L'efficacité de la lutte biologique comme moyen de protection des récoltes est fortement impactée par des interactions inter- et intra- spécifiques.

En conséquence, les effets Allee (ou densité dépendance positive) que peuvent subir certains agents de lutte biologique devraient être pris en compte pour modéliser la lutte biologique et définir des stratégies d'introduction d'auxiliaires.

Nous allons étudier ce problème au travers de deux modèles de complexité croissante: le premier se concentrant uniquement sur la dynamique des prédateurs dont l'établissement est freiné par un effet Allee fort, et le second, modélisant à la fois la dynamique des proies et des prédateurs.

Dans le second cas, l'objectif est l'éradication des nuisibles malgré une efficacité réduite des prédateurs lorsqu'ils sont à faible densité.

En considérant une lutte biologique augmentative par des introductions de prédateurs de manière périodique, nous montrons qu'en cas de succès, le contrôle des nuisibles est amélioré dans les deux cas en privilégiant les introductions importantes et espacées aux introductions faibles mais plus fréquentes.

The efficiency of biological control as crop protection methodology is deeply impacted by inter- and intra-specific interactions.

As such, Allee effects among biocontrol agents such as pest predators should be taken into account to design biological control schemes.

We investigate this problem through two models of increasing complexity: the first one concentrates on the predator dynamics whose establishment is hampered by a strong Allee effect and the second one models both predator and prey dynamics.

In the latter case, pest eradication is targeted despite diminished predation efficiency when predator density is low.

Considering augmentative biological control through periodic impulsive predator releases we show that, when it succeeds, pest control is accelerated in both models by taking rare and large releases over frequent and smaller ones.

Modelling the dynamics of introduced populations is a challenge of main importance in conservation and restoration ecology.

Since introductions may occur repeatedly, we provide a model in which population growth is represented by an Ordinary Differential Equation disrupted by discrete time introduction events stochastically distributed in propagule size and over time.

Because introduction schemes involve essentially small population sizes, the model includes strong demographic Allee effects, leading the population to extinction when its size is below some threshold.

Moreover, introduction success can be hampered by environmental stochasticity, such as the occurence of catastrophes caused by external factors, that can drastically reduce the number of individuals in the population.

Assuming constant propagule pressure, i.e. the mean number of individuals introduced by unit time is constant, we investigate introduction strategies over the trade-off ranging from frequent and small sizes introductions to rarer and larger ones.

The computation of the probability to reach a target population level, where the population is deemed established, leads to an implicit equation of the Mean First Passage Time at this target. A fixed point study proves that there exists a unique solution to this equation, iteratively computed to identify the introduction strategy leading to the population target size in least time.

Litterature reports that, in case of strong Allee effects, it is preferable to favor rare and large introductions. Here we show how environmental stochasticity coupled to stochastic fluctuations in propagule size and introduction timing makes intermediate strategies the ones that minimize the time to population establishment.

Modelling the dynamics of introduced populations is a challenge of main importance in conservation and restoration biology. By assuming that introductions may occur repeatedly, we provide a model in which the population growth is represented by an Ordinary Differential Equation. Population growth is modified by discrete introduction events. Introduction events have a random propagule size and are distributed randomly in time.

Because the considered introduction schemes involve essentially small population sizes, the model can include strong demographic Allee effects, which implies that a population is doomed to extinction when its size is below some threshold. Moreover, invasion success can be hampered by environmental stochasticity, such as the occurence of catastrophes caused by external factors, that can drastically reduce the number of individuals in the population. This is also included in the model.

Assuming constant propagule pressure, i.e. the mean number of individuals introduced by unit time is constant, we investigated introduction schemes over a trade-off ranging from frequent and small sizes introductions to rarer and larger ones. The computation of the probability to reach a target size leads to an integral equation of the Mean First Passage Time (MFPT) to reach the target. A fixed point study proved that there exists a unique solution to this equation, which can be numerically computed to identify the introduction strategy leading to the population target size in least time.

To support our investigations, we proceeded to a numerical computation of the MFPT using Monte Carlo simulations of a purely stochastic model representing population growth with a birth-death process. Results of the stochastic differential equation and the purely stochastic process were compared.

Literature reports that, in case of strong demographic Allee effects, it is preferable to favor rare and large introductions. Here we show how environmental stochasticity arising as catastrophes, coupled to stochastic fluctuations in propagule size and introduction timing, can result in the mean time to population establishment being minimized for intermediate strategies.