BIOL 475 Lab 3: Estimating Population Size                                                      Fall 2009

 

Introduction

 

        The size of a population is one of its most important attributes.  Population size has critical consequences for potential rates of evolution (gene flow, founder effects, etc.) and vulnerability to extinction. The ability to measure population size strongly influences our efforts to assess the impacts of various environmental factors (abiotic, biotic, natural or anthropogenic).  In addition, knowing the relative abundance of species in a habitat can give us some important information about community structure. Finally, observing the changes in populations of organisms through time yields insight into the natural variability inherent in populations and the ability to identify trends through time in response to external forcing agents. Population size can be expressed as the absolute number of organisms in an area under consideration (such as the number of squirrels on the College campus), or, alternatively as population density (the number of squirrels per unit area, such as 2 squirrels per tree or 20 squirrels per 100m2).

        Although it is extremely important to know the population size of the organism(s) under study, measuring it presents a number of problems. First, organisms differ in their level of detectability (how easy it is to find them), either because of their behavior, size, coloration, or habitat. In general, in natural systems, it would not be practical to attempt to count every individual in the system. Even when the U.S. government spends tens of millions of dollars to conduct a national census to estimate the size (and character) of the human population, the raw counts are often not accurate. Ecologists usually need to gather this kind of information with tens of dollars. Therefore, we must resort to estimating population size through sampling. There are a variety of different methods to do this, each with associated assumptions. The best estimates are those for which you can calculate a measure of certainty—a confidence interval—to give you an idea of how accurate your estimate is. Ideally, we use a 95% confidence interval, which identifies the spread, or range of values between which we are reasonably certain lies the ÔtrueÕ population size. If we were to sample this same population again and again, each time calculating an estimated population density, then 95% of these samples would estimate the population size to be within the confidence interval. This gives us an indication of how close we probably are to a real measure of population size. It tells us how ÒgoodÓ our estimate is. In general, the larger the sample size we take, the better is our estimate of true population size.  In designing a sampling method for collecting data, we try to use a sample size that gives us a reasonably good estimate of population size but which minimizes the effort or expense needed to make the sample.

        Because there are so many different kinds of organisms, each with its own behavior and natural history, estimating the size of a population in nature takes planning, effort, and ingenuity. It also requires that you know something about the basic biology of the organism you are measuring. Different sampling methods are appropriate for organisms that are stationary (such as plants or intertidal invertebrates) and for those that move (most terrestrial and aquatic animals). For stationary organisms, sampling usually involves the use of permanent quadrats, or sampling enclosures, which are randomly placed in the population, and within which the number of organisms is then counted at intervals.  Mobile organisms can also be censused by using sampling quadrats, by trapping animals, by spending a certain constant amount of time searching through the habitat, or by various other means. Once again, the main goal of an ecologist is to determine the most accurate method to use that best suits the organism and the resources available to the ecologist.

        In this weekÕs lab, we are going to estimate the population size of grasshoppers inhabiting an old field. Grasshoppers will be our focal organism because they are present in high numbers, are relatively easy to catch, are unlikely to leave the field in three days and they donÕt bite or sting! The old field we will be sampling in is a habitat island, in that it is surrounded on all sides by areas unlikely to be appealing to grasshoppers. We are going to use and evaluate two different methods to estimate population size: mark-recapture and depletion, sometimes known as Ôcapture per unit effortÕ. I guarantee that assumptions will be violated! But, the key in ecology is to violate as few assumptions as possible, while analyzing how these violations might affect the outcome.

 

 Methods: Estimating Population Size in Mobile Organisms

 

I. Mark-Recapture Method

 

        The simplest form of this method is called the Lincoln-Peterson Index. It consists of taking a random sample of individuals from a population, marking the individuals, and releasing them back into the population. After an appropriate amount of time (which will depend on the biology of the organism), a second sample is taken and the number of marked and unmarked individuals in the second sample is counted. If certain assumptions are met, then the proportion of marked individuals in the second sample is an estimate of the percentage of the total population that comprised the initial sample. For this method to yield a reliable estimate, the following assumptions must be met:

 

a)       Marked and unmarked individuals mix randomly after the first capture

b)       The population is closed (no emigration or immigration & no births or deaths)

c)       All individuals have an equal probability of capture

d)       All sampling is done at random.

e)       Being captured once does not affect the probability of being captured again later.   

