Lab 4. MARK-RECAPTURE SAMPLING

Transcription

1 Mark-recapture Sampling 1 Lab 4. MARK-RECAPTURE SAMPLING I. Introduction One of the most basic field problems in ecology is the determination of how many individuals of a species there are in a given area. The task of enumeration is relatively straightforward for nonmobile or sessile organisms. However, mobile organisms present a suite of problems for a researcher interested in ascertaining the abundance of these organisms. One method used to estimate population sizes is the capture-recapture or mark-recapture technique. The premise of this technique is that one catches a random sample of a population, marks individuals, releases them so that they remix with the rest of the population, and then catches a second random sample of the population. Population size is then estimated from the proportion of the second sample that bears a mark from the first capture period. Generally speaking, if the population is large, the marked individuals will have become diluted within it, and only a few would be expected to appear in the second sample. If assumptions about the sampling and animals distribution are correct, then the proportion of marked individuals in the second sample is the same as that in the entire population. II. Background Assumptions Like all estimation procedures, a number of assumptions must be met to validly use this method: 1. The two samples taken from the population must be random samples. That is, all individuals in the population have an equal and independent chance of being captured during the time of sampling. An adequate interval of time between captures must be given to allow dispersal of the marked animals throughout the population.. There is no change in the ratio of marked to unmarked animals. This means that during the time from initial capture to recapture, there must be no significant addition of unmarked animals to the population through births or immigration. 3. Similarly, population losses from mortality and emigration must remove the same proportion of marked and unmarked individuals. 4. Marking of individuals does not affect their mortality. 5. Individuals do not lose marks. It is called Peterson s method (Peterson 1896) by fisheries biologists, Lincoln s method (Lincoln 1930) by mammalogists and ornithologists, and the Lincoln-Peterson index by ecologists who are appreciative of the efforts of both contributors to this methodology. Surprisingly though, Peterson did not mean for it to be used for population-size estimation, and Lincoln was scooped by 13 years by another researcher, Dahl (LeCren 1965). III. Calculations Great, but how is this index calculated? Glad you asked. The total population may be estimated as follows:

2 Mark-recapture Sampling 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: M R (Equation 1) N n or N n (Equation ) M R Equation 1 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 the population. Equivalently, 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. Rearrangement of either equation yields the following; Mn N (Equation 3) R Example calculation Are you like me, would an example help solidify your understanding of the theory behind this method of population-size estimation? OK, suppose you take 100 white balls out of a pot having an unknown number of white balls, paint them black, return them to the pot, and mix all the balls in the pot thoroughly. If you then take 150 balls from the pot and find 5 of them to be black, then M 100, n 150, R 5, and the unknown total number of balls could be estimated using Equation 3 from above: N R Mn ( 100)( 150) balls However, Equation 3 may overestimate the population size (i.e., it is biased) when samples are relatively small (Chapman 1951). N C is a nearly unbiased estimate of population size if the number of recaptured animals, R, is at least 8 (Krebs 1989). This bias can be reduced by computing ( M + 1)( n + 1) Nc 1 (Equation 4) R + 1

3 Mark-recapture Sampling 3 From the example above with the white balls, ( )( ) Nc ,51 N C 1 6 N C N C balls The approximate variance, s, of this estimate is ( M + 1)( n + 1)( M R)( n R) ( R + 1) ( R + ) s (Equation 5) From the example above with the white balls, s s ( )( )( 100 5)( 150 5) ( 5 + 1) ( 5 + ) 14,978,15 18,5 s s 88.5 With the standard deviation, s, (simply calculating the square root of the variance, s ) 95% and 99% confidence limits on the population estimate are given by N (or N C ) (s) (95% confidence limits) (Equation 6) and N (or N C ) +.58(s) (99% confidence limits) (Equation 7) For the above example, the 95% confidence interval (CI) for N C could be calculated as 95% CI N C (s) (88.5) The 95% confidence interval (41.1, 759.1) Thus, we could say with 95% confidence that the true population size (total number of balls in the pot) is between 41.1 and balls. As you might assume, one generally can compare the similarity in population estimates between two populations (or two time periods for the same population) by simply calculating the confidence limits of an estimate for both populations and determining whether these limits overlap. If the confidence limits do not overlap, we generally consider them statistically different.

