This repository contains the MATLAB scripts used for an undergraduate group research project that I participated in at the Mathematical and Theoretical Biology Institute (MTBI) 2011 Summer program. The paper may be found here:
J. Ames, A. Feiler, G. Mendoza, A. Rumpf, and S. Wirkus. Determination of Tucson, Arizona as an Ecological Trap for Cooper's Hawks (Accipiter cooperii). Unpublished manuscript, 2011, https://mtbi.asu.edu/2011-2.
The project involved studying a protozoan disease (Trichomonas gallinae) as it affects the Cooper's Hawk (Accipiter cooperii). Several mathematical models were created to study this disease, including a deterministic ODE-based model and several stochastic analogs of the deterministic model. The programs included in this repository were used to generate the computational results in the paper.
I would not really expect these files to be of use to anyone outside of our research group, and most of them will not make sense unless you have read the paper (linked above), but they are provided here for anyone interested. The individual files are described below. Note that the name of our research group was "Fancy Birds", which is why many of the files are named that.
Description of the function.
> command line input (shown as "---" if it was called by another function rather than directly from the command line)
Used to plot the real H* boundary for d vs σ with varying β. Included in paper as Figure 6.
> beta_sigma_d
Used to plot the real H* boundary for β vs σ with varying d. Included in paper as Figure 5.
> d_sigma_beta
Used to plot the real H* boundary for β vs d with varying σ. Included in paper as Figure 7.
> sigma_d_beta
Used to combine the results from beta_sigma_d.m, d_sigma_beta.m, and sigma_d_beta.m into a single 3D plot. Included in the paper as Figure 8.
> sigma_beta_d_3d_corner
Used to generate a bifurcation diagram for H* versus β. Included in paper as Figure 9.
> equilibrium_bifurcation_beta
Used to generate a bifurcation diagram for H* versus d (as a percentage). Included in paper as Figure 10.
> equilibrium_bifurcation_deaths
The main stochastic model utilizing a Markov chain with event rates based on our system of ODEs. Allows the user to specify initial conditions and the σ value. Outputs a vector of the total number of each event type which occurred during the simulation, as well as a plot of each population class over time. Used to generate Figure 14. A cleaner version of this file is included in Appendix C under the name hawk_markov.m.
> fancy_birds(1000000,1825,200,200,100,0,0.423,1) for Figure 14 (showing 10 realizations with hold on)
Runs fancy_birds.m many times and averages the final statistics from each realization. Used to obtain the average population growth for a variety of σ values. The results from these runs are plotted in Figure 12.
> fancy_birds_comparison(250,[[0:0.01:0.1],[0.2:0.1:1]])
The same as fancy_birds.m, but allows the user to specify β instead of σ.
---
The same as fancy_birds_comparison.m, but instead runs fancy_birds_beta.m for a variety of β values. The results from these runs are plotted in Figure 11.
> fancy_birds_comparison_beta(250,linspace(0.0005,0.0035,21))
The same as fancy_birds.m, but allows the user to specify d instead of σ.
---
The same as fancy_birds_comparison.m, but instead runs fancy_birds_d.m for a variety of d values. The results from these runs are plotted as Figure 13.
> fancy_birds_comparison_d(250,linspace(0,0.025,26))
The alternate, more realistic stochastic model. Used to track various classes of a hawk population for a specified amount of time. Outputs a vector of various statistics about the process results, as well as a plot of either every individual class or the classes grouped into adults and nestlings.
> fancier_birds(365,200,1) for Figure 15
> fancier_birds(1825,200,2) for Figure 16 (showing 10 realizations with hold on)
The same as fancier_birds.m, but allows the user to specify a d value.
---
Runs fancier_birds_d.m many times and averages the final statistics from each realization. Used to obtain the average population growth from our default parameters, discussed in Section 3.3.
> fancier_birds_comparison_d(1000,0.41)
Function containing the equations for system (1)-(4).
---
Calls newmodel.m and plots the solution of the ODE in days, with our current parameters. Produces Figure 2
> plotNM(365)
To produce Figure 3 we change the values of d=.73/40 (73% die from the disease), γ=.27/40 (27% recovers from the disease) and run for 600 days.
> plotNM(600)
Figure 4 is given by changing values of γ=.26/40 (26% recovers from the disease), d=.74/40 (74% die from the disease) and run for 365 days.
> plotNM(365)