to estimate population size, survival, or movement. When capturing and marking organisms, ecologists need to consider the welfare of the organisms. If the chosen identifier harms the organism, then its behavior might become irregular. Notation Let N = Number of animals in the population n = Number of animals marked on the first visit K = Number of animals captured on the second visit k = Number of recaptured animals that were marked A biologist wants to estimate the size of a population of turtles in a lake. She captures 10 turtles on her first visit to the lake, and marks their backs with paint. A week later she returns to the lake and captures 15 turtles. Five of these 15 turtles have paint on their backs, indicating that they are recaptured animals. This example is (n, K, k) = (10, 15, 5). The problem is to estimate N. Lincoln–Petersen estimator The Lincoln–Petersen method (also known as the Petersen–Lincoln index or Lincoln index) can be used to estimate population size if only two visits are made to the study area. This method assumes that the study population is "closed". In other words, the two visits to the study area are close enough in time so that no individuals die, are born, or move into or out of the study area between visits. The model also assumes that no marks fall off animals between visits to the field site by the researcher, and that the researcher correctly records all marks. Given those conditions, estimated population size is: Derivation It is assumed that all individuals have the same probability of being captured in the second sample, regardless of whether they were previously captured in the first sample (with only two samples, this assumption cannot be tested directly). This implies that, in the second sample, the proportion of marked individuals that are caught () should equal the proportion of the total population that is marked (). For example, if half of the marked individuals were recaptured, it would be assumed that half of the total population was included in the second sample. In symbols, A rearrangement of this gives the formula used for the Lincoln–Petersen method. Sample calculation In the example (n, K, k) = (10, 15, 5) the Lincoln–Petersen method estimates that there are 30 turtles in the lake. Chapman estimator The Lincoln–Petersen estimator is asymptotically unbiased as sample size approaches infinity,