Bunker Hill Community College Simulation of Estimation of Population Size Paper


BEFORE YOU BEGIN: Review, in depth, the document in “General Course Information” titled “How to Write Your Lab Report”. In addition, review the examples provided, and make use of the template that is found in that area. In order to be considered complete, all lab reports must include the required five sections (intro, objectives, hypothesis, results, and discussion). And lastly, consider the depth and substance of the discussion sections in the examples provided. You are expected to include the same level of depth in your own discussion section.IntroductionIf you were to go into an ecosystem, lets say a field, and then you spent some time trying to capture a few organisms, let’s say crickets – it is very unlikely that you caught all of the crickets in that field. The fact is you caught some fraction of the entire population of crickets in the area.You can think of it like a fraction:Let’s call the entire population N.Let’s call the number caught n1.So, we get:number of crickets caught (n1) / the entire cricket population (N)Now let’s pretend that you put a small paint mark on the crickets that you caught and then put them back where you caught them. The next day you go out and catch some crickets again. You will probably catch some that you marked with paint and some new ones. The number of marked (recaptured crickets) compared to the total number of crickets that you caught on the second try is a fraction:Let’s call the total number of crickets caught on the second day n2Let’s call the number of marked or recaptured crickets RAs a result:marked or recaptured crickets on 2nd day = Rtotal number of crickets caught 2nd day = n2In most cases the ratio of R/n2 is similar to the n1/N. So the ratio of recaptured crickets to total number of crickets caught on the second day is similar to the number of crickets caught on the first day compared to the total number of crickets in the area sampled (or cricket population).By combining the fractions we getN = ( n1· n2)/RN = total populationn1 = total organisms captured on the first dayn2 = total organism captured on the second dayR = total number recaptured organisms on the second dayIf we capture organisms one day, mark them, release them, then go back on a second day and capture organisms again we can use the formula above to estimate the entire population of that organism in the area.Let’s use our crickets as an example.ExampleDay 1: We capture 23 crickets in 4 m2 area (this is our n1) – we mark them with a little dot of painton their backs – we let them go in the same place where we caught them.Day 2: We go to the same 4 m2 plot. We catch 21 crickets (this is our n2). Of the 21 crickets we catch on this day 10 are marked with little a paint dots. Thus, we recaptured 10 crickets (this is our R).We use the formula to estimate the number of crickets in our plot:N = (n1· n2)/R = (23 x 21)/10 = cricket population is 48.3 crickets/ 4m2Required MaterialsPart 1 – One or two sheets of paper.Part 2 – meter stick or tape measurewhite out or painttoothpickscissorsProcedureHere you will create a pretend population of animals (small squares of paper) and then simulate the capture recapture method of estimating populations. You will be using the capture recapture formula (seen above) three times and then taking an average.Getting StartedFirst you will make your pretend animal population.Using scissors and a piece of paper, cut out 200 small squares (2cm X 2cm). The squares do not have to be exactly the same just make sure you have 200 of them.Spread the square out evenly over a table surface.The table surface will be acting as the ecosystem sampling area and the squares are your pretend animals.Part 1: Simulating the capture of animals day 1 (getting n1)After spreading the squares out close your eyes and randomly put one hand down on the surface of the table.Pick up all of the squares underneath your hand and place them on the side.Do this two more times in different locations.Count up the total number of pieces of paper you have sampled (three tries).This will represent the captured animals on day 1. Record this number as n1.Part 2: Simulating the recapture of animals day 2 (getting n2 and R)With a pen put a #1 on all of the pieces of paper, then return then to the table.Mix all of the paper pieces together (the ones mark with #1 and the ones that you did not pick up) and spread them out again on the table surface.Once mixed, randomly select your paper animal squares again as you did before.Count up the total number of captured pieces of paper on this second try – record this number as your n2.Then count how many of the pieces picked up this second time have the #1 on them.Record them as recaptured animals or R.Part 3: Estimating the population of your paper square animals.Using the formula for estimating the population (shown above) calculate the N -population of paper animals.n1 = number of pieces of paper capture on the first try (three handfuls)n2 = number of pieces of paper captured on the second try (three handfuls).R = the number of n2 pieces that were marked #1.Calculate the population of your paper bugsN = n1· n2 / RRecord your estimated population.Now repeat the procedures followed to estimate the population two more times (remember you don’t have to really wait 24 hrs between n1 and n2, this is just a simulation).Average your three population calculations.Results SectionUsing a table or just text, write out the data collected for the paper simulation portion of this lab.Include, the your n1, n2, R and N for each of your trials.Then calculate the average N for each of the trials.Discussion SectionLook at the following questions and be sure to include them in your discussion section.Did the mathematical estimate of population come out close to 200? Why or why not?In the real world with real animals what factors might influence this type of capture recapture calculation?Why would we even need mathematical formulas to calculate population?Remember in this simulation you created the animals and already knew the population. Would this happen in the real world?

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