 

II. Depletion Method

 

        The depletion method is based on the idea of diminishing returns, and makes the same assumptions as the mark-recapture technique. If successive collections are made from a population and the individuals collected are not returned to the population, then a gradual decrease in the population size will result as individuals are removed. If the same effort is made to capture organisms during each collecting period, then a gradual decrease in the number collected will also occur. If the number caught during each sampling period is plotted as a function of the cumulative number collected, then the points theoretically should fall along a straight line (see below). We can use this line to predict how many individuals would have been accumulated had we been able to capture every one. The point on the line where the catch per unit effort equals 0 corresponds to the value of X where all members of the population have been captured, i.e., the estimated population size, N. This is shown on the following graph:

 

                       

 

 

                                    Catch per unit effort plotted as a function of the

                                    cumulative number collected prior to the current sampling period.

 

                                   

Sampling Procedure

 

Although we will calculate our estimates of the grasshopper population size separately for each method, we will partially combine the sampling effort to maximize our sampling efficiency (i.e., get the largest sample in the shortest amount of time). To accomplish this, we will mark off two sets of three 5 X 5 meter sampling quadrats. The locations of these quadrats will be randomly determined. Once the locations are decided on, a barrier to immigration and emigration will be constructed using 8 bamboo polls, bridal veiling, and a few binding clips (if you canÕt do an ecological study with materials bought at exclusively at a discount store, then youÕre doing something wrong). Once the structure is complete, students in each group should identify a pair of grasshopper catchers, a data-logger, and a team of grasshopper markers.

 

For sampling done within the quadrats as part of the depletion method, the unit of effort we will be using for this exercise is hand collection (with optional butterfly nets) over 15 minute intervals. During this time, all grasshoppers encountered by either of the two collectors will be caught and placed in a ziplock bag. At the end of the 15 minutes, collection will cease and the collectors will hand the bags to the data-logger, who will count and record the number of grasshoppers, and pass them to the marking team. The marking team will carefully transfer the grasshoppers to a marking chamber (plastic box) and apply a touch of white-out to the thorax of the animal. Marked grasshoppers will be placed back into their original ziplock bags. This procedure will be repeated a minimum of 4 times. Once the four collections have been collected, counted and marked, we will dismantle the enclosures and release the marked individuals back into randomly selected locations in the field.

 

As a class, we will conduct an immediate recapture effort once the grasshoppers are released. Students will spread out and catch as many grasshoppers as we can in the time we have. Be careful not to TRY and get marked individuals; instead, go for whatever individuals you come across. Our goal is to measure the proportion of individuals in our sample that are marked. I will attempt to repeat this the recapture on Monday afternoon if I can round up some help. The justification for doing the recapture twice is that we will most likely be violating assumption (b) stated above. Although I chose this field because it is surrounded by unlike vegetation  and so is effectively a somewhat closed system, we cannot prevent deaths from occurring over the course of even 2 days (i.e., some of these grasshoppers will be eaten by SOMETHING). In this case, we may be violating assumption (a), as the marked grasshoppers may not be randomly dispersed among the population. Still, the difference between these two recapture attempts should tell us some interesting things.        

 

Estimating Population Size

 

I. Mark-Recapture. Because (hopefully) two separate recapture attempts were performed, we will have two separate population size estimates. Each should be calculated as follows.

 

        The raw data for the calculations are as follows:

            M        = number of individuals marked and released in the initial sample.

            C         = total number of individuals captured in the second sample.

            R         = number of marked individuals recaptured in the second sample.

