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.

Figure 1. Domain of parasitoid extinction (black) and persistence (white) as a function of parasitoid searching efficiency (a) and host finite rate of increase (λ) for three intensities of a mate-finding Allee effect: no Allee effect (α = 0), mild effects (α = 5), strong effects (α = 20).

Other assumptions are a random distribution of parasitoid attacks (k = 10) and a medium intraspecific competition in the host population (b = 1.5). Two different domains of extinction can be distinguished: the upper domain corresponding to high parasitoid efficiency and low host finite rate of increase and the lower domain, corresponding to low parasitoid efficiency and high host finite rate of increase.

Figure 2. Domain of parasitoid extinction (black) and persistence (white and gray) as a function of parasitoid searching efficiency (a) and host finite rate of increase (λ) for three intensities of a mate-finding Allee effect (no Allee effect: α = 0; mild effect: α = 5; strong effect: α = 20) and two levels of intraspecific competition in the host population (under-compensated competition: b = 0.8; over-compensated competition: b = 3.2).

A random distribution of parasitoid attacks is assumed (k = 10). Parasitoid persistence is underpinned by qualitatively distinct dynamics; white: asymptotic stability; light gray: damped oscillations; dark gray: cycles or chaos.

Figure 3. Domain of parasitoid extinction (black) and persistence (white and gray) as a function of parasitoid searching efficiency (a) and host finite rate of increase (λ) for three intensities of a mate-finding Allee effect (no Allee effect: α = 0; mild effect: α = 5; strong effect: α = 20) and two distributions of parasitoid attack (random: k = 10; aggregated: k = 0.8).

Intraspecific competition in the host population is assumed moderate (b = 1.5). Parasitoid persistence is underpinned by qualitatively distinct dynamics; white: asymptotic stability; light gray: damped oscillations; dark gray: cycles or chaos.

Figure 4. Bifurcation diagrams for hosts (black) and parasitoids (gray) populations, as a function of the intensity of a mate-finding Allee effects (α).

Population characteristics: a) , , , ; b) , , , ; c) , , , . The black curve on parasitoid graphics represents .

Figure 5. Minimum initial population density triggering parasitoid establishment (F_crit) as a function of parasitoid searching efficiency (a) and the intensity of Allee effects (α).

Parameter values: b = 1.5, , , K = 500.

Figure 6. Residual host abundance after parasitism (N _max) without (α = 0) and with (α = 20) a strong mate-finding Allee effect and either a random (κ = 10) or aggregated (κ = 0.8) distribution of attacks, as a function of parasitoid searching efficiency (a) and host finite rate of increase (λ).

Intraspecific competition in the host population was assumed medium ()