BIOL 217 ESTIMATING ABUNDANCE Page 1 of 10 A calculator is needed for this lab. Abundance can be expressed as population size in numbers or mass, but is better expressed as density, the number of individuals per unit area or volume. For example, the population density of human populations is often measured in individuals per square kilometer. Zooplankton density might be better measured as individuals per liter. Because usually we usually cannot count all the individuals in a population, ecologists have devised many different methods to estimate population size or density. In this laboratory, we will examine some of these methods. You will do the sampling work in pairs. Absolute density is the actual number per spatial unit. When it is not possible to measure absolute density, we must settle for estimates of relative density, also called indices of relative abundance. Measures of relative density allow us to compare the relative sizes of different populations or of the same population at different times. Methods for Measuring Relative Density When information is needed about density, but it is not feasible to measure absolute density, it is often possible to assess relative density by one of several methods. If the main interest is in discovering whether populations are more abundant in one place than another or are increasing or decreasing over time, estimates of relative density can be sufficient. Sometimes a broader effort to establish relative densities across an area can be linked to a more limited effort to obtain absolute densities in a few locations. Such an approach can save a lot of time and money, although it might not be quite as good. NUMBER OF ARTIFACTS OR SIGNS - Examples are counts of bird nests, cicada exoskeletons, butterfly cocoons, crayfish chimneys, and fecal pellets for many animals. HUNTING, TRAPPING, AND FISHING RECORDS - Pelt records for animals sold by North American trappers go back over 150 years for some mammals. CATCH PER UNIT EFFORT (CPUE) - This method assumes that when organisms are more abundant, more will be caught for each unit of sampling effort. CPUE indices are used widely by fishery biologists to gauge trends in fish stocks. In fish studies, CPUE is often expressed as number of fish caught or weight per haul of a net. Relative abundance of insects on plants may be represented by insects per sweep of a net. The line transect method is a special case of CPUE. Nothing is caught, but animals are observed as the investigator walks at a constant pace along a line of predetermined distance. The assumption is simply that more animals will be seen when abundance is greater.
Methods of Measuring Absolute Density Total Counts Population size is determined exactly by counting all individuals. Total counts can sometimes be made for large plants, less often for territorial birds and lizards. Human censuses often attempt to reach total counts, but encounter many problems. Total counts are not possible for many mobile organisms, such as adult insects and vertebrates, or for organisms that are overwhelmingly abundant, such as bacteria and algae. Organisms that are cryptic (difficult to detect), such as camouflaged moths that look like bark and perch on trees, would be underestimated by total counts. The other techniques of estimating absolute density rely on small samples from which the density of the entire population is extrapolated. Quadrat (Plot) Sampling In this approach, all individuals in a manageably small region (called a quadrat) are counted. Strictly speaking, a quadrat is square, and typically it is, but the term quadrat is often used for a plot of any shape. For terrestrial organisms, quadrats are typically areas, but for aquatic species and soil organisms, they may be volumes. After many quadrats have been sampled, the average density for the entire area can be calculated. Suppose you counted 19 small beetles in a sample of 1/100 of a square meter. You could estimate the absolute density as 1900 per square meter. Actually, you would not have much confidence in this extrapolation unless you knew beforehand that density was constant in the area. To increase confidence, you would need to count beetles in lots of quadrats and use the average density for all quadrats as the estimate. Three things are required for quadrat sampling to give valid results: 1) The number of individuals in each quadrat must be counted accurately. 2) The area of each quadrat must be known. In practice, quadrats of equal size are usually used, but this is not necessary. 3) Quadrats must be representative of the area. If densities on the quadrats counted do not adequately reflect densities of the entire area, the extrapolation will be inaccurate. Representativeness is achieved by random sampling of the quadrats from the larger area. In random sampling, the entire area is first mapped into quadrats, each of which is assigned a number. A quick way to do that is to use a random number table (included here, but also found in many statistics books and computer programs.) to select which quadrats will be sampled. The crucial factor in random sampling is that each quadrat has an equal chance of being selected. This prevents biases of ecologists toward sampling mainly in areas of higher (or lower) than average density. A typical finding is that a species is more abundant in some habitats and microhabitats than others. If subregions are likely to differ in abundance, we can use stratified random sampling, in which the total region studied is divided into subregions, each of which is sampled randomly. Subregions may correspond, for example, to identifiable habitats, different
