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					                            POPULATION DENSITY LAB
        Although density is usually an important population characteristic in ecological studies, it
is often difficult to accurately measure. There have been many techniques designed for
estimating population density, each with their own particular strengths and weaknesses. In this
lab, we will examine two techniques for density estimation: “mark and recapture” and quadrat
sampling. These are most appropriately used for mobile animal populations and sessile animal
or plant populations, respectively.

EXERCISE 1: Mark and recapture techniques

        In these techniques, a sample of organisms, usually mobile animals, is captured from the
population whose density we wish to estimate and an identifying mark is applied to them. In
practice, these marks can be of many types, including radio collars in large mammals, leg bands
in birds, fin clipping in fish, etc. The marked animals are released back into the original
population, and after a period of time a second sample is captured. The size of the population is
related to the fraction of individuals in the second sample which carry marks.
        Slightly different mark-recapture techniques must be applied to populations that are open
(meaning that individuals may migrate into and out of the population, be born, or die) or closed
(where the population does not change size during the study period). In this example, we will
examine the use of the Petersen technique, which is the simplest mark-recapture technique and is
used to study closed populations.

        In the Petersen method, the size of the population at the time of marking N is related to
three variables:

         N = C*M / R

where:          M = number of individuals marked in the first sample
                C = total number of individuals captured in the second sample
                R = number of individuals in the second sample which are marked

         To illustrate this, do the following:

Part 1
1. Grab several handfuls of beans (at least 100) and place then into a paper bag.
2. Mark 10 of the beans with a wax pencil so that you can clearly identify them as being
   “marked”. This is your initial marked sample, so M = 10.
3. Shake the bag and then withdraw 10 beans. This is your second sample, so C = 10.
4. Count the number of beans in the sample that are marked (= R) and record your answer in
   Table 1. Replace your beans into the bag.
5. Estimate the size of your bean population N by dividing M*C by the number of marked beans
   in your sample.
6. Repeat steps 3 through 5 nine more times and average the population estimates you obtained
   in each trial to get an overall population size estimate.
Part 2
    Repeat part 1 with the exception of taking 20 beans from the bag with each sample instead of
10. Thus, C for each pop. size estimate here will be 20 instead of 10.

Part 3
    Repeat part 2 after taking 10 unmarked beans from the bag and adding marks to them. In this
set of estimates, M = 20 and C = 20.

After you are finished, count the beans in your bag to determine the actual bean population size.

             TABLE 1: Petersen mark-recapture estimates for bean “population”
              C = 10                  C = 20                    C = 20
              M = 10                  M = 10                    M = 20
Trial         # of        Population # of          Population # of           Population
              marked      size        marked       size         marked       size
              beans in    estimate    beans in     estimate     beans in     estimate
              sample (R) ( = 100/R)   sample (R) ( = 200/R)     sample (R) ( = 400/R)

estimated      --------------              --------------              --------------
pop size


1. How did your various average estimated population sizes compare to the actual size? Which
combination of C and M gave you the best estimate? Which gave you the worst?

2. If you were trying to estimate the population density of a real species why might you have to
sacrifice some accuracy in your estimation?

3. What do you have to assume to be true in order to believe your estimates of population size?
What might happen in a real population of animals that would affect your results? (Give at least
two assumptions)
EXERCISE 2: Quadrat techniques

        For immobile animals or plants, our job of estimating density is made somewhat easier.
Here, we could simply count up the number of organisms within our known study area and
directly calculate the actual population density. In practice, however, it is usually impractical to
count an entire population, so we usually do counts in a number of replicated small areas known
as quadrats and use the average density in these quadrats as our estimated (but not necessarily
“real”) density.
        In deciding how to sample our population, we must make a couple of choices.
Specifically, we must decide:

         1. the number of quadrats we will sample
         2. the size of the quadrats used (e.g. 0.1 m2, 0.25 m2, 0.5 m2, etc.)
         3. where we will put the quadrats

Before proceeding, answer the following questions:

1. What would be the advantage of increasing the number of quadrats sampled? What would
be the disadvantage or cost of increasing this number?

2. What would be the advantage of increasing the size of quadrats sampled? What would be the
disadvantage or cost of increasing the size?

