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Chapter 6
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Biophysical models of small pelagic fish
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Christophe Letta, Kenneth A. Roseb, Bernard A. Megreyc
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a
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Oceanography Department, Rondebosch, 7701, South Africa,
[email protected]
Institut de Recherche pour le Développement, UR ECO-UP, University of Cape Town,
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b
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LA 70803, USA,
[email protected]
Department of Oceanography and Coastal Sciences, Louisiana State University, Baton Rouge,
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c
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Fisheries Science Center, Seattle, WA 98115, USA,
[email protected]
National Oceanic and Atmospheric Administration, National Marine Fisheries Service, Alaska
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1
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Biophysical models of fish early life stages are used to simulate the dynamics of eggs and larvae
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in virtual marine environments. Environments are characterised by temporally dynamic three-
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dimensional fields of physical (e.g., current velocities, temperature) and biogeochemical (e.g.,
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phytoplankton and zooplankton concentrations) variables provided by hydrodynamic or
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hydrodynamic-biogeochemical coupled models. These fields are used as inputs to fish models
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that simulate the dynamics of eggs and larvae including their transport, growth, mortality and
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behavioural processes (Figure 1). Biophysical models of early life stages are ready for
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investigating the effects of climate change on egg and larval growth, mortality, and spatial
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distributions. The quality of the predictions of the biophysical models will depend on sufficient
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accuracy in the physical and biogeochemical models under climate change scenarios, whether the
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spatial and temporal scales of the physical and biogeochemical model predictions are appropriate
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to be used as inputs to biophysical fish models, and the degree to which the growth (including
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feeding), mortality (including predation), and behaviour-based movement processes represented
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in the biophysical model have adequate species-specific and site-specific details.
29 30
Many questions related to the effects of climate change on fish population dynamics (e.g.,
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sustainable harvest) require the inclusion of juvenile and adult life stages in the biophysical
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models. Unlike for eggs and larvae for which physics plays a dominant role in their movement,
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behaviour plays an important role in the movement of juvenile and adult fish. Biophysical models
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that include the adult life stages of fish is an area of high research interest but will likely be used
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for general analysis of climate effects or application to a few, extremely well-studied species and
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locations. The uncertainty in how to model movement will limit the development of a generally
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agreed upon modelling approach that has helped advance the early life stage models. Continued
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efforts on adult models is necessary in order to get to “end-to-end” (physics to fish), full life cycle
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models capable of addressing the long-term consequences of climate change on fish and fisheries.
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Abstract
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The objective of this chapter is to provide an overview of biophysical models of marine fish
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populations, with a particular focus on those applied, or potentially applicable, for examining the
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consequences of climate change on small pelagic fish species. We focus on models that include
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physics and are therefore spatially-explicit, and review models under the categories of those that
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include lower trophic level dynamics (NPZ), early life stages of fish (eggs and larvae), and
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juvenile and adult stages. We first give an overview of the methods that are used to represent
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transport, growth, mortality, and behaviour in biophysical models of early life stages. Second, we
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detail several case studies of such models, focusing on those applied to anchovy and sardine in
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SPACC regions and those involving small pelagic fish in “non-SPACC” regions. Some questions
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related to climate change require models that include juveniles and adults. Models that include
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juveniles and adults differ from the early life stage models in the important role played by
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behaviour in fish movement. We briefly discuss several approaches used for modelling
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behavioural movement of fish, and then summarize several case studies of biophysical models
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that include adults that are relevant, or potentially relevant, to small pelagic species. Finally, we
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conclude with a discussion of the potential use of biophysical models of early life stages and
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adults for investigating some of the issues associated with forecasting the effects of climate
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change on small pelagic fish species.
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1 Introduction
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Understanding and forecasting the effects of climate change on small pelagic fish involves
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coupling the physics and lower trophic level dynamics to the growth, mortality, reproduction, and
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movement processes of key life stages that govern fish recruitment and population dynamics.
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Fish exhibit large changes in body weight, and often dramatic changes in body form, habitat
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usage, and diet, with ontogenetic development through the egg, larval, juvenile, and adult life
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stages. Early life stages (eggs and larvae) are heavily influenced by advective processes, which
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determine where they go in the system and to what environmental conditions they are exposed.
