Modeling prey behavior in response to fear of predation
Modeling prey behavior in response to fear of predation lead image
In nature, prey animals constantly worry about predators. Predation and the fear of predation impact every animal’s actions, including behaviors around reproduction and care for offspring. This means that extensive predation can not only reduce the number of living individuals of a prey species, but can also impact the number of future individuals.
Zhang et al. developed a mathematical model to study the effect of fear on prey behavior.
“The reduction of the number of sparrow offspring is not only related to the direct predation of predators, but also related to the fear from predators,” said author Yonggui Kao. “In this paper, we study the influence of the fear effect on the behavior of the sparrow and its predator population from the perspective of mathematics and biology.”
The researchers modeled their system using a fractional-order differential equation that enables more detail and a memory response. They identified three relevant parameters for their model: the fear felt by prey species, the availability of shelter from predators, and the order of the fractional derivative.
At lower orders, the end state of the system was heavily impacted by the initial conditions, which more closely mirrors real-world scenarios. For instance, with a strong memory response, the predator and prey populations tended to reach a stable equilibrium, suggesting the importance of memory for stable coexistence.
The team plans to use their method to study more complex biological systems, as well as determine more of the theoretical implications of their model.
“For example, the first derivative can represent the change rate of population, so we are curious about the biological meaning of the fractional derivative,” said Kao.
Source: “Impact of fear effect and prey refuge on a fractional order prey-predator system with Beddington-DeAngelis functional response,” by Na Zhang, Yonggui Kao, and Binfeng Xie, Chaos (2022). The article can be accessed at https://doi.org/10.1063/5.0082733 .
