The minimalist conjecture predicts that, in quadratic twist families of abelian varieties, half have rank 0 and half have rank 1. This fits into the larger picture of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics, which predict the distribution of Selmer groups of these abelian varieties. In joint work with Jordan Ellenberg, we prove a version of these heuristics: over function fields over the finite field F_q, we show that the above heuristics are correct to within an error term in q, which goes to 0 as q grows. The main inputs are a new homological stability theorem in topology for a generalized version of Hurwitz spaces and an expression of average sizes of Selmer groups in terms of the number of rational points on these Hurwitz spaces over finite fields.