My research focuses on developing mathematical frameworks to incorporate novel kinds of individual information (incorporating different sources of heterogeneity). For example, the first part of my thesis is focused on incorporating some memory into matrix population models (building so called second-order matrix models). The second part of my thesis will be about incorporating simple Mendelian recombination into a matrix population model. Combining the powerful demographic approach of matrix models with Mendelian genetics leads to a model with eco-evolutionary interactions and feedbacks. We apply this model to study genotype coexistence, pesticide resistance and assortative mating. This work is part of Hal Caswell's advanced ERC grant entitled "Individual stochasticity and population heterogeneity in plant and animal demography."