The effect of yield: The pairs of red and blue lines show the effect of altering the productivity of the environment on the approach to equilibrium. The solid lines represent a yield of 7000 kcal/ha, the dashed lines represent a yield 3x as large, and the short dashes represent a 6x yield. The low yield population is below adequate nutrition from the start and fertility falls and mortality rises smoothly as food availability declines. The local slopes of these vital rates are generally small indicating a slow approach to equilibrium. This effect is driven by the slow growth of the population. The other two yields cause the population to grow at its maximum rate until it falls below E=1 and vital rates begin to fall. The moderate yield population experiences hunger first. In each, the approach to equilibrium is rapid once E has fallen below 1. The notes on the right of the graph indicate the equilibrium state of the population. Ê refers to food availability at equilibrium. Lifespan and population size at equilibrium are e 0 hat and Nhat, respectively. For a thorough explanation see Lee and Tuljapurkar (2008), Puleston and Tuljapurkar (2008), and Lee et al. (2009). Ê : e 0 hat: 30.0 Nhat : 2799 Ê : e 0 hat: 30.0 Nhat: Ê : e 0 hat: 30.0 Nhat : 27287

The effect of background mortality: The pairs of red and blue lines show the effect of altering life expectancy from birth when food is plentiful. The lines represent a life expectancy of 30 years (solid), 45 years (dashes) and 60 years (small dashes). In the harsh environment, the maximum growth rate is relatively small so the approach to equilibrium is long and it experiences adequate nutrition for almost 1200 years here. Although mortality is high from the beginning, it changes very little at equilibrium, due to the fact that equilibrium food availability is fairly high. The fast-growing population in the cushy environment approaches equilibrium quickly and experiences a large drop in quality of life after about 225 years, when it falls below adequate nutrition. At equilibrium lifespan is longest in the favorable environment, but not much different from the other two scenarios. Ê : e 0 hat: 26.8 Nhat : Ê : e 0 hat: 30.0 Nhat: Ê : e 0 hat: 34.0 Nhat : 16075

The effect of fertility: The pairs of red and blue lines show the effect of altering the total fertility rate when food is plentiful. Generally, lower maximum fertility means lower mortality at equilibrium, as shown by the height at which the lines intersect. When E=1 the low fertility population’s TFR is 2 daughters per mother, the moderate one’s is 3, and the high population’s TFR is 4. Mortality tends to be more responsive than fertility in this model, so when fertility is high at E=1, the gap between the vital rates is closed by a marked rise in mortality as the population approaches equilibrium. The result is higher fertility and mortality at equilibrium than in the other scenarios. The high-fertility population also grows quickly, thus experiences hunger before the others, and moves from E=1 to equilibrium food availability with the greatest slope. Ê : e 0 hat: 35.3 Nhat : Ê : e 0 hat: 25.4 Nhat: Ê : e 0 hat: 20.4 Nhat : 15956

The effect of fertility elasticities: The pairs of red and blue lines show the effect of altering the elasticities of the age-specific fertility rates. The elasticities describe how responsive fertility is to changes in food availability. The three levels of elasticities here are 0.5x the empirical estimates, the empirical estimates, and 2x empirical. Greater elasticities mean a steeper drop in fertility to a given change in food availability, and are associated with higher levels of food availability at equilibrium. Changing the elasticities alters how the gap between births and deaths when food is plentiful (and the population is growing) will be closed. High fertility elasticities mean that fertility will be expected to drop more sharply as the population grows, and thus mortality will rise less. Low elasticities of fertility mean that mortality will be high at equilibrium, as it has to rise sharply to meet fertility. Ê : e 0 hat: 28.3 Nhat : Ê : e 0 hat: 30.0 Nhat: Ê : e 0 hat: 32.3 Nhat : 12959

The effect of survival elasticities: The pairs of red and blue lines show the effect of altering the elasticities of the age-specific survival probability. The range of elasticities is identical to the fertility example. The pattern is the complement of the previous one. If survival elasticities are low, they don’t change much as food availability drops and much more of the gap between births and deaths is closed by movement in fertility. Generally, high elasticities are associated with high food availability at equilbrium. This occurs because a small drop in E from 1 results in a large decrease in the vital rates and consequently the growth rate, which must fall to replacement level for the population to achieve equilibrium. Elasticities may be changed by behavior, meaning that in response to a change in food availability a population may actively alter the survival probability of one or more ages. Ê : e 0 hat: 31.8 Nhat : Ê : e 0 hat: 30.0 Nhat: Ê : e 0 hat: 28.5 Nhat : 12478

Growth trajectories: These three graphs describe the change in (from top) population size, food availability (E) and the exponential growth rate. Food availability is high initially, when a group of 200 people live on a rich land. The population grows at its maximum rate for about 225 years, when it becomes so large that the land cannot provide enough calories to fully feed the population. The green line crosses the dashed one, representing E=1 at this point. The result is that the growth rate begins to fall from its maximum and move towards r=0 (equilibrium). The population trajectory slowly bends over as E and r fall and moves towards an equilibrium defined largely by demography and its interaction with the environment and the population’s behavior.

Population structure: The blue line represents what the age structure (equivalent to the age pyramid) looks like when the population is small and is growing at its maximum rate. It is generally young, a feature of such populations. At equilibrium infant mortality is generally fairly high, and fertility rates are lowered. Mortality is higher across the board, but food availability has the greatest negative effects on the oldest and youngest ages. The equilibrium population is older on average.