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Risk-Pooling and Herd Survival: An Agent-Based Model of a Maasai Gift-Giving System

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Abstract

We use agent-based modeling to study osotua, a gift giving system used by the Maasai of East Africa. Osotua’s literal meaning is “umbilical cord,” but it is used metaphorically to refer to a specific type of gift-giving relationship. Osotua relationships are characterized by respect, responsibility and restraint. Osotua partners ask each other for help only if they are in need and provide help only when asked and only if they are able. We hypothesize that under the ecologically volatile conditions in which Maasai pastoralists have traditionally lived, such a system is particularly suited to risk pooling. Here we explore whether osotua increases the viability of herds by comparing herd survivorship and stability under osotua rules to a) no exchange and b) probabilistic rules for requesting and giving livestock. Results from this model suggest that this gift-giving system can dramatically increase herd longevity through a limited pooling of risk.

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Notes

  1. The ethnic landscape in the Mukogodo region is complex. In 1971, Mukogodo community leaders successfully petitioned the Kenyan government to refer to them as Maasai, although more specific ethnic identities (e.g., Mukogodo, Mumonyot, Digirri, Ilng’wesi, and LeUaso) remain important locally. Because Cronk's work on the osotua norm involved interviewees and game-players from throughout the region, we refer to them collectively as Maasai. For more information about the history of ethnic identities in the Mukogodo area, see Cronk (2004).

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Acknowledgements

An early version of this work was presented at the Institute for Advanced Study in Princeton, New Jersey. We thank workshop participants for their helpful comments. We also thank the members of the Rutgers Behavioral Ecology Lab, who provided helpful feedback regarding the manuscript and Liz Dong for editorial assistance. This material is based upon work supported by the National Science Foundation under Grant No. SES-0345945 Decision Center for a Desert City (DCDC) and Grant F32 CA144331. Any opinions, findings and conclusions or recommendation expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

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Authors and Affiliations

  1. University of Arizona, Tucson, AZ, USA

    C. Athena Aktipis

  2. Arizona State University, Phoenix, AZ, USA

    C. Athena Aktipis

  3. Rutgers University, New Brunswick, NJ, USA

    Lee Cronk & Rolando de Aguiar

Authors
  1. C. Athena Aktipis
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  2. Lee Cronk
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  3. Rolando de Aguiar
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Corresponding author

Correspondence to C. Athena Aktipis.

Appendix: Model Description

Appendix: Model Description

The model description offered below follows the standardized ODD protocol for describing individual and agent based models (Grimm and Railsback 2005; Grimm et al. 2006).

Purpose

Here we use an agent-based model of the Maasai pastoral system to investigate whether the gift-giving norms associated with osotua give rise to limited risk pooling. This model allows us to investigate whether the osotua rule increased overall herd survivorship and decreased the variability of survivorship within dyads.

State Variables and Scales

In this model time is represented discretely. Space is not explicitly modeled. Herd growth dynamics and volatility are implemented with global variables while the herd size and giving/asking rules are agent variables (Table 2). During each time period, agents execute the commands described in the schedule.

Table 2 Overview of state variables associated with each type of entity
Full size table

Process Overview and Scheduling

This model proceeds in discrete time steps, and entities execute procedures according to the following ordering:

  1. 1.

    For each actor, herds change in size:

    • Herds increase in size according to growth rate

    • Herds decrease in size by volatility size every volatility rate years

    • If herd size is above herd max it is set to herd max

    • Herd size is rounded to nearest integer

  2. 2.

    Requests are made:

    • If no exchange, no requests are made

    • If asking is probablistic, requests made according to asking rate

    • If giving is osotua, requests are made if herd size is below herd min

  3. 3.

    Requests are fulfilled

    • If no exchange, no requests are made

    • If asking is probablistic, requests fullfilled according to giving rate and giving proportion

    • If giving is osotua, requests are made if herd size is above herd min

  4. 4.

    Actors removed from the population if two consecutive rounds occur where cattle holdings are below herd min.

  5. 5.

    Age of actors incremented by 1

Design Concepts

Emergence

In this model, risk pooling emerges from interactions between agents.

Prediction

Agents in this model lack the ability to predict outcomes of future environmental variability or future social interactions. They do not integrate information across time periods.

Sensing

Agents receive requests from their interaction partners and are able to examine their own resource holdings before fulfilling requests.

Interaction

Agents interact by making and fulfilling requests for cattle.

Stochasticity

Herd growth and environmental volatility both have stochastic components.

Observation

Reported data are averaged from 10,000 runs for each of the five conditions. Simulations were run until both agents were removed from the population (i.e., dropped below the viability threshold for more than 2 consecutive time periods).

Initialization

All runs were initialized according to default parameters in Table 3.

Table 3 Initial and default values for all variables
Full size table

Input

In order to make our model of the Maasai pastoral system as realistic as possible, the following parameter values and assumptions about herd dynamics were based on existing scholarship (Dahl and Hjort 1976).

Growth Rate

We used a 3.4% growth rate with an SD of 2.53 based on Dahl and Hjort’s (1976, p. 66) estimate the growth rate in “normal” conditions to be 3.4%, with a maximum possible growth rate of roughly 11% and a minimum of approximately −6% (in the diminishing herds example). Dahl and Hjort estimates of these numbers are based on both empirical evidence and analytical modeling.

Herd Size

Initial herd sizes in our model were 70, with a minimum of 64 and a maximum of 600. These values were derived from Dahl and Hjort (1976, p. 178) who state that a herd of 64 cattle is sufficient to sustain a reference family. Herd sizes described in the text range from 60–100 cows and herds larger than 600 are not considered viable (Dahl and Hjort 1976, p. 158).

Volatility

We used a volatility rate of .1, meaning that on average a disaster (e.g., drought or disease) occurred every 10 years. In our model, this disaster reduced the cattle herd by 30% on average, with a SD of 10%. Dahl and Hjort (1976, pp. 114–130) note that these disasters occur approximately every 10–12 years based on empirical data, and that the population decline (during disasters that occur every 10 years) should not be more than approximately 28%, based on analytical models.

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Aktipis, C.A., Cronk, L. & de Aguiar, R. Risk-Pooling and Herd Survival: An Agent-Based Model of a Maasai Gift-Giving System. Hum Ecol 39, 131–140 (2011). https://doi.org/10.1007/s10745-010-9364-9

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