UNCORRECTED PROOF YTPBI: 2113 Model 5G pp. 1–10 (col. fig: nil) ARTICLE IN PRESS Theoretical Population Biology xx (xxxx) xxx–xxx Contents lists available at ScienceDirect Theoretical Population Biology journal homepage: www.elsevier.com/locate/tpb Population and prehistory III: Food-dependent demography in variable environments Charlotte T. Lee a,∗ , Cedric O. Puleston b , Shripad Tuljapurkar b a Biological Science, Florida State University, Tallahassee, FL 32306, USA b Biological Sciences, Stanford University, Stanford, CA 94305, USA article info Article history: Received 9 April 2009 Available online xxxx Keywords: Human demography Environmental fluctuation Food ratio Well-being Preindustrial population Production Consumption abstract The population dynamics of preindustrial societies depend intimately on their surroundings, and food is a primary means through which environment influences population size and individual well-being. Food production requires labor; thus, dependence of survival and fertility on food involves dependence of a population’s future on its current state. We use a perturbation approach to analyze the effects of random environmental variation on this nonlinear, age-structured system. We show that in expanding populations, direct environmental effects dominate induced population fluctuations, so environmental variability has little effect on mean hunger levels, although it does decrease population growth. ∧ The growth rate determines the time until population ∧ is limited by space. ∧ This limitation introduces a tradeoff between population density and well-being, so population effects become more important than the direct effects of the environment: environmental fluctuation increases mortality, releasing density dependence and disproportionately raising average well-being for survivors. We discuss the social implications of these findings for the long-term fate of populations as they transition from expansion into limitation, given that conditions leading to high well-being during growth depress well-being during limitation. © 2009 Published by Elsevier Inc. 1. Introduction 1 History and prehistory provide abundant evidence that human 2 populations shape and are shaped by their environment (e.g, Kirch, 3 1994; Vitousek et al., 2004). The environment plays a role in 4 the demographic and cultural fates of many societies, including 5 whether they are in some sense sustainable (see Kirch, 2007 for 6 a comparison of four cases). This paper completes a quantitative 7 framework for examining how environment, demography, and 8 society jointly affect human population dynamics. Our framework 9 (Lee and Tuljapurkar, 2008; Puleston and Tuljapurkar, 2008) 10 explicitly links population and environment by describing the 11 nonlinear feedbacks between food supply, human mortality ∧ , 12 fertility, population density, growth ∧ and age structure. This 13 theory of food-dependent demography is an essential first step 14 in linking the biological and social mechanisms that drive 15 macro-demographic change, and advances the development of 16 a quantitative foundation for the study of the joint evolution 17 of human biology and culture (Weiss, 1976). Here we examine 18 the demographic consequences of an environmentally driven, 19 stochastic, year-to-year variation in food supply. 20 ∗ Corresponding author. E-mail address: ctlee@bio.fsu.edu (C.T. Lee). Previously we analyzed two demographic regimes that describe 21 preindustrial populations. In one, population is not limited by 22 space and eventually grows at an asymptotic rate determined by 23 food availability (Lee and Tuljapurkar, 2008). Food availability rel- 24 ative to need depends on environment and on population demog- 25 raphy and social factors, loosely defined to include such factors as 26 labor and technology. Food-dependent growth eventually leads to 27 a regime in which space limits food production, and the popula- 28 tion reaches an equilibrium density likewise determined by the 29 environment (including available space), demography, and soci- 30 ety (Puleston and Tuljapurkar, 2008). The former regime describes 31 populations colonizing or expanding into a new area. The latter 32 describes populations that are constrained within some spatial re- 33 gion, e.g., by physical or climatic factors. In both, we quantify rel- 34 ative food availability using the food ratio, which is the number of 35 calories available to consume in a given year relative to the num- 36 ber of calories needed to maximize survival and fertility. The food 37 ratio is a measure of food consumption relative to ideal levels, and 38 thus describes hunger and its effects on population well-being as 39 reflected in age-specific mortality and fertility rates. Our theory of 40 food-dependent demography allows us to ask how environmen- 41 tal factors (such as climate and soil properties) and human fac- 42 tors (such as crop choice, labor organization ∧ and harvest efficiency) 43 act via food to influence populations’ fates. Thus, it is a foundation 44 for the quantitative study of human-environment interactions in 45 preindustrial societies. 46 0040-5809/$ – see front matter © 2009 Published by Elsevier Inc. doi:10.1016/j.tpb.2009.06.003 Please cite this article in press as: Lee, C.T., et al., Population and prehistory III: Food-dependent demography in variable environments. Theoretical Population Biology (2009), doi:10.1016/j.tpb.2009.06.003