Quantitative Models of Social-Ecological-Technical Systems

Feedback control systems in general exhibit inherent robustness-fragility tradeoffs. That is, by becoming very robust to a given set of disturbances for maintaining stability, feedback systems necessarily introduce hidden fragilities …

Here, a simple model of a subsistence economy based solely on the cultivation of maize and agave is presented. While maize is an annual plant that humans can eat and …

Animated demonstration of the Lorenz model and its sensitivity to initial conditions. The simulation starts with twenty points very close to each other, and follows them as they move further …

This is a two-sector growth model that couples the dynamics of human demographics and a renewable resource base. The two sectors are agricultural and manufacturing sectors. To capture both the positive (Malthusian) …

This model tells a story of resilience of a rangeland system in Australia. Anderies et al. (2002) provides the following overview of the model. \"We developed a stylized mathematical model …

This is the original Brander-Taylor Easter Island model. Brander and Taylor (1998) describes the model as the following: \"The paper presents a general equilibrium model of renewable resource and population …

This is a model for the coupled dynamics of conflict between two different user groups regarding their socioeconomic choice (between cooperative and non-cooperative collective action) and nutrient loading input level …

The model of Tsembaga agro-ecology explores the coupled dynamics involving population growth, renewable resource base, resource consumption by humans, and the self-regulating effect of cultural ritual. The model demonstrates that …

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This model explicitly incorporates the immigration and emigration processes in the context of three-trophic-level systems (e.g., a stream reach), and reveals how the coupled populations will change in response to the …

This is an ecological-economic model that endogenizes discontinuous change between states of fire-driven, semi-arid rangelands which may exist in varying degrees as grassland and woodlands depending partly on the given …

 The authors address the question of how infrastructure design affects SES sustainability in two stages. First, they explore the effects of design variations in shared infrastructure on long-term system behavior …

in this model, cumulative density of forest resources and population density use generalized logistic models with predatory-prey type nonlinear interactions. The model is an effort to capture not only the …

This is a standard Gordon-Schaefer model that simulates a simple open-access fishery in discrete time. A fishery stock grows logistically and is harvested by humans. Fishers always exert too much …

The dynamic model for poverty traps contains parameters as government policies and technologies, and variables such as income, expenditures, assets holdings and anthropometric status. This dynamic model for poverty traps …

HANDY is a 4-variable thought-experiment model for interaction of humans and nature. The focus is on predicting long-term behavior rather than short-term forecasting. Carrying Capacity is developed as a practical …

# Eqn 1:#β(Q) is the introduction rate#β0 represents the maximal rate of introduction in the proliferating phase#θ1 is the value for which β reaches half of its maximal value#n is …

The life table model is one of the type of survival analysis which pertains to \"time to event\". The information that were accumulated throughout the study is one of the …

A modified Lotka-Volterra system in which multiple consumers and resource systems are connected by both consumer-consumer and consumer-resource links. Consumers represent cities, and thus exhibit nonlinear scaling behaviors as population …

This simple model was developed by Edward Lorenz in 1963 to study fluid mechanics (based on Navier-Stokes equations). It is the first ever model of a chaotic dynamical system. Chaos arises …

Symmetric competition model

Most models of Malthusian population dynamics specify logistic growth to a carrying capacity, but the historical record of agrarian societies strongly suggests that repeated cycles of overshoot and collapse (so-called …

This discrete time model represents a coupled system as seen through talk turns in a conversation between a wife and husband where each exerts influence dynamically on the other. Cook …

This model is a modification of an older model by Camporeale and Ridolfi (2006) that studied the influence of river flow variability on the distribution of biomass of riparian vegetation. …

Exploring the dynamic feedbacks between biological and cultural evolutionary systems is critical to understanding the origins of modern human behavior. The authors present a population dynamics model using ordinary differential …

This model explores the long-term dynamic interaction between the exploitation of natural resources and population growth. This is a variant of Brander and Taylor (1998). The reference article, D'Alessandro (2007), …

This is a simple model of a prey–predator system in two areas, one of which receives fishing activity (fishing ground) and another that does not (MPA: marine protected area). Takashina …

This model describes the Pezzey-Anderies extension to the Brander-Taylor Easter Island model. In addition to the parameters in the Brandor-Taylor model, Pezzey and Anderies have introduced $tax$ and $h_m$. Pezzey …

This is a simple predator-prey model with type I or II functional response (depending on parameter choices). The model is also known as the Lotka–Volterra equation. Prey grows logistically and …

In this case, the surface water level is modeled by a first order differential equation. There are six sections with equal area that are allocated water based on institutions that …

This is a refined model of robustness and vulnerability trade-off of Pumpa irrigation system

This is a simple model with reciprocal feedbacks between social and ecological dynamics of farmland abandonment. With the rising urbanization, human migration to urban centers have increased significantly around the …

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 …

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), …

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 …

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.\" …

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, …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

This model is a very simple regional growth model with a single global externality.