Biol 380 - General Ecology
Kasmer

ESTIMATING THE SIZE OF ANIMAL POPULATIONS

To understand how different physical or biological factors influence the distribution or abundance of species, we usually need to measure changes in population abundances over space or time. However, it usually is not possible to obtain a complete count or census of a natural population of animals (and it is often difficult even for plants!). For this reason, ecologists generally have to rely on some kind of estimate of abundance or density. For example, one may count the number of singing males of a species of bird in a given community or defined area and then estimate the size of the breeding population by assuming that for every male there is one female. Or one may count the individuals in a sample area and then extrapolate to the larger area in which the whole population is assumed to live. Because each method has different assumptions and hence, different strengths and weaknesses, it is recommended (though rarely done) that at least two estimation methods be used and compared in any population study.

In this lab you will estimate the size of populations of brine shrimp (Artemia salina) in small aquaria.  Although there are two basic population estimation techniques for mobile organisms (mark-and-recapture and catch-per-unit-effort sampling, which is also referred to as depletion sampling), you will be using only the mark-recapture technique.  In addition, you will be examining or thinking about the assumptions of each model and their validity for different kinds of species.  As will be the case for most labs this semester, you will write up the lab in its entirety in your laboratory notebook.  The carbons for this lab will be due at the beginning of class on a date TBA.

The Mark and Recapture Technique

The mark and recapture method involves marking a number of individuals in a natural population, returning them to that population, and subsequently recapturing some of them as a basis for estimating the size of the population at the time of marking and release. This procedure was first used by C.J.G. Petersen in studies of marine fishes and F.C. Lincoln in studies of waterfowl populations, and is often referred to as the Lincoln Index or the Petersen Index. It is based on the principle that if a proportion of the population was marked in some way, returned to the original population and then, after complete mixing, a second sample was taken, the proportion of marked individuals in the second sample would be the same as was marked initially in the total population. That is,

R (marked recaptures) / C (total in second sample)  =  M (marked initially) / N (total pop. size)

The accuracy of this method rests on a number of assumptions, including the following:

1). During the interval between the preliminary marking period and the subsequent recapture period, nothing has happened to upset the proportions of marked to unmarked animals (that is, no new individuals were born or immigrated into the population, and none died or emigrated).

2). The chances for each individual in the population to be caught are equal and constant for both the initial marking period and the recapture period. That is, marked individuals must not become either easier or more difficult to catch.

3). Sufficient time must be allowed between the initial marking period and the recapture period for all marked individuals to be randomly dispersed throughout the population (so that assumption 2 above holds).  However, the time period must not be so long that assumption 1 breaks down.

4). Animals are not affected by their marks (i.e., their survival, catchability, ability to migrate, reproductive ability in the time interval are all unaffected by the marks).

5). Animals do not lose their marks.

There are a number of modifications of this simplest form of mark-and-recapture methods. These are presented in Cox (1996; Exercise 10), Brower et al. (1997) and in Krebs (1999).  (Ask me if you are interested in looking at any of these sources.)

MATERIALS AND METHODS

If we were working with natural populations of animals in the field, we might mark animals in two different areas on one day, and re-sample these same areas for marked animals several days later. If animals in the two areas are marked with a different color, it would be possible to determine whether migration occurred between the populations. Benthic aquatic animals (e.g., insect larvae, clams) can be sampled with kick nets, small terrestrial insects can be sampled with sweep nets, and larger animals (e.g., birds, mammals) can be captured with traps or by other means. The number of animals taken from each area would be recorded, and the animals are marked and returned to the area they came from. It is also necessary to estimate the size of the area sampled if you wanted to report the results in terms of density (# per unit area or volume), rather than merely total population size.

In lab, you will work in small groups. Each group will be given an aquarium (beaker) containing an unknown number of brine shrimp in a clear 1% NaCl solution.  I will also provide beakers containing brine shrimp that have been swimming around in a salt solution to which a non-toxic dye has been added (2.5ml of a 0.1% methylene blue solution per 100ml of salt solution), so that these brine shrimp have been dyed blue.  Rather than actually trying to mark brine shrimp that are initially captured (I have absolutely no idea how that could be done!), you will replace them (one-for-one) with the dyed brine shrimp; thus each group will remove a sample of undyed brine shrimp from the aquarium, and replace them with an equivalent number of dyed brine shrimp.   The group will then resample their population, and based on the sample, estimate the size of their population of animals.  Finally, each group will determine both the standard errors and the 95% confidence interval of their estimate, using formulae described below.

