Structural complexity characterizes our representations of dissipative structures. As a mechanistic concept, when referred to natural systems it generates perplexity in the face of logically sound models. Natural selection is a simple mechanistic concept, whose logic is well exemplified in genetic algorithms. While biological traits and functions do appear to have been subjected to selective culling, current neo-Darwinian theory is unable to account for the evolution of traits or functions when many of these are taken as the separate objects of independent fitness functions. Soft selection, acting in a phenotypically holistic manner, does model selection acting upon structurally complex systems with many traits and functions, but does not account for the evolution of specific traits or functions. It is further suggested that selection cannot be other than a weak force in the early, generative stages of complex life histories, and that this is a good thing, preserving their generativity. I conclude that natural selection theory by itself cannot account for increases in structural complexity.