Body size variation is an enigma. We do not understand why species achieve the sizes they do, and this means we also do not understand the circumstances under which gigantism or dwarfism is selected. We develop size-structured integral projection models to explore evolution of body size and life history speed. We make few assumptions and keep models simple: all functions remain constant across models except for the one that describes development of body size with age. We set sexual maturity to

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... ccur when size attains 80% of the asymptotic size, which is typical of a large mammal, and allow negative density dependence to only affect either reproduction or juvenile survival. Fitness -the quantity that is maximized by adaptive evolution -is carrying capacity in our models, and we are consequently interested in how it changes with size at sexual maturity, and how this association varies with development rate. The simple models generate complex dynamics while providing insight into the circumstances when extremes of body size evolve. The direction of selection leading to either gigantism or dwarfism crucially depends on the proportion of the population that is sexually mature, which in turn depends on how the development function determines the survivorship schedule. The developmental trajectories consequently interact with size-specific survival or reproductive rates to determine the best life history and the optimal body size emerges from that interaction. These dynamics result in trade-offs between different components of the life history, with the form of the trade-off that emerges depending upon where in the life history density dependence operates most strongly. Empirical application of the approach we develop has potential to help explain the enigma of body size variation across the tree of life.