Emmanuelle Augeraud-Véron

Assessing the Impact of Bycatch on Dolphin Populations: The Case of the Common Dolphin in the Eastern North Atlantic

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.

Discontinuous initial value problems for functional differential-algebraic equations of mixed type

We study the well-posedness of initial value problems for nonlinear functional differential-algebraic equations of mixed type. We are interested in solutions to such problems that admit a single jump discontinuity at time zero. We focus specially on the question whether unstable equilibria can be stabilized by appropriately choosing the size of the jump discontinuity. We illustrate our techniques by analytically studying an economic model for the interplay between inflation and interest rates. In particular, we investigate under which circumstances the central bank can prevent runaway inflation by appropriately hiking the interest rate.

Continuous-Time Overlapping Generations Models

Age structured populations are studied in economics through overlapping generations models. These models allow for a realistic characterization of life-cycle behaviors and display intertemporal equilibrium that are not necessarily efficient. This article uses the latest developments in continuous time overlapping generations models to show the influence of the vintage structure of the population on the volatility of intertemporal prices. Permanent cycles can be found on the neighborhood of steady-states while the transitional dynamics are generically governed by short run fluctuations.

The Dispersion of Age Differences between Partners and the Asymptotic Dynamics of the HIV Epidemic

In this paper, the effect of a change in the distribution of age differences between sexual partners on the dynamics of the HIV epidemic is studied. In a gender- and age-structured compartmental model, it is shown that if the variance of the distribution is small enough, an increase in this variance strongly increases the basic reproduction number. Moreover, if the variance is large enough, the mean age difference barely affects the basic reproduction number. We, therefore, conclude that the local stability of the disease-free equilibrium relies more on the variance than on the mean.

Optimal Control for a Groundwater Pollution Ruled by a Convection---Diffusion---Reaction Problem

We consider an optimal control problem of underground water contaminated by agricultural pollution. The economical intertemporal 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-dimensional domain. We prove the existence of a global optimal solution under various regularity assumptions and for a wide variety of boundary conditions. We also provide an asymptotic controllability result.

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

In this paper, we study an economic model, where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton–Jacobi–Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits.