Mark-recapture Methods Field Exercise # 1. Estimating the population size of a mobile animal: Water striders (Gerris sp.)

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1 1 Biology 317 Principles of Ecology September 21, 28, 2017 Mark-recapture Methods Field Exercise # 1 Estimating the population size of a mobile animal: Water striders (Gerris sp.) Gerris sp. (Hemiptera: Gerridae) is an abundant water strider in Illinois. Gerrids live on the water surface, preying upon organisms caught in the surface film or emerging through it. In western Illinois, gerrids overwinter as adults in leaf litter or protected vegetation along the banks of streams. We will carry out a mark-recapture study of gerrids on South Creek or Snake Den Creek at Green Oaks to address the following question: What is the size of the population of water striders living in the section of stream that we sample? As you watch and chase gerrids, keep other questions in mind, e.g.: Are gerrids actively selecting certain types of microhabitats? If so, why? How could you test hypotheses your observations have suggested? Today we will capture and mark as many gerrids as possible from within a reach of South Creek and/or Snake Den Creek at Green Oaks. You should divide into groups of about 4 to 5 each. Two people should take turns netting the gerrids, and storing them in inflated ziplock bags which contain a little stream water. Pass these bags to the rest of the group who will mark the water striders. The markers will count all water striders captured and paint small dots of "white out" on the backs of the water striders (make sure not to mark their stomachs). At the end of the afternoon the water striders will be returned to the area of the stream from which they were captured. We hope to mark about 200 individuals. On next Thursday we will return to the stream section we sampled and capture as many marked and unmarked gerrids as possible. Keep all the water striders in inflated ziplock bags until the end of the exercise to minimize double counting. Record the number of marked and unmarked individuals. Data Analysis 1. We will compute the estimated size of the gerrid population using Petersen's index for mark - recapture studies. Petersen developed the method as part of a study examining recaptures of marked fish in Denmark. Interestingly, the first known use of markrecapture methods was done to estimate human population size in London in the 16th

2 2 Century. Apparently, people were marked with chalk and counted when encountered again. Before discussing the method, we need to consider the assumptions of the Petersen index. In order for the method to provide an accurate estimate of population size, the following assumptions must be met: 1. The population is closed, so that N (the actual population size) does not change during the course of the study. In other words, we assume there are no changes in the population due to births, deaths, or movements of the animals during the study. For this to be a reasonable assumption, the population must be sampled at short time intervals. 2. All animals have the same chance of getting caught in the first sample. 3. Marking individuals does not affect their later catchability. We also assume that marking individuals does not increase their risk of mortality. 4. Animals do not lose marks between the two sampling periods. 5. All marks are reported on discovery in the second sample. Here are the measurements we will make in the field: n 1 = number of individuals marked in the first sample n 2 = total number of individuals captured in the second sample m 2 = number of individuals in second sample that are marked From these measurements, we obtain an estimate of: N = size of population at time of mark - recapture study We can estimate N by using a proportionality argument: N = n 2 n 1 m 2 this can be rearranged to: N = (n 1 )(n 2 ) m 2 We could calculate N using the above formula, which is the original Petersen index. Unfortunately, further study has shown that the original formula tends to overestimate the true population size, so instead we will calculate N using a modified equation which has been shown to be an unbiased estimator of N:

3 3 N = (n 1 + 1) (n 2 + 1) - 1 (m 2 + 1) 2. After we calculate N, we need to ask ourselves how reliable are these estimates of population size? To answer this question, a statistician constructs confidence intervals around the estimate. A confidence interval is a range of values which is expected to include the true population size a given percentage of the time. Typically confidence intervals are calculated for 95%, so that 95% of the time your confidence interval would include the true population size. The high and low values of a confidence interval are called the confidence limits. Clearly, we want the confidence intervals to be as small as possible (small in range) so that we have a better estimate of the true population size. Confidence intervals are an important guide to the precision of our estimate. If a Petersen population estimate has a wide confidence interval, we should not place too much faith in it. Often a larger sample size that includes a high percentage of recaptured individuals will provide narrow confidence intervals. There are several methods with which to construct confidence intervals. We will concentrate on one of them developed by Greenwood and Robinson. I have included the example labeled Box 3.4 (from Sunderland 2006) showing how to calculate the confidence intervals. First calculate P: p = m 2 /n 2 Then we calculate two values W 1, W 2 : W 1, W 2 = p + [1/(2n 2 ) { square root p(1-p)(1-m 2 /n 1 )/(n 2-1)}] W 1 = higher value; W 2 = lower value Then Lower Confidence Limit (LCL) = n 1 / W 1 Upper Confidence Limit (UCL) = n 1 / W 2 3. For this lab exercise, you will: A. Calculate estimated population sizes (N) for the water striders in South Creek at Green Oaks using the unbiased estimator of the Petersen Index. B. Calculate confidence intervals for both estimates of population size, using the formula given in Box 3.4. C. Calculate the relative precision of the estimate the quantity Q explained in Box 3.4 so Q = 200 (square root N/n 1 n 2 ) D. Present the data in either table(s) or figure(s).

4 4 E. Discuss the data obtained in the study. F. Present hypotheses and possible explanations for why water striders are present in certain portions of the stream. References: Greenwood, J.J.D. and R.A. Robinson General Census Methods in Ecological Census Techniques: A Handbook. 2 nd.ed. ed. by W.J. Sutherland. Cambridge University Press. pp

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