Counting Beans; Adventures in Population-size Estimation

Ecology Lab

Rob Bierregaard

Introduction

            Ecologists nearly always want to know how many of their study organisms there are in a given population. However, it is rarely is it possible to count whatever it is that is being studied. Plants are often too numerous to count, and mobile organisms rarely cooperate—they’re often cryptic, frightened by the presence of the researcher, or simply moving around too much for the census taker to know whether an individual spotted has already been counted or not.

            Population biologists have therefore developed a number of techniques to estimate population sizes. These take the form of counting some subsamples of the population and then extrapolating average counts to a larger population. With plants, subsamples are taken to estimate population density in a given area. With mobile organisms, trapping and marking or trapping and removing individuals are the basis for population size estimates.

            In last week’s lab, we used a number of these techniques to estimate the population of laboratory beans found in the blue-tray habitat.

Methods

            We were given a small jar full of white beans and a blue tray, conveniently gridded out to help us sample the bean population.

            Our first sampling technique was to guess how many beans were in the jar. We then released the population into their “habitat” and shook the tray to scatter the beans. We then used quadrat and transect sampling to estimate the overall population size. Finding an average number of beans in a quadrat or transect, we extrapolated this mean to the whole population. Because there are 100 quadrats in the blue tray, we multiplied our mean number of beans/quadrat times 100 quadrats/tray. The ratio for transects was 10.

            We next used two techniques that are appropriate for mobile orgainisms. First we “trapped” and marked 50 beans by replacing 50 white beans with 50 red ones. Three random samples were then taken from the whole population, and the ratio of marked (red) to unmarked beans was used to estimate the total population size. Then we sampled without replacement. 10 samples were taken based on a standard trapping effort. We placed the top of a jar that (about 10 cm in diameter) on the tray and removed all the beans under it. The tray was shaken again and another sample taken. The number of beans taken in each successive sample was plotted against the cumulative number of beans captured. We calculated a regression through these points and used the x intercept as one estimate of the total population size. We also used a formula (see worksheet) with these same numbers to come up with another estimate. Our final estimate was the average of these two numbers.

            Finally, we used point-quadrat and random-pairs techniques to come up with our last two estimates. These techniques are based on randomly choosing a point and measuring the distance to neighboring beans. (See worksheet for details).

            After counting the actual number of beans, we calculated the percent error ((est-true)/true) for each technique. The class data were posted on our website so we could compare the different teams’ results.

            To compare the different sampling systems, I looked at the average (absolute value) and standard deviation of the percent error for each technique for the six teams.

Results.

            There was a wide range of mean percent error for the different techniques (Table 1). The best two techniques were quadrats and point-quarter, with mean percent errors of 22.51% and 24.55%, respectively. Quadrats and transects had the least variation (lowest standard deviations). The removal technique was by far the worst, with an average percent error of 122%!

  Table 1. Mean percent error and standard deviation for seven different population size estimates.

Discussion

            With the notable exception of the removal technique, the sampling procedures we used gave us fairly comparable levels of accuracy, with percent error ranging from 23-37%. All but the removal procedure gave us substantially better estimates than guessing, which is somewhat reassuring. It would be interesting to take additional samples to see if our estimates improved or if this is the best level of accuracy we can expect with these population sizes and techniques. It is certainly possible that our beans were not really randomly distributed before sampling, which would violate assumptions inherent in the various calculations.

There was clearly a serious problem with the removal trapping procedure. Looking at the class data, there were three groups with wildly bad estimates (as high as 240%!), while three had reasonable values. This strongly suggests that the three outlier groups did something different from the other three groups. Perhaps their populations weren’t adequately randomized before each sample was removed. Or maybe they didn’t really randomly sample. (The estimates are especially affected by large numbers captured in the later samples.)

A lesson learned here is that we need to understand the assumptions of the sampling procedure. Violating these assumptions can lead to very inaccurate estimates of population size.