[Re] Chaos in a Three-Species Food Chain

2019 Replication of Hastings & Powell (1991)

This project is a replication and implementation in Julia v1.3.1 of Hastings & Powell (1991), a classic paper in ecological modelling. Full reference to the original article:

Hastings, A., & Powell, T. (1991). Chaos in a Three-Species Food Chain. Ecology, 72(3), 896–903. https://doi.org/10.2307/1940591

The goal of this project was to test if the results of the original paper could be reproduced, as well as to provide a fully reproducible version for it on GitHub.

The reproduction was successful for all important results and was published in ReScience C (also archived on Zenodo). The open review is available here.

As a bonus, we represented the dynamics of the three-species system in the following animated 3D GIF:

Model reproduction

All the scripts required to reproduce the model are in the code/ subfolder. They assume that code/ is used as the working directory.

Initial setup

To reproduce our project, we recommend the following steps as initial setup, assuming Julia v1.3.1 is already installed:

Clone this repository

git clone https://github.com/BIO6032/2019_replication_HastingsPowell_1991.git

Launch Julia in the repository, then set code/ as the working directory:

cd("code")

Run the following commands to install the exact versions of packages (as specified in the Project Environment)

import Pkg; Pkg.activate(".")
Pkg.instantiate()

Running the model

After setup, main.jl can be run to reproduce all figures in a single call.

include("main.jl") # make sure you ran cd("code") to set the correct working directory

Note that this is not an especially intensive task. On an ordinary laptop, it takes about 1 minute, 2.00 GB of memory and uses a single core. However, if using the packages for the first time, precompiling may take an additional 5 minutes (Julia has to do this after installing or changing versions).

Alternatively, individual scripts in code/ (producing one figure each) can be run separately, either line-by-line in a terminal or through a Julia IDE, such as Juno or Julia for VS Code. However, be sure to run these lines from main.jl first:

import Pkg; Pkg.activate(".")
using DifferentialEquations
using Plots
include("HPmodel.jl")

The GIF can be reproduced by running the figure2D-gif.jl script. This is longer than for the core figures and takes about 8-10 minutes.

include("figure2D-gif.jl")

Notes on possible warnings

┌ Warning: dt <= dtmin. Aborting. There is either an error in your model specification or the true solution is unstable.
└ @ DiffEqBase ~/.julia/packages/DiffEqBase/gTsoC/src/integrator_interface.jl:333

This warning is expected in the code/figure4.jl and code/figureS1.jl scripts. It will be repeated a few times, as the model does not converge to a solution for a few higher parameter values. We chose to leave it as is to warn potential users at this.

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS
GKS: can't connect to GKS socket application
Did you start 'gksqt'?

This graphics display error sometimes happens on Linux, but the figures should be produced anyways. It can likely be fixed by installing additional dependencies -- see this issue.

Article reproduction

Our article uses the ReScience C journal template. All elements are in the article/ subfolder. Instructions to reproduce the article are provided in the subfolder README.