It has been argued that hunter-gatherers’ food-sharing may have provided the basis for a whole range of social interactions, and hence its study may provide important insight into the evolutionary origin of human sociality. Motivated by this observation, we propose a simple network optimization model inspired by a food-sharing dynamic that can recover some empirical patterns found in social networks. We focus on two of the main food-sharing drivers discussed by the anthropological literature: the reduction of individual starvation risk and the care for the group welfare or egalitarian access to food shares, and show that networks optimizing both criteria may exhibit a community structure of highly-cohesive groups around special agents that we call hunters, those who inject food into the system. These communities appear under conditions of uncertainty and scarcity in the food supply, which suggests their adaptive value in this context. We have additionally obtained that optimal welfare networks resemble social networks found in lab experiments that promote more egalitarian income distribution, and also distinct distributions of reciprocity among hunters and non-hunters, which may be consistent with some empirical reports on how sharing is distributed in waves, first among hunters, and then hunters with their families. These model results are consistent with the view that social networks functionally adaptive for optimal resource use, may have created the environment in which prosocial behaviors evolved. Finally, our model also relies on an original formulation of starvation risk, and it may contribute to a formal framework to proceed in this discussion regarding the principles guiding food-sharing networks.