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FIGURE 2.4. Results of dynamic simulation of foraging/framing preference model using reasonable values from Mikea research (see text).

hatsake. Consistent with time allocation data, all six household members forage while only the adolescents and adults contribute agricultural labor (Tucker and Young 2005). The simulation begins in the month of July, which is typically the time of year when Mikea decide whether and to what extent they should cultivate maize in the coming year; D begins 303 days before the maize harvest. The household imagines a three-hectare cleared hatsake. The anticipated value of this field is 930 kg/ha times 3640 kcal/kg times three hectares: A begins at approximately 10,000,000 kcal. The daily gain from foraging is provided by mean age and sex-specific net acquisition rates reported in Tucker and Young (2005) times the average duration of tuber foraging trip, 300 minutes; g = 39,400 kcal/day spent foraging.

I assume that Mikea discount future agricultural rewards at the average rates revealed experimentally. Because this simulation involves large rewards and long-scale delays, the appropriate discount rates are those revealed in the sacks of maize experiment: k = 2.00/month (Tucker and Steck in prep). I convert this into the daily rate of k = 0.066/day.

To begin with, let us assume that a day's agricultural labor contributes a = 500,000 kcals to the final harvest. At this rate, the household will have to work 20.3 days to achieve an A of 10,000,000 kcals. Let us further assume the hunger penalty is 0.5k (0.033/day). The results of this simulation are presented in Figure 2.4. The inset demonstrates oscillating values before the convergence point. The convergence point occurs on day 19. Up to this point, the household spends alternating days foraging and farming. They only contribute half the labor (ten days) to farming that they originally anticipated, and the final harvest is 5,000,000 kcal.

What happens if the discount rate is increased? Recall that preliminary experiments revealed that Mikea who primarily forage discount future sacks of maize at 3.9/month (0.13/day). Changing k by this magnitude has little effect on the model's predictions, except that one day fewer is spent farming, and the final reward is 4,500,000 kcal. At k = 0.4/day, only six of the anticipated 20 days of agricultural labor are invested, producing a final reward of only 3,000,000 kcal.

What happens if the discount rate is decreased? As k approaches zero, more days are spent farming. If we use the midpoint of Pender's (1996) value for Indian peasants, converted to days (0.0016/day), the household

FIGURE 2.5. Results of dynamic simulation of foraging/farming preference model when the hunger penalty is reduced by an order of magnitude (see text).

accomplishes 13 days of agricultural labor. Because h is a fraction of k, the small h means value does not oscillate, and the 13 days are spent consecutively. The final harvest is 6,500,000 kcal. If k = 0, there is no discounting, and every day is spent farming.

What happens if the hunger penalty is decreased? Resetting k at 0.066/day, h is then reduced by an order of magnitude (0.0033/day). Results are displayed in Figure 2.5. The number of days spent farming remains at ten, but preference switches between foraging and farming at a different frequency. Six days of farming occur before the household is hungry enough to be forced into foraging; two days of foraging are required before the household can farm again. An artifact of the simplifying assumptions of this model is that increasing h beyond 0.5k has no effect on the model, for no matter how grave the effect of hunger after a day spent farming, a day of foraging resets k to its initial value.

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