Simpson's Index is represented by which formula?

Simpson's Index, often used in ecology to measure biodiversity, assesses the probability that two individuals randomly selected from a sample will belong to the same species. The correct formula for Simpson's Index is indeed represented by the expression 1 minus the fraction of the product of the number of individuals in a species (n) taken two at a time over the total number of individuals (N) taken two at a time. This way, the formula effectively calculates diversity by reflecting how many different species are present in the community and their relative abundances.

Specifically, the formula, D = 1 - (n(n-1))/(N(N-1)), indicates that as the value of D approaches 1, it implies a high level of diversity within the habitat, meaning species are more evenly distributed. Conversely, a value closer to 0 suggests that one or few species dominate the environment, indicating lower biodiversity. This approach emphasizes the importance of both the number of species and their population sizes in determining overall ecological diversity.

Other formulas provided do not effectively convey the intended measurement of biodiversity as Simpson's Index. They either represent unrelated concepts or do not properly integrate the necessary aspects of abundance and species richness that are captured in the correct formula.