.R. 2003. Index values rarely constitute reliable information. Wildlife Society Bulletin 31(1): 288-291.

Boonstra, R. and Krebs, C.J. 1976. The effect of odour on trap response in Microtus townsendii. Journal of Zoology (London) 180(4): 467-476. Doi: 10.1111/j.1469-7998.1976.tb04692.x.

Broekhuis, F. and Gopalaswamy, A.M. 2016. Counting cats: Spatially explicit population estimates of cheetah (Acinonyx jubatus) using unstructured sampling data. PLoS ONE 11(5): e0153875. Doi: 10.1371/journal.pone.0153875.

Efford, M.G. and Fewster, R.M. 2013. Estimating population size by spatially explicit capture–recapture. Oikos 122(6): 918-928. Doi: 10.1111/j.1600-0706.2012.20440.x.

Efford, M.G., Dawson, D.K., and Borchers, D.L. 2009. Population density estimated from locations of individuals on a passive detector array. Ecology 90(10): 2676-2682. Doi: 10.1890/08-1735.1

Engeman, R.M. 2003. More on the need to get the basics right: population indices. Wildlife Society Bulletin 31(1): 286-287.

Krebs, C.J. and Boonstra, R. 1984. Trappability estimates for mark-recapture data. Canadian Journal of Zoology 62 (12): 2440-2444. Doi: 10.1139/z84-360

Leslie, P.H., Chitty, D., and Chitty, H. 1953. The estimation of population parameters from data obtained by means of the capture-recapture method. III. An example of the practical applications of the method. Biometrika 40 (1-2): 137-169. Doi:10.1093/biomet/40.1-2.137

McKelvey, K.S. & Pearson, D.E. (2001) Population estimation with sparse data: the role of estimators versus indices revisited. Canadian Journal of Zoology, 79(10): 1754-1765. Doi: 10.1139/cjz-79-10-1754

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