The forecasting of the future growth of world population is of critical importance to anticipate and address a wide range of global challenges. The United Nations produces forecasts of fertility and world population every two years. As part of these forecasts, they model fertility levels in post-demographic transition countries as tending toward a long-term mean, leading to forecasts of flat or declining population in these countries. We substitute this assumption of constant long-term fertility with a dynamic model, theoretically founded in evolutionary biology, with heritable fertility. Rather than stabilizing around a long-term level for post-demographic transition countries, fertility tends to increase as children from larger families represent a larger share of the population and partly share their parents' trait of having more offspring. Our results suggest that world population will grow larger in the future than currently anticipated.