Many cancers arise as a result of the accumulation of mutations and their subsequent clonal expansions through epithelial tissue. This process leads to a spatially heterogeneous, evolving premalignant tissue that forms fertile ground for the growth of neoplasms. In fact, several clinical studies have correlated genetic diversity within premalignant tissue with a higher chance of progression to cancer. Thus we aim to develop a quantitative understanding of the temporal dynamics of diversity in a spatially structured population. In this talk I will discuss a stochastic spatial model of the emergence and spread of new types in a population. I will discuss and characterize several measures of diversity (both spatial and non spatial) within a spatially evolving population. In particular, how do the temporal dynamics of diversity depend on the parameters of the tissue and selective advantage of mutants? If time permits, I will also discuss the application of this model to designing sampling procedures in suspected premalignant tissue.