Main answer:
The population size (Nc) of the vole population = 444.44
The standard error (SE) of Nc = 48.85
The population density of the vole population = 0.44 per meter square.
Step-by-step explanation:
To estimate the population size and density of the vole population, the Lincoln-Peterson method with Chapman's correction is used. In this method, the ratio of marked to captured individuals in the first and second captures is used to estimate the population size.
Based on the given information:
M = 80 (voles captured in the first capture)
C = 50 (voles captured in the second capture)
R = 18 (marked voles in the first capture)
Using the Lincoln-Peterson formula, Nc = (M × C) / R, we can calculate the estimated population size:
Nc = (80 × 50) / 18 = 444.44
The standard error (SE) of the estimated population size can be calculated using the Chapman's correction formula:
SE = √((Nc × (N - R) × (N - C)) / (R × (R - 1)))
Since the population size (N) is unknown, we assume it to be larger than the estimated population size (Nc). Given that the study area is 100x100 meters, N can be approximated as 10,000 (100 × 100).
SE = √((444.44 × (10000 - 18) × (10000 - 50)) / (18 × (18 - 1))) = 48.85
The population density is the population size divided by the area of the study. In this case, since the study area is 100x100 meters, the population density would be:
Population density = Nc / (100 × 100) = 444.44 / 10000 = 0.044
Learn more about:
The Lincoln-Peterson method with Chapman's correction is a commonly used method to estimate population size when capturing and marking individuals. It assumes that the marking does not significantly affect the behavior or survival of the individuals. The standard error provides an estimate of the uncertainty associated with the population size estimate. It is important to note that population estimates are subject to various assumptions and limitations, and additional sampling or statistical techniques may be required for more accurate estimates in different scenarios.