The “pleiotropy-barrier” model. (A) The “pleiotropy-barrier” model posits a dynamic process that new genes evolve adaptively more quickly compared with older
genes. It suggests that older genes undergo stronger purifying selection because their multiple functions (usually adverse
pleiotropy) act as a “barrier-like” factor to hinder fixations of mutations that might otherwise be beneficial for novel phenotypes.
(B) The logistic function between relative pleiotropy P(t) and evolutionary time t, 
, where P_max represents the maximum relative pleiotropy. The k is the growth rate parameter, which controls how quickly the phenomenon approaches the maximum value. A higher k value means faster growth initially.
