Does the evolution of complex life depend on the stellar spectral energy distribution?

This paper presents the proportional evolutionary time hypothesis, which posits that the mean time required for the evolution of complex life is a function of stellar mass. The "biological available window" is defined as the region of a stellar spectrum between 200 to 1200 nm that generates free energy for life. Over the $\sim$4 Gyr history of Earth, the total energy incident at the top of the atmosphere and within the biological available window is $\sim$10$^{34}$ J. The hypothesis assumes that the rate of evolution from the origin of life to complex life is proportional to this total energy, which would suggest that planets orbiting other stars should not show signs of complex life if the total energy incident on the planet is below this energy threshold. The proportional evolutionary time hypothesis predicts that late K- and M-dwarf stars (M < 0.7 M$_{\odot}$) are too young to host any complex life at the present age of the universe. F-, G-, and early K-dwarf stars (M > 0.7 M$_{\odot}$) represent the best targets for the next generation of space telescopes to search for spectroscopic biosignatures indicative of complex life.