Hadza hunter-gatherers, social networks, and models of cooperation

At the heart of the Great Lakes region of East Africa is Tanzania — a republic comprised of 30 mikoa, or provinces. Its border is marked off by the giant lakes Victoria, Tanganyika, and Malawi. But the lake that interests me the most is an internal one: 200 km from the border with Kenya at the junction of mikao Arusha, Manyara, Simiyu and Singed is Lake Eyasi. It is a temperamental lake that can dry up almost entirely — becoming crossable on foot — in some years and in others — like the El Nino years — flood its banks enough to attract hippos from the Serengeti.

For the Hadza, it is home.

The Hadza number around a thousand people, with around 300 living as traditional nomadic hunter-gatherers (Marlow, 2002; 2010). A life style that is believed to be a useful model of societies in our own evolutionary heritage. An empirical model of particular interest for the evolution of cooperation. But a model that requires much more effort to explore than running a few parameter settings on your computer. In the summer of 2010, Coren Apicella explored this model by traveling between Hadza camps throughout the Lake Eyasi region to gain insights into their social network and cooperative behavior.

Here is a video abstract where Coren describes her work:

The data she collected with her colleagues (Apicella et al., 2012) provides our best proxy for the social organization of early humans. In this post, I want to talk about the Hadza, the data set of their social network, and how it can inform other models of cooperation. In other words, I want to freeride on Apicella et al. (2012) and allow myself and other theorists to explore computational models informed by the empirical Hadza model without having to hike around Lake Eyasi for ourselves.

The Hadza live in small temporary camps of around 30 individuals, with an average of adults per camp for the 17 camps in Apicella et al. (2012).^[1] Within hunter-gatherer camps — including the Hadza — there is camp-wide sharing of food (Marlowe, 2004; Gurven, 2004), of responsibility for child care (Henry, et al., 2005; Crittenden & Marlowe, 2008; Hill & Hurtado, 2009), and of the daily chores like acquisition of food, construction and maintenance of living spaces, and transportation of children and possessions (Hill, 2002). In a cross-cultural meta-analysis of 32 present-day foraging societies — including the Hadza — Hill et al. (2011) showed that their camps have low levels of close kin (usually less than 10%; in the Hadza specifically ranging on average from 4.1% for a focal male to 5.5% for a focal female) and experience a constant flow of individuals between camps. As Coren highlighted in the above video, the Hadza camps are very dynamic, relocating every 4 to 6 weeks and sometimes dissolving into or merging with other camps.

This flow of individuals between camps is not random, however. Individuals have preferences for camp-mates and Apicella et al. (2012) measured these preferences by asking each adult to nominate a few other individuals that they would prefer to have as camp-mates for their next camp.^[2] In this study, men only nominated other men and women other women, resulting in two disjoint graphs with a total of 205 individuals (nodes) and 1263 future camp-mate nominations (directed edges) and around 46% of the edges being between camps. Apicella et al. (2012) presented these graphs in figure 1c (and the within-vs-between camp nominations in figure S4). Since an important step towards working with data is to have that data, preferably in a machine friendly format, I focused on this figure. Although I have met Coren Apicella once before, I didn’t feel comfortable emailing her for her raw data — especially since I didn’t have a specific purpose for it in mind — so Marcel Montrey and I extracted the adjacency matrix from figure 1c by hand.^[3]

Graph of the Hadza future camp-mate preference, based on data from Apicella et al. (2012). Left graph is women and right graph is men. Nodes are sized in proportion to their in-degree.

But what are we to make of this data? Apicella et al.’s (2012) first step was to compare to other networks or models of networks that we often discuss. Compared to a random network with the same number of edges and nodes, they found:

• that the degree-distribution has significantly fatter tails,
• differences in its degree of reciprocity, with an Hadza being 37.6 to 51.4 times more likely to name as a desired campmate somebody who named them as a desired campmate,
• higher than expected associativity between in- and out-degree: agents that name more agents were also more likely to be named more themselves.
• homophily in traits like age, height, weight, body fat, handgrip strength, and level on contribution in a public-goods game.^[4]

For empirical comparisons, they considered 142 socioeconomic networks of US students from the National Longitudinal Study of Adolescent Health (for design, see: Harris et al., 2009), and two similar sized networks (N = 181, N = 251) of adult subsistence-farming villagers in Honduras that were shared with them by Derek K. Stafford (forthcoming; also, see Stafford et al., 2010). Although these comparison networks used different questions (roughly: “who are your friends?”) to generate their directed edges, the Hadza network parameters fell within the ranges observed in these comparison networks. But that is of interest to us, only if we expect these parameters to be relevant and determinant for the sort of questions we want to ask. It is not always clear to me that this is the case.