depths in a water column, or simply to spatially defined subregions. Stratified random sampling allows different estimates for the subregions and prevents areas from being overlooked. It is usually not possible to guess the number of quadrats needed to obtain a good estimate unless previous studies are available for the organism and its habitat. A practical method for determining the number of quadrats needed is to construct a performance curve. The cumulative average density is plotted against the number of quadrats sampled. For a small number of quadrats, the average density is liable to fairly large fluctuation, but the average density stabilizes as the number of quadrats sampled increases. When the density stabilizes, enough quadrats have been sampled to give a reasonably good estimate of absolute density. Quadrat Sampling Example The following exercise is designed to show how sampling accuracy improves with increased effort. A gridded figure with a bunch of dots will be projected on-screen. It shows the position of pill bugs (Armadillidium sp.), also known affectionately as roly polies, and less affectionately as woodlice, across a sampling area (like in an ivy patch ). The total sampling area has been divided into 80 quadrats of equal size (10 cm 2 ). In the upper left hand corner of each quadrat is its two digit identification number. We will sample this population, in one case using the random number table provided, you will pick a series of quadrats, count the number of individuals (dark dots) in each quadrat selected, and, using the worksheet below, collect some data and construct performance curves, adding a point for each quadrat sampled, and estimating density. In using a random number table, you would not want to start at the same point time after time. Begin by haphazardly selecting a two digit column and a row. The two digit number specifies the first quadrat to be sampled. The next quadrat sampled has the identification number equal to the two digit number in the same columns and the next lower row. Mark-Recapture This method is good for mobile and cryptic animals. Animals are caught, given permanent marks, released at the point of capture, and allowed time to resume normal activity. At some later time, animals are collected again from the same population. The proportion of marked individuals and the original number marked are used to estimate the size of the population. Alternative names for this method are capture-recapture and mark-release-recapture. Some common methods of marking are: turtles-notches in the margins of shells; lizardsclipping toes, series of color-coded beads tied to tail or shoulder, paint; fishelectrocautery, fin- clipping, tags; alligators-plastic tags on tail; birds-leg bands; and mammals-radio collars, ear tags.
Suppose we have marked and released animals and have made a second census in which both marked and unmarked individuals have been captured. To estimate the total population, we need to know only two things: 1) the proportion of the total population that is marked. 2) the number of marked animals alive at the time of the second census. If captures are made randomly with respect to whether an animal has been caught and marked before, a sample caught at any given time should have the same proportion of marked individuals as the entire population. Let M = number of marked individuals in the entire population, N = number of individuals in the entire population, R = number of marked individuals in the second sample, and C = total number of individuals caught in the second sample. R/C = M/N Due to random sampling effects, this equation only approximates equality. When would the equality be exact? The assumption that animals are captured randomly is crucial for estimating the proportion of animals marked. It means that marking does not affect the probability of capture. If this assumption is false, the estimate will be wrong. If animals are easier to recapture (trap-happy) than unmarked individuals, what does that do to your estimation? Under what circumstances might trap-happiness occur? The number of marked individuals alive in the population is harder to estimate than their proportion because the marked population can changes between sampling periods due to death and emigration. It turns out that there are many versions of mark-recapture estimation, and the basis for their variation often relates to ways of estimating the number marked and alive. For the simplest methods using only two censuses, marks need only indicate that the animals have been captured. Some of the more sophisticated methods require marks allowing recognition of each unique individual. The more complex approaches help to account for potential biases, some of which are mentioned above, but might include immigration, emigration, births, deaths, and variation in catchability. How are mark-recapture estimates related to total counts? If we make a total count, we know the population size exactly. In a mark-recapture census, suppose that we capture only one in 1000 individuals and only catch 20 individuals in each sampling interval. There is a good chance that we may not have any marked individuals in our second sample. It is easy to see that the population size would be overestimated. Also, the smaller the number of individuals captured in the second census, the more likely that there will be large deviations by chance alone from the true proportion of marked individuals. Thus, the larger the proportion of the population sampled, the better will be the Lincoln-Petersen estimate. At very high sampling percentages, a close