When we meet, each group will have to design their own technique for capturing brine shrimp from their aquaria, so think about how you might do this before we actually meet.  The aquaria will be 500-ml beakers, and the brine shrimp are small enough to be sucked up using a disposable pipette with a large opening, or with small fishnets (both of which will be provided).  

Note that you will also want to consider how brine shrimp behave (e.g., do they swim around near the top or bottom, sides or middle of their containers, or all around in the water?  Thus it will be necessary to observe them for a while before actually coming up with a protocol for capturing them.

As a last step for the lab, you will also need to figure out the actual size of the population of brine shrimp in your aquaria, so that you can see how closely your estimate of population size (from the mark-recapture study) corresponds to the actual size of the population.  (Note that this is usually impossible to do in the field, and that this is a distinct advantage to working with artificial populations in the lab!)

At the end of class, we will compile and share the results obtained by the different groups.

DATA ANALYSIS

The mark-recapture analysis was shown earlier in the handout. In addition, it is described in Krebs (1989), which also describes several methods of calculating the 95% confidence limits of the estimates. Most basically, solving for N gives an estimate of the total population size:

                N = ( C * M ) / R

However, it has been shown that using this formula often overestimates the true size of a population, so the following unbiased formulation is preferred:

N = [(M+1)(C+1) / (R+1)] - 1

As in all estimates, it is also useful to have some information about the uncertainty of the estimate (as measured by the standard error, and/or by 95% confidence intervals).   The standard error of the estimate of N is given by the following formula:

SE = sqrt { [(M+1)(C+1)(M-R)(C-R)] / (R+1)2(R+2) }

The standard error gives an idea of where the sample mean is likely to be found if the experiment were conducted repeatedly.  From the standard error, we can also calculate the 95% confidence limits of the estimate (which defines the range of values within which the true population size is likely to lie with 95% certainty), using the following formula:

95% confidence interval = N  +  (1.96)(SE)

There are alternative ways of estimating the 95% confidence interval, depending on the ratio of marked:unmarked individuals in the second sample and the total number of animals in the second sample. 

Note also that there is an alternative formula for estimating N (which is:  N = [M(C+1)]/(R+1) )that should be used if you sample with replacement (as would occur if you merely observed, rather than removed individuals in the second sample).  Refer to Krebs (1999) to learn more about these (and many more!) alternatives.

 

Things to do/questions to address in your lab notebook:

1.  In the form of an appropriately titled and constructed bar chart, show for both your group's population and one other group's population the true population size of brine shrimp in your group's container (note that this means you must actually determine this), your unbiased estimate  of the population size (calculated from the mark-recapture data), the standard error of your estimate (shown as an error bar), and the 95% confidence interval of your estimate (shown as a second error bar).  

2.  Based on the bar chart you generated (above), does there seem to be significant difference in the size of the two populations of brine shrimp?  Explain.

3.  How accurate is your estimate of the size of the population of brine shrimp in your container?  Support your answer by referring to empirical observations, as well as to your statistical results.

4.  Discuss what factors might account for any differences in the relative sizes of the standard errors for the two populations that you graphed, or that might account for differences in the relative accuracy of your estimated population sizes of the two populations.

5.   Evaluate how well you think you were able to satisfy each of the assumptions of the mark-recapture technique.

6.   If migration occurred in a natural population being studied, how would this influence the reliability of your estimate of population size determined using the mark-and-recapture technique? Would your population estimate be too high or too low, or would you not be able to predict how your estimate would be biased? (Remember: migration consists of both immigration and emigration.) 

7.   Discuss the kind of bias you would expect to be generated in the estimate of population size (and/or its confidence interval) if each of the remaining assumptions were violated.  (For example: If such-and-such an assumption is not met, would it cause the size of the population be expected to be overestimated? underestimated? unbiased?  Would the confidence interval be expected to be larger, smaller or unchanged from when all assumptions are met? . . . and then do the same for each of the other assumptions.)  Note that it is possible that violating several different individual assumptions may have the same effects, so work out your answers on scratch paper before committing them to your notebook - you may be able to save yourself some time, space and effort!

REFERENCES

Brower, J.E., J.H. Zar, and C.N. vonEnde. 1997. Field & Laboratory Methods for General Ecology. 4/e. Boston: WCB/McGraw-Hill.

Cox, G.W. 1996. Laboratory Manual of General Ecology. 7/e. Dubuque, IA: Wm.C.Brown.

Krebs, C.J. 1999. Ecological Methodology. 2/e. NY: Benjamin/Cummings.

Southwood, T. R. E. and P.A. Henderson.  2000. Ecological Methods. 3/e. Malden, MA: Blackwell Science.

Zippin, C. 1958. The removal method of population estimation. J. Wildlife Management 22:82- 90.