Exploring inbreeding dynamics by considering reproductive bound and polygyny

Inbreeding is a clinically significant measure of a population dependent on human social structures including the population size or the cultural traits. Here, we propose an expanded and elaborate model to analyze the inbreeding within a population where explicit polygyny and inbreeding bounds are taken into account. Unlike the models presented so far, we implemented biologically realistic assumptions that there is the disproportionate probability of males to reproduce (polygyny) and female reproduction is bounded. Using the proposed model equations, we changed the parameters that represent the polygyny degree, the female reproductive bound correlated to the mutation rate, and the total population size. The disappearance of the polygyny that numerous human societies experienced results in the long-lasting effect of the decreasing inbreeding coefficient. Decreased female reproductive bound correlated with a higher mutation rate reveals similar results. After the effect of each factor is analyzed, we modeled the dynamics of the inbreeding coefficient throughout an imaginary human population where polygyny disappears and late marriage becomes prevalent. In this group, the population size gradually and exponentially increases reflecting the traits of prehistoric human society and rising agricultural productivity. To observe how late and less marriage, the feature of the modern developed society, affects the inbreeding dynamics, the female reproductive bound and the population size were assumed to decrease after the population upsurge. The model can explain the decreasing trend of the prehistoric inbreeding coefficient of the actual human population and predict how the trend will be shifted when traits of modern societies continue.