The gradual changes which happen in species or creatures , is called evolution . The evolution process depends on the population of the reproducer species like viruses . In a population , the species interact and evolute . The interaction among species , determines the structure . If we have a fixed population including two species with a reproduction rate (fitness) of 1 and r with no mutation during the evolution , at the end , only one of the species will cover and fix all the population . To investigate the effect of population structure on evolutionary dynamics , the evolution graph theory is employed , and to model the method of mutation expansion , the Moran process is employed . According to Moran’s birth-death process , each time one species with probability proportional to its fitness is chosen for reproduction and it replaces its offspring in to one of its neighbors randomly . The present study investigated a well-known issue in evolutionary dynamics . Numerically , in complete , random and scale free graphs , this study investigated the method of mutation species expansion with time , once for different fitness , fixed size and population structure and once more for different population size , fixed fitness and population structure .