Verdy Ariane

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Verdy
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Ariane
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  • Preprint
    Sensitivity analysis of reactive ecological dynamics
    ( 2008-02) Verdy, Ariane ; Caswell, Hal
    Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.
  • Article
    Putting it all together: Adding value to the global ocean and climate observing systems with complete self-consistent ocean state and parameter estimates.
    (Frontiers Media, 2019-03-04) Heimbach, Patrick ; Fukumori, Ichiro ; Hill, Christopher N. ; Ponte, Rui M. ; Stammer, Detlef ; Wunsch, Carl ; Campin, Jean-Michel ; Cornuelle, Bruce D. ; Fenty, Ian ; Forget, Gael ; Kohl, Armin ; Mazloff, Matthew R. ; Menemenlis, Dimitris ; Nguyen, An T. ; Piecuch, Christopher G. ; Trossman, David S. ; Verdy, Ariane ; Wang, Ou ; Zhang, Hong
    In 1999, the consortium on Estimating the Circulation and Climate of the Ocean (ECCO) set out to synthesize the hydrographic data collected by the World Ocean Circulation Experiment (WOCE) and the satellite sea surface height measurements into a complete and coherent description of the ocean, afforded by an ocean general circulation model. Twenty years later, the versatility of ECCO's estimation framework enables the production of global and regional ocean and sea-ice state estimates, that incorporate not only the initial suite of data and its successors, but nearly all data streams available today. New observations include measurements from Argo floats, marine mammal-based hydrography, satellite retrievals of ocean bottom pressure and sea surface salinity, as well as ice-tethered profiled data in polar regions. The framework also produces improved estimates of uncertain inputs, including initial conditions, surface atmospheric state variables, and mixing parameters. The freely available state estimates and related efforts are property-conserving, allowing closed budget calculations that are a requisite to detect, quantify, and understand the evolution of climate-relevant signals, as mandated by the Coupled Model Intercomparison Project Phase 6 (CMIP6) protocol. The solutions can be reproduced by users through provision of the underlying modeling and assimilation machinery. Regional efforts have spun off that offer increased spatial resolution to better resolve relevant processes. Emerging foci of ECCO are on a global sea level changes, in particular contributions from polar ice sheets, and the increased use of biogeochemical and ecosystem data to constrain global cycles of carbon, nitrogen and oxygen. Challenges in the coming decade include provision of uncertainties, informing observing system design, globally increased resolution, and moving toward a coupled Earth system estimation with consistent momentum, heat and freshwater fluxes between the ocean, atmosphere, cryosphere and land.
  • Thesis
    Dynamics of marine zooplankton : social behavior ecological interactions, and physically-induced variability
    (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2008-02) Verdy, Ariane
    Marine ecosystems reflect the physical structure of their environment and the biological processes they carry out. This leads to spatial heterogeneity and temporal variability, some of which is imposed externally and some of which emerges from the ecological mechanisms themselves. The main focus of this thesis is on the formation of spatial patterns in the distribution of zooplankton arising from social interactions between individuals. In the Southern Ocean, krill often assemble in swarms and schools, the dynamics of which have important ecological consequences. Mathematical and numerical models are employed to study the interplay of biological and physical processes that contribute to the observed patchiness. The evolution of social behavior is simulated in a theoretical framework that includes zooplankton population dynamics, swimming behavior, and some aspects of the variability inherent to fluid environments. First, I formulate a model of resource utilization by a stage-structured predator population with density-dependent reproduction. Second, I incorporate the predator-prey dynamics into a spatially-explicit model, in which aggregations develop spontaneously as a result of linear instability of the uniform distribution. In this idealized ecosystem, benefits related to the local abundance of mates are offset by the cost of having to share resources with other group members. Third, I derive a weakly nonlinear approximation for the steady-state distributions of predator and prey biomass that captures the spatial patterns driven by social tendencies. Fourth, I simulate the schooling behavior of zooplankton in a variable environment; when turbulent flows generate patchiness in the resource field, schools can forage more efficiently than individuals. Taken together, these chapters demonstrate that aggregation/ schooling can indeed be the favored behavior when (i) reproduction (or other survival measures) increases with density in part of the range and (ii) mixing of prey into patches is rapid enough to offset the depletion. In the final two chapters, I consider sources of temporal variability in marine ecosystems. External perturbations amplified by nonlinear ecological interactions induce transient excursions away from equilibrium; in predator-prey dynamics the amplitude and duration of these transients are controlled by biological processes such as growth and mortality. In the Southern Ocean, large-scale winds associated with ENSO and the Southern Annular Mode cause convective mixing, which in turn drives air-sea fluxes of carbon dioxide and oxygen. Whether driven by stochastic fluctuations or by climatic phenomena, variability of the biogeochemical/physical environment has implications for ecosystem dynamics.