TY - JOUR
T1 - Ecological and evolutionary dynamics of two-stage models of social insects with egg cannibalism
AU - Kang, Yun
AU - Rodriguez-Rodriguez, Marisabel
AU - Evilsizor, Stephen
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - 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.
AB - 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.
KW - Backward bifurcation
KW - Cannibalism
KW - Ecological dynamics
KW - Evolutionary dynamics
KW - Forward transcritical bifurcation
KW - Stage-structure model
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U2 - 10.1016/j.jmaa.2015.04.079
DO - 10.1016/j.jmaa.2015.04.079
M3 - Article
AN - SCOPUS:84945280082
SN - 0022-247X
VL - 430
SP - 324
EP - 353
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -