Mathematical models for host-parasitoid interactions and biological control of Drosophila suzukii

This thesis treats mathematical models for host-parasitoid interactions. It is composed of three parts. In the first part, a class of such models is analyzed theoretically. It focuses on the phenomena of multiple coexistence equilibria of competing parasitoid species. The second part is about a model for determining how a parasitoid release should be timed to optimally control the invasive fruit fly Drosophila suzukii. The third part analyzes an experiment for releasing parasitoids in a greenhouse which is infested by D.suzukii. The models presented are used to discuss how to improve such biological control strategies

Multiple coexistence equilibria in a two parasitoid-one host model

Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two parasitoids that attack different juvenile stages of a common host. Their main result was that coexistence of the parasitoids is only possible when there is sufficient variability in the maturation delays of the host juvenile stages. Here, we analyze the phenomenon of coexistence in that model more deeply. We show that with some distribution families for the maturation delays, the coexistence equilibrium is unique, while with other distributions multiple coexistence equilibria can be found. In particular, we find that stable coexistence does not necessarily require mutual invasibility

Open field trials of food-grade gum in California and Oregon as a behavioral control for Drosophila suzukii Matsumura (Diptera: Drosophilidae).

The invasion of Drosophila suzukii, spotted-wing drosophila, across Europe and the US has led to economic losses for berry and cherry growers, and increased insecticide applications to protect fruit from damage. Commercial production relies heavily on unsustainable use of conventional toxic insecticides. Non-toxic insecticide strategies are necessary to alleviate the disadvantages and non-target impacts of toxic conventional insecticides and improve Integrated Pest Management (IPM). A novel food-grade gum deployed on dispenser pads (GUM dispensers) was evaluated to mitigate D. suzukii crop damage in five commercial crops and nine locations. Trials were conducted at a rate of 124 dispensers per hectare in cherry, wine grape, blueberry, raspberry, and blackberry in California and Oregon, USA during 2019 and 2020. The majority of trials with the food-grade gum resulted in a reduction of D. suzukii egg laying in susceptible fruit. In some cases, such damage was reduced by up to 78%. Overall, results from our meta-analysis showed highly significant differences between GUM treatments and the untreated control. Modeling simulations suggest a synergistic reduction of D. suzukii damage when used in combination with Spinosad (Entrust SC) insecticide. These data illustrate commercial value of this tool as a sustainable alternative to manage D. suzukii populations within a systems approach

Reversible phenotypic plasticity with continuous adaptation

We introduce a novel model for continuous reversible phenotypic plasticity. The model includes a one-dimensional environmental gradient, and we describe performance of an organism as a function of the environmental state by a Gaussian tolerance curve. Organisms are assumed to adapt their tolerance curve after a change of the environmental state. We present a general framework for calculating the genotype fitness if such adaptations happen in a continuous manner and apply the model to a periodically changing environment. Significant differences of our model with previous models for plasticity are the continuity of adaptation, the presence of intermediate phenotypes, that the duration of transformations depends on their extent, fewer restrictions on the distribution of the environment, and a higher robustness with respect to assumptions about environmental fluctuations. Further, we show that continuous reversible plasticity is beneficial mainly when environmental changes occur slow enough so that fully developed phenotypes can be exhibited. Finally we discuss how the model framework can be generalized to a wide variety of biological scenarios from areas that include population dynamics, evolution of environmental tolerance and physiology