For at least the past 5 decades, population genetics, as a field, has worked to describe the precise balance of forces that shape patterns of variation in genomes. The problem is challenging because modeling the interactions between evolutionary processes is difficult, and different processes can impact genetic variation in similar ways. In this paper, we describe how diversity and divergence between closely related species change with time, using correlations between landscapes of genetic variation as a tool to understand the interplay between evolutionary processes. We find strong correlations between landscapes of diversity and divergence in a well-sampled set of great ape genomes, and explore how various processes such as incomplete lineage sorting, mutation rate variation, GC-biased gene conversion and selection contribute to these correlations. Through highly realistic, chromosome-scale, forward-in-time simulations, we show that the landscapes of diversity and divergence in the great apes are too well correlated to be explained via strictly neutral processes alone. Our best fitting simulation includes both deleterious and beneficial mutations in functional portions of the genome, in which 9% of fixations within those regions is driven by positive selection. This study provides a framework for modeling genetic variation in closely related species, an approach which can shed light on the complex balance of forces that have shaped genetic variation.