Quick Start

Social Ostracism and Resource Management

Model Type
SES Library XPP model

This replicator dynamics model considers the case of a common-pool resource system where social ostracism may be used to compel non-complying harvesters to avoid over-exploitation of the resource base. Here, non-compliant harvesters (i.e., defectors) are identified by their payoff strategy and incur an 'ostracism' penalty proportional to the number of compliant harvesters (i.e., co-operators) in the system. When the ostracism effect is equivalent to the number of compliant harvesters and the resource inflow rate is constant, regime shifts are removed from the purely social and ecological subsystems in the model. However, bifurcations remain possible due to the interactions between the social and ecological components. Changing the cost of effort, strength of ostracism, or multiple drivers readily triggers a regime shift.

No scenarios available.

No animations available.

Name Initial Value Description
$R$ - The number of units of a generic resource (e.g., harvestable fish count)
$f_c$ - The fraction of co-operators in the system
Name Default Value Description
$c$ - The constant inflow rate of the resource
$d$ - Stock accumulation constraint
$R_{max}$ - Maximum resource count that can be accumulated by harvesters
$k$ - Stock accumulation constraint
$q$ - The catchability of the resource
$n$ - Total number of harvesters
$e_c$ - Level of effort exerted by the co-operators
$e_d$ - Level of effort exerted by the defectors
$\gamma$ - Factor of total productivity
$a$ - Elasticity of total effort
$b$ - Elasticity of the resource stock
$w$ - Costs of harvesting per unit of effort
$h$ - Maximum sanctioning level possible
$t$ - Sanctioning effectiveness threshold
$g$ - Growth rate of ostracism effectiveness
$$$\dot{R} = c - d(R/R_{max})^k - qER$$$
$$$\dot{f_c} = f_c(1-f_c)(U_c - U_d)$$$
$$$E = n[f_c e_c + (1-f_c)e_d]$$$
$$$f(E,R) = \gamma E^a R^b$$$
$$$U_c = e_c \big(\frac{f(E,R)}{E} - w \big )$$$
$$$U_d = e_d \big(\frac{f(E,R)}{E} - w \big ) - ilde{w0}(f_c) \frac{e_d - e_c}{e_d}$ $$
$$$ ilde{w}(f_c) = he^{(te^{ [g f_c]})}$$$
laderegimeshifts.ode
Loading source code...

Download Source File (laderegimeshifts.ode)

The source code file can be used with XPP/XPPAUT or other simulation tools.

Loading model data...