Ecology

The DiffEQPlotter explores graphical solutions to differential equation systems. Nine equation system families are provided - some simple algebraic systems, some ecology models, and some limit cycles. Each can be tuned by setting constants. Paired time plot and phase plot show the behavior of the system (trajectory) from any selected starting point. The phase plot also shows the "nullclines" (where the derivative of each equation is zero), and a vector field showing the tendency of the system across a grid over the plane.

Though not "fractals" software, it was developed for the same mathematics professor, Michael Frame of Yale University.

Predator/Prey with Functional Response is Predator/Prey plus a first scenario to explore Types I, II, and III functional response, the function that relates predator consumption rate to prey abundance. This is the variant of Predator/Prey assigned in class at Yale.

Diversity Metrics explores species diversity measures. There are 625 possible worlds to explore (four preset). The user samples the species landscape by positioning sample plots or transects one by one, or by using an autosample button. Diversity metrics include the species-area curve, the Shannon-Weaver index, the Simpson index, and beta diversity. Used in teaching Conservation Biology at Yale.

Metapopulation Models are stochastic models of populations of populations (islands and mainland, with and without a rescue effect). Used to teach Landscape Ecology and Conservation Biology at Yale.

Population Growth Models provides 2 plots to help compare the different basic population growth models of ecology. Multiple functions and parameterizations of those functions can be added to either plot.

Density Dependence explores exponential population growth with and without density dependence.

Predator/Prey explores predator/prey coupled population equations. Starting from simple linear codependence, successive scenarios add saturation to the predator, then logistic growth to the prey, then predator interference. At Yale, we assign the functional response variant of this.

Explores Lotka-Volterra Competition models on a time series. Same interface as Predator/Prey, but for a different two-species interaction.

Exploitation Ecosystems is an introduction to classical theory on 3-trophic level food chains, across a gradient of plant carrying capacities, with choice of two models to control carnivore deathrate.

Density-Dependent Growth and Ricker Diagrams explores how chaos emerges in population ecology. No longer used - see FracDyn for a more mathematical treatment.