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Part 2: ARTIFICIAL POPULATIONS

Part 2: ARTIFICIAL POPULATIONS
(1) Petersen Method:
We will use mark-recapture techniques to estimate the number of marbles in a bucket (known to contain 1000 marbles). For this experiment 400 of the marbles are 'marked' (M) (=one colour), wheras the other 600 are unmarked (a different colour). You will sample this bucket using two different sampling sizes (400 and 50), and with and without random mixing. The four combinations of these two factors are labelled a1, a2, b1 and b2 in the text below:
(a.1)
• Mix the marbles thoroughly before you sample
• Take a haphazard sample of 400 (C) marbles from the bucket.
• Then count how many are marked (R). Write this down.
• Return all the marbles to the container (except on third time you repeat this: see a2)
Repeat this sample of 400 for a total of three times.

(a.2)
Following your third sample of (a1), return the marked marbles to the bucket last.

• Without mixing before you sample, take a haphazard sample of 400 marbles
• Then count how many are marked (R). Write this down.
• Return all the marbles to the container

Repeat this sample of 400 for a total of three times.

(b.1) Follow the instructions for a1, except make your sample size (C) = 50, not 400. Again, you will repeat for a total of three times.
(b.2) Follow the instructions for a2, except make your sample size (C) = 50, not 400. Again, you will repeat for a total of three times.
For your lab report, calculate the estimated population size and its 95% confidence limits for each of your nine samples. You can do this later, so that you don’t run out of time to do the rest of the practical work.
Note that this is sampling without replacement. What does this mean? It means that you do not pick up a single marble, record if it is marked or not, return it to the bucket before picking up another marble. If you had done this, it would be called “sampling with replacement”. Instead, put the marble aside! With this sampling protocol, there is no chance of recording the same individual marble multiple times. Obviously, at the end of the sample period, with or without replacement, the marked individuals all end up back in the population.
(2) Schnabel Method:
This is a technique applicable to a multiple census over a short time period when the population can be assumed to be constant in size. A supply of artificial "animals" is provided in the form of dried white beans. Count out a known population of 200 beans.
• Sample the beans by removing a small sample of 10-30 beans (Ct).
• Count the number of beans that are already marked in this sample (Rt)
• Mark the beans that are not already marked (Ut). Note that in the first sample there will be no marked animals. If you find you have some marked animals in the first sample you are doing something wrong!
Also note that

for this population with no accidental deaths. Follow this sequence:
MIXING — SAMPLING — COUNTING MARKED AND UNMARKED — MARKING — RETURNING ALL BEANS TO THE POPULATION
and repeat for a total of 7 times.
For your lab report (ie. do this later): Tabulate your data as shown in Table 2.2 (page 36 of Krebs, 1999) and calculate the estimated population size and its 95% confidence limits using both the original Schnabel estimator and the Schumacher-Eschmeyer estimator.
Be sure to follow the sequence listed above!
(3) Jolly-Seber Method:
This technique is applicable to open populations which are sampled many times over a long time period. We will apply the method to three artificial populations (our friends the beans) with known parameters. One population is constant in size, one is declining, and one is increasing. In every case the sequence of operations is as follows:
MIXING — SAMPLE RANDOMLY — COUNT MARKED AND UNMARKED AND RECORD WHEN LAST MARKED — MARK ALL BEANS — RETURN ALL BEANS — MIX —- REMOVE RANDOMLY (=natural mortality) — ADD UNMARKED BEANS (=births).
The 'remove randomly' represent emigration and mortality from predation, disease, bad weather, etc. and these beans are thrown away because in the real world you would never see these animals. The 'add unmarked ' represents births and immigration.
In each experiment the population size, survival rate and dilution rate are known for each sample time. You can thus compare the estimated population parameters from the Jolly-Seber model with their known values.
Note that the sequence above will be repeated 7 times for each population, representing seven different months of sampling.

Each group will do one of the following three experiments:

Exp # Starting Population Time Sample Remove Add Unmarked Size Size (Deaths) (Births)
# 1
200 1 60 40 40
2 60 40 40
3 60 40 40
4 60 40 40
5 60 40 40
6 60 40 40
7 60 - -
----------------------------------------------------------------------------------------------------------------------
# 2
200 1 60 40 0
2 60 32 0
3 60 26 0
4 60 20 0
5 60 18 0
6 60 13 0
7 51 - -
----------------------------------------------------------------------------------------------------------------------

Exp # Starting Population Time Sample Remove Add Unmarked Size Size (Deaths) (Births)
# 3
10 1 4 1 9
2 8 2 16
3 13 3 29
4 25 6 52
5 45 10 94
6 50 19 169
7 50 - -

Record your data as you proceed in the form of Table 2.3 (page 43), filling in one column of the table for each of the seven samples.

Exchange your data with that of two groups who did the other experiments. You will analyze the results for all three experiments as follows.
Use the Jolly-Seber model to estimate population size, probability of survival, and number of new recruits added for each of the sampling periods. Calculate the 95% confidence interval only for the estimate of population size (follow the complex formula on p47 of Krebs using Excel).
YOUR DISCUSSION IN THE COMBINED REPORT ON THE ARTIFICIAL AND CRAB POPULATIONS SHOULD INCLUDE, BUT NOT BE LIMITED TO ANSWERS TO THE FOLLOWING QUESTIONS (AS WELL AS THOSE AT THE END OF THE CRAB LAB):

1. What sample size should you use in the Petersen method to obtain accurate estimates of population size for our marble population? see p 29-32 in Krebs.
2. Do the confidence limits for the Petersen and Schnabel data on the artificial population all overlap the known value of N? Why or why not?
3. What level of accuracy has been achieved for the three sampling experiments? What effect has sampling as in a.2 and b.2 (without mixing) had on accuracy and precision of your estimates? When using mark-recapture techniques on biological populations, what analogous situations might arise that have a similar effect on estimates of N? (you will want to read Chp 2 in Krebs to answer these questions)

REFERENCES
Carothers, A.D. 1973. Capture-recapture methods applied to a population with known parameters. J. Anim. Ecol. 42: 125-146.
DeLury, D.B. 1968. the estimation of population size by a marking and recapture procedure. J. Fish. Res. Bd. Canada 18:19-25.
Manly, B.F.J. 1971. A simulation study of Jolly's method for analyzing capture-recapture data. Biometrics 27: 415-424.
Robson, D.S. and H.A. Regier. 1964. Sample size in Petersen mark-recapture experiments. Trans Amer. Fish. Soc. 93: 215-226.
Roff, D.A. 1973. On the accuracy of some mark-recapture estimators. Oecologia 12: 15-34.
Seber, G.A.F. 1982. The Estimation of Animal Abundance and Related Parameters. 2nd Ed. Griffin, London. Chapters 3-5.



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