My urge to have social network data on hunter-gatherers comes from the apparent importance and pervasiveness of study of spatial structure in the mathematical models of evolutionary game theory. The idea is to cut out the network-modeling middleman. Instead of trying to figure out what sort of network families are like real networks, and then running games on those families, why not run games directly on empirically observed networks? Unfortunately, there is a tension between the sort of networks anthropologists and sociologists collect, and the sort of networks that evolutionary game theorists model. The typical approach to networks in EGT is to have the edges of the graph determine the pairs of agents that interact during the game and for reproduction or imitation.^[5] Since we usually consider symmetric games, we usually also want symmetric graphs.^[6] So an obvious approach is to symmetrize the Hadza network by saying that the agents will interact symmetrically if either one initiates, and that ‘future camp-mate’ is a proxy for friend and friendship is a proxy for frequent interaction. This makes for easy integration of the Hadza network into existing models, but throws away our knowledge of how the Hadza actually interact with each other; which is mostly at the level of a camp.

Instead, we could structure models using Coren’s data in terms of camps, and have inviscid interactions within each camp. Unfortunately, if the camps are then allowed to grow or survive in proportion to the camps’ total (or average) payoff — from whatever interactions you choose to model — then we will have built group-selection into our models. If, instead, we keep the camps fixed, with only (payoff independent) migration between camps then we are in a setting similar to Tarnita et al.’s (2009) evolutionary set theory. This approach can also promote cooperation, but in a more subtle way than direct selection on groups. We can then use the graph of cross-camp future campmate nominations from supplementary figure S4 as a migration graph. Imagine a dynamics where at each time-step, an ego is selected at random^[7] and given the opportunity to migrate to the camp — potentially the same camp as they are already in — of one of the alters that the ego nominated as a preferred future camp-mate. Further, we can periodically dissolve and then reform the camp-mate networks according to the preferences that Coren collected. One way might be to (1) select egos at random, (2) create a new camp for them if they are not already part of a camp, and (3) let them invite those who they wish to have as campmates to their camp. This would reflect that — although the migration or visitation is very common — whole camps move around 6 to 12 times a year; the number and size of camps also fluctuates throughout the season, with fewer larger camps forming during the late dry season and wet season when berries are common (Marlowe, 2002; 2010). This approach allows us to use Coren’s social network not as the interaction (and/or reproduction/imitation) graph, but as a meta-network that informs how we update the interaction graph.

The approaches in the last two paragraphs differ in the extent you have to depart from domain-knowledge about the empirical data was gathered versus how much you have to adjust existing modeling tools. The first integrated better with the theoretical work on EGT, and the latter with the empirical work in anthropology. In the end, how much you adjust your tools or how far you depart from the data is a choice similar to finding your preferred tool-problem pairing. I can see myself both using the symmetrized network as a backdrop for existing projects like the evolution of useful delusions (Kaznatcheev, et al., 2014), and extending evolutionary set theory as a basis for a model closer to the Hadza empirical model. I’ll keep you updated on both, dear reader.

Notes and References

1. Here there seems to significant variance between years or seasons. The data used by Hill et al. (2011), for example, reported 17 camps with a total of 406 adults — so around 23.9 adults per camp. I am not sure what, if anything, to make of this.
2. Apicella et al. (2012) also constructed a gift network by asking individuals to choose recipients for a total of 3 sticks of honey. The sticks could not be kept, but you could choose to send more than one of your sticks to the same person, resulting in a weighted directed graph. Many of the general properties I discuss later for the campmate-network also held for this one, but the network itself was not explicitly presented in the paper (or the supplemental materials). Since I could not work with it directly, I didn’t discuss it further in this post.
3. The crowded representation in figure 1c and errors in transcription introduce some discrepancy between the numbers reported in Apicella et al. (2012) and the graphs we recovered. In particular, our graphs have a total of 94 men and 97 women, and 340 and 506 edges in the male and female graphs, respectively. This is 14 individuals and 417 nominations short of the 205 individuals and 1263 nominations that the authors report. So don’t use our count as an authoritative data set. For my own purposes, I will ask Coren for the actual raw data if I find a question that I think computational modeling can answer.
4. While visiting the camps, Coren engaged the Hadza in a public goods game. Although researchers have asked the Hadza to play several economic games before — usually the ultimatum or dictator game (for example, see Henrich et al., 2001) — this was their first time playing the public goods game. The payoffs were in honey — their very most preferred food (Marlowe & Berbesque, 2009) — and measured in sticks. Each participant was endowed with 4 sticks of honey, and any that they donated to the public good were multiplied by a factor of 3 and — after all adult camp-mates made their contribution decisions in private — were distributed among all adults in the camp. All camps had more than 4 adult residents.
5. Of course, we can also follow Ohtsuki et al. (2007) and use different interaction and replacement graphs. It is easier to justify the Hadza network as a replacement by imitation network, by saying that the edges are friendship ties; and to use camp level inviscid interaction as I discuss in the next paragraph. Of course, if the full meta-network approach of the next paragraph is adapted, then the Hadza network is used to update camps, but the interaction and imitation networks can be set by the inviscid camp structure itself.
6. Alternatively, one can embrace the directed edges by modifying the evolutionary game theory models and concentrating on non-symmetric games like ultimatum or dictator. This would connect to a large behavioral economics and anthropology literature (like Henrich et al., 2001) and some modeling literature (like Nowak et al., 2000).
7. Selecting egos at random independent of their fitness or strategy is a potentially unreasonable simplification. When a Hadza leaves their camp, it is usually for some reason like a dispute or resource shortage which can be closely linked to one’s payoff from or strategy in cooperative interactions. Fortunately, these sorts of conditional migration strategies are already being explored by researchers like C. Athena Aktipis (2004).

