This document summarizes a model of the relationship between foraging effort, resource density, and social change in hunter-gatherer societies. The model assumes open access to resources and examines how individual foragers increasing their extraction per unit area impacts the resilience of the forager-resource system. It outlines the assumptions of the model, equations for resource growth and harvest, conversion of biomass to energy, time allocation dynamics, and how the system responds to changes in foraging effort and population density. Simulation results show the maximally resilient system occurs at a population density of 0.5.

1. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Intensification, Tipping Points, and Social
Change in a Coupled Forager-Resource
System
Jacob Freeman1 John M. Anderies 1
1 The School of Human Evolution and Social Change
Arizona State University
CUNY Human Ecodynamics Workshop
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

2. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Outline
1 Motivation
2 The Foraging Effort Model
3 Analysis: Resilience and Social Change
4 Discussion
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

3. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Question
Question: Given the open-access nature of resources
among hunters and gatherers, if individual foragers extract
more resources per unit area, how does this behavior
impact the resilience of a forager-resource system?
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

4. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Basic Assumptions
1 Foragers groups primarily exploit open-access resources
within a habitat and this habitat is embedded in a
landscape of habitats
2 The interpretation of the model is restricted to the use of
stationary resources
3 Forager population density is a parameter
4 Foraging effort (e) is interpreted as time spent harvesting
resources (workdays per day)
5 Two energy targets motivate behavior, c and γ
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

5. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Resource Growth and Harvest
x
G(x) = rx(1 − ) (1)
K
resource growth rate
0 resource density K
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

6. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Resource Growth and Harvest
H(x, e) = ph(x, e) (2)
h(x, e) = qxe (3)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

7. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
The Conversion of Biomass to Energy
α = le(−mp) (4)
efficiency of converting biomass into energy (α)
1
m = 0.5
m = 0.8
0
forager group density (p)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

8. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
The Conversion of Biomass to Energy
α = le(−mp) (4)
efficiency of converting biomass into energy (α)
1
m = 0.5
m = 0.8
0
forager group density (p)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

9. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Time Allocation
δ = γ − αh(x, e) (5)
16 Jacob Freeman, John M. A
1
Region 2a. Resource density is high enough to
meet basic metabolic needs. Thus, foragers attempt
Region 1. Resource density is so low
to meet their daily energy goal of g by changing
that more foraging effort is required to
effort in proportion to their energy deficit. That is
Foraging deficit, d
meet basic metabolic needs than for-
D(x, e) ⇡ a1 d so that de/dt ⇡ a1 d . Here, d > 0 so
agers are willing to tolerate (or are cap-
foraging effort will increase.
bable of). Foragers reduce effort at a
0 constant rate. That is, D(x, e) ⇡ a2 so
that
de
⇡ a2 .
dt Region 2b. As in Region 2a, but here, d < 0 so
foraging effort will decrease.
-1
0 c 3
Harvest per unit foraging effort, ah(x, e)/e
Fig. 2 Foraging effort decision dynamics. The different regions in the daily energy deficit - daily energy harvest plane generate a simple d
heuristic for forager groups. See Box 2 for the mathematical details of the function used to represent these different regions.
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

10. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
The Story
dx
= G(x) − H(x, e) (6)
dt
de
= D(x, e). (7)
dt
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

11. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
The Maximally Resilient System: p=0.5
2.5
a
2
foraging Effort
1.5
Foraging effort
1 (S)
(S)
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Resourcedensity
resource Density
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

12. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
The Resilient but Vulnerable System: p=0.7
2
(Z) bb
(U)
(Z)
1.5
foraging Effort
(U)
Foragingeffort
1
(S)
(S)
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
resource density
Resource Density
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

13. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
The Degraded System: p=0.8
2
(Z) cC
1.5 (Z)
foraging Effort
Foragingeffort
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Resource Density
resource density
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

14. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Institutions and Windows of Vulnerability
. 00 . 20 . 40 . 60 . 80 1. 00 1. 20
1. 40 window of vulnerability 1. 40
equilibrium foraging effort (e*)
1. 20 1. 20
1. 00 1. 00
αh(x,e)/e = c
. 80 . 80
αh(x,e)/e > c
. 60 . 60
. 40 . 40
. 20 . 20
. 00 . 20 . 40 . 60 . 80 1. 00 1. 20
forager group density (p)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

15. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
Institutions and Windows of Vulnerability
. 00 . 20 . 40 . 60 . 80 1. 00 1. 20
1. 40 window of vulnerability 1. 40
equilibrium foraging effort (e*)
1. 20 1. 20
1. 00 αh(x,e)/e = c 1. 00
. 80 . 80
. 60 αh(x,e)/e > c . 60
. 40 . 40
. 20 . 20
. 00 . 20 . 40 . 60 . 80 1. 00 1. 20
forager group density (p)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

16. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
1 The very success of an adaptation at the level of an
individual forager group can create system-level
vulnerabilities that subsequently feed back to cause
emergent social change.
2 A looming tipping point creates uncertainty and associated
risk for foragers.
3 Alternatives adaptive strategies: relocate, reform or control
4 Freeman, J. and Anderies J. M. 2012. Intensification,
Tipping Points, and Social Change in a Coupled
Forager-Resource System. Human Nature (DOI)
10.1007/s12110-012-9154-8
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

17. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
1 The very success of an adaptation at the level of an
individual forager group can create system-level
vulnerabilities that subsequently feed back to cause
emergent social change.
2 A looming tipping point creates uncertainty and associated
risk for foragers.
3 Alternatives adaptive strategies: relocate, reform or control
4 Freeman, J. and Anderies J. M. 2012. Intensification,
Tipping Points, and Social Change in a Coupled
Forager-Resource System. Human Nature (DOI)
10.1007/s12110-012-9154-8
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers

18. Motivation
The Foraging Effort Model
Analysis: Resilience and Social Change
Discussion
1 The very success of an adaptation at the level of an
individual forager group can create system-level
vulnerabilities that subsequently feed back to cause
emergent social change.
2 A looming tipping point creates uncertainty and associated
risk for foragers.
3 Alternatives adaptive strategies: relocate, reform or control
4 Freeman, J. and Anderies J. M. 2012. Intensification,
Tipping Points, and Social Change in a Coupled
Forager-Resource System. Human Nature (DOI)
10.1007/s12110-012-9154-8
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers