## 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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## 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 |

## Leukopoiesis Model | Model |

# 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 sen- sitivity of the rate of reintroduction#Q is the quiscent cells# Eqn 2:#k(W) is the differentiation rate#k0 is a proportionality coefficiet#m and θ2 depend on the growth factors responsible for maturation of considered white blood cells#W is lymphocytes (T, B, or NK)# Eqn 3:#Kv is the differentiation rate to... | 03 Oct 2016 |

## Life table | Model |

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 advatage of this method.This often used in demographics and epidemiology but can also be used on agricultural economics. Sperling and Loevinsohn (1992) used this method in analyzing varietal diffusion for beans in which the main objective is to know howm nay technology adopters remains after a time period. | 30 Nov 2017 |

## Living in a network of scaling cities and finite resources | Model |

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 increases w.r.t. harvest rate and harvest conversion efficiency. Populations can also migrate between cities along a welfare-dependent gradient.Analysis of the model for a simple dyadic network reveals that the basic Lotka-Volterra formulation can lead to... | 30 Sep 2016 |

## Lorenz Model | Model |

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 when a deterministic, nonlinear dynamical system exhibits long-term unpredictability in behavior due to sensitivity to initial conditions.The model is a three-dimentional system of differential equations. Specifically, the model describes the convection motion of a fluid in a small idealized "Rayleigh-... | 09 Aug 2016 |

## Lotka-Volterra Competition | Model |

Symmetric competition model | 09 Aug 2016 |

## Malthusian Population Growth and Crisis in Pre-Industrial Agrarian Societies | 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 "Malthusian crises") are endogenous to population dynamics (see Nefedov, 2013 for details and citations). In this model, Nefedov (2013) explicitly models harvest surplus production as the carrying capacity of an agricultural population. When population pressure drives the... | 01 Oct 2016 |

## Mathematics of Marital Conflict | Model |

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 et al. (1995) develop this entirely social model based on empirical observations of marital conflict in the Gottman Love Lab, a University of Washington social laboratory studying marital conflict and resolution. The authors developed this model, then confirmed the model through turn-wise application of the... | 30 Nov 2017 |

## Measuring Riparian Width | Model |

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. The new and modified model defines an upper or hillside bound of riparian vegetation, in addition to the lower bound defined in the older model, and thus clearly delineate riparian width. The assumptions made in the model include:(1) Only one species is considered, thus ignoring interspecific dynamics. (2... | 30 Nov 2017 |

## Modeling Human Ecodynamics and Biocultural Interactions in the Late Pleistocene of Western Eurasia | Model |

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 equations and agent based modeling to delineate the consequences of differing mobility strategies expressed as reproduction potential at the population level for Late Pleistocene hominins in Western Eurasia (i.e., modern Homo sapiens and Neanderthals). The model... | 29 Nov 2017 |

## Non-linear dynamics of population and natural resources: The emergence of different patterns of development | Model |

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), gives the following description of the model. "Two new assumptions are introduced: i) the disaggregation of the ecological complex into two different resources; ii) irreversibility —namely, an inexorable tendency to exhaustion when the renewable resource stock is below a certain... | 09 Aug 2016 |

## Paradox of marine protected areas: suppression of fishing may cause species loss | Model |

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 et al. 2012 gives the following description of the model. "A number of fish and invertebrate stocks have been depleted by overexploitation in recent years. To address this, marine protected areas (MPAs) are often established to protect biodiversity and recover stocks. We analyzed the potential impact of... | 09 Aug 2016 |

## Pezzey-Anderies Model | Model |

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 and Anderies (2003) gives the following overview: "We extend the Brander–Taylor model of population and resource development in an isolated society by adding a resource subsistence requirement to people's preferences. This improves plausibility; amplifies population overshoot and... | 09 Aug 2016 |

## Predator-Prey Model | Model |

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 is harvested by predators. In the model, predators are specialists (i.e., they eat only one particular prey species for survival and growth), and their predation pattern can be either type I or II functional response. In type I, the predation rate depends only on the prey density ($b=0$), i.e., how... | 09 Aug 2016 |

## Pumpa Irrigation System | Model |

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 determine how long each sector receives water, and in what order. Water is allocated to a given sector by opening and closing gates along the irrigation canals. Based on these allocations, each sector maintains a crop yield depending on the amount of time that maintains their water level within the bounds of a desired... | 09 Aug 2016 |