approximation to the total count can be obtained. Recall, however, that mark-recapture methods are used because total counts are not possible. There are many approaches to mark-recapture, but the simplest is the Lincoln-Petersen Method. While it is simple, it should impress upon you the basics of mark-recapture. There are only 2 censuses. First, animals are caught, marked, and released. A second sample is later caught and checked for marks. This method assumes that the population is closed. This means that it has no births, deaths, immigration, or emigration, no change in composition at all. Due to this limitation, the time between censuses must be short. Because the Lincoln-Petersen method assumes that no losses of marked animals occur between samples, we know M, the total number of marked individuals. Once we have the second sample, we also know the numbers of marked, recaptured (R) and total individuals (C) in the second sample. Only N is unknown, and can be calculated as CM N = -------- R This estimate of population size can readily be converted to density by dividing N by the area occupied. Suppose you sample bass in an 8 hectare pond and mark and release 20 bass. After a few days you sample again and catch 40 bass, of which 10 are marked. How many bass are in the pond? What is their population density? Lincoln-Peterson Method Example Place about 250ml of beans in a dish. Close your eyes and take a good handful out and put them on the bench top. Mark the sampled beans with a blue dot, count those beans and begin to fill out the table on your worksheet. Return them to the container and thoroughly mix the beans. Take a second sample. Record numbers of beans with and without blue dots. Calculate a Lincoln-Petersen size estimate for the whole bean population. Mark all the beans from the second beaker sample, even those already having blue dots, with a blue line before returning them to the container and mixing again. Take a third sample, recording the number of beans marked with the pattern for the previous sample. For the third sample, you would count only beans having a blue line as being marked. Those having only a blue dot would be considered unmarked for this sample. So - those having both a blue line and a blue dot would be counted as marked as if only having the blue line. Then mark all beans in the beaker with a dot of a different color.
Repeat this procedure until you have marked 10 beakers full of beans, using a color and line-dot combination unique to each sample. Finally, take an eleventh sample and use the results to calculate the tenth estimate of population size. If several Lincoln-Petersen estimates are made for a single population, we can use the mean of all estimates as the best estimate of abundance. Furthermore, we can calculate confidence limits for the estimate. We can obtain the standard deviation from: to get a measure of variation of all of the estimates around the mean. We can then divide that by the square root of the sample size to get the standard error of the mean (SE): It turns out that about 2/3s of all of the measures will be within 1 SE of the mean, and about 95% of them within 2 SE. To be precise, the 95% confidence limits of the estimate are given as + 1.96 SE (+ 2 SE includes 95.4% of the observations). Confidence limits (intervals) are a good way to depict variation in a way that is easily visualized and shows how confident we are about our measurements. They can also be used to quickly ascertain if two means are different if the means + SEs of two data sets do not overlap, they are probably significantly different.
Estimating Abundance Worksheet Name Lab (i.e., 1-3) Turn in this lab before you leave. Value: 10 pts. Quadrat Sampling Sample # From 00 From 79 Random 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 In the pill bug grid, starting with cell 00, count the sample number and enter into table to left. Do this for the first 15 cells. Do the same, but work backward from cell 79. Now, using the random number table, select cells randomly and sample 30 cells, entering the data into the table as above. Using the data you collected, build a graph, showing all three data sets. Make sure you label your axes and provide a caption. What do you conclude the density of these pill bugs to be per meter? How many quadrats were needed to get an accurate density? Did you encounter any problems with your sampling? What would your solution be? Mark-Recapture If previously marked animals are more prone to avoid recapture ( trap-shy ), what will that do to our population estimate? Show this using the mark-recapture formula. What would happen to your Lincoln-Petersen estimate if immigration were occurring?
