Evolutionary dynamics of a multi-trait semelparous model

Amy Veprauskas, Jim M Cushing

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider a multi-trait evolutionary (game theoretic) version of a two class (juvenile-adult) semelparous Leslie model. We prove the existence of both a continuum of positive equilibria and a continuum of synchronous 2-cycles as the result of a bifurcation that occurs from the extinction equilibrium when the net reproductive number R0 increases through 1. We give criteria for the direction of bifurcation and for the stability or instability of each bifurcating branch. Semelparous Leslie models have imprimitive projection matrices. As a result (unlike matrix models with primitive projection matrices) the direction of bifurcation does not solely determine the stability of a bifurcating continuum. Only forward bifurcating branches can be stable and which of the two is stable depends on the intensity of between-class competitive interactions. These results generalize earlier results for single trait models. We give an example that illustrates how the dynamic alternative can change when the number of evolving traits changes from one to two.

Original languageEnglish (US)
Pages (from-to)655-676
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number2
DOIs
StatePublished - Mar 1 2016

Fingerprint

Evolutionary Dynamics
Leslie model
Projection Matrix
Continuum
Bifurcation
Branch
Primitive Matrix
Reproductive number
Evolutionary Game
Matrix Models
Model
Extinction
Cycle
Generalise
Alternatives
Interaction
Class

Keywords

  • Bifurcation
  • Evolutionary dynamics
  • Juvenile-adult dynamics
  • Stability
  • Synchronous cycles

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Evolutionary dynamics of a multi-trait semelparous model. / Veprauskas, Amy; Cushing, Jim M.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 21, No. 2, 01.03.2016, p. 655-676.

Research output: Contribution to journalArticle

@article{527898dbbdfb493fbf50dd10bccfa152,
title = "Evolutionary dynamics of a multi-trait semelparous model",
abstract = "We consider a multi-trait evolutionary (game theoretic) version of a two class (juvenile-adult) semelparous Leslie model. We prove the existence of both a continuum of positive equilibria and a continuum of synchronous 2-cycles as the result of a bifurcation that occurs from the extinction equilibrium when the net reproductive number R0 increases through 1. We give criteria for the direction of bifurcation and for the stability or instability of each bifurcating branch. Semelparous Leslie models have imprimitive projection matrices. As a result (unlike matrix models with primitive projection matrices) the direction of bifurcation does not solely determine the stability of a bifurcating continuum. Only forward bifurcating branches can be stable and which of the two is stable depends on the intensity of between-class competitive interactions. These results generalize earlier results for single trait models. We give an example that illustrates how the dynamic alternative can change when the number of evolving traits changes from one to two.",
keywords = "Bifurcation, Evolutionary dynamics, Juvenile-adult dynamics, Stability, Synchronous cycles",
author = "Amy Veprauskas and Cushing, {Jim M}",
year = "2016",
month = "3",
day = "1",
doi = "10.3934/dcdsb.2016.21.655",
language = "English (US)",
volume = "21",
pages = "655--676",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",
publisher = "Southwest Missouri State University",
number = "2",

}

TY - JOUR

T1 - Evolutionary dynamics of a multi-trait semelparous model

AU - Veprauskas, Amy

AU - Cushing, Jim M

PY - 2016/3/1

Y1 - 2016/3/1

N2 - We consider a multi-trait evolutionary (game theoretic) version of a two class (juvenile-adult) semelparous Leslie model. We prove the existence of both a continuum of positive equilibria and a continuum of synchronous 2-cycles as the result of a bifurcation that occurs from the extinction equilibrium when the net reproductive number R0 increases through 1. We give criteria for the direction of bifurcation and for the stability or instability of each bifurcating branch. Semelparous Leslie models have imprimitive projection matrices. As a result (unlike matrix models with primitive projection matrices) the direction of bifurcation does not solely determine the stability of a bifurcating continuum. Only forward bifurcating branches can be stable and which of the two is stable depends on the intensity of between-class competitive interactions. These results generalize earlier results for single trait models. We give an example that illustrates how the dynamic alternative can change when the number of evolving traits changes from one to two.

AB - We consider a multi-trait evolutionary (game theoretic) version of a two class (juvenile-adult) semelparous Leslie model. We prove the existence of both a continuum of positive equilibria and a continuum of synchronous 2-cycles as the result of a bifurcation that occurs from the extinction equilibrium when the net reproductive number R0 increases through 1. We give criteria for the direction of bifurcation and for the stability or instability of each bifurcating branch. Semelparous Leslie models have imprimitive projection matrices. As a result (unlike matrix models with primitive projection matrices) the direction of bifurcation does not solely determine the stability of a bifurcating continuum. Only forward bifurcating branches can be stable and which of the two is stable depends on the intensity of between-class competitive interactions. These results generalize earlier results for single trait models. We give an example that illustrates how the dynamic alternative can change when the number of evolving traits changes from one to two.

KW - Bifurcation

KW - Evolutionary dynamics

KW - Juvenile-adult dynamics

KW - Stability

KW - Synchronous cycles

UR - http://www.scopus.com/inward/record.url?scp=84954526745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84954526745&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2016.21.655

DO - 10.3934/dcdsb.2016.21.655

M3 - Article

AN - SCOPUS:84954526745

VL - 21

SP - 655

EP - 676

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 2

ER -