Ecosystem Viable Yields

The World Summit on Sustainable Development (Johannesburg, 2002) encouraged the application of the ecosystem approach by 2010. However, at the same Summit, the signatory States undertook to restore and exploit their stocks at maximum sustainable yield (MSY), a concept and practice without ecosystemic dimension, since MSY is computed species by species, on the basis of a monospecific model. Acknowledging this gap, we propose a definition of "ecosystem viable yields" (EVY) as yields compatible i) with guaranteed biological safety levels for all time and ii) with an ecosystem dynamics. To the difference of MSY, this notion is not based on equilibrium, but on viability theory, which offers advantages for robustness. For a generic class of multispecies models with harvesting, we provide explicit expressions for the EVY. We apply our approach to the anchovy--hake couple in the Peruvian upwelling ecosystem

Guaranteed Inertia Functions in Dynamical Games.

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the controls regulating viable evolutions. For tychastic systems (parameterized systems where the parameters are tyches, disturbances, perturbations, etc.), the palicinesia of a tyche measure the worst norm over time of the velocities of the tyches. The palicinesia function is the largest palicinesia threshold c such that all evolutions with palicinesia smaller than or equal to c are viable. For dynamical games where one parameter is the control and the other one is a tyche (games against nature or robust control), we define the guaranteed inertia function associated with any initial state-control-tyche triple the best of the worst of the norms of the velocities of the controls and of the tyches and study their properties. Viability Characterizations and Hamilton-Jacobi equations of which these inertia and palicinesia functions are solutions are provided.Viability; dynamical games; inertia function; Tychastic systems; palicinesia;

A metapopulation model with Markovian landscape dynamics

We study a variant of Hanski's incidence function model that allows habitat patch characteristics to vary over time following a Markov process. The widely studied case where patches are classified as either suitable or unsuitable is included as a special case. For large metapopulations, we determine a recursion for the probability that a given habitat patch is occupied. This recursion enables us to clarify the role of landscape dynamics in the survival of a metapopulation. In particular, we show that landscape dynamics affects the persistence and equilibrium level of the metapopulation primarily through its effect on the distribution of a local population's life span.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes

We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We propose several necessary conditions and a sufficient one. The hierarchy between these conditions is studied via suitable counterexamples. Equivalence criteria are given in abstract form for general dynamics and algebraic form for systems with constant coefficients or continuous switching. The problem is motivated by the study of lysis phenomena in biological organisms and price prediction on spike-driven commodities.Comment: Mathematics of Control, Signals, and Systems, Springer Verlag (Germany), 2015, online first http://link.springer.com/article/10.1007/s00498-015-0146-