Evolutionary explanations of mental disorders are a longstanding aim of evolutionary psychiatry, but have suffered from complexities including within-disorder heterogeneity and environmental effects of contemporary societies obscuring possible ancestral functions. Studying the relevant processes of human evolution directly is not possible, so hypotheses have remained speculative, exaggerating "just-so storytelling" critiques. This is despite significant evidence existing in genetics, neuroscience and epidemiology, all of which bears some inferential relevance to evolutionary hypotheses, but which is often not marshalled in a systematic way. To utilise this evidence best to investigate evolutionary explanations of psychiatric (or other) traits we present a novel framework of evidence synthesis and analysis and exemplify it by systematically reviewing evidence related to autism. In the five stages of this "DCIDE framework" analysis, Description identifies a trait to explain and Categorisation initially excludes verifiably non-adaptive cases by utilising evidence from genetics, neuroscience, and environmental factors. Integration then hones a target for adaptive explanation by considering evidence of age of onset, environmental effects, duration, prevalence and sex differences, incorporating relevant correlated traits visible to selection. Evolutionary hypotheses are then Depicted and Evaluated for their ability to explain all the evidence at hand, using standardised areas of evidence and theoretically motivated principles (e.g. traits arising at birth and lasting for life have different plausible explanations than traits arising in adolescence and receding in adulthood). Competing evolutionary hypotheses can thus be systematically compared for their sufficiency in explaining a wide range of available evidence. In the DCIDE review of autism, when Described with current diagnostic criteria, up to 20% of cases Categorise as non-adaptive, primarily caused by de novo mutations and environmental trauma. The remaining cases are eligible for adaptive explanation. For Integrating genetically correlated phenotypes, evidence of high prevalence of subclinical familial traits and camouflaged female cases is necessary. Competing Depictions contrast a high intelligence by-product hypothesis with social niche specialisation for high "systemising" cognition. In Evaluation, broad evidence supports the social niche hypothesis while the intelligence by-product hypothesis fails to predict various lines of evidence. This provides not only the most robust synthesis of autism research relevant to evolutionary explanation to date, but is a first example of how the structure of the DCIDE framework can allow improved systematic evolutionary analysis across psychiatric conditions, and may also be adopted to strengthen evolutionary psychology more generally, countering just-so storytelling and cherry-picking critiques.