A Mathematician from RUDN University Refined the Model of Predator-Prey Relations in the Wild

A Mathematician from RUDN University Refined the Model of Predator-Prey Relations in the Wild

The traditional mathematical model of predator-prey relations in the wild does not take into account indirect nonlocal interactions. However, according to a mathematician from RUDN University, they affect the dynamics of predators and prey in a system, and the nature of this effect is sensitive to the initial conditions.

Ecologists use mathematical models of ecosystems to understand their structure and predict their development. Predator-prey is one of the basic models of this kind. With its help scientists can for instance calculate changes in the numbers of carnivores and herbivores depending on numerous conditions: the breeding of the latter, starvation of the former, amounts of prey eaten by predators, migrations, and so on. However, this model only takes into account local interactions, i.e. direct interactions between predators and prey in each given spatial location, while actual ecosystems also include nonlocal ones. A mathematician from RUDN University working together with his colleagues from the UK and India enhanced the standard predator-prey model taking these less obvious factors into account. Using his work, ecologists will be able to better understand developments in natural systems.

One example of natural nonlocal interactions is arid regions. To grow there, plants need to have a vast root system to collect moisture from large territories, not just from the vicinity of their location. Mathematically, this nonlocality is expressed as an integral that sums up the effect of the whole system at each given point. The competition for food among herbivores is also nonlocal, so a model has to take into account the integral amount of food in a system, not at each particular place.

“Nonlocal properties of movement are of interest for researchers; however, the nonlocal origin of this dynamics is often discarded. Still, there are a lot of natural systems with nonlocal interactions. One of the best examples may be the vegetation-water system, especially in semi-arid regions. There, nonlocality is a direct result of extensive root networks. We have confirmed that the nonlocality of intraspecific interactions can be the cause of different system dynamics in the predator-prey model,” said Prof. Sergey Petrovskii from RUDN University.

The team tested their concept using computer modeling and found out that even if a system initially has equal numbers of carnivores and herbivores, after some time their quantities start to grow differently at different points due to nonlocal interactions. As a result, the total quantity of the system becomes dominated either by predators or prey, and different spatial patterns are formed. Another feature of a nonlocal system is bistability, i.e. possible coexistence of two patterns. This is an important attribute of nonlocality. It is the initial conditions that determine which pattern eventually succeeds.

Other participants of the study represented the University of Leicester (UK).

 An article about his work was published in the Communications in Nonlinear Science and Numerical Simulation journal.

News
All news
Science
23 Jun
Scientists Reveal the Water Column of the Yamal Lakes Can Be a Microbial Filter

Scientists from the Winogradsky Institute of Microbiology RAS, RUDN University, St. Petersburg State University and the Tyumen Scientific Centre SB RAS studied the microbial communities from several lakes of the Yamal Peninsula. It turned out that methanotrophs (bacteria that use methane as a source of energy) consume methane more actively in the deep mature lakes of the peninsula than in small thermokarst lakes. In this regard, methane emissions into the atmosphere from the surface of deep lakes are low, and only small (relatively younger thermokarst lakes with constitutional ground ice) can make a significant contribution to methane emissions in the north of Western Siberia. Thus, bacteria perform an important function for the climate balance — they reduce the emission of methane into the atmosphere.

Science
20 Jun
RUDN University Physicists Determine the Optimal Conditions for Holding High-Energy Plasma Clouds in Pyrotron

RUDN University physicists have described the conditions for the most efficient operation of long mirror-based variant of cyclotron in the autoresonance mode. These data will bring better understanding of plasma processes in magnetic traps.

Science
16 Jun
The new protocol will allow to obtain bioactive compounds bypassing by-products

Chemists from Russia and the USA have improved the method of creating bioactive indole-acetonitrile compounds. Previously, in the course of their synthesis, by-products were obtained — a new method allows them to be avoided. This increases the yield of the final product to 81%.