The dynamics of early human populations depend on food availability, but food supply is itself a dynamic quantity that depends on natural and human factors such as climate, soil nutrient status, caloric demand, and labor supply. We present an age-structured model for humans that explicitly includes the dynamic links between food supply, mortality and fertility rates, population growth rate and age structure, caloric need, and labor. We focus on preindustrial agricultural populations in an expansion phase of population growth, where we assume that arable land area is not limiting. This focus is relevant to the early stages of any society's adoption of agriculture, or to the success of colonization of new areas by agriculturalists (as throughout Polynesia, for example). We provide numerical solutions, analytic approximations, and stability analysis for the asymptotic population growth rate in a constant environment, and show how this growth rate depends on environmental productivity, on the functional relationship between vital rates and food, and on quantities such as the population average ages of food production and consumption. As previous work on preindustrial agroecosystems shows that yields can be surprisingly variable, we then allow environmental productivity to vary through time. We demonstrate strong effects of variability on the stochastic population growth rate, variance, and demographic measures of quality of life. We discuss the implications of these findings for population growth and well-being in preindustrial agricultural societies, as well as for robust quantitative modeling of coupled human-natural systems.