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There are many models that have coupled physics with eggs and larvae dynamics, and examined
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how physical transport under different conditions can affect the growth and mortality rate
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experienced by individuals during these early life stages (Werner et al., 2001; Runge et al., 2005;
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Miller, in press). The “Workshop on advancements in modeling physical-biological interactions
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in fish early-life history: recommended practices and future directions” held on 3-5 April 2006 in
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Nantes, France (co-chairs: A. Gallego, E. North and P. Petitgas), attracted more than 50
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participants from 14 countries, an indication of the international interest in the topic. There are
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now modelling tools that allow designing simulations coupling physics with ichthyoplankton
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dynamics (e.g., Ichthyop, Lett et al., submitted, http://www.eco-up.ird.fr/projects/IBM.htm).
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Many questions posed about climate effects on fish and fisheries can be only partially answered
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by models that predict growth and survivorship to the larval or early juvenile life stage.
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Recruitment for some species may not be determined until later in the life cycle than is simulated
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with these early life stage models. Furthermore, some questions require simulating the effects of
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climate on adults (e.g., how will climate affect migration, spatial distributions and spawning
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success), and other questions require multi-generational simulations that include all life stages in
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order to forecast the long-term consequences of climate effects (e.g., climate effects on
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sustainable harvest levels). The coupling of physics and the lower trophic levels to models that
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include the adult life stages is much less common than models restricted to early life stages.
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Biophysical models that include adult life stages are being increasingly considered and their use,
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especially with the need to investigate the effects of climate and fishing in marine ecosystems,
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will accelerate over the next decade (Travers et al., submitted).
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The objective of this chapter is to provide an overview of biophysical models of fish, with a
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particular focus on those applied, or potentially applicable, for examining the consequences of
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climate change on small pelagic species. We consider models of early life stages and models that
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include adults. Our review is not intended to be comprehensive, and others have previously
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reviewed biophysical models of marine populations (Werner et al., 2001; Runge et al., 2005;
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Miller, in press). We focus our review on models of fish that include physics and possibly lower
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trophic level dynamics; inclusion of physics implies the models must be spatially-explicit. We
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divided these models into two general categories: single-species individual-based models (IBMs)
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of fish early life history and models of adult stages (either adults only, or full life cycle that
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include all life stages). In the early life stage IBMs, the abiotic environment is described with
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outputs from a hydrodynamic model, or by a hydrodynamic model coupled to a biogeochemical
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(e.g., NPZ) model. Werner et al. (2001) classified IBMs in which the physics is used for transport
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but the biotic (NPZ) environment is absent or represented by static prey fields derived from field
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data as “hydrodynamics and simple behaviors” or “hydrodynamics and static prey”. Building on
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the classification proposed by Werner et al., we also include in our review IBMs that use outputs
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of biogeochemical models as a dynamic representation of the prey for the fish, and these we term
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“hydrodynamics and dynamic prey”. The adult models are much less common and, while we
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focus on models that are spatially explicit and coupled to hydrodynamic and biogeochemical
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models, we also include models that do not fulfil all of the criteria. We included some adult
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models because they could be adapted to examine questions about climate change effects that
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require the inclusion of adult life stages.
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This chapter is organized as follows. First, we give an overview of the methods used to represent
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transport, growth, mortality, and behaviour of individuals in biophysical models of early life
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stages. Second, we detail several case studies of such models, organized by models of anchovy
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and sardine in SPACC regions (first in the Benguela upwelling system, then in other major
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upwelling systems), and for small pelagic fish in general in “non-SPACC” regions. We then turn
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to models that include adults. Because fish behaviour comes much more into play when adult
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stages are considered, advective transport is no longer sufficient and we discuss methods used to
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represent movement. We then detail several case studies of biophysical models that include adults
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that are relevant, or potentially relevant, to small pelagic species and climate change. Finally, we
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conclude with a discussion of the potential use of these biophysical models to investigate some of
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the issues raised in the context of climate change.
