## Browse quantitative models header

There follows a list of quantitative models in the SES Library.

There follows a list of quantitative models in the SES Library.

Title | Type |
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## A model of robustness tradeoffs in social-ecological system | Model |

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 to disturbances outside this set. Even a small unanticipated disturbance can initiate cascading system-wide failures as a result. The model presented here demonstrates this phenomenon. In Anderies et al. (2012), an agricultural production system is illustrated as... | 09 Aug 2016 |

## A Two-Sector Growth Model: Economic Development, Demographics, and Renewable Resources | Model |

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) and negative (modern growth) type relationships between population growth and output, it is important to model the shifting composition of output from agricultural to manufacturing as growth occurs. Thus, the model is a two sector (productions and consumptions in... | 09 Aug 2016 |

## Analyzing the Impact of Agave Cultivation on Famine Risk in Arid Pre-Hispanic Northern Mexico | Model |

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 store, agave is a perennial plant that can be used for multiple purposes: as edible materials yielding caloric values and as fiber materials for producing items like clothing, ropes, and baskets. This model tries to capture the essence of a cultivation strategy of a portfolio of plants that have differing levels of sensitivity... | 09 Aug 2016 |

## Animated demonstration of the Lorenz Model | Model |

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 away. The starting values differ in the fifth and sixth significant digits of a single coordinate. The Lorenz model was developed by Edward Lorenz in 1963 to study fluid mechanics.The model is a three-dimentional system of differential equations. Specifically, the model describes the convection motion of a... | 09 Aug 2016 |

## Australian Rangelands Model | Model |

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 to explore the effects of physical, ecological, and economic factors on the resilience of a managed fire-driven rangeland system. Depending on grazing pressure, the model exhibits one of three distinct configurations: a fire-dominated, grazing-dominated, or shrub-dominated rangeland system. Transaction costs... | 09 Aug 2016 |

## Biodiversity, resilience and the control of ecological-economic systems: the case of fire-driven rangelands | Model |

This case explores semi-arid rangelands which may exist in varying degrees as grassland and woodlands. Depending partly on the soil conditions, more sandy favoring woodlands and more clay favoring grasslands, as well as the behavior of fire and herbivores, an optimally controlled management of this environment looks at the interaction of these elements. In particular, the time horizon of the management planning can heavily influence paths and conditions of the system. By controlling... | 01 Oct 2016 |

## Brander-Taylor Model | 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 dynamics related to the Lotka-Volterra predator-prey model, with man as the predator and the resource base as the prey. We apply the model to the rise and fall of Easter Island, showing that plausible parameter values generate a 'feast and famine" pattern of cyclical adjustment in... | 09 Aug 2016 |

## Conflict between groups of players in coupled socio-economic and ecological dynamics | Model |

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 into a lake water system. Suzuki and Iwasa (2009),gives the following overview of the model. "Conflict among multiple groups is a major source of difficulty in environmental conservation. People are often divided into various groups that have different social factors, sometimes ... | 09 Aug 2016 |

## Coupled population dynamics in an open, three-trophic-level system | Model |

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 primary-productivity gradients (e.g., r, K). In contrast, traditional simple food-chain models study mostly two-trophic-level system which can be open or close. More interstingly, though not reflected here, there are two contrasting models presented in the paper:... | 09 Oct 2016 |

## Culture and Human Agro-ecosystem Dynamics: the Tsembaga of New Guinea | Model |

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 the cultural ritual of Tsembaga (Kaiko) can stabilize the Tsembaga population and its resource level. This is achieved by attenuating wildly fluctuating limit cycles of population and resource levels down to desirable small-amplitude cycles. Anderies (1998) describes... | 09 Aug 2016 |

## Demographic-Fiscal Model of the Growth and Collapse of Agrarian States | Model |

The Demographic-Structural theory is an empirically derived theory of the breakdown and collapse of agrarian states, originally posited by Jack Goldstone's (1991) work on Early Modern Engalnd, France, the Ottoman Empire, and Ming China. Pulling together opposing Marxist and Malthusian expanations of state collapse, the Demographic Structural theory suggests that population pressure among the general populace and among elites places fiscal pressures on the state. When the state becomes insolvent... | 02 Oct 2016 |

## Effect of infrastructure design on commons dilemmas | Model |

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 a model system. They examine two types of distribution infrastructure, one with and one without upstream−downstream asymmetry, and different threshold characteristics of infrastructure maintenance. Second, they evaluate how these design variations influence the robustness of... | 09 Oct 2016 |

## Effects of population and population pressure on forest resources and their conservation: a modeling study | Model |

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 effect of population density on forest resources (a logistic model), but also the effect of population pressure on forest resources, which grows proportionally to population density and is limited by the carrying capacity of the forest. Additionally, it models the effect of economic... | 01 Oct 2016 |

## Fishery Model | Model |

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 effort and harvest fish at a level that is socially NOT optimal. This happens because fishers are driven to harvest until their net profit drops down to zero. A socially optimal level of harvesting effort is attained when marginal cost of harvesting effort and marginal revenue from harvesting become... | 09 Aug 2016 |

## Human and nature dynamics (HANDY): Modeling inequality and use of resources in the collapse or sustainability of societies | Model |

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 measure for forecasting collapses. A sustainable steady state is shown to be possible in different types of societies but over-exploitation of either Labor or Nature results in a societal collapse. | 09 Oct 2016 |