Dynamics of a single species evolutionary model with Allee effects

Kang, Yun; Udiani, Oyita

doi:10.1016/j.jmaa.2014.03.083

Cited by 35 publications

(36 citation statements)

References 39 publications

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“…The evolutionary extension of this model used the approach of evolutionary game theory introduced in the book of [41] but also the recent work of [5,6,21]. We assume that: a) There is a phenotypic trait u and its related trait function φ(u) that is related to the life history parameters of social insects, which ultimately determines the ecological dynamics for a given trait value; and b) The selection of trait depends on the gradient of the fitness of the colony (i.e., the total population of the immature-and mature-class).…”

Section: Discussionmentioning

confidence: 99%

“…In this section, we derive the evolutionary model extended from the ecological model (1) by using the evolutionary game theory (EGT) approach stated in [5,21,41]. Our primary purpose of studying this extended evolutionary model is to obtain insights on how the strategy of egg cannibalism in social insects may impact the dynamical outcomes in the EGT setting.…”

Section: The Evolutionary Model and Its Dynamicsmentioning

confidence: 99%

“…By using the modeling methodology for Evolutionary Game Theory (EGT) presented in Vincent and Brown [41] but also see [6,21,30], we derive an evolutionary model from the ecological model (1) as follows:…”

Section: The Evolutionary Model and Its Dynamicsmentioning

confidence: 99%

“…Our two-stage single-species model of social insect populations consists of egg and mature stages, in which the mature stage cannibalizes the egg population. The extended evolutionary version uses the framework of evolutionary game theory used in [4,21,41]. We aim to apply this model and its extended evolutionary version to study the following ecological questions:…”

Section: Introductionmentioning

confidence: 99%

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

Kang

Rodriguez-Rodriguez

Evilsizor

2015

Journal of Mathematical Analysis and Applications

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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.

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Section: Discussionmentioning

confidence: 99%

Section: The Evolutionary Model and Its Dynamicsmentioning

confidence: 99%

Section: The Evolutionary Model and Its Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kang

Rodriguez-Rodriguez

Evilsizor

2015

Journal of Mathematical Analysis and Applications

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“…The Allee effect is therefore important in conservation of endangered and exploited species. " During the last decades, many scholars studied the influence of Allee effect, see [1,[34][35][36][37][38][39][40][41][42] and the references cited therein. Kang and Yakuba [37] studied the population dynamics of a two-species discrete-time competition model where each species suffers from either predator saturation induced Allee effects or mate limitation induced Allee effects.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of a commensal symbiosis model involving Allee effect and one party can not survive independently

Chen

2018

Adv Differ Equ

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A two-species commensal symbiosis model involving Allee effect and one party can not survive independently is proposed and studied in this paper. Sufficient conditions which ensure the local and global stability of the boundary equilibrium and the positive equilibrium are obtained, respectively. Numeric simulations show that with the increasing of Alee effect, the system takes much longer time to reach its stable steady-state solution, though the Allee effect has no influence on the final density of the species. The Allee effect has instable effect on the system, however, such effect is controllable.

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Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator

Chen

Feng

Song

2023

Acta Math. Appl. Sin. Engl. Ser.

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Dynamics of a single species evolutionary model with Allee effects

Cited by 35 publications

References 39 publications

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

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

Dynamic behaviors of a commensal symbiosis model involving Allee effect and one party can not survive independently

Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator

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