Why are Homo sapiens the only human species living on this planet? Homo sapiens have lived on this planet for about 300,000 years. During most of their existence, early modern humans shared this planet with other archaic humans, such as Neanderthals and Denisovans. Why did the other archaic humans become extinct? To explore this question, this study develops a Malthusian model with natural selection of human species to explore how population dynamics of one group of humans may cause the extinction of another group. In my model, different groups of humans engage in hunting-gathering. The larger group of humans can occupy more land. Therefore, the expansion of one population causes the other population to shrink in a Malthusian economy. Which human population shrinks or even becomes extinct depends on structural parameters in the Malthusian model.