A Computational Approach to Identifying Evolutionarily Stable Strategies in Mammalian Search Behaviour

Authors: L. A. Terpsma, R. Martinez-Garcia, C. H. Fleming, W. F. Fagan, J. M. Calabrese, M. J. Noonan

Understanding how organisms navigate their environment under landscape changes is increasingly important under rapid human-induced changes, yet predictive models often fail to incorporate ecological constraints which govern animal movement. This study aims to investigate how mammalian movement strategies adapt to variation in resource distribution using a computational approach. We developed a stochastic system, grounded in allometric scaling relationships, where individual movement behaviour emerges from interaction with variable resource landscapes and energetic costs, evolving over evolutionary time. Our results indicate that search strategies in a population stabilise over time, with emergent optima dependent on landscape composition. A fundamental trade-off between search efficiency and movement speed, emerges as a result of energetic constraints. Higher resource availability reduced ballistic length scale ($l_v$) (Gamma GLM: $\beta = -1.35 \times 10^{-4}$, $p = 0.00448$) and increased movement speed non-linearly (Nonlinear least squares (Michaelis-Menten): $a = 5.22$, $p < 0.001$, $b = 1079$, $p < 0.001$), suggesting individuals rely less on slow long-distance movement when resources are energetically rich. In contrast, when resources are highly clustered, we found $l_v$ decreased (Gamma GLM: $\beta = -0.00794$, $p = 0.183$), along with speed (Gamma GLM: $\beta = -0.0136$, $p < 0.001$), suggesting search strategy relies on maintaining position within a resource cluster. Resource unpredictability has found to have no significant effect on movement, but further investigation is warranted in this domain. Overall, our findings highlight the importance of incorporating ecological constraints into predictive movement models to better capture biologically plausible dynamics. This framework provides a generalisable approach for predicting how environmental change may influence animal movement, with potential applications in conservation planning and broader relevance to understanding movement processes across various ecological systems.

Repository Contents

Each folder contains another README file which describes each component in greater detail.

• simulation_scripts/ contains the R script files for the necessary functions and simulation code.
• figure_scripts/ contains functions and scripts necessary to create all figures presented in the figures folder.
• figures/ contains all figures of simulation results.
• presentations/ contains files used for presentation of the project, such as posters and slideshows.
• writing/ contains the manuscript and supplementary materials.

Start Here

The below provides details on the workflow needed to reproduce simulations. The R files listed below are found in the simulation_scripts folder.

• 01-prey-functions.R: functions for generating prey only simulations
• 02-prey-simulation.R: workflow for simulating evolution of prey search behaviour over evolutionary timescales.

R Environment and Packages

Simulations, models, and generation of all figures were conducted in the R statistical package (v.4.5.2 R Core Team 2025) using the RANN (v. 2.6.2), spatstat.random (v.3.4-2), spatstat.geom (v. 3.6-0), ctmm (v. 1.2.0), extraDistr (v. 1.10-0), mgcv (v. 1.9-3), tictoc (v. 1.2.1), tidyverse (v. 2.0.0), gridExtra (v. 2.3), viridis (v. 0.6.5), propagate (v. 1.1-0), patchwork (v. 1.3.2), and scico (v. 1.5.0.9000) packages.

Auguie B (2017). gridExtra: Miscellaneous Functions for "Grid" Graphics. doi:10.32614/CRAN.package.gridExtra https://doi.org/10.32614/CRAN.package.gridExtra, R package version 2.3, https://CRAN.R-project.org/package=gridExtra.

Baddeley A, Rubak E, Turner R (2015). Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press, London. ISBN 9781482210200, https://www.routledge.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/Baddeley-Rubak-Turner/p/book/9781482210200/.

Fleming CH, Calabrese JM (2023). ctmm: Continuous-Time Movement Modeling. doi:10.32614/CRAN.package.ctmm https://doi.org/10.32614/CRAN.package.ctmm, R package version 1.2.0, https://CRAN.R-project.org/package=ctmm.

Izrailev S (2024). tictoc: Functions for Timing R Scripts, as Well as Implementations of "Stack" and "StackList" Structures. doi:10.32614/CRAN.package.tictoc https://doi.org/10.32614/CRAN.package.tictoc, R package version 1.2.1, https://CRAN.R-project.org/package=tictoc.

Jefferis G, Kemp SE, Arya S, Mount D (2024). RANN: Fast Nearest Neighbour Search (Wraps ANN Library) Using L2 Metric. doi:10.32614/CRAN.package.RANN https://doi.org/10.32614/CRAN.package.RANN, R package version 2.6.2, https://CRAN.R-project.org/package=RANN.

Pedersen T, Crameri F (2025). scico: Colour Palettes Based on the Scientific Colour-Maps. R package version 1.5.0.9000, commit e94d08c334c8de7ba5dd0c405baeb578a5d2651c, https://github.com/thomasp85/scico.

Pedersen T (2025). patchwork: The Composer of Plots. doi:10.32614/CRAN.package.patchwork https://doi.org/10.32614/CRAN.package.patchwork, R package version 1.3.2, https://CRAN.R-project.org/package=patchwork.

Simon Garnier, Noam Ross, Robert Rudis, Antônio P. Camargo, Marco Sciaini, and Cédric Scherer (2024). viridis(Lite) - Colorblind-Friendly Color Maps for R. viridis package version 0.6.5.

Spiess A (2026). propagate: Propagation of Uncertainty. doi:10.32614/CRAN.package.propagate https://doi.org/10.32614/CRAN.package.propagate, R package version 1.1-0, https://CRAN.R-project.org/package=propagate.

Wickham H, Averick M, Bryan J, Chang W, McGowan LD, François R, Grolemund G, Hayes A, Henry L, Hester J, Kuhn M, Pedersen TL, Miller E, Bache SM, Müller K, Ooms J, Robinson D, Seidel DP, Spinu V, Takahashi K, Vaughan D, Wilke C, Woo K, Yutani H (2019). “Welcome to the tidyverse.” Journal of Open Source Software, 4(43), 1686. doi:10.21105/joss.01686 https://doi.org/10.21105/joss.01686.

Wolodzko T (2023). extraDistr: Additional Univariate and Multivariate Distributions. doi:10.32614/CRAN.package.extraDistr https://doi.org/10.32614/CRAN.package.extraDistr, R package version 1.10.0, https://CRAN.R-project.org/package=extraDistr.

Wood, S.N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3-36