Lincoln-Petersen Example Following the directions given in the lab, fill out the table below. SAMPLE MARK # MARKED RECAPTURED # SAMPLED ESTIMATED N 1 BLUE DOT ------ ------ 2 BLUE LINE 3 4 5 6 7 8 9 10 11 ------ Calculate the mean population estimate and the 95% confidence limits and show them here: Mean = + SE beans. Count all the beans in your population. What is it? Discussion - How does the total count compare with the Lincoln-Petersen estimate? Is the total count within the confidence limits?
RANDOM NUMBER TABLE 11164 36318 75061 37674 26320 75100 10431 20418 19228 91792 21215 91791 76831 58678 87054 31687 93205 43685 19732 08468 10438 44482 66558 37649 08882 90870 12462 41810 01806 02977 36792 26236 33266 66583 60881 97395 20461 36742 02852 50564 73944 04773 12032 51414 82384 38370 00249 80709 72605 67497 49563 12872 14063 93104 78483 72717 68714 18048 25005 04151 64208 48237 41701 73117 33242 42314 83049 21933 92813 04763 51486 72875 38605 29341 80749 80151 33835 52602 79147 08868 99756 26360 64516 17971 48478 09610 04638 17141 09227 10606 71325 55217 13015 72907 00431 45117 33827 92873 02953 85474 65285 97198 12138 53010 94601 15838 16805 61004 43516 17020 17264 57327 38224 29301 31381 38109 34976 65692 98566 29550 95639 99754 31199 92558 68368 04985 51092 37780 40261 14479 61555 76404 86210 11808 12841 45147 97438 60022 12645 62000 78137 98768 04689 87130 79225 08153 84967 64539 79493 74917 62490 99215 84987 28759 19177 14733 24550 28067 68894 38490 24216 63444 21283 07044 92729 37284 13211 37485 10415 36457 16975 95428 33226 55903 31605 43817 22250 03918 46999 98501 59138 39542 71168 57609 91510 77904 74244 50940 31553 62562 29478 59652 50414 31966 87912 87154 12944 49862 96566 48825 96155 95009 27429 72918 08457 78134 48407 26061 58754 05326 29621 66583 62966 12468 20245 14015 04014 35713 03980 03024 12639 75291 71020 17265 41598 64074 64629 63293 53307 48766 14544 37134 54714 02401 63228 26831 19386 15457 17999 18306 83403 88827 09834 11333 68431 31706 26652 04711 34593 22561 67642 05204 30697 44806 96989 68403 85621 45556 35434 09532 64041 99011 14610 40273 09482 62864 01573 82274 81446 32477 17048 94523 97444 59904 16936 39384 97551 09620 63932 03091 93039 89416 52795 10631 09728 68202 20963 02477 55494 39563 82244 34392 96607 17220 51984 10753 76272 50985 97593 34320 96990 55244 70693 25255 40029 23289 48819 07159 60172 81697 09119 74803 97303 88701 51380 73143 98251 78635 27556 20712 57666 41204 47589 78364 38266 94393 70713 53388 79865 92069 46492 61594 26729 58272 81754 14648 77210 12923 53712 87771 08433 19172 08320 20839 13715 10597 17234 39355 74816 03363 10011 75004 86054 41190 10061 19660 03500 68412 57812 57929 92420 65431 16530 05547 10683 88102 30176 84750 10115 69220 35542 55865 07304 47010 43233 57022 52161 82976 47981 46588 86595 26247 18552 29491 33712 32285 64844 69395 41387 87195 72115 34985 58036 99137 47482 06204 24138 24272 16196 04393 07428 58863 96023 88936 51343 70958 96768 74317 27176 29600 35379 27922 28906 55013 26937 48174 04197 36074 65315 12537 10982 22807 10920 26299 23593 64629 57801 10437 43965 15344 90127 33341 77806 12446 15444 49244 47277 11346 15884 28131 63002 12990 23510 68774 48983 20481 59815 67248 17076 78910 40779 86382 48454 65269 91239 45989 45389 54847 77919 41105 43216 12608 18167 84631 94058 82458 15139 76856 86019 47928 96167 64375 74108 93643 09204 98855 59051 56492 11933 64958 70975 62693 35684 72607 23026 37004 32989 24843 01128 74658 85812 61875 23570 75754 29090 40264 80399 47254 40135 69916