Invasion-controlled pattern formation in a generalized multispecies predator-prey system

D. Bazeia, B. F. De Oliveira, A. Szolnoki

Research output: Contribution to journalArticle

Abstract

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey-type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.

Original languageEnglish
Article number052408
JournalPhysical Review E
Volume99
Issue number5
DOIs
Publication statusPublished - May 20 2019

Fingerprint

predators
Predator-prey System
Invasion
Pattern Formation
Predator-prey
games
transition points
autocorrelation
Intransitive
Spatial Autocorrelation
extinction
rocks
Even number
Odd number
Extinction
Order Parameter
decay
Model
Decay
Game

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Invasion-controlled pattern formation in a generalized multispecies predator-prey system. / Bazeia, D.; De Oliveira, B. F.; Szolnoki, A.

In: Physical Review E, Vol. 99, No. 5, 052408, 20.05.2019.

Research output: Contribution to journalArticle

@article{5335f4fa3c1a44a892d6bf14a5b1bfff,
title = "Invasion-controlled pattern formation in a generalized multispecies predator-prey system",
abstract = "Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey-type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.",
author = "D. Bazeia and {De Oliveira}, {B. F.} and A. Szolnoki",
year = "2019",
month = "5",
day = "20",
doi = "10.1103/PhysRevE.99.052408",
language = "English",
volume = "99",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Invasion-controlled pattern formation in a generalized multispecies predator-prey system

AU - Bazeia, D.

AU - De Oliveira, B. F.

AU - Szolnoki, A.

PY - 2019/5/20

Y1 - 2019/5/20

N2 - Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey-type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.

AB - Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey-type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.

UR - http://www.scopus.com/inward/record.url?scp=85066763645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066763645&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.99.052408

DO - 10.1103/PhysRevE.99.052408

M3 - Article

VL - 99

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5

M1 - 052408

ER -