Reciprocal altruism and food sharing decisions among Hiwi and Ache hunter–gatherers

Abstract

The common occurrence of food transfers within human hunter–gatherer and forager–horticulturalist groups presents exciting test cases for evolutionary models of altruism. While kin biases in sharing are consistent with nepotism based on kin selection, there is much debate over the extent to which reciprocal altruism and tolerated scrounging provide useful explanations of observed behavior. This paper presents a model of optimal sharing breadth and depth, based on a general non-tit-for-tat form of risk-reduction based reciprocal altruism, and tests a series of predictions using data from Hiwi and Ache foragers. I show that large, high variance food items are shared more widely than small, easily acquired food items. Giving is conditional upon receiving in pairwise interactions and this correlation is usually stronger when the exchange of value rather than quantities is considered. Larger families and low producing families receive more and give less, consistent with the notion that marginal value may be a more salient currency than quantity.

Appendices

Appendix 1a

For a fixed producer priority level at F−A, it will be more beneficial to share to an additional individual when V(n)>V(n−1).

$${\left( {F - A} \right)}^{{\text{c}}} + n{\left( {\frac{{PA}}{n}} \right)}^{{\text{c}}} > {\left( {F - A} \right)}^{{\text{c}}} + {\left( {n - 1} \right)}{\left( {\frac{{PA}}{{n - 1}}} \right)}^{{\text{c}}} $$

(4)

$${\left( {\frac{n}{{n - 1}}} \right)}^{{1 - {\text{c}}}} > 1$$

(5)

The inequality (Eq. 5) is true when c<1. Therefore it will always be better to increase sharing breadth when the value function is characterized by a diminishing returns curve.

Appendix 1b

It will be advantageous for an acquirer to share with n individuals, and not hoard, when V(n)>V(0). We can calculate the minimal probability that makes sharing a better option than hoarding:

$${\left( {F - A} \right)}^{{\text{c}}} + n{\left( {\frac{{PA}}{n}} \right)}^{{\text{c}}} > F^{{\text{c}}} $$

(6)

$$ \Rightarrow p_{{\min }} > \frac{n}{A}{\left( {\frac{{F^{{\text{c}}} - {\left( {F - A} \right)}^{{\text{c}}} }}{n}} \right)}^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle {\text{c}}$}}} $$

(7)

Appendix 2

For all simulations, F=100, N=20, and r=10. Figures 3a–c allow for half the individuals to reciprocate with p ₁=0.8, while the other half reciprocate with p ₂=0.2. In Fig. 4, p ₁=0.5 and p ₂=0.3. In each graph, I consider the acquirer giving 25%, 50%, 75%, and 100% of their acquisition to anywhere from 1 to 20 recipients. Several diminishing value functions, including the natural logarithmic function and power functions of degree between 0.3 and 0.6 were evaluated. The value function used for presentation is a square root function (c=0.5), although other value functions give similar qualitative results. In terms of identifying an intermediate optimal breadth and depth, the square root function will be more conservative than the logarithmic function because the former is less steeply declining than the latter. The dashed horizontal line in each figure gives the baseline benefit (F−A)^c from hoarding. Return values V(n) are calculated according to Eqs. 4 and 5. See also Fig. 5. Details about the figures are given in the text.

Fig. 3a–c

Simulations of the sharing breadth–depth model. Resource package size F=100. Horizontal line represents the expected value if none is given away. V(n) refers to the expected value an acquirer will receive over a relevant time period from sharing 25%, 50%, 75%, and 100% of a resource. Ten individuals return food with a probability p ₁=0.8, and ten with probability p ₂=0.2. The variable q describes the probability that two foragers return food to an acquirer on the same day, and varies in a q=0.1, b q=0.5, and c q=0.9

Fig. 4a–b

Simulations of the sharing breadth-depth model. Similar to Fig. 3b, c, except resource package size is reduced, F=10, and p ₁=0.5, and p ₂=0.3 in (b). Horizontal line represents the expected value if none is given away

Fig. 5a–c

Graphs of V(n) with linear cost function (n × cost). Similar to Fig. 4b, with a cost a c=0.03, b c=0.05. In part c the cost c=0.1 and probability of simultaneous returns q=0.5