Host coexistence in a model for two host–one parasitoid interactions

Abstract

Building from a continuous-time host-parasitoid model introduced by Murdoch et al. (Am Nat 129:263-282, 1987), we study the dynamics of a 2 host-parasitoid model assuming, for the sake of simplicity, that larval stages have a fixed duration. If each host is subjected to density-dependent mortality in its larval stage, we obtain explicit conditions for the existence of an equilibrium where the two host species coexist with the parasitoid. However, if host demography is density-independent, equilibrium coexistence is impossible. If at least one of the 1 host-parasitoid systems has an oscillatory dynamics (which happens under some parameter values), we found, through numerical bifurcation, that coexistence is favoured. Coexistence between the two hosts may occur along a periodic solution even without density-dependence. Models of this type may be relevant for the use of parasitoids as biocontrol agents of insect pests.

Stability, bifurcation analysis, and chaos control of a discrete bioeconomic model

“…Since then, the model has attracted the attention of many authors. [2][3][4][5][6] As we know, discrete-time models exhibit much more complex dynamics than the continuous-time models. Several researchers have studied various discrete host-parasitoid models in different biological contexts.…”

“…The exploitation of biological resources and harvesting of populations are common in fisheries, forestry, agriculture, and wildlife management. 2 Furthermore, biological resources are frequently harvested for profit nowadays. As a result, population dynamics with harvesting have become a very important topic in mathematical bioeconomics.…”

“…In 1935, researchers Nicholson and Bailey 1 introduced a discrete‐time host‐parasitoid system to study stability of the coexisting equilibrium. Since then, the model has attracted the attention of many authors 2–6 . As we know, discrete‐time models exhibit much more complex dynamics than the continuous‐time models.…”

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“…Tang and Chen (see [6]) and Xu and Mark (see [7]) show that many forms of complex dynamics are observed not only in hostparasitoid interaction model with Holling-type functional response but also a mutual interference host-parasitoid model. Clamer and Pugliese (see [8]) studied the dynamics of a 2 hostCparasitoid model assuming, and obtained explicit conditions for the existence of an equilibrium where the two host species coexist with the parasitoid. However, if host demography is density-independent, equilibrium coexistence is impossible.…”

Complex Non-Unique Dynamics in a Host-Parasitoid Model Incorporating Clumping Effect

“…Tang and Chen (see [6]) and Xu and Mark (see [7]) show that many forms of complex dynamics are observed not only in hostparasitoid interaction model with Holling-type functional response but also a mutual interference host-parasitoid model. Clamer and Pugliese (see [8]) studied the dynamics of a 2 hostCparasitoid model assuming, and obtained explicit conditions for the existence of an equilibrium where the two host species coexist with the parasitoid. However, if host demography is density-independent, equilibrium coexistence is impossible.…”