Fisheries interactions have been implicated in the decline of many marine vertebrates worldwide. In the eastern North Atlantic, at least 1000 common dolphins (Delphinus delphis) are bycaught each year, particularly in pelagic pair-trawls. We have assessed the resulting impact of bycatch on this population using a demographic modeling approach. We relied on a sample of females stranded along the French Atlantic and western Channel coasts. Strandings represent an extensive source of demographic information to monitor our study population. Necropsy analysis provided an estimate of individual age and reproductive state. Then we estimated effective survivorship (including natural and human-induced mortality), age at first reproduction and pregnancy rates. Reproductive parameters were consistent with literature, but effective survivorship was unexpectedly low. Demographic parameters were then used as inputs in two models. A constant parameter matrix proposed an effective growth rate of −5.5±0.5%, corresponding to the current situation (including bycatch mortality). Subsequently, deterministic projections suggested that the population would be reduced to 20% of its current size in 30 years and would be extinct in 100 years. The demographic invariant model suggested a maximum growth rate of +4.5±0.09%, corresponding to the optimal demographic situation. Then, a risk analysis incorporating Potential Biological Removal (PBR), based on two plausible scenarii for stock structure suggested that bycatch level was unsustainable for the neritic population of the Bay of Biscay under a two-stock scenario. In depth assessment of stock structure and improved observer programs to provide scientifically robust bycatch estimates are needed. Effective conservation measures would be reducing bycatch to less than 50% of the current level in the neritic stock to reach PBR. Our approach provided indicators of the status and trajectory of the common dolphin population in the eastern North Atlantic and therefore proved to be a valuable tool for management, applicable to other dolphin populations.

In this paper, the dynamic behavior of the capital growth rate is analyzed using an overlapping-generations model with continuous trading and finitely lived agents. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewisedefined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle-point trajectory that converges to a unique steady-state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.JEL Classification: D50, D90.

We consider an optimal control problem of underground water contaminated by agricultural pollution. The economical inter-temporal objective takes into account the trade off between fertilizer use and cleaning costs. It is constrained by a hydrogeological model for the spread of the pollution in the aquifer. This model consists in a parabolic partial differential equation which is nonlinearly coupled through the dispersion tensor with an elliptic equation, in a three-Communicated by Bernard Dacorogna

A mathematical model has been developed to study the spread of the COVID-19 epidemic in France. To calibrate the model, data from the French Public Health Agency was examined. The spread of the epidemic greatly depends on lockdown measures (referred to in France as ‘confinement’). The aim of this paper is to predict the expected evolution of the epidemic based on the various possible scenarios for ending the lockdown. The spread of the disease, and its re-emergence, will be determined by these scenarios.