In the spring, a group of biologists caught and tagged 500 wolves in a wilderness area. These animals were then released. A couple of months later, 200 wolves were caught and 75 of them had tags. Estimate the wolf population in this wilderness area.
Please check if my solution is correct:
75/200 is the percent of wolves caught that had tags;
75/200=500/N
75N=200x500
N=1333.333
Thanks in advance.
Yes, your answer is correct.
To check, compare
75/200=0.375
500/1333.333=0.375
However, biologists use a more elaborate method to calculate.
The proportional method used above assumes replacement of the sample after each recapture, which is not (usually) the case. When the recaptured sample is taken without replacement, the estimate will change, especially when the size of recaptured population is a significant proportion of the whole population. The technique used by biologists uses the hypergeometric distribution.
Fortunately, in this case, the most probable population size is still 1333 using the hypergeometric distribution, so yes, your answer is correct both ways.
Thank you very much.
You're welcome!
To estimate the wolf population in the wilderness area, you can use the tag-recapture method. This method assumes that the proportion of tagged wolves in the second capture is proportional to the proportion of tagged wolves in the overall population.
First, you correctly calculated the percent of wolves caught that had tags: 75/200 = 0.375, or 37.5%.
Next, you set up a proportion equation with this known percentage:
0.375 = 500/N
To solve for N (the total population), you can cross-multiply:
0.375N = 500
Now, divide both sides of the equation by 0.375 to isolate N:
N = 500 / 0.375
Calculating the value, N ≈ 1333.333.
Based on your calculations, you estimated the wolf population in the wilderness area to be approximately 1333.333. However, since a population cannot have a fractional value, you should round this number to the nearest whole number.
Therefore, the estimated wolf population in the wilderness area is approximately 1333 wolves.