Group selection and inclusive fitness are not equivalent; the Price equation vs. models and statistics

► We show how using the Price equation can lead to claims that are not correct. ► The Price equation is used for the claim that group selection and inclusive fitness are equivalent. ► With a counterexample, we show where this argument is not correct. ► We explain why the Price equation is claimed to be dynamically insufficient. ► We determine what “Price's theorem” must be.