Modeling the ecological consequences of land-use policies in an urbanizing region

Tenley M Conway1, Richard G Lathrop

  • 1Department of Geography, University of Toronto at Mississauga, 3359 Mississauga Road North, Mississauga, ON, L5L 1C6, Canada. Tenley.conway@utoronto.ca

Related Concept Videos

Threats to Biodiversity01:50

Threats to Biodiversity

There have been five major extinction events throughout geological history, resulting in the elimination of biodiversity, followed by a rebound of species that adapted to the new conditions. In the current geological epoch, the Holocene, there is a sixth extinction event in progress. This mass extinction has been attributed to human activities and is thus provisionally called the Anthropocene. In 2019 the human population reached 7.7 billion people and is projected to comprise 10 billion by...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Manipulation and Analysis01:21

Manipulation and Analysis

GIS manipulation and analysis functions are vital for decision-making and planning. These activities range from data retrieval tasks, such as selecting information based on specific criteria, to advanced analytical techniques that address complex spatial problems.One critical GIS analysis method is overlaying, which combines multiple data layers to examine impacts. For example, overlaying a river-dammed lake boundary with road networks can identify affected infrastructure. Another common...
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...