Abstract
Rates of evolution are fundamental to understand the processes that shaped the history of life. The predominant view holds that high rates of phenotypic evolution result from lineage transitions across peaks in an adaptive landscape, with subsequent slow-downs, but evidence remains debated. I developed a phylogenetic "diffused Brownian motion" model that characterizes nuanced variations in evolutionary rates and use it to comprehensively assess body size evolution and its underlying rates for 2,950 extinct and 792 extant species that span over 450 Mys of evolution. I find that evolutionary rates do not conform to expectations from adaptive landscape theory, but rather have been stable, unaffected by the accumulation of phenotypic disparity. Long-term evolutionary trends, such as several net increases in clade-average body size, result both from sustained evolution at the lineage level and the sorting of species phenotypes and their underlying evolutionary rates at the clade level, sometimes acting in opposite directions. These findings substantiate an active role of species in shaping their environment that generate continuous novelty of life forms.