Aktipis, C.A. (2004). Know when to walk away: contingent movement and the evolution of cooperation. Journal of Theoretical Biology, 231(2): 249-260.

Apicella, C.L., Marlowe, F.W., Fowler, J.H., & Christakis, N.A. (2012). Social networks and cooperation in hunter-gatherers. Nature, 481 (7382), 497-501 PMID: 22281599

Crittenden, A. N., & Marlowe, F. W. (2008). Allomaternal care among the Hadza of Tanzania. Human Nature, 19(3): 249-262.

Gurven, M. (2004). To give and to give not: the behavioral ecology of human food transfers. Behavioral and Brain Sciences, 27(04), 543-559.

Harris, K.M., C.T. Halpern, E. Whitsel, J. Hussey, J. Tabor, P. Entzel, & Udry, J.R. (2009) The National Longitudinal Study of Adolescent to Adult Health: Research Design. [online].

Kaznatcheev, A., Montrey, M., & Shultz, T.R. (2014). Evolving useful delusions: Subjectively rational selfishness leads to objectively irrational cooperation. Proceedings of the 36th annual conference of the cognitive science society. arXiv: 1405.0041v1.

Marlowe, F. (2002). Why the Hadza are still hunter-gatherers. Ethnicity, huntergatherers, and the ‘Other’, ed. S. Kent, 247-81.

Marlowe, F.W. (2004). What explains Hadza food sharing? Research in Economic Anthropology, 23: 69-88.

Marlowe, F. W., & Berbesque, J. C. (2009). Tubers as fallback foods and their impact on Hadza hunter‐gatherers. American Journal of Physical Anthropology, 140(4): 751-758.

Marlowe, F.W. (2010). The Hadza: hunter-gatherers of Tanzania (Vol. 3). Univ. of California Press.

Nowak, M. A., Page, K. M., & Sigmund, K. (2000). Fairness versus reason in the ultimatum game. Science, 289(5485): 1773-1775.

Ohtsuki, H., Pacheco, J. M., & Nowak, M. A. (2007). Evolutionary graph theory: breaking the symmetry between interaction and replacement. Journal of Theoretical Biology, 246(4): 681-694.

Hill, K. (2002). Altruistic cooperation during foraging by the Ache, and the evolved human predisposition to cooperate. Human Nature, 13(1): 105-128.

Hill, K., & Hurtado, A. M. (2009). Cooperative breeding in South American hunter–gatherers. Proceedings of the Royal Society of London B: Biological Sciences, rspb20091061.

Hill, K. R., Walker, R. S., Božičević, M., Eder, J., Headland, T., Hewlett, B., … & Wood, B. (2011). Co-residence patterns in hunter-gatherer societies show unique human social structure. Science, 331(6022): 1286-1289.

Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H., & McElreath, R. (2001). In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies. American Economic Review, 91(2): 73-78.

Henry, P.I., Morelli, G.A., & Tronick, E.Z. (2005). Child caretakers among Efe foragers of the Ituri forest. Hunter-gatherer childhoods: Evolutionary, developmental, and cultural perspectives, 191-213.

Stafford, D., Hughes, A. D., & Abel, B. (2010). A Pictures is Worth a Thousand Words: Photographic Identification in Rural Networks and an Introduction to Netriks. Meeting of Networks in Political Science [online pdf]

Stafford, D. (forthcoming). The Left Hand: How Power-Asymmetries Structure Cooperative Behavior. U. Michigan (Ann Arbor) Ph.D. dissertation

Tarnita, C., Antal, T., Ohtsuki, H., & Nowak, M. (2009). Evolutionary dynamics in set structured populations. Proceedings of the National Academy of Sciences, 106(21): 8601-8604

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