Archive for category: Biology

Introduction

None of the numerous techniques available for estimating the size of animal populations is foolproof, and none can apply equally well to all populations. Some population sampling methods can yield reasonably good size estimates only for small and relatively immotile animals. This lab presents a popular method useful for estimating the population size of a single species of highly mobile animal, such as most vertebrates. It is called the capture-recapture, or mark-recapture, technique. In honor of some early contributors to its development, fishery biologists refer to the basic procedure as Peterson’s method, ornithologists and mammalogists call it Lincoln’s method, and diplomatic ecologists refer to it as the Lincoln-Peterson method.

Lincoln-Peterson Method

A number of individuals from a population of interest are captured, marked by some identifiable means, and released within a short period of time (e.g., a day). At a later date (perhaps after a week or two), a second sample of individuals is taken from the population. Some of the individuals in this second sample may be identified as being members of the first sample because they were previously marked. Obviously, if the population is large, the marked individuals will have become “diluted” within it, and only very few would be expected to appear in the second sample. But if the population is relatively small, then more previously marked animals would be in the second sample. Indeed, if certain assumptions about sampling and the animals’ distribution are correct, then the proportion of marked individuals in the second sample is the same as that in the entire population, and the total population may be estimated as follows.

Assume the total population size to be estimated contains N individuals. From this population, take a sample of M individuals, mark these animals, and return them to the population. At a later time, take a second sample of n individuals from the population; this sample contains R recaptured animals (i.e., individuals captured and marked in the first sampling). Then the population size, N may be estimated by the following considerations:

The first equation says that the proportion of marked animals in the entire population is equal to the proportion of marked animals in a random sample taken from that population. Equivalently, the second equation says that the ratio of the total population to the number of animals marked on the first date is equal to the ratio of the number caught on the second date to the number that were recaptured on the second date. By rearrangement of the above equations,

so this equation estimates the population size, N.

The theory behind this method of population size estimation is exemplified by laboratory exercises using inanimate objects, as indicated in the following example. Suppose you take 200 white balls out of a pot having an unknown number of white balls, paint them black, return them to the pot, and mix all balls in the pot thoroughly. If you then take 250 balls from the pot and find 50 of them to be black, then M=200, n=250, R=50, and the unknown total number of balls (N) could be estimated using this equation:

Note that if someone came along after you replaced the marked balls in the pot and removed 100 balls at random, you would still have the same ratio of white to black balls in the pot, and therefore you would still estimate the original number of balls. This situation is analogous to random mortality or random emigration in a population. The following assumptions must be met to validly use this capture-recapture procedure.

1. No trap bums. All individuals in the population have an equal and independent chance of being captured during the time of sampling. That is, the two samples taken from the population must be random samples.
2. No change in the ratio of marked to unmarked animals. During the time from initial capture to recapture, there must be no significant additions of unmarked animals to the population through births or immigration, and population losses from death and emigration must remove the same proportion of marked and unmarked animals. The estimation procedure will work if mortality or emigration occurs randomly for marked and unmarked animals, for then the ratio n/R will be unaltered. If there are additions of new individuals to the population but no mortality then N will be an estimate of the population size at the time the second sample is taken. If there is both mortality and recruitment, then this method will overestimate the size of the population at the time of either of the two samples.
3. Marked animals mix with unmarked. Marked animals distribute themselves homogeneously with respect to unmarked ones so that unmarked animals have the same opportunity for capture in the second sample as do marked ones. That is, there must be a random distribution of marked individuals throughout the entire population, and marking an animal must not affect the subsequent likelihood of that animal’s being recaptured. One must be careful not to alter the catchability of an animal by the acts of capturing and marking it; this can happen if the catching or marking technique causes significant changes in the animal’s behavior or vigor.

These assumptions require a good deal of knowledge of the natural history of the species under study. When applying this technique, you should know the following.

1. Reproductive history of the population. Are young being added to the population? Is the catchability of animals changing during the period of measurement due to reproduction-induced changes in behavior?
2. Mortality pattern of the species. Is the population undergoing a decline? Remember that the population may experience mortality without affecting the population estimate, as long as mortality affects the marked and unmarked alike.
3. Effects of marking on the behavior and physiology of the animal. Is the animal’s movement or behavior altered? Is the probability of mortality changed?
4. Seasonal patterns of activity and movement. Do not use this method during hibernation or migration seasons.
5. Biases in the capture of the animals. Do different individuals, sexes, or ages avoid capture or become prone to capture? Is the animal highly mobile or relatively sessile?

In addition, of course, one must use a marking technique enduring enough so the marks will last from the time of marking until the time of recapture.

Schnabel Method

In order to get a good estimate from the Lincoln-Petersen method, you must mark a significant fraction of the population you are estimating. This is not always practical. An alternative is to sample repeatedly from a population with fewer marked individuals. This repeated sampling is called the Schanbel method and is in essence a weighted mean of a series of Lincoln-Petersen estimates. The Schnabel estimate of population size is:

As with all population estimates made from samples, there is an uncertainty caused by the error associated with examining a sample rather than the entire population. A measure of this error that expresses the uncertainty of a capture-recapture population estimate is the variance. For the Schnabel estimate, this is computed on the reciprocal of the population density 1/N as:

Procedure

1. You will be given a paper bag that contains an unknown (by you) number of white beans. Pull 10 beans from the bag and replace with black beans. Shake the bag and pull another 10 beans out of the bag. Note the number of black beans in this sample. From this data calculate the estimated population size (N) and the variance.

Pull another 10 white beans from the bag and replace with 10 black beans. Resample and recalculate N and the variance. Repeat this, replacing 10 beans at a time until the number of black beans in the bag is 200. Recalculate N and the variation for each 10-bean addition of black beans. How does the number of marked individuals in the population affect your population size estimate and standard error?

2. Now, violate the assumptions of the estimate. Repeat 1 above. This time, with each addition of black beans to the population, chuck the white beans back in as well. How does a growing population affect your estimates?
3. Repeat 1 above. This time, with each addition of black beans to the population, don’t shake the bag before sampling. How does a growing population affect your estimates?

Graph your results.