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2 Biophysical models of early life stages
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2.1 Modelling the fish egg and larval environment
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2.1.1 The abiotic environment
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The abiotic environment for the fish eggs and larvae is usually provided by simulations of
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hydrodynamic models. In some studies, field data were directly used to generate the needed
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physics for model simulations (e.g., Heath et al., 1998; Rodríguez, 2001; Santos et al., 2004). The
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hydrodynamic models were generally used to provide temporally dynamic, 3-dimensional fields
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of physical variables such as current velocities, temperature, and salinity.
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2.1.2 The biotic environment
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The use of biogeochemical models or field data to generate the biotic environment for the fish
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eggs and larvae has received less consideration. Most applications focus on the prey field for
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influencing the feeding and growth rates of the fish larvae. Prey fields have been generated as
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input to the early life stage models using biogeochemical models (e.g., Hinckley, 1999; Koné,
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2006), interpolated from field data (e.g., Hinrichsen et al., 2002; Lough et al., 2006), or assessed
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using remotely-sensed data (e.g., Bartsch and Coombs, 2004). On the other hand, use of models
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or data to specify spatially and temporally varying predation on fish eggs and larvae is rare (but
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see Suda and Kishida, 2003; Suda et al., 2005; Vikebø et al., in press). Predation is usually
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considered part of the total mortality rate, with the changing vulnerability of early life stages
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represented by mortality rates being stage-specific or size-dependent.
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2.2 Modelling fish egg and larval dynamics
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Most biophysical models of the early life stages are individual-based models (Lagrangian),
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although a few models used an Eulerian approach (e.g., Zakardjian et al., 2003, who applied their
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model to zooplankton dynamics). There are a variety of different methods for coupling a
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hydrodynamic model to an individual-based model of eggs and larvae (Hermann et al., 2001).
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Most common is to run the hydrodynamic model, store the outputs, and then use the outputs as
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inputs to the fish model (Figure 1).
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Figure 1
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2.2.1 Transport
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v Transport of individuals in biophysical models consists in updating the individuals’ position x
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using the following equation:
166 r r r dx / dt = u + u ′
(1)
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r The deterministic advection term u is typically derived from spatial and temporal interpolations r of the flow fields provided by the hydrodynamic model. A stochastic term u ′ is often added to
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take into account the small-scale fluctuations in the currents that are lost due to the grid resolution
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of the hydrodynamic model and temporal averaging of the hydrodynamic model outputs. The
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stochastic term is often represented using an ad-hoc diffusion term (i.e., a random walk process)
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or using a random displacement process if a spatially non-uniform diffusivity is used (North et
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al., 2006; Huret et al., in press). Recent theoretical results using the dispersal characteristics of
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drifters show promise for objectively specifying the stochastic term (Haza et al., in press).
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Equation (1) is numerically integrated using schemes such as a forward Euler or a Runge-Kutta.
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Ådlandsvik (abstract 1 ) has recently proposed several standard test cases to evaluate the advection
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scheme used in biophysical models. Some studies have specifically attempted to “validate” the
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flow fields and the transport scheme used by comparing trajectories of virtual and real drifters
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(Gutiérrez et al., 2004; Thorpe et al., 2004; Edwards et al., 2006; Fach and Klinck, 2006).
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2.2.2 Growth
183
1
Ådlandsvik, B. The particle-tracking method for transport modelling. Workshop on advancements in modeling physical-biological interactions in fish early-life history: recommended practices and future directions. Nantes, France, April 3-5, 2006.
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A general relationship between the attributes of individuals (e.g., length L and age) and
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environmental variables (e.g., temperature T and food biomass F ) was proposed by Heath and
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Gallego (1997) to simulate growth:
187 t = age
Lage =
∫ f (age) f 1
2
(T ) f 3 ( F )dt
(2)
t =0
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In most biophysical models, the growth algorithm used various simplified versions of equation
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(2) in which stage durations (e.g., Miller et al., 1998), length (e.g., Fox et al., 2006), or weight
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(e.g., Vikebø et al., 2005) were functions of temperature only. When the effect of prey fields on
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growth was considered, relatively more complex bioenergetics sub-models were developed (e.g.,
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Hinckley, 1999; Megrey and Hinckley, 2001; Hinrichsen et al., 2002; Lough et al., 2005). These
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bioenergetics models allow for weight and temperature effects on consumption and the loss terms
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(respiration, egestion, excretion), and use the prey field information to determine the actual
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realized consumption rate. There is an extensive set of bioenergetics models for fish, many of
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which use the same notation and formulations in what is termed the Wisconsin model that allows
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for easy inter-specific and inter-life stage comparisons (Ney, 1993; Hanson et al., 1997).
