A large lake contains an abundance of rainbow trout. You capture 75 trout, tag and then release them. You then capture another sample of 200 trout. Of the 200 trout in this second sample, 15 have tags.
a) Estimate the number of trout in the lake using the mark-recapture technique.
b) What assumptions do you make when using the mark-recapture technique? state 2 assumptions and explain why they are important.
Answer to question 1
Question: a) Estimate the number of trout in the lake using mark-recapture technique.
Explanation: Let, calculate by The Lincoln – Petersen method:
N = Number of animals in the population =?
n = Number of animals marked on the first visit=75
K = Number of animals captured on the second visit=200
k = Number of recaptured animals that were marked=15
Estimated population size is,
Question: b) What assumption do you make when using the mark-recapture technique?
State at least 2 assumptions explain why they are important.
The Lincoln Petersen method (Petersen Lincoln index / Lincoln index) can be used to measure population size if only two visits are made to the study area.
1. This technique assumes that the study population is “closed”. Videlicet, the 2 visits to have a look at place are near sufficient in time in order that no individuals die, are born, or pass into or out of the study area between visits.
Importance: Individuals with marks have the equal opportunity of survival as other members of the population. It is critical to pick out a marking method that does not harm your animal.
2. The model additionally assumes that no marks fall off animals between visits to the field site by way of the researcher, and that the researcher expertly records all marks.
Importance: Births and deaths do no longer occur in good sized numbers among the time of release and the time of recapture. If marked animals die and are replaced with newborns, then you will recapture few or no marked animals, and your estimate will be too disproportionate This is not a huge difficulty in research of box turtles, but can considerably have an effect on estimates for expeditiously breeding organisms.
Answer to question 2
Number of samples captured and tagged, M = 75
Number of samples captured second time(with and without tags), C = 200
Number of samples recaptured (with tags) = 15
According to Mark-recapture technique,
Estimated number of individuals,
If any of the assumptions are violated, it may change the accuracy of the estimated population.
1. If there is no marked individuals in the recaptured samples, R = 0 and the result is undefined, mark more individuals and try again.
2.There should not be immigration into or emigration out of the population.
3. There shall be no mortality between the marked and the recaptured times.
4. The mark must not get washed away or wear off.
Answer to question 3
Whenever there are limitations in counting the population directly, such as in fishes or frogs or highly motile creatures, various methods have been developed to do an estimation of the population. One such method is the mark-recapture technique which gives very reliable and reproducible results when done correctly and if the assumptions hold good for that period of estimation.
The given data is:
N = Population = ?
M = Population Marked = 75
S = Sample size of second capturing = 200
R = number of marked trouts recaptured = 15
The formula to be used is:
Rearranging it for the unknown (N)
Thus the estimated population of trout by the mark-recapture method is 1000 trouts.