Jacob Freeman (ASU) Mutual feedback between resource base and foraging decisions on the evolution of...

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



Outline

1 Motivation

2 The Foraging Effort Model

3 Analysis: Resilience and Social Change

4 Discussion




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?




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




Resource Growth and Harvest

G(x) = rx(1 − xK) (1)

reso

urc

e g

row

th r

ate

resource density K0




Resource Growth and Harvest

H(x ,e) = ph(x ,e) (2)

h(x ,e) = qxe (3)




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




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.




The Story

dxdt

= G(x)− H(x ,e) (6)

dedt

= D(x ,e). (7)




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)




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)




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




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


equili

bri

um

fora

gin

g e

ffort

(e*)




Institutions and Windows of Vulnerability

window of vulnerability

αh(x,e)/e > c

αh(x,e)/e = c


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




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


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