Fig. 1.

Population dynamics of a scientific field, depending on its power ($1-\beta$), significance ($\alpha$), and homophilous bias ($ϵ$). (A and B, Left) Graphs display [2], which relates the Youden index ($J$) to the share of Better scientists in the tenured population ($\sigma$). (A and B, Right) Graphs are phase lines for [5], which describes how the share of Better scientists ($\sigma$) evolves over time. (A) High power: $1-\beta \ge \alpha +ϵ/\left(1+ϵ\right)$. When a science has high power, the Better paradigm necessarily prevails. (B) Low power: $1-\beta <\alpha +ϵ/\left(1+ϵ\right)$. When a science has low power, the Worse paradigm may prevail; this happens when many scientists initially believe in the Worse paradigm [$\sigma \left(0\right)<\sigma *$].