A double-spiral maze and hi-resolution tracking pipeline to study dispersal by groups of minute insects.

Minute insects such as parasitic micro-wasps have high basic and applied importance for their widespread use as biocontrol agents. Their dispersal is a phenotype of particular interest. Classically, it is evaluated using field releases, but those are time consuming, costly, and their results highly variable, preventing high-throughput and repeatability. Alternatively, dispersal can be studied using small-scale assays, but those neglect important higher-scale processes. Consequently, proper evaluation of dispersal is often complicated or lacking in academic studies and biocontrol breeding programs. Here we introduce a new method, the double-spiral maze, that allows the study of spatial propagation of groups of micro-wasps at relevant scales (several hours and meters), retaining high throughput and experimental power. The method records the location of every individual at every time, enabling accurate estimates of diffusion coefficients or other dispersal metrics. We describe this affordable, scalable, and easy-to-implement method, and illustrate its application with a species of agricultural interest.

Two models of interfering predators in impulsive biological control.

In this paper, we study the effects of Beddington-DeAngelis interference and squabbling, respectively, on the minimal rate of predator release required to drive a pest population to zero. A two-dimensional system of coupled ordinary differential equations is considered, augmented by an impulsive component depicting the periodic release of predators into the system. This periodic release takes place independently of the detection of the pests in the field. We establish the existence of a pest-free solution driven by the periodic releases, and express the global stability conditions for this solution in terms of the minimal predator rate required to bring an outbreak of pests to nil. In particular, we show that with the interference effects, the minimal rate will only guarantee eradication if the releases are carried out frequently enough. When Beddington-DeAngelis behaviour is considered, an additional constraint for the existence itself of a successful release rate is that the pest growth rate should be less than the predation pressure, the latter explicitly formulated in terms of the predation function and the interference parameters.

A mechanistic investigation of the algae growth "Droop" model.

In this work a mechanistic explanation of the classical algae growth model built by M. R. Droop in the late sixties is proposed. We first recall the history of the construction of the "predictive" variable yield Droop model as well as the meaning of the introduced cell quota. We then introduce some theoretical hypotheses on the biological phenomena involved in nutrient storage by the algae that lead us to a "conceptual" model. Though more complex than Droop's one, our model remains accessible to a complete mathematical study: its confrontation to the Droop model shows both have the same asymptotic behavior. However, while Droop's cell quota comes from experimental bio-chemical measurements not related to intra-cellular biological phenomena, its analogous in our model directly follows our theoretical hypotheses. This new model should then be looked at as a re-interpretation of Droop's work from a theoretical biologist's point of view.

Nonlinear control for algae growth models in the chemostat.

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells' growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.

Robust regulation of anaerobic digestion processes.

This paper deals with the problem of controlling anaerobic digestion processes. A two-step (i.e. acidogenesis-methanization) mass balance model is considered for a 1 m3 fixed bed digester treating industrial wine distillery wastewater. The control law aims at regulating the organic pollution level while avoiding washout of biomass. To this end, a simple output feedback controller is considered which regulates a variable strongly related to the Chemical Oxygen Demand (COD). Numerical simulations assuming noisy measurements first illustrate the robustness of this control procedure. Then, the regulating procedure is implemented on the considered anaerobic digestion process in order to validate and demonstrate its efficiency in real life experiments.