Influence of Intrapredatory Interferences on Impulsive Biological Control Efficiency

Abstract

International audienceIn this paper, a model is proposed for the biological control of a pest by its natural predator. The model incorporates a qualitative description of intrapredatory interference whereby predator density decreases the per capita predation efficiency and generalises the classical Beddington-DeAngelis formulation. A pair of coupled ordinary differential equations are used, augmented by a discrete component to depict the periodic release of a fixed number of predators into the system. This number is defined in terms of the rate of predator release and the frequency at which the releases are to be carried out. This formulation allows us to compare different biological control strategies in terms of release size and frequency that involve the same overall number of predators. The stability properties of the zero-pest solution are analysed. We obtain an upper bound on the interference strength (the biological condition) and a minimal bound on the predator release rate (the managerial condition) required to eradicate a pest population. We demonstrate that increasing the frequency of releases reduces this minimal rate and also increases the rate of convergence of the system to the zero-pest solution for a given release rate. Additionally, we show that other conclusions are to be expected if the interferences between predators have weaker or stronger effects than the generalised Beddington-DeAngelis formulation proposed in this paper

Natural enemies deployment in patchy environments for augmentative biological control

“…As in the present study, they have shown that the threshold predator release rate ensuring the stability of the pest-free solution was an increasing function of the release period and that pest eradication was faster for smaller values of the release period. Here, the spatial structure of the environment seems thus to have the very same effects as direct inter-predator competition in Nundloll et al [15,16].…”

“…In previous studies, Nundloll et al [15,16] considered augmentative biological control in spatially implicit pest-predator models in which predators suffer from negative density dependence. As in the present study, they have shown that the threshold predator release rate ensuring the stability of the pest-free solution was an increasing function of the release period and that pest eradication was faster for smaller values of the release period.…”

“…Therefore, it is important to investigate which strategy (T, p) would yield faster convergence rate of the pest population to zero. As shown in [16], this can however not be achieved by simply comparing the largest modulus λ(T, p) of the eigenvalues of M, which yield the slowest dynamics of the discrete system, in order to evaluate the convergence rate of the semi-discrete system. Indeed, when comparing two strategies with identical λ, the one with a smaller T will converge faster to pest eradication in actual time than the one with a larger one.…”

Semidiscrete biomass dynamic modeling: an improved approach for assessing fish stock responses to pulsed harvest events

“…Additionally, conservation and supplementation stocking can be discrete efforts occurring for a number of aquatic and terrestrial species. The present study focuses on a nuisance population of common carp as an example; however, this approach could also be applied to pest suppression occurring in agroecosystems (i.e., predator releases, pesticides) (Lu et al 2003;Nundloll et al 2010). Accounting for these events occurring over a short period of time relative to the annual period using semidiscrete models can potentially improve understanding and management of population dynamics in a variety of systems and circumstances.…”

A population model with birth pulses, age structure, and non-overlapping generations

“…Whilst our model is new, as far as we are aware, we note that a number of other models of populations subject to birth pulses and age structure have been studied in recent years [7,[22][23][24]. Furthermore, hybrid systems have been investigated in many other contexts, including (but not limited to) vaccination strategies [2,20,28], chemotherapeutic treatment of diseases [12,18], and pest control [16,17,26,27,30,33,36].…”