On differentiating selective and neutral evolutionary processes - ABSTRACT At the founding of population genetics in the early 20th century, S. Wright and R.A. Fisher developed much of the mathematical and conceptual framework underlying the study of population-level processes dictating variation observed within- and between-species. However, as evidenced by decades of published interactions, they held strongly differing views regarding the relative importance of adaptive vs. non-adaptive processes in driving evolution. As pointed out by J. Crow (2008), these issues were not really resolved, but rather they were abandoned in favor of more tractable studies. With the proposal of the Neutral Theory by M. Kimura and T. Ohta, the relative contribution of stochastic effects, as earlier advocated by S. Wright, received renewed attention. In the following decades, further theoretical development as well as the availability of large-scale sequencing data have indeed overwhelmingly justified the important role of genetic drift. However, subsequent research related to linked, rather than direct, selection effects have re-ignited previous debates. Namely, whether the large class of strongly and weakly deleterious variants hypothesized under the Neutral Theory, and their related linked selection effects (i.e., background selection), are sufficient to explain genome wide patterns of variation; or whether a more predominant class of beneficial variants, and their related linked selection effects (i.e., selective sweeps), are required. The primary difficulty in answering this question stems from our lack of an appropriate neutral null model - that is, a model incorporating genetic drift as modulated by a realistic demographic history, as well as a realistic distribution of fitness effects summarizing the pervasive effects of both direct and linked purifying selection. Without this null model incorporating these evolutionary processes that are certain to be occurring, it is simply not feasible to quantify the periodic frequency with which adaptive processes are additionally acting to shape patterns of polymorphism and divergence. Future work will focus on the necessary theoretical and statistical developments for application to organisms characterized by small progeny distributions within the context of the Wright-Fisher model and Kingman coalescent (e.g., humans), as well as large progeny distributions within the context of the Moran model and multiple-merger coalescent (e.g., viruses). In total, the product of this research will be a framework for inferring evolutionarily appropriate null models applicable widely across the tree of life, that will enable the field to directly address this long- standing and fundamental debate, and to accurately identify genomic targets of adaptation.