How did humans evolve from individualistic foraging to collective foraging with sex differences in food production and widespread sharing of plant and animal foods? While current models of food sharing focus on meat or cooking, considerations of the economics of foraging for extracted plant foods (e.g., roots, tubers), inferred to be important for earlier hominins (∼ 6–2.5 mya), suggest that hominins shared such foods. Here we present a conceptual and mathematical model of early hominin food production and sharing, prior to the emergence of frequent scavenging, hunting and cooking. We hypothesize that extracted plant foods were vulnerable to theft, and that male mate-guarding protected females from food theft. We identify conditions favoring plant food production and sharing across mating systems (i.e., monogamy, polygyny, promiscuity), and we assess which mating system maximizes female fitness with changes in the energetic profitability of extractive foraging. Females extract foods and share them with males only when: i) extracting rather than collecting plant foods pays off energetically; and ii) males guard females.