BY 450 - ECOLOGY SPRING 2005
LABORATORY EXERCISE
ESTIMATING POPULATION SIZE, DENSITY, AND DISPERSION
PART I - MARK AND RECAPTURE TECHNIQUES
In this exercise, we will employ the Lincoln-Petersen index to estimate population size using a mark-recapture technique. Given our constraints on time, the application of the techniques to a natural population will be difficult. We will, instead, use the technique to estimate the "population size" of peas in a fish bowl.
The procedure is quite simple. The first step is the collection of a sample of organisms from the population of interest. You will accomplish this by using the "pea sampler" provided. Mark the organisms (peas) collected in this sample by marking them on both sides with an indelible pen in such a way that you will recognize them when you see them again. Then return the marked organisms to the population (put the peas back in the bowl). Record the number of marked organisms, M1.
You must now allow time for the marked organisms to distribute themselves among the population. In fact, you will hasten the process by covering the bowl and shaking it vigorously for a few minutes. Then, collect another sample from the population of interest. Observe the organisms in your sample carefully. Record the total sample size (n) and the number of marked organisms (recaptures) in the sample (R). Then, use the Lincoln-Petersen method of estimating the population size:
Actually, statistical theory tells us that the estimate arrived at by this equation is slightly biased, i.e. it overestimates the population size. An unbiased estimate can be obtained as:
The standard error of the estimate can be calculated as:
Using this method, determine your estimate for the population size of peas in your bowl. Do this twice, once with a small "pea sampler" and a second time with a larger sampler.
Small Sample / Large SampleNumber of peas marked (M)
Number of peas in
second sample (n)
Number of marked peas in second sample (R)
Estimate of population size
Standard error for
estimate
95% Confidence interval for population size
(Estimate ± 2 S.E.)
Actual Number ______
Discussion: In the space below, discuss your results. How might they have differed if you had used a larger sampler? Smaller? What must be true about the “organisms” for this technique to yield accurate results?
PART 2 - ESTIMATE OF DENSITY AND DISPERSION USING QUADRAT SAMPLES
A primary focus of ecology is the abundance of organisms in their environment. Generally, absolute abundance is of less interest than density, the abundance of organisms per unit area or volume. There are many different approaches to the estimation of density. One of the most straightforward is the use of the quadrat sample.
On the map provided, each of the different symbols represents the stem of a type of plant. Stars represent starflowers, suns signify sunflowers, squares are a type of mint and triangles a type of sedge. You are to take random quadrats (Hint: use a random number table or a calculator) using the "sampler" provided. We will assume that these quadrats represent 1 m2. Count the types of each plant contained in the quadrat. Count the plant if more than half of the symbol is within the sampler. If it is split exactly, count it on the north and south side of the sampler, but not the east or west side. Take 10 quadrat samples, and record your data in the table below. For each species, calculate the mean density and the sample variance of the density. If you are uncertain how to do this, ASK!
Sample # / Starflower / Sunflower / Mint / Sedge1
2
3
4
5
6
7
8
9
10
SX
SX2
As discussed in class, the ratio of the variance to the mean is an indicator of dispersion. In random dispersal patterns, the variance and the mean are usually similar in magnitude. Organisms showing a uniform dispersion pattern usually have variances that are smaller than the mean, while the reverse is true of aggregated or clumped patterns.
For each of the species in this exercise, calculate the Var/Mean ratio, and record it in the space provided. Then discuss the significance of these ratios:
Complete the table below:
Mean density
Variance
V/M
Significance?
Now, for one species only (Starflower) employ a Poisson distribution to predict the number of quadrats containing a given number of flowers. Compare the expected number to the observed number. Finally, conduct a Chi-Square Goodness of Fit test to determine if the observed numbers differ significantly from the expected.
X / P(X) / Expected / Observed / C20
1
2
3
4
5
6
7
8
Discuss your results: