Evolution Equation Models for the Advective Transport During Spring and the Fasting Physiology During Winter of Age-0 Pacific Herring in Prince William Sound, Alaska. Results from Projects J, U, T and I of the Sound Ecosystem Assessment Program.
Berenstein, Carlos A.
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Two models are presented which together address the objective of the Sound Ecosystem Assessment Program to quantitatively represent the time evolution of age-0 (first year of life) subpopulations of Pacific herring <i>(Clupea pallasi).</i><p> For these models the first year of life is represented as hatching followed by three disjoint time intervals, with each interval characterized by a single dominant process: spring through mid-summer, advective transport of larvae; mid-summer through fall, feeding and growth; and winter through early spring, fasting. Models were developed for the first and third time intervals; these two are the subject of this report.<p> The model for advective transport and fate of larvae is the result of three separate model developments: the implementation of the Mellor-Blumberg 3D primitive equation circulation model for PWS (Wang, Mooers and others, J. SEA); the representation of larval advection as composite Lagrangian particles (Wang, M. Jin and others, J. SEA); and the representation of larval initial conditions, behavior and mortality (Norcross and others, T. SEA).<p> A primary application is the losses for an age-0 subpopulation in PWS due to advection of larvae out of PWS. It is shown that the assumption of a constant, spatially uniform predation loss rate greatly simplifies the comparison of the time evolution of loss due to advection relative to that due to predation. This comparison is applied to a full simulation for 1996 with the result that the advective loss is negligible.<p> After the period of advective drift the age-0 subpopulation ceases to make significant spatial movements and is represented as a discrete collection of stationary subpopulations indexed by site. For the fasting period and for each site-indexed subpopulation the following is assumed: <i>i.)</i> observable initial physiological conditions at an observable initial time for fasting; <i>ii.)</i> observable environmental forcing during fasting; <i>iii.)</i> total fasting until an observable end-of-fast time in spring.<p> During the fasting period the four non-negligible tissue types--lipid, protein, ash, and water--are represented as an initial value problem for a system of ordinary differential equations, and fasting survival is represented as a region of viability in a four-dimensional physiology space (Patrick, Mason and others, J.SEA). The model is calibrated using laboratory studies of fasting (Paul, U SEA), and validated using the two observables physiology and survival for a set of study sites (U. SEA and T. SEA).<p> Both models are required for the determination of the time evolution of the age-0 subpopulation. The site-specific fasting survival is useful only in the context of the global distribution of the subpopulation among the possible sites. This distribution at the start of fasting is approximately given by the distribution at the end of the period of larval drift.