Modern economies generate immensely diverse complex goods and services by coordinating e↵orts and know-how of people in vast networks that span across the globe. This increasing complexity puts us under the pressure of acquiring an ever-increasing specialized and yet diverse skill portfolio in order to stay e↵ective members of a complex economy. Here, we analyze the skill portfolios of workers in an e↵ort to understand the latent structure and evolution of these portfolios. Analyzing the U.S. survey data (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019) and 20 million resumes, we uncover a tree structure of vertical skill dependencies such that skills that only a few jobs need (specialized) are located at the leaves under the broadly demanded (general skills). The resulting structure exhibits an unbalanced tree shape. The unbalanced shape allows the further categorization of specialized skills: nested, branching out of a deeply rooted sturdy trunk reflecting a dense web of common prerequisites, and un-nested, lacking such support. Our longitudinal analyses show individuals indeed become more specialized, going down the nested paths as moving up the career ladder to enjoy higher wage premiums. The specialization, however, is most likely accompanied by demands for a higher level of general skills, and furthermore, specialization without the strengthening of general skills is deprived of wage premiums. We examine the geographic and demographic distribution of skills to explain disparities in wealth. Finally, historical changes in occupation skill requirements show these branches have become more fragmented over the decade, suggesting the increasing labor gap.