Abstract
Biodiversity refers to the variety and variability of life at the levels of genes, individuals, species, populations, communities, regions, landscapes, etc, and therefore is inherently under a hierarchical structure. Biodiversity includes three aspects: genetic diversity, species (taxonomic) diversity and ecosystem (functional) diversity. In genetics, researchers often describe the process of genetic evolution by complex mathematical model, and then based on the selected model, some genetic diversity indices in terms of model parameters are derived. The most widely used model is the infinite allele model (IAM) for mutation under the finite island model (FIM) framework. Chao et al. (2015b) derived the formulas for the expected values of various gene diversity indices under the assumption of IAM model for an isolated population and for multiple subdivided populations (i.e., two-level hierarchy). Gaggiotti et al. (2018) developed allelic diversities under a three-level hierarchy (i.e., an entire area includes several regions and each region includes several islands/communities) without using any genetic models; they advocated the use of Shannon entropy and its corresponding dissimilarity index because of their good monotonicity properties. This thesis extends Chao et al.’s formulas to three-level hierarchical structure under the IAM-FIM framework. The theoretical formulas for genetic alpha, beta and gamma diversities at each level are derived in terms of model parameters for Shannon entropy-based and hetrozygosity-based measures. The resulting formulas are also compared with the results obtained from Gaggiotti et al. (2018). Simulation results show that when a gene pool is at equilibrium, the proposed three-level theoretical formulas match well with the simulated diversities. Two real genetic data were analyzed to illustrate the application of the proposed formulas. In addition, an online software with simple interactive interface using R language and network package Shiny is developed to facilitate the computations of the proposed formulas in this paper for users without R background.