Ecological and evolutionary dynamics of two-stage models of social insects with egg cannibalism

Yun Kang, Marisabel Rodriguez-Rodriguez, Stephen Evilsizor

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Cannibalistic interactions between different developmental stages in a population are prevalent among many groups of animals and social insects. Cannibalism plays an important role in the population outcomes and represents an adaptive strategy in which parents consume some offspring to increase their current and/or future reproductive success. To understand how egg cannibalism affects ecological dynamics and evolutionary outcomes, we propose a simple two-stage ecological model and its evolutionary model by using the framework of evolutionary game theory. Our analytical study shows that: 1. At the population level, a large rate of egg cannibalism can lead to a forward transcritical bifurcation, characterized by the emergence of a globally stable interior equilibrium, while a small rate of egg cannibalism can lead to a backward subcritical bifurcation, which generates strong Allee effects. 2. When the environment is harsh, egg cannibalism can prevent extinction in both the ecological and the evolutionary setting. In addition, evolution preserves strong Allee effects by choosing the trait with the smaller cannibalism rate. 3. Evolution may decrease or increase the fitness of the colony by decreasing or increasing the total population size. 4. The trait function is very important since it can affect permanence of the system. These results suggest that cannibalism behavior is indeed an adaptive strategy when the availability of food is scarce and the nutrient is limited. Additionally, cannibalism may be averted by defensive behaviors or other adaptations that serve to their age distribution, and it may be also a mechanism that can generate strong Allee effects.

Original languageEnglish (US)
Pages (from-to)324-353
Number of pages30
JournalJournal of Mathematical Analysis and Applications
Volume430
Issue number1
DOIs
StatePublished - Oct 1 2015

Fingerprint

Social Insects
Allee Effect
Two-stage Model
Evolutionary Dynamics
Adaptive Strategies
Game theory
Transcritical Bifurcation
Backward Bifurcation
Nutrients
Evolutionary Game Theory
Ecological Model
Animals
Permanence
Availability
Population Size
Extinction
Fitness
Interior
Decrease
Interaction

Keywords

  • Backward bifurcation
  • Cannibalism
  • Ecological dynamics
  • Evolutionary dynamics
  • Forward transcritical bifurcation
  • Stage-structure model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Ecological and evolutionary dynamics of two-stage models of social insects with egg cannibalism. / Kang, Yun; Rodriguez-Rodriguez, Marisabel; Evilsizor, Stephen.

In: Journal of Mathematical Analysis and Applications, Vol. 430, No. 1, 01.10.2015, p. 324-353.

Research output: Contribution to journalArticle

Kang, Yun ; Rodriguez-Rodriguez, Marisabel ; Evilsizor, Stephen. / Ecological and evolutionary dynamics of two-stage models of social insects with egg cannibalism. In: Journal of Mathematical Analysis and Applications. 2015 ; Vol. 430, No. 1. pp. 324-353.
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