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2.2.3 Mortality
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Mortality has been represented in early life stage models in a variety of ways, including constant
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rates (e.g., Brown et al., 2005; Tilburg et al., 2005), and depending on life stage (e.g., Miller et
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al., 1998), length (e.g., Hinckley, 1999), weight (e.g., Brickman et al., 2001), temperature (e.g.,
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Mullon et al., 2003), and growth rate (e.g., Hinrichsen et al., 2002; Bartsch and Coombs, 2004).
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Suda and colleagues (Suda and Kishida 2003; Suda et al., 2005) is one of the few examples that
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included inter-specific effects and density dependent effects on mortality. Vikebø et al. (in press)
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considered predation rates on larvae as functions of their size and light intensity. The high
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mortality rates of early life stage IBMs can result in numerical problems because many
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individuals need to be followed in order to obtain enough survivors to allow analysis of the
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results. One method for dealing with the high mortality problem is to use the concept of super-
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individuals (Scheffer et al., 1995), in which each simulated individual is assumed to represent
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some number of identical population individuals (e.g., Hinckley, 1999; Megrey and Hinckley,
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2001; Allain, 2004; Bartsch and Coombs, 2004). Rather than mortality resulting in the removal of
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model individuals, the worth of each super-individual is decreased based on the mortality rate.
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Models that use super-individuals can therefore use a constant, and a priori determined, number
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of model individuals throughout their simulations. Caution is needed in using super-individuals to
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ensure numerical accuracy of model simulations. When processes are density-dependent or the
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introduction of new individuals occurs over an extended period of time or space, proper balancing
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of how new super-individuals are introduced (number, initial population number they represent,
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timing and spatial location of their introduction) is needed to ensure accurate model results.
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2.2.4 Behaviour
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Egg buoyancy schemes have been included in determining the vertical position of individuals.
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Typically, a vertical velocity term is used that is assumed to be proportional to the difference
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between egg density and water density. Egg densities have been assumed to be constant (e.g.,
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Parada et al., 2003; North et al., 2005), stage-dependent (e.g., Hinckley, 1999), and time-
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dependent (e.g., Brickman et al., 2001). Because growth, mortality, and horizontal advection are
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all functions of depth, a key behavioural trait for drifting larvae is vertical positioning (Fiksen et
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al., in press). It is therefore no surprise that vertical migration of larvae has received a lot of
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attention, even in early works (Bartsch et al., 1989). Most studies use a diel vertical migration
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scheme (e.g., Rice et al., 1999; Peliz et al., in press), but other vertical migration approaches
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include the use of a depth-by-age curve (Ådlandsvik et al., 2004), stage-specific vertical
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velocities (Pedersen et al., 2006), and length-specific depth distributions (Bartsch and Coombs,
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2004). Vikebø et al. (in press) have used an approach where larvae are assumed to know the
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conditions within the upper 100 m and to migrate where they have an optimal blend of growth
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and survival. Horizontal swimming of larvae has also been considered in a few studies
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(Rodríguez et al., 2001; Yeung and Lee, 2002; Fox et al., 2006; Fiksen et al., in press). Specific
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experiments have been conducted to assess swimming abilities of larvae, and described as an
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integral part of the modelling process (e.g., Guizien et al., 2006). To our knowledge, schooling
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behaviour, which commonly appears in small pelagic fish larvae (Hunter and Coyne, 1982), has
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never been taken into account. However, there are many models of schooling that focus on how
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schools form and persist (reviewed in Lett and Mirabet, submitted).
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2.3 Case studies
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2.3.1 Models of anchovy and sardine in the Benguela upwelling system
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Most biophysical models of early life stages developed for the Benguela Current upwelling
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system have focused on anchovy (Engraulis encrasicolus) in the southern Benguela (Huggett et
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al., 2003; Mullon et al., 2003; Parada, 2003; Parada et al., 2003; Skogen et al., 2003; Koné,
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2006). Early life stage models have also been developed for sardine (Sardinops sagax) in the
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southern Benguela (Miller, 2006; Miller et al., 2006) and in the northern Benguela (Stenevik et
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al., 2003). All these models, except Koné (2006), fall into the “hydrodynamics and simple
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behaviors” category; Koné’s (2006) model is an example of an “hydrodynamics and dynamic
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prey” IBM.
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Most of these Benguela Current models used the same regional PLUME configuration (Penven,
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2000; Penven et al., 2001) of the ROMS hydrodynamic model (Shchepetkin and McWilliams,
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2005). The PLUME configuration covers the southern Benguela from 28 to 40°S and from 10 to
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24°E, at a horizontal resolution ranging from 9 km at the coast to 16 km offshore and with 20
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terrain-following vertical levels. Koné (2006) used the same PLUME configuration of ROMS but
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coupled with a biogeochemical model (Koné et al., 2005). Skogen et al. (2003) and Stenevik et
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al. (2003) used a different configuration and the NORWECOM hydrodynamic model (Skogen,
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1999). This configuration covered the whole Benguela area, from 12 to 46°S and from 4 to 30°E,
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at a horizontal resolution of 20 km and with 18 terrain-following vertical levels.
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Recently, the ROMS model has been applied to the Benguela region using an embedding
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procedure that places a high-resolution small-scale (child) grid nested into a low-resolution large-
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scale (parent) grid (Penven et al., 2006a). The parent grid covers the whole southern Africa from 10
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5 to 46°S and from 2°W to 54°E, at a horizontal resolution of 0.25° ranging from 19 km in the
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south to 27 km in the north (Southern Africa Experiment or SAfE, Penven et al., 2006b). The
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first child grid (SAfE south coast) was designed to study the interactions between the Agulhas
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and Benguela systems and covers the area from 28 to 39ºS and 12 to 27ºE at a horizontal
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resolution of about 8 km (N. Chang, personal communication). The second child grid (SAfE west
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coast) was designed to encompass most of the Benguela from 18 to 35ºS and 10 to 20ºE, and also
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has a horizontal resolution of about 8 km (J. Veitch, personal communication). The parent and
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child grids have 32 terrain-following vertical levels. Hydrodynamics provided on the SAfE west
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coast child grid was recently used in a Lagrangian model (Lett et al., in press).
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The development of anchovy early life stage models for the southern Benguela that used the
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PLUME configuration of ROMS has followed a step-by-step progression from simple to more
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complex models. The first model developed by Huggett et al. (2003) only tracked eggs and larvae
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with transport completely determined passively by currents. Parada et al. (2003) introduced a
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buoyancy scheme for the eggs, and Parada (2003) added temperature-dependent and stage-
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dependent growth and mortality, and vertical swimming behaviour of larvae. A synthesis of these
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simulation experiments can be found in Mullon et al. (2003). Koné (2006) then added food-
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dependency to the temperature-dependent larval growth.
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The progression of anchovy model development provides an opportunity for determining how
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increasing biological complexity affected model results. All of these models used the same
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configuration of the same hydrodynamic model (PLUME implementation of ROMS), and all
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relied on the same method for designing simulations and analysing the results. Simulations were
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performed using all combinations of pre-defined parameter values, and using comparable
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graphical and statistical analysis to determine the effects of the parameters and their interactions
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on the output variables. The main output variable used was the percentage of larvae transported
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from the anchovy spawning grounds near the South African south coast to nursery grounds off
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the west coast. This percentage was referred to as the simulated transport success. The major
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results from the progression of models and analyses were:
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1) Simulated transport success has a strong seasonal pattern, peaking in the austral spring and summer time periods (October to March).
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2) There is little chance for virtual eggs released on the eastern side of the spawning grounds to be transported to the west coast. 3) Simulated transport success is highest for an egg density of 1.025 g.cm-3, and use of this density generated results similar to those obtained using purely passive transport. 4) Simulated transport success increases with spawning depth within 0 to 75 m.
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These modelling results corresponded reasonably well to the field observations of anchovy in the
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southern Benguela. The main spawning season of anchovy is austral spring and summer, with
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major spawning areas located in the western and central parts of the spawning grounds. Measured
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egg density is about 1.025 g.cm-3. However, anchovy eggs are mainly found in the upper 20 m
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and rarely deeper than 60 m (Dopolo et al., 2005). Preliminary results obtained from an anchovy
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biophysical model using new hydrodynamics (SAfE south coast implementation of ROMS)
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suggest a slight decrease of simulated transport success with spawning depth, which is more in
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accordance with the observations.
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While the early life stage models of the Benguela described above used hydrodynamics based on
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seasonal forcing, other models (Skogen et al., 2003; Stenevik et al., 2003; Miller, 2006; Miller et
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al., 2006) used hydrodynamics based on interannual forcing. Interannual indices of retention or
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transport success derived from these models did not correlate well with time-series of sardine
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recruitment (Stenevik et al., 2003; Miller, 2006; Miller et al., 2006). However, the main objective
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of these analyses was on investigating the factors that affected retention and transport of sardine
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eggs and larvae, and not on deriving indicators of recruitment success. Skogen et al. (2003)
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showed that different indices of transport to the South African west coast were correlated to
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anchovy recruitment. The contrasting results of model-derived indices being correlated or not
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correlated with recruitment data was also found in other studies. Parada et al. (in press) found that
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pre-recruitment indices and retention indices derived from their walleye pollock (Theragra
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chalcogramma) model were not correlated with recruitment estimates in the Gulf of Alaska,
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while Baumann et al. (2006) found significant correlations between a drift index and sprat
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(Sprattus sprattus) recruitment success in the Baltic Sea. The recent availability of interannual
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simulations covering the period 1957–2001 for the SAfE south coast and SAfE west coast
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333
implementations (N. Chang and J. Veitch, personal communications), presents an opportunity for
334
attempting to correlate model-generated indices to recruitment data for the Benguela region.
335 336
The numerical experiments performed by Mullon et al. (2002), Lett et al. (2006) and Lett et al.
337
(in press) provide some basic building blocks for analyses of anchovy and sardine early life stage
338
dynamics. Mullon et al. (2002) developed an evolutionary model that explored how
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environmental constraints (e.g., avoiding offshore advection and cold water) affect the spatial and
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temporal patterns in spawning. These relatively simple constraints imposed for multiple
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generations led to the selection of spawning patterns that were in surprisingly good agreement
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with those observed for anchovy and sardine in the southern Benguela. This approach of allowing
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the temporal and spatial patterns in spawning to emerge from a selective process and
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environmental conditions offers an alternative to the usual approach of specifying the location
345
and timing of egg deposition that is used in most biophysical models.
346 347
Lett et al. (2006) used a Lagrangian approach to simulate and quantify enrichment and retention
348
processes in the southern Benguela. These two processes, along with the concentration process,
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form a triad of processes that are fundamental for the survival and recruitment of early life stages
350
of pelagic fish (Bakun, 1996). The results of Lett et al. (2006) reinforce the view of Cape
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Agulhas as a “dividing line” in the southern Benguela pelagic fish recruitment system, with a
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transport-based subsystem to the west and a retention-based subsystem to the east. These two
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subsystems were considered by Miller (2006) and Miller et al. (2006) in their sardine biophysical
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model. Lett et al. (in press) also used a Lagrangian approach to investigate the processes
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responsible for the absence of anchovy and sardine spawning in the central Benguela off the
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Lüderitz region. They examined the flow field and temperature conditions that particles would
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experience in the Lüderitz region, and concluded that the combination of a surface hydrodynamic
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and a subsurface thermal barrier could limit the possibility for anchovy and sardine
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ichthyoplankton to be transported from the southern to the northern Benguela. Recent remote
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sensing data also suggested a poor trophic environment in the Lüderitz region (Bartholmae and
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Basson, submitted; Demarcq et al., in press).
362
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2.3.2 Models of anchovy and sardine in other upwelling systems
364 365
We are not aware of biophysical models of anchovy early life stages developed in Eastern
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Boundary Current upwelling systems outside the Benguela. A preliminary biophysical model of
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sardine (Sardina pilchardus) has been developed in the Iberian system (Santos et al. 2005). Other
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models of sardine, in the Kuroshio Current (Sardinops melanostictus, Heath et al., 1998) and in
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the Iberian (Santos et al., 2004) upwelling systems, used hydrodynamics derived from field data.
