TY - JOUR
T1 - Dynamics of an ant-plant-pollinator model
AU - Wang, Yuanshi
AU - DeAngelis, Donald L.
AU - Nathaniel Holland, J.
N1 - Funding Information:
This work was supported by NSF of Guangdong S2012010010320 to Y. Wang, and was supported by NSF Grants DEB-0814523 and DEB-1147630 to J. N. Holland and D. L. DeAngelis. D. L. DeAngelis acknowledges the support of the US Geological Survey Southeastern Ecological Science Center.
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - In this paper, we consider plant-pollinator-ant systems in which plant-pollinator interaction and plant-ant interaction are both mutualistic, but there also exists interference of pollinators by ants. The plant-pollinator interaction can be described by a Beddington-DeAngelis formula, so we extend the formula to characterize plant-pollinator mutualisms, including the interference by ants, and form a plant-pollinator-ant model. Using dynamical systems theory, we show uniform persistence of the model. Moreover, we demonstrate conditions under which boundary equilibria are globally asymptotically stable. The dynamics exhibit mechanisms by which the three species could coexist when ants interfere with pollinators. We define a threshold in ant interference. When ant interference is strong, it can drive plant-pollinator mutualisms to extinction. Furthermore, if the ants depend on pollination mutualism for their persistence, then sufficiently strong ant interference could lead to their own extinction as well. Yet, when ant interference is weak, plant-ant and plant-pollinator mutualisms can promote the persistence of one another.
AB - In this paper, we consider plant-pollinator-ant systems in which plant-pollinator interaction and plant-ant interaction are both mutualistic, but there also exists interference of pollinators by ants. The plant-pollinator interaction can be described by a Beddington-DeAngelis formula, so we extend the formula to characterize plant-pollinator mutualisms, including the interference by ants, and form a plant-pollinator-ant model. Using dynamical systems theory, we show uniform persistence of the model. Moreover, we demonstrate conditions under which boundary equilibria are globally asymptotically stable. The dynamics exhibit mechanisms by which the three species could coexist when ants interfere with pollinators. We define a threshold in ant interference. When ant interference is strong, it can drive plant-pollinator mutualisms to extinction. Furthermore, if the ants depend on pollination mutualism for their persistence, then sufficiently strong ant interference could lead to their own extinction as well. Yet, when ant interference is weak, plant-ant and plant-pollinator mutualisms can promote the persistence of one another.
KW - Acyclicity
KW - Extended Beddington-DeAngelis functional response
KW - Mutualism
KW - Persistence
KW - Stability
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U2 - 10.1016/j.cnsns.2014.06.024
DO - 10.1016/j.cnsns.2014.06.024
M3 - Article
AN - SCOPUS:84908653975
VL - 20
SP - 950
EP - 964
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 3
ER -