The "Vicar of Bray" hypothesis (or Fisher-Muller Model) attempts to explain why sexual reproduction might have advantages over asexual reproduction - sexual populations having the ability to out-compete asexual populations because they evolve more rapidly in response to environmental changes. The offspring of a population of sexually reproducing individuals will show a more varied selection of phenotypes and they will therefore be more likely to produce a strain that can survive a change in the ecology of the environment in which they live. Under the Vicar of Bray hypothesis, sex benefits a population as a whole, but not individuals within it, making it a case of group selection.
The hypothesis originated with August Weismann (1889) and takes its current popular name after the Vicar of Bray, a semi-fictionalised cleric who retained his ecclesiastic office by quickly adapting to the prevailing religious winds in England, switching between various Protestant and Catholic rites as the ruling hierarchy changed. Most biologists accepted a mathematized version of this explanation as providing one of the most important reasons for the prevalence of sexual reproduction in the natural world until the Williams Revolution (George C. Williams's critiques of group selection) re-examined the implicit group-selectionist character of the argument and led to a gene-centered view of evolution in the 1960s. As of 2016 a more popular explanation for the evolutionary origin and maintenance of sex comes in the form of the Red Queen Hypothesis, which instead proposes that sex benefits individual genes directly.