AUTHOR BLOG: Citizen-Science Data and Capture-Mark-Recapture Models to Estimate Numbers of Rare Species

Andrew Dennhardt

Linked paper: Applying citizen-science data and mark–recapture models to estimate numbers of migrant Golden Eagles in an Important Bird Area in eastern North America by A.J. Dennhardt, A.E. Duerr, D. Brandes, and T.E. Katzner, The Condor: Ornithological Applications 119:4, November 2017.

Have you ever looked to the autumn sky above and wondered how many of your favorite feathered friends are out there, as they migrate southward each year? If so, then you are not alone. A common goal in ecology has been to estimate the abundance of wild populations. From basic counts to educated guesses, historically, people have tried it all. During and even before the work of Sir Ronald Fischer, the father of modern statistics, applied mathematics aided in population estimation—for humans and wild animals alike.

F.C. Lincoln (1930) is credited with one of the first modern attempts to approximate population abundance of wild animals based on a sample of marked individuals (Bailey 1952, Le Cren 1965). The premise of his approach, co-credited to C. G. Johannes Petersen (1894) and commonly called capture-mark-recapture (CMR), was simple: trap a random set of animals of the same species in an area, mark those you caught with a unique tag, release them back into the wild for a period of time, return to the same area once more and randomly trap individuals of that same species again, and record which previously tagged individuals, if any, came back to the area. In brief, when you know the proportion of individuals you recaptured the second time, you can assume that you trapped the same proportion of the total population when you trapped the first time. The math is straightforward, too: if you have an initial sample of animals captured, marked, and released back into the wild, M, and multiply that by the total number of animals sampled a second time, n, then you can divide that quantity by the number of marked animals in that second sample, m, and approximate true population size, N.

In our paper, we used modern statistical advancements in CMR to estimate abundance of Golden Eagles (Aquila chrysaetos), a species of conservation concern in the United States, using an unusual approach. In effect, we did not physically capture, mark, or recapture individual animals in the wild; rather, we did so virtually in a computing environment with the help of observational data collected by some savvy citizen-scientists.

Golden Eagles in eastern North America face lethal and sub-lethal threats, many of which are human caused. However, these eagles are rarely seen, broad-ranging, and difficult to capture in the wild because they often avoid areas of human activity. Despite this fact, citizen-scientists observe Golden Eagles frequently and regularly during their annual spring and autumn migrations in Pennsylvania, U.S.A. Moreover, Golden Eagle movements are highly stereotyped, especially in autumn, bringing them within a few hundred meters of hawk counters on ridgetops in the Appalachian Mountains. Better still, because of past telemetry studies, we know how fast Golden Eagles fly when they migrate. Hawk counters collect their data on Golden Eagles and other migrant species and archive their observations in an online database, With assistance from managers of the archive, our research team gained permission and access to download historic count data on migrating Golden Eagles observed using the Kittatinny Ridge during their peak migration period, November, over a 10 year period from 2002 to 2011.

Now, here’s where things get really exciting (well, they do for me, at least!). Because (a) historic hawk-count data included information on the timing of Golden Eagles migrating southward past monitoring sites along the Kittatinny, (b) telemetry data gave us an idea of how fast they fly while migrating in autumn, and (c) we could measure the distance between each of the monitoring sites they passed, we could then estimate how long it would take eagles to travel between pairs of sites. Using a customized computer program, we matched records of Golden Eagles together, from site to site, such that we could know when observers at one site counted a bird that had probably been counted at a previous site (i.e. eagles became “captured,” “marked,” and “recaptured”).

Using these virtual data on matched eagle observations, we developed what are commonly called encounter histories. In brief, encounter histories comprise a sequence of 1s and 0s unique to each eagle. In a given sequence, a 1 represents either the event of first “capture and marking” or a subsequent “recapture” after being previously marked and released back into the wild, and a 0 represents an event when an eagle was not “captured or recaptured” at a previous or subsequent migration monitoring site. For modern CMR approaches, extensions of Lincoln (1930) and Petersen’s (1894) early work, encounter histories are the necessary input data for a statistical model. Because we were interested in estimating eagle abundance in a particular area (i.e. the Kittatinny Ridge) over time, we chose the Population Analysis (POPAN) Jolly-Seber model—the right tool for the job.

Most exciting for us, our methodology worked. We produced population abundance estimates for Golden Eagles migrating along the Kittatinny Ridge each autumn. To boot, two sets of our estimates followed the necessary rules (e.g., statistical model goodness-of-fit tests) for us to consider them reliable by modern CMR standards. Together, our best models estimated that approximately 1,350 Golden Eagles migrated along the Kittatinny Ridge each November, 2002–2011.

In the end, we feel that we have produced a useful framework for evaluating other migratory bird populations based on similar data and known movement behaviors. Our proposed methodology not only builds upon the legacy of modern CMR work, but is also far more cost-effective than physical CMR and other costly survey techniques. In the case of fixed-wing aircraft surveys for Golden Eagles in the western United States alone, our work costs far less than the annual ~$320,000 necessary to implement such surveys. Most importantly, such an achievement was only made possible by the tireless work of numerous dedicated citizen-scientists, whose standardized and centrally managed data can provide wildlife researchers and managers with quality information useful in conservation decisions. To our friends at the Hawk Migration Association of North America, for all of their data collection and management year-in and year-out, our team is abundantly grateful—pun intended!


Bailey, N. T. J. 1952. Improvements in the interpretation of recapture data. Journal of Animal Ecology 21:120–127.

Le Cren, E. D. 1965. A note on the history of mark-recapture population estimates. Journal of Animal Ecology 34:453–454.

Lincoln, F. C. 1930. Calculating waterfowl abundance on the basis of banding returns. Circulation of the U.S. Department of Agriculture No. 118.

Petersen, C. G. J. 1894. On the biology of our flat-fishes and on the decrease of our flat-fish fisheries: with some observations showing to remedy the latter and promote the flat-fish fisheries in our seas east of the Skaw. Report of the Danish Biological Station No. IV (1893–94).

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s