Discrete Logistic Population Growth Models

An interactive Shiny application for exploring deterministic, discrete, density-dependent logistic population growth models.

Overview

This app provides two tabs, each implementing a different parameterisation of the discrete logistic growth model:

1. r discrete model — uses the discrete growth factor r_d:

   N_t+1 = N_t + r_d N_t (1 − N_t / K)

2. λ (lambda) discrete model — uses the finite rate of increase λ:

   N_t+1 = λ N_t (1 − N_t / K)

A third tab provides background on the models, their assumptions, and references.

Features

• Adjustable sliders for starting population (N), carrying capacity (K), growth rate (r or λ), and time (t).
• Real-time plots of population size over time and rate of population change vs. population size.
• Demonstrates stable equilibria, damping oscillations, limit cycles, and chaotic dynamics depending on the growth rate.
• Plot lines turn red when growth-rate parameters enter the chaotic regime.

Running the App

Prerequisites

• R (≥ 3.5)
• R package: shiny
• Quarto (for rendering the .qmd documentation files)

Render Documentation

Before launching the app for the first time (or after editing any .qmd file), render the HTML includes:

# From the project directory
for f in *.qmd; do quarto pandoc "$f" -o "${f%.qmd}.html" --mathjax --from markdown; done

Launch

# From the project directory
shiny::runApp()

Or open app.R in RStudio and click Run App.

References

• Gillman, M. (2005). Population Dynamics: Introduction. Encyclopedia of Life Sciences.
• Gillman, M. (2009). An Introduction to Mathematical Models in Ecology and Evolution: Time and Space. Wiley-Blackwell.
• Gotelli, N. J. (2001). A Primer of Ecology (3rd ed.). Sinauer Associates.