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