BIOL 217 ESTIMATING ABUNDANCE Page 1 of 10

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1 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.

2 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

3 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.

4 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

5 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.

6 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 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.

7 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 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?

8 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 BLUE LINE 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?

9 RANDOM NUMBER TABLE

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