Post on 27-Jun-2015
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Intensification, Tipping Points, and SocialChange in a Coupled Forager-Resource
System
Jacob Freeman1 John M. Anderies 1
1The School of Human Evolution and Social ChangeArizona State University
CUNY Human Ecodynamics Workshop
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
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
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Question
Question: Given the open-access nature of resourcesamong hunters and gatherers, if individual foragers extractmore resources per unit area, how does this behaviorimpact the resilience of a forager-resource system?
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Basic Assumptions
1 Foragers groups primarily exploit open-access resourceswithin a habitat and this habitat is embedded in alandscape of habitats
2 The interpretation of the model is restricted to the use ofstationary resources
3 Forager population density is a parameter4 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
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Resource Growth and Harvest
G(x) = rx(1 − xK) (1)
reso
urc
e g
row
th r
ate
resource density K0
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
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
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
The Conversion of Biomass to Energy
α = le(−mp) (4)
m = 0.5
m = 0.8
effi
cien
cy o
f co
nve
rtin
g b
iom
ass
in
to e
ner
gy
(α)
forager group density (p)
0
1
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
The Conversion of Biomass to Energy
α = le(−mp) (4)
m = 0.5
m = 0.8
effi
cien
cy o
f co
nve
rtin
g b
iom
ass
in
to e
ner
gy
(α)
forager group density (p)
0
1
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Time Allocation
δ = γ − αh(x ,e) (5)16 Jacob Freeman, John M. Anderies
Fora
ging
defic
it,d
Region 1. Resource density is so lowthat more foraging effort is required tomeet basic metabolic needs than for-agers are willing to tolerate (or are cap-bable of). Foragers reduce effort at aconstant rate. That is, D(x,e)⇡�a2 sothat
dedt
⇡�a2.
Harvest per unit foraging effort, ah(x,e)/ec0
-1
1
0
3
Region 2a. Resource density is high enough tomeet basic metabolic needs. Thus, foragers attemptto meet their daily energy goal of g by changingeffort in proportion to their energy deficit. That isD(x,e)⇡ a1d so that de/dt ⇡ a1d . Here, d > 0 soforaging effort will increase.
Region 2b. As in Region 2a, but here, d < 0 soforaging effort will decrease.
Fig. 2 Foraging effort decision dynamics. The different regions in the daily energy deficit - daily energy harvest plane generate a simple decisionheuristic 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
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
The Story
dxdt
= G(x)− H(x ,e) (6)
dedt
= D(x ,e). (7)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
The Maximally Resilient System: p=0.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.5
1
1.5
2
2.5
resource density
fora
gin
g e
ffort
a
(S)Fo
rag
ing
Eff
ort
Resource Density
(S)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
The Resilient but Vulnerable System: p=0.7
(Z)
(S)
(U)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.5
1
1.5
2
fora
gin
g e
ffort
resource density
b
(U)
Fo
rag
ing
Eff
ort
Resource Density
(S)
b(Z)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
The Degraded System: p=0.8
0 0.2 0.4 0.6 0.8 1 1.2 1.4
resource density
0
0.5
1
1.5
2
fora
gin
g e
ffort
(Z)
Cc(Z)
Fora
gin
g E
ffort
Resource Density
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Institutions and Windows of Vulnerability
1. 201. 00. 80. 60. 40. 20. 00
1. 201. 00. 80. 60. 40. 20. 00
1. 40
1. 20
1. 00
. 80
. 60
. 40
. 20
1. 40
1. 20
1. 00
. 80
. 60
. 40
. 20
window of vulnerability
αh(x,e)/e > c
αh(x,e)/e = c
forager group density (p)
equili
bri
um
fora
gin
g e
ffort
(e*)
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
Institutions and Windows of Vulnerability
window of vulnerability
αh(x,e)/e > c
αh(x,e)/e = c
forager group density (p)
equili
bri
um
fora
gin
g e
ffort
(e*)
1. 201. 00. 80. 60. 40. 20. 00
1. 201. 00. 80. 60. 40. 20. 00
1. 40
1. 20
1. 00
. 80
. 60
. 40
. 20
1. 40
1. 20
1. 00
. 80
. 60
. 40
. 20
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
1 The very success of an adaptation at the level of anindividual forager group can create system-levelvulnerabilities that subsequently feed back to causeemergent social change.
2 A looming tipping point creates uncertainty and associatedrisk for foragers.
3 Alternatives adaptive strategies: relocate, reform or control4 Freeman, J. and Anderies J. M. 2012. Intensification,
Tipping Points, and Social Change in a CoupledForager-Resource System. Human Nature (DOI)10.1007/s12110-012-9154-8
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
1 The very success of an adaptation at the level of anindividual forager group can create system-levelvulnerabilities that subsequently feed back to causeemergent social change.
2 A looming tipping point creates uncertainty and associatedrisk for foragers.
3 Alternatives adaptive strategies: relocate, reform or control4 Freeman, J. and Anderies J. M. 2012. Intensification,
Tipping Points, and Social Change in a CoupledForager-Resource System. Human Nature (DOI)10.1007/s12110-012-9154-8
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers
MotivationThe Foraging Effort Model
Analysis: Resilience and Social ChangeDiscussion
1 The very success of an adaptation at the level of anindividual forager group can create system-levelvulnerabilities that subsequently feed back to causeemergent social change.
2 A looming tipping point creates uncertainty and associatedrisk for foragers.
3 Alternatives adaptive strategies: relocate, reform or control4 Freeman, J. and Anderies J. M. 2012. Intensification,
Tipping Points, and Social Change in a CoupledForager-Resource System. Human Nature (DOI)10.1007/s12110-012-9154-8
Jacob Freeman, John M. Anderies The Resilience of Hunter-Gatherers