 

        The population estimate is based on the assumption that, if we mark a certain proportion of the population, we should recover an equivalent fraction of marked animals at a later sampling time. If, at the second sampling interval, 12% of the animals we capture are marked, and if (as the assumptions above state) every animal is equally likely to be captured, then we can assume that, in our first census, we marked that same fraction of the total population.

 

                                    M/N = R/C                                                                               

 

        By rearranging this equation, we obtain the Lincoln-Peterson Index, which gives us an

 estimate of population size (N):

 

                                    N = MC/R                                                                              

 

        Confidence intervals for N are calculated as follows. Let us define the following variables:

 

            p          = decimal fraction of marked animals that were in the second sample.

                        = R/C

 

            q          = decimal fraction of unmarked animals that were in the second sample.

                        = 1-p

 

        Then, the 95% Confidence Interval is expressed as:

 

                        95% C.I. = p ± 1.96                                                               

 

 

        We can say, therefore, that this interval will include the true proportion of marked individuals 95% of the time.

 

                        ( p - 1.96 ) and  ( p + 1.96 )                                     

 

Similarly, we can be 95% sure that the actual population size lies within the range,

 

                        (N - 1.96 N) and  ( N + 1.96 N)      

 

 

II. Depletion Method

 

        The four values you obtained by sampling (the catch per unit effort) are to be plotted as Y values. The cumulative numbers of grasshoppers collected in all the samples up until that time (i.e, the total number of grasshoppers removed from the population in all the samples prior to the current sample) are to be plotted as X values. In the first sample, Y will be the number of grasshoppers you sampled in the first 15 minute increment, and X will be zero (since, prior to this sample, no grasshoppers had yet been removed from the population). In sample 2, Y will again be the number captured in that second sample interval, and X will be the number of grasshoppers removed from the population in all the previous samples (in this instance, those taken at sample 1).            Theoretically, we expect the values of Y to decrease linearly as X increases. This means, biologically, that as we remove more and more individuals from the population (X increases), the number of grasshoppers we encounter in each successive unit effort should decline (Y decreases; i.e., the points should lie along a straight line).  However, because of sampling error, the relationship might not be exactly a straight line; there will be error around the predicted line. Plot the data points for each of the study quadrats, fit a straight line to the data and calculate the x intercept when y = 0 (see figure above). [hint: use Excel to fit a line to the data. Then, once you have the equation for the line, you can solve for x] Biologically, this method says that, when we have removed so many organisms from the population that we do not capture any more in a sampling interval, we have essentially collected all the individuals in the population- and this is, by definition, the population size. So when the catch per unit effort is 0, the cumulative prior catch is an estimate of N.

 

Because we used quadrats for this method instead of sampling the entire field, the population estimate will actually be for the quadrat (25 square meters). Therefore, we must scale our estimates up to match the entire area of the field, partially using the technique of proportional sampling. This method works only if you know the size of the range of the population (Rp), and assumes that individuals are uniformly distributed throughout the populationÕs range. The formula we will use to estimate the population of the field (Np) is:

 

Np = (NsRp)/Rs

 

Where Ns is the number of estimated individuals in our study plot, Rp is the range of the population (size of the field) and Rs is the area of the study plot (25 square meters).

 

Once you have calculated the six estimates of the population size of grasshoppers in this field, calculate the mean and the 95% confidence interval about the mean [hint: the 95% confidence interval in this situation is calculated as 1.96*(the standard deviation)].

 

Assignment due Friday October 2

 

1.     Calculate the Lincoln-Peterson Index using the class recapture data (to be posted by Tuesday morning) along with the 95% confidence intervals. This will give you an estimate of the number of grasshoppers in the field. Based on the characteristics of the field we sampled in, which assumptions do you think were violated most significantly and what effect do you think this might have on our population estimate?

2.     Calculate Np using the Depletion Method described above based on the data from ONE quadrat. Which assumptions of this method do you think were violated most significantly in our sample and what effect do you think this might have on our population estimate?

3.     Which method do you think gives the most accurate estimate of population size for this particular field?