Quantitative Models of Social-Ecological Systems

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Type

Waterwheel Model

Model
This model describes the dynamics of a waterwheel. The wheel has 10 cups that are filled when as they pass over the top of the arc of the wheel (imagine a Ferris wheel where instead of seats there are buckets. Water is flowing down on the Ferris wheel filling the buckets). The weight of the water makes the wheel turn. However, in this model, the buckets leak. So if the flow of the water from the top is too slow, some interesting motion can occur. This waterwheel model is a perfect physical...
09 Aug 2016

Two-actor conflict with time delay: A dynamical model

Model
Based on previous mathematical studies, the authors created a model to analyze the conflict dynamics between two actors. In this model, they modified previous nonlinear dynamical models by Liebovitch et al. (2008) and Liebovitch, Vallacher, & Michaels (2010) by considering nonlinear delayed response between two actors. The results of the model show that under certain initial and feedback conditions, a stable neutral equilibrium of conflict may destabilize for some critical values of time...
05 Oct 2016

Tourists and traditional divers in a common fishing ground

Model
A social-ecological model of a fishing ground open to eco-tourism is presented here. To assess the impact of introducing eco-tourism on the welfare of the fishing association and on the resource level, Lee and Iwasa (2011) constructs a model in which the fishing association charges an entrance fee to tourists. The level of the fee is chosen to regulate tourist number as well as maximing benefits accrued to the fishing association (combined revenue from tourism and conventional fishing by...
09 Aug 2016

The inevitability of surprise in agroecosystems

Model
This is a simple model of competition between noxious and benigne weeds in an agroecosystem based on predator-prey dynamics. The interesting aspect of this model is that it demonstrates the inevitability of surprises in system behavior - meaning that for some systems, early warning signals (e.g, increased variance or autocorrelatin) are almost non-existent prior to critical transitions in systems. The reference article, Vandermeer (2011), gives the following overview. "Many critical...
09 Aug 2016

The Evolution of Social Norms in Common Property Resource Use

Model
This is a simple evolutionary game model (based on replicator equations) that couples evolution of users' social norms and renewable resource dynamics. The reference article, Sethi and Somanathan (1996), provides the following overview of the model. "The problem of extracting commonly owned renewable resources is examined within an evolutionary-game-theoretic framework. It is shown that cooperative behavior guided by norms of restraint and punishment may be stable in a well-defined sense...
09 Aug 2016

The effect of scaling and connection on the sustainability of a socio-economic resource system

Model
Most modeling exercises on resource-population dynamics of a socio-economic system assume that many growth-related phenomena are linearly related to population size. The model presented here departs from this linear thinking by exploring potential non-linear relationships, or power-law scaling behaviors, with population size. For example, twice as many people do not mean that twice as much resources are required to maintain existing population. Similarly, twice as many people do not necessarily...
09 Aug 2016

The Discrete Logistic

Model
The logistic is the simplest representation of population dynamics  that contains a minimum level of biological realism.  If we imagine a  population of individuals at time t, the number of individuals in the next period (periods can range from seconds to days to decades depending on the organism) is the number of individuals now plus the number of births minus the number of deaths.  If we assume in the simplest case there are no environmental constraints on births or deaths...
09 Aug 2016

The coupled dynamics of human socio-economic choice and lake water system: the interaction of two sources of nonlinearity

Model
Here, we present a model of the coupled dynamics between human socioeconomic choice (between cooperative and non-cooperative collective action) and nutrient loading input level into a lake water system. Suzuki and Iwasa (2008) explains the model as the following. "In the model, many players choose one of the two options: a cooperative and costly option with low phosphorus discharge, and an economical option with high phosphorus discharge. The choice is affected by an economic cost, a social...
09 Aug 2016

Subtle global bifurcation with dramatic ecological consequences in a simple population model

Model
This model presents an example of a global bifurcation (a heteroclinic connection). The model is a three-dimensional system with two resources and a single consumer, where one of the resources is fixed and the other is reproductive. By assuming that, for all values of resource consumers (C) below its carrying capacity (K), the fixed resource facilitates the consumption of the reproductive resource, the system can be reduced to a two-dimensional system. The reference article, Vandermeer and King...
09 Aug 2016

Spread of ideas based on epidemiological models

Model
Models inspired by epidemiology and informed by the sociology of the spread dynamics, are applied to the diffusion of a specific scientific idea. Although the example will clearly not cover everyclass of ideas, it will point to features of epidemic models that apply to idea diffusion. It will alsoreveal features of these models that require modification, thereby producing more realistic candidate models.At the onset of the spread of the idea, most of the population will be in the susceptible...
07 Oct 2016

Social Ostracism and Resource Management

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...
07 Oct 2016

Simple Model of Farming/Gathering Transition

Model
This is a stylised model capturing "the interdependencies of foraging, farming and productivity of an ecosystem" and can be used to "explore alternative scenarios of niche construction and ecological inheritance." The model has two components, forest growth and time allocated to either foraging or farming, coupled together. Three basic model assumptions are 1) individuals are households, 2) households choose to produce either tree seeds or maize and 3) territory is open access. Allocation of...
06 Oct 2016

Robustness, institutions, and large-scale change in social-ecological systems: the Hohokam of the Phoenix Basin

Model
This is a model that illustrates the relationship among levels of (1) population, (2) human-made capital, (3) natural capital , and (4) resource consumption. The key insight to be gained from the model is that as the ratio of capitalization in human-made infrastructure over human population is varied in the parameter space, the dynamics of natural capital changes and becomes vulnerable to different disturbance regimes. That is, as humans grow in population and over-invest in capitalization/...
09 Aug 2016

Robustness and Resilience across Scales: Migration and Resource Degradation in the Prehistoric U.S. Southwest

Model
This is a simple model that integrates 1) resource-population dynamics, 2) population migration, and 3) spatial heterogeneity in biophysical conditions (i.e., soi fertility). The reference article, Anderies and Hegmon (2011), gives the following abstract of the model. "Migration is arguably one of the most important processes that link ecological and social systems across scales. Humans (and other organisms) tend to move in pursuit of better resources (both social  and  environmental).  Such ...
09 Aug 2016

Resource Dynamics Under Harvest and Sunk Cost Effects

Model
This is a simple model for resource dynamics under harvest. The authors added expected effects of investment in fixed structures on the dynamics of settlement. These sunk-cost effects are not included in this simple model.The authors introduce a model of logictically regrowing resource exploited by a consumer. There is only one variable, which is level of local renewable sources. Parameters are: local renewable resources (R), settlement of humans (H), maximum growth rate (g), maximum level of...
29 Nov 2017