Extra Food Could Let Predators and Prey Coexist in Cubic Herds

When fish school, krill swarm, or birds flock, the animals often assemble into three-dimensional aggregations that can be idealized as a cubic herd.

The study, published in Advances in Continuous and Discrete Models, proposes and analyzes a prey-predator model in which prey form a cubic herd while predators have access to additional food sources.

The authors, Priyanka Basak, Aniket Banerjee, and Debaldev Jana, first establish the mathematical foundations of the system.

Central to the analysis is the parameter A, which measures the amount of additional food available to predators. The team performs a bifurcation analysis with respect to this parameter, showing how the qualitative behavior of the system changes as food supply varies. Numerical simulations support the analytical findings throughout.

The study also extends the analysis into space. The researchers derive conditions for Turing instability, the mechanism by which a stable uniform state can spontaneously give rise to spatial patterns, and verify these conditions both analytically and numerically.

One of the most striking results concerns bistability. According to the model, increasing the amount of additional food can induce bistability, allowing two different equilibria to coexist simultaneously.

The same increase in additional food also promotes the formation of spatial spot patterns in the model. These patterns, arising through Turing-type mechanisms, illustrate how localized clustering can emerge in prey-predator systems when prey exhibit cubic herd behavior and predators are supplementally fed.

The authors conclude that additional food is crucial for supporting predator persistence and maintaining ecological balance in prey-predator systems exhibiting cubic herd behavior. As a theoretical contribution, the work offers a framework for understanding how herd geometry and food supplementation jointly shape coexistence, though the findings rest on model analysis and simulation rather than direct field observations.

Subject of Research: A mathematical prey-predator model with cubic herd behavior of prey and additional food for predators

Article Title: Significance of additional food in a prey-predator model with cubic shape herd behavior of prey

Article References: Basak, P., Banerjee, A., & Jana, D. (2026). Significance of additional food in a prey-predator model with cubic shape herd behavior of prey. Advances in Continuous and Discrete Models. https://doi.org/10.1186/s13662-026-04138-4

Image Credits: AI Generated

DOI: 10.1186/s13662-026-04138-4

Keywords: prey-predator model, additional food, cubic herd behavior, Beddington-DeAngelis, bifurcation, Turing instability, bistability, spatial patterns, ecological balance, mathematical biology, Significance, additional