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However, three anchovy (Engraulis ringens) biophysical models using hydrodynamics provided
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by ROMS are under development for the Humboldt Current upwelling system (Brochier et al.,
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submitted; Brochier et al., abstract 2 ; Soto-Mendoza et al., abstract 3 ; Chai et al., abstract 4 ), and
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there are anchovy models in the vicinity of major upwelling systems. Models exist for European
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anchovy (Engraulis encrasicolus) in the Bay of Biscay (Allain et al., 2003; Allain, 2004; Allain
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et al., in press; A. Urtizberea, personal communication) and for Japanese anchovy (Engraulis
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japonicus) in the Yellow Sea (Hao et al., 2003). Models of the early life stages of taxa in
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upwelling systems besides small pelagic fish include crab (Carcinus maenas) in the Iberian
378
upwelling system (Marta-Almeida et al., 2006; Peliz et al., in press), zooplankton in the
379
California Current upwelling system (Carr et al., in press), and blue shrimp (Litopenaeus
380
stylirostris) and brown shrimp (Farfantepenaeus californiensis) in the Gulf of California
381
(Marinone et al., 2004).
382 383
Santos et al. (2004) used a combination of measured and modelled velocities to estimate the
384
surface flow field experienced by particles during an upwelling event off Portugal, and obtained
385
qualitatively similar patterns of retention at the shelf-break for modelled particles and for
386
observed sardine eggs and larvae. In the same region, Marta-Almeida et al. (2006) used the 2
Brochier, T., Tam, J. and Ayón, P. IBM for the anchovy in the northern Humboldt Current ecosystem: identification of processes affecting survival of early life stages. International Conference on The Humboldt Current System: Climate, ocean dynamics, ecosystem processes, and fisheries. Lima, Peru, November 27 - December 1, 2006. 3
Soto-Mendoza, S., Castro, L., Parada, C., Colas, F., Donoso, D. and Schneider, W. Modeling the egg and early larval anchoveta (Engraulis ringens) transport/retention in the southern spawning area of the Humboldt Current. International Conference on The Humboldt Current System: Climate, ocean dynamics, ecosystem processes, and fisheries. Lima, Peru, November 27 - December 1, 2006.
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Chai, F., Shi, L., Xu, Y., Chao, Y., Rose, K., Chavez, F. and Barber, R. T. Modeling Peru upwelling ecosystem dynamics: from physics to anchovy. International Conference on The Humboldt Current System: Climate, ocean dynamics, ecosystem processes, and fisheries. Lima, Peru, November 27 - December 1, 2006.
14
387
ROMS model on a domain extending from 37.5 to 44.3°N and 12.8 to 8.4°W and simulated
388
different vertical migration behaviours of crab larvae. They showed that migrating larvae were
389
retained within the inner shelf under a wider range of upwelling and downwelling conditions than
390
non-migrating larvae. This was further studied by Peliz et al. (in press). They used a 3-level
391
embedding procedure in ROMS, with a high-resolution (~2 km) small-scale domain nested into a
392
medium-resolution (~6 km) medium-scale domain, both nested into a low-resolution (~16 km)
393
large-scale domain. They showed that a model including both diel vertical migration for larvae
394
and river outflow allowed simulating patterns of crab larvae concentrations that were closer to the
395
observed patterns than when only one of the two processes was included (Figure 2). This is a
396
good example of modelling study using a pattern-oriented approach (Grimm et al. 2005). We can
397
anticipate a similar study on sardine (Santos et al., 2007) to complement the preliminary one of
398
Santos et al. (2005), as data on the vertical distribution and behaviour of sardine larvae have
399
recently been collected off Portugal (Santos et al., 2006).
400 401
Figure 2
402 403
Allain and colleagues (Allain et al., 2003; Allain 2004; Allain et al., in press) used
404
hydrodynamics derived from the MARS 3-dimensional circulation model (Lazure and Dumas, in
405
press) that covered the Bay of Biscay south of 49°N and east of 8°W at a 5 km horizontal
406
resolution with 30 terrain-following vertical levels. Allain et al. (2003) used virtual passive buoys
407
released in the simulated flow fields to reconstruct the putative origins in time and space of
408
collected anchovy larvae and juveniles. Allain (2004) and Allain et al. (in press) used a
409
biophysical model of anchovy that included transport, growth, and mortality. They used the
410
super-individual approach (Scheffer et al., 1995), with each simulated buoy representing a large
411
number of eggs, larvae, and juveniles. Every time step, each buoy was characterized by a
412
distribution of growth rates (function of age and the physical environment it experienced) and by
413
a survival probability (the probability that growth rates in the distribution were above a pre-
414
defined age-specific and stage-specific threshold). They used the simulations to form an index of
415
recruitment (survival rate multiplied by egg production, summed over the year and spatial
416
domain) that correlated remarkably well to a (short) time-series of anchovy recruitment data.
417
15
418
Rodríguez et al. (2001) released particles in a static two-dimensional flow field calculated from
419
observations to assess the potential for retention of organisms around the Canary Island of Gran
420
Canaria. They showed that particles released north of Gran Canaria would need limited
421
“swimming ability” (speeds of ~0.5 cm.s-1) in order for them to be retained, whereas those
422
particles released east or west of Gran Canaria would require a much stronger swimming ability
423
(>5 cm.s-1) in order to be retained. Hunter (1977) reported mean swimming speeds of 0.3–0.45
424
cm.s-1 for early (5 mm) northern anchovy (Engraulis ringens) larvae at 17° to 18°C. A
425
configuration of ROMS for the northern Canary is under development (E. Machu, personal
426
communication). This configuration uses an embedding procedure with a parent grid covering the
427
area from 10 to 40°N and -5.5 to 30°W at a horizontal resolution of 1/4°, and a child grid from 21
428
to 32.5°N and 9 to 20.5°W at a horizontal resolution of about 8 km. A biophysical model will be
429
developed in the near future to study sardine early life history in this region (T. Brochier and A.
430
Ramzi, personal communications).
431 432
Lett et al. (2007) used a similar approach for the northern Humboldt upwelling system as Lett et
433
al. (2006) did in the southern Benguela. They derived indices of enrichment, concentration, and
434
retention based on Lagrangian simulations using hydrodynamics from a regional ROMS
435
configuration. This configuration covered the domain off Peru from 20°S to 3°N and 90 to 70°W
436
at a horizontal resolution of 1/9° (~10 km) and with 32 terrain-following vertical levels (Penven
437
et al., 2005). Lett et al. (2007) analysed the spatial distribution and seasonal variability in the
438
simulated indices, and discussed their results in relation to the distributions of anchovy
439
(Engraulis ringens) eggs and larvae off Peru. A coastal area of enhanced enrichment was
440
identified between Punta Falsa and Pisco (6°–14°S), which corresponds to the zone where most
441
anchovy eggs and early larvae are found. Preliminary modelling results suggest that the early life
442
stages of anchovy are found mainly in the northern part of this zone (6°–9°S) because this area
443
provides high retention and concentration. Another striking characteristic of anchovy spawning in
444
the region is the bimodal seasonal pattern, with peaks in January-March and August-October. A
445
biophysical model of anchovy early life stages is currently being developed to better understand
446
the bimodal spawning pattern in this region (Brochier et al., submitted). Other biophysical
447
models of the early life stages of anchovy are under development for the northern Humboldt (Y.
16
448
Xu, personal communication) and southern Humboldt (S. Soto-Mendoza, personal
449
communication) upwelling systems.
450 451
Heath et al. (1998) used static two- and three-dimensional flow fields calculated from
452
observations for two years to assess the dispersal of sardine (Sardinops melanostictus) eggs and
453
larvae in the Kuroshio Current upwelling system. They obtained very different results for the two
454
years, with most egg production being transported towards the Kuroshio Current extension in the
455
first year, while most of it was retained in the coastal areas in the second year. In contrast, using
456
different scenarios for transport (without and with diffusion) and for behaviour (without and with
457
vertical redistribution of individuals according to observed depth distributions) had