Quantitative Models of Social-Ecological Systems

Title
Type

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

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

Model
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02 Oct 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

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

Ecological-economic model for optimal control of fire-driven, semi-arid rangelands

Model
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 soil conditions. More sandy soils will result in woodlands, whereas clay soils will more likely result in grasslands. One of the critical features of this model is the existence and impact of fires on these different types of rangelands. Grasslands may build up biomass and create...
01 Oct 2016

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

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

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

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

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

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

Lotka-Volterra Competition

Model
Symmetric competition model
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

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