A theoretical study to introduce an index of biodiversity and its corresponding index of evenness based on mean deviation

In the present study, we propose a new biodiversity index and the corresponding index of evenness. These indices are based upon the mean deviation of the number of individuals belonging to a species in a collection of biological organisms. There is an arbitrary parameter in our model whose value can be adjusted to change the sensitivity of any of these two indices to the variations of the population of different species in a sample, caused by various factors. With the help of a hypothetical dataset regarding the populations of six species in six different collections, we have calculated the indices defined in this article and also determined the values of some commonly used indices. It is observed that the changes in the new indices are sufficiently greater than the changes in other indices, due to the changes in the composition of a sample. Loss or gain of species is likely to be better reflected in the values of the new indices compared to the most widely used indices of biodiversity and evenness. We have shown the effect of variation of the parameter that controls the efficiency of the new indices. The characteristics of the new indices and their comparison with the other indices have been depicted graphically.