On the feasibility of saltational evolution

One of the key tenets of Darwin’s theory that was inherited by the Modern Synthesis of evolutionary biology is gradualism, that is, the notion that evolution proceeds gradually, via accumulation of “infinitesimally small” heritable changes 1,2 . However, some of the most consequential evolutionary changes, such as, for example, the emergence of major taxa, seem to occur abruptly rather than gradually, as captured in the concepts of punctuated equilibrium 3,4 and evolutionary transitions 5,6 . We examine a mathematical model of an evolutionary process on a rugged fitness landscape 7,8 and obtain analytic solutions for the probability of multi-mutational leaps, that is, several mutations occurring simultaneously, within a single generation in one genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multi-mutational leap is low, and accordingly, their contribution to the evolutionary process is minor at best. However, such leaps could become an important factor of evolution in situations of population bottlenecks and elevated mutation rates, such as stress-induced mutagenesis in microbes or tumor progression, as well as major evolutionary transitions and evolution of primordial replicators.