4 Mark-recapture Sampling 4 The precision with which the capture-recapture technique estimates population size is inversely dependent on the number of marked animals recaptured. Thus, attempt to obtain a reasonably large R by making n large. Several newer, alternative methods use theory and sampling procedures based on multiple markings and/or multiple recaptures for more complex study designs. These include the Schnabel method (relaxes single marking and single recapture assumption) and the Jolly-Seber method (relaxes closed population and survival assumptions). Keep in mind that a population estimate is different from a density estimate. How so? Density estimates refer to a number of individuals per unit area, so one must know the exact amount of area from which animals were trapped. This is a tricky proposition for live-trapping studies, as much research has shown that animals of different species, ages, or sexes may be drawn to traps to differing degrees. Thus, it is difficult to determine exactly how much area is being trapped. Population estimates simply yield a relative abundance or number of individuals per sampling effort (i.e., number/trapline or number/watershed). The data you will analyze for this lab are real data collected from an ongoing study on Konza Prairie. You will use raw data sheets from live-trapping of small mammals to calculate population estimates and confidence intervals, compare effects of a treatment (fire frequency) on abundance of small mammals, and determine whether this real-world example is valid in light of the inherent assumptions of the Lincoln-Peterson index. Brief explanation of the data sheets The six data sheets at the end of this lab are the results from live trapping done on the Switch Lines on Konza Prairie. The study site is two watershed treatment units (R01A and R0A) that bound each other in the southwestern corner of Konza. Unit R0A had been burned every spring from Unit R01A went unburned during that same time period (except for a wildfire in 1994). Beginning in 001, the treatments were switched on the two watersheds, with R01A being burned annually, and R0A no longer being burned. The data you will be using were collected on June 6 and 7, 001; exactly two months after the first planned burn on R01A in 0 years. Six traplines are located on the site; three in watershed unit R0A, and three in treatment unit R01A. Two of the traplines in each watershed have 0 stations each, whereas the 3 rd trapline in each has only 10 stations. Two large (7.6 x 8.9 x.9 cm) Sherman live traps were set at each station, for a total of 00 traps set across the entire site each night. Traps were baited with a kiss of peanut butter and rolled oats, a delicious concoction which rodents (and hungry graduate students) cannot resist. Most of the notation on the data sheet is selfexplanatory, but some parts require explanation. About 15 species of small mammals can be captured on Konza, but the following abbreviations will be most useful for this exercise: PL Peromyscus leucopus (white-footed mouse), PM Peromyscus maniculatus (deer mouse), SH Sigmodon hispidus (hispid cotton rat), and NF Neotoma floridana (Eastern woodrat). Mass is in grams. Toe clipping is a marking technique used to uniquely identify individuals, so each toe clip number identifies a different individual in the population.

5 Mark-recapture Sampling 5 Mark-Recapture Sampling Questions (0 pts. total) Due March 4, Give a population estimate and 95% confidence interval for all rodents (all species combined) on: a) the entire study site; b) each of the two treatment watershed units separately.. Give a population estimate and 95% confidence interval for only white-footed mice (Peromyscus leucopus) on the entire study site. 3. Give a population estimate and 95% confidence interval for only deer mice (Peromyscus maniculatus) on the entire study site. Note: you should not need to calculate anything new to answer this question. 4. Compare the total rodent abundance (all species combined) on the two watershed units. Does fire treatment appear to affect abundance of rodents in tallgrass prairie? How did you decide if differences were significant? 5. Were the assumptions of the Lincoln-Peterson index satisfied for this study? Related References Brower, J. E., J. H. Zar, and C. N. von Ende Field and laboratory methods for general ecology, 4 th Ed. W.C. Brown Publishing, Boston. Chapman, D. G Some properties of the hypergeometric distribution with applications to zoological censuses. University of California Publications in Statistics 1: Krebs, C. J Ecological Methodology. Harper Collins Publishers, New York. LeCren, E. D A note on the history of mark-recapture population estimates. Journal of Animal Ecology 34: Lincoln, F. C Calculating waterfowl abundance on the basis of banding returns. U.S. Department of Agriculture Circular No. 118:1-4. Peterson, C. G. J The yearly immigration of young plaice into the Limfjord from the German Sea. Report of the Danish Biological Station (1895) 6:5-84.