3. How should you arrange your quadrats? What would be the best method for determining
where they should be placed?

Part 1

1. Lay out a 10 meter transect in the study area
2. Within each 1 meter section lay out 3 10 by 10 cm (= 0.01m2) quadrats and count the number
   of acorns within each. Use the random number table to locate your quadrats within the
   section. As you count the acorns in each quadrat, keep track of the time it takes. Record your
   data in Table 2.
3. Repeat step 2 using 2 25 by 25 cm (= 0.0625 m2) quadrats instead.
4. Repeat step 2 using a single 50 by 50 cm ( = 0.25 m2) quadrat for each section
5. In Table 3, calculate (using Excel) the mean density per quadrat, the variance in density per
    quadrat, and the average time spent counting per quadrat for each quadrat size. To
    standardize your results on a per meter2 basis, simply divide your results per quadrat by the
    relative area – e.g.:

Mean number per m2 =            (mean number per 0.01 m2) / 0.01, or
                                (mean number per 0.0625 m2) / 0.0625, or
                                (mean number per 0.25 m2) / 0.25
For variances, the square of the conversion factor is used:

Variance per m2 =      (variance per 0.01 m2) / (0.01)2 , or
                       (variance per 0.0625 m2) / (0.0625)2 , or
                       (variance per 0.25 m2) / (0.25)2

                                   TABLE 2: Quadrat counts

Sample              # of plants Time spent # of plants Time spent # of plants Time spent
                    in 10x10               in 25x25               in 50x50
                    cm quadrat             cm quadrat             cm quadrat
                   Table 3: Average quadrat densities and time expenditures

                            10 by 10 cm               25 by 25 cm               50 by 50 cm
                            quadrats                  quadrats                  quadrats
Mean # / quadrat
Variance / quadrat
Mean # / m2
Variance / m2
Average time spent
counting quadrat

Part 2

Wiegert (1962) proposed that one method for determining optimum quadrat size was to
minimize the product:

         (relative cost of counting quadrat) * (relative variability for quadrat size)

We can calculate relative cost for each quadrat size by:

         Relative cost = (Ave. time to sample one quadrat) / (Minimum time for all sizes)

and relative variance by:

         Relative variance = (variance for quadrat size) / (minimum variance for all sizes)

Using these relationships, fill in the table below:

Quadrat size      Variance per      (1) Relative      Average time (2) Relative          Product of
                  m2                variance          cost         time cost             (1) * (2)

10 x 10 cm
25 x 25 cm
50x 50 cm

1. Looking at the variances alone, which quadrat size had the highest variance? Which had the
   lowest? By this standard, which would be the best quadrat size to use in counting this plant?
   (Think about the way t-tests work when answering this question!)

2. Using Wiegert’s method, which would be the best quadrat size? What tradeoff do you make
   when using this method?

3. Besides the time actually spent counting the quadrats and monetary expenses, what other
   “costs” might be involved in ecological studies that these calculations don’t take into
   account? How important would these be in designing a study?

4. What problems did you run into when using quadrats? Why might this method be a less than
   perfect way of estimating population density?

EXERCISE 3: Dispersion patterns

         In addition to giving us information regarding population density, quadrat studies can
also tell us something about the way the population is spatially distributed. In an evenly
distributed population, each quadrat should contain roughly the same number of individuals.
Thus the variability in the counts (as measured by the standard deviation or variance) should be
close to 0 and the ratio of variance/mean should be close to 0 as well. Conversely, some
quadrats scattered through clumped populations should have a large number of individuals (if
you happen to “hit” a clump), while others will have very few. Thus, quadrat counts for a
clumped population should have high variability and the ratio of variance/mean will be >> 1.
Randomly distributed populations follow a statistical distribution called the Poisson distribution
in which the variance of measurements is equal to the mean of the measurements. In this case
the variance in quadrat counts would be equal to the mean count and the ratio variance/mean  1.
Thus, we can determine the spatial pattern of a population simply by knowing the mean number
and variance found in counts of its density:

Variance/mean ratio           Dispersion pattern
       0                            uniform
       1                            random
       >> 1                          clumped

Using your quadrat counts above determine how the acorn population is distributed at different

Quadrat size       Mean density        Variance            Variance/mean       Distribution
10x10 cm
25x25 cm
50x50 cm


1. Would you expect the dispersion pattern you see in a population to change with quadrat size?
Why or why not? Give an example of how the dispersion pattern seen in a population might
change with scale.

2. What dispersion pattern did you find for acorns? Why did you see this pattern? What does
this mean for the tree?

3. Do you think the pattern you observed for acorns is the “real” pattern? What other factors
might be influencing the distribution of acorns? If you could measure the “real” pattern what do
you think it would look like? Why might it look this way?

Shared By:
Jun Wang Jun Wang Dr
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