cademic science is a culturally evolved social institution with formal rules, norms and conventions. However, in recent years, scientists have begun to examine the utility of even longstanding characteristics of this institution 1-3 . For example, it is now widely recognized that preferentially valuing positive over negative results can generate publication bias, which distorts the published literature 4,5 ; evaluating scientists based on their number of publications can cause a myopic focus on productivity at the expense of rigour 6 ; and rewarding scientists based on the prestige of the journal in which they publish may incentivize scientists to present their work in an overly positive light, submit low-quality papers to high-impact journals and engage in other questionable research practices [7][8][9][10][11][12] .The priority rule is a particularly longstanding scientific norm, in which individuals who are first to make discoveries receive disproportionate credit relative to all other individuals who provide solutions to the same problem 13,14 . Famously, Charles Darwin was motivated to publish his writings on evolution by means of natural selection in part because of a concern that he would lose priority to Alfred Russel Wallace, who had developed a similar idea. In his famous letter to Charles Lyell, Darwin proclaimed "I rather hate the idea of writing for priority, yet I certainly should be vexed if any one were to publish my doctrines before me" 15 . Rewards for priority take on various forms, including eponymy (that is, naming a scientific discovery after the scientist who discovered it), financial prizes (for example, the Nobel prize), an increased probability of publishing in high-impact journals, and better professional positions and speaking engagements 3,13,16,17 . Little research explicitly documents the career repercussions of losing a priority race (that is, getting scooped). However, one survey of physical and biological scientists found that over 60% of scientists reported being scooped at some point in their careers 18 , and a recent study among structural biologists found that scooped papers received 28% fewer citations and were 18% less likely to appear in a top-ten journal 19 . This suggests that scientists have significant incentives to compete over priority of discovery.Given its role as a major incentive, how does rewarding priority of discovery affect scientific inquiry? Rewards for priority can

Differences in social norms are a key source of behavioral variation among human populations. It is widely assumed that a vast range of behaviors, even deleterious ones, can persist as long as they are locally common because deviants suffer coordination failures and social sanctions. Previous models have confirmed this intuition, showing that different populations may exhibit different norms even if they face similar environmental pressures or are linked by migration. Crucially, these studies have modeled norms as having a few discrete variants. Many norms, however, have a continuous range of variants. Here we present a mathematical model of the evolutionary dynamics of continuously varying norms and show that when the social payoffs of the behavioral options vary continuously the pressure to do what others do does not result in multiple stable equilibria. Instead, factors such as environmental pressure, individual preferences, moral beliefs, and cognitive attractors determine the outcome even if their effects are weak, and absent such factors populations linked by migration converge to the same norm. The results suggest that the content of norms across human societies is less arbitrary or historically constrained than previously assumed. Instead, there is greater scope for norms to evolve towards optimal individual or group-level solutions. Our findings also suggest that cooperative norms such as those that increase contributions to public goods might require evolved moral preferences, and not just social sanctions on deviants, to be stable.

In the version of this article initially published, the disclosure of a financial competing interest was inadvertently omitted: author Leonid Tiokhin is co-founder of the company Red Team Market, which provides independent, paid criticism of scientific research. This error has been corrected in the PDF and HTML versions of this article.