DOI: 10.5061/dryad.p2ngf1w4x
title: Code from: Spatial heterogeneity modulates dispersal effects on metapopulation abundance: insights from a graphical approach

description: This Dryad package contains source code for generating schematic figures
 that illustrate equilibrium geometry in a family of
 ecological/population-dynamics models. The scripts focus on (i) a logistic
 growth model and (ii) consumer–resource / predator–prey extensions with
 Type I and Type II (Holling) functional responses. Across alternative
 assumptions about the relationship between intrinsic growth rate (r) and
 carrying capacity (K) (i.e., different r–K relationships or trade-offs),
 the code computes equilibrium conditions and visualizes how equilibrium
 solutions lie on, or are constrained by, characteristic ellipses in
 parameter/state space. The archive is code-only and does not include
 empirical datasets; no simulated datasets are required for reuse. Running
 the scripts reproduces the conceptual diagrams by deterministically
 evaluating equilibrium expressions and/or numerical solutions on
 user-specified parameter grids, and outputs publication-ready figures
 (e.g., PDF/PNG) along with intermediate objects (e.g., coordinates of
 ellipses and equilibrium points) when enabled. Reuse potential includes
 (a) reproducing or adapting schematic figures for manuscripts, theses, and
 teaching materials, (b) extending to alternative functional responses or
 additional biological processes, and (c) sensitivity exploration of how
 assumed r–K relationships reshape equilibrium structure. The package
 contains no personal, sensitive, or confidential information and raises no
 human- or animal-subject ethical concerns. Files are intended for open
 reuse consistent with Dryad’s licensing requirements.
description: # Code from: Spatial heterogeneity modulates dispersal effects on
 metapopulation abundance: insights from a graphical approach Dataset DOI:
 [10.5061/dryad.p2ngf1w4x](https://doi.org/10.5061/dryad.p2ngf1w4x) ##
 Description of the data and file structure This Dryad package contains
 source code for generating schematic figures that illustrate equilibrium
 geometry in a family of ecological/population-dynamics models. The scripts
 focus on (i) a logistic growth model and (ii) consumer–resource /
 predator–prey extensions with Type I and Type II (Holling) functional
 responses. Across alternative assumptions about the relationship between
 intrinsic growth rate (*r*) and carrying capacity (*K*) (i.e., different
 *r–K* relationships or trade-offs), the code computes equilibrium
 conditions and visualizes how equilibrium solutions lie on, or are
 constrained by, characteristic ellipses in parameter/state space. The
 archive is **code-only** and does not include empirical datasets; no
 simulated datasets are required for reuse. Running the scripts reproduces
 the conceptual diagrams by deterministically evaluating equilibrium
 expressions and/or numerical solutions on user-specified parameter grids,
 and outputs publication-ready figures (e.g., PDF/PNG) along with
 intermediate objects (e.g., coordinates of ellipses and equilibrium
 points) when enabled. ### Files and variables #### File: code.R
 **Description:**  Code to analyze how dispersal shapes metapopulation size
 in logistic models and how predator dispersal affects predator and prey
 metapopulation abundance in predator–prey models with Type I and II
 functional responses. ## Code/software R