Dual fear mechanisms shaping stochastic population dynamics under the Allee effect
Abstract
Traditional population models that include predator–prey interactions attribute demographic changes directly to predation-related effects. However, predator-induced fear in prey has increasingly been recognised as an important factor shaping population dynamics. In this study, we propose a cubic population model in which fear acts through two distinct functional channels for a single-species population exhibiting the Allee effect. In this model, fear reduces the intrinsic growth rate through a multiplicative suppression mechanism while also playing an integrated role in modulating the growth and interaction dynamics by rescaling the saturation structure of the Holling type III interaction term. The stochastic extension of the model is described by a Langevin formalism containing correlated additive and multiplicative Gaussian noise, and the steady state probability distribution (SSPD) is analytically obtained using the corresponding Fokker–Planck equation. The analytical solution is validated by numerical simulations. The SSPD reveals both noise-induced transitions and fear-controlled regime changes between low- and high-density states, with the dual-channel structure producing structural competition and non-monotonic changes in the distribution. These are analysed through phenomenological bifurcation (P-bifurcation) diagrams and three-dimensional distribution surfaces. Additionally, statistical properties, parameter sensitivity, and escape dynamics are investigated through normalised moments, Fisher information, and mean first-passage time (MFPT) calculations. Notably, our model treats fear as an independent control parameter and provides a theoretical mechanism capable of generating qualitatively contrasting population responses across parameter regimes, while also offering a framework for examining critical transition dynamics of potential relevance to conservation and management.
Related
- Spatiotemporal dynamics in a diffusive Leslie–Gower model: Turing instability and bifurcations with prey Allee effect and predator fear effect
- Spatial Dynamics in a Diffusive Leslie–Gower Predator–Prey Model with Allee Effect, Harvesting, and Cooperative Hunting
- Stochastic SEIR dynamics via graph Laplacian diffusion under transmission uncertainty
- Investigating the deterministic and stochastic dynamics of Monkeypox: a hybrid numerical approach using spectral method and feedforward neural networks
- Cooperativity through Allee Effects drives growth of diffuse midline gliomas impacting the optimal scheduling of therapeutic interventions
BibTeX
@article{gultekin2026dual,
title = {{Dual fear mechanisms shaping stochastic population dynamics under the Allee effect}},
author = {Özgür Gültekin and Mirza Muradli},
journal = {Scientific Reports},
year = {2026},
month = oct,
doi = {10.1038/s41598-026-70008-4},
url = {https://www.nature.com/articles/s41598-026-70008-4},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Dual fear mechanisms shaping stochastic population dynamics under the Allee effect
AU - Özgür Gültekin
AU - Mirza Muradli
PY - 2026
DA - 2026/10/01
JO - Scientific Reports
DO - 10.1038/s41598-026-70008-4
UR - https://www.nature.com/articles/s41598-026-70008-4
AB - Traditional population models that include predator–prey interactions attribute demographic changes directly to predation-related effects. However, predator-induced fear in prey has increasingly been recognised as an important factor shaping population dynamics. In this study, we propose a cubic population model in which fear acts through two distinct functional channels for a single-species population exhibiting the Allee effect. In this model, fear reduces the intrinsic growth rate through a multiplicative suppression mechanism while also playing an integrated role in modulating the growth and interaction dynamics by rescaling the saturation structure of the Holling type III interaction term. The stochastic extension of the model is described by a Langevin formalism containing correlated additive and multiplicative Gaussian noise, and the steady state probability distribution (SSPD) is analytically obtained using the corresponding Fokker–Planck equation. The analytical solution is validated by numerical simulations. The SSPD reveals both noise-induced transitions and fear-controlled regime changes between low- and high-density states, with the dual-channel structure producing structural competition and non-monotonic changes in the distribution. These are analysed through phenomenological bifurcation (P-bifurcation) diagrams and three-dimensional distribution surfaces. Additionally, statistical properties, parameter sensitivity, and escape dynamics are investigated through normalised moments, Fisher information, and mean first-passage time (MFPT) calculations. Notably, our model treats fear as an independent control parameter and provides a theoretical mechanism capable of generating qualitatively contrasting population responses across parameter regimes, while also offering a framework for examining critical transition dynamics of potential relevance to conservation and management.
SN - 2045-2322
ER -