Host-Parasitoid Dynamics and the Success of Biological Control When Parasitoids Are Prone to Allee Effects

Abstract

In sexual organisms, low population density can result in mating failures and subsequently yields a low population growth rate and high chance of extinction. For species that are in tight interaction, as in host-parasitoid systems, population dynamics are primarily constrained by demographic interdependences, so that mating failures may have much more intricate consequences. Our main objective is to study the demographic consequences of parasitoid mating failures at low density and its consequences on the success of biological control. For this, we developed a deterministic host-parasitoid model with a mate-finding Allee effect, allowing to tackle interactions between the Allee effect and key determinants of host-parasitoid demography such as the distribution of parasitoid attacks and host competition. Our study shows that parasitoid mating failures at low density result in an extinction threshold and increase the domain of parasitoid deterministic extinction. When proned to mate finding difficulties, parasitoids with cyclic dynamics or low searching efficiency go extinct; parasitoids with high searching efficiency may either persist or go extinct, depending on host intraspecific competition. We show that parasitoids suitable as biocontrol agents for their ability to reduce host populations are particularly likely to suffer from mate-finding Allee effects. This study highlights novel perspectives for understanding of the dynamics observed in natural host-parasitoid systems and improving the success of parasitoid introductions.

A host–parasitoid system with predation-driven component Allee effects in host population

“…Proof The positive invariance follows directly from continuity argument since N = 0 and P = 0 are invariant manifolds for system (3). We now show the boundedness of system (3) in R 2 + .…”

“…According to Lemma 2.1, we also know that the host is persistent in its single state (i.e. P = 0) for system (3). In order to show that the host is persistent Thus, the host is persistent in system (3) …”

“…Weak Allee effects are the cases when there is no such critical threshold but still there is a positive correlation between the per capita growth and population density or size at low population densities/sizes. Excellent reviews on Allee effects and their ecological implications can be found in [7] and some related recent work can be found in [1,3,14,15,25,29,34,35,41,45,50].…”

“…In recent years, there are fair amount of mathematical modelling work in studying the dynamics of host-parasitoid systems subject to Allee effects based on the modified discrete-time NicholsonBailey model (see, e.g. [3,25,26,30,31,34]) in addition to the approaches of the differential equations (e.g. see the work of Hilker et al [21], Morozov et al [38], Petrovskii et al [42]).…”

Global dynamics and bifurcation analysis of a host–parasitoid model with strong Allee effect

“…Most parasitoid larva require a specific life stage of the host, so parasitoid and host generations are linked to each other. Consequently, the interaction between host and parasitoid is often modelled by using a discrete-time step corresponding to the common generation length of host and parasitoid [3,6,8]. The following classical Nicholson-Bailey model is a famous example for host-parasitoid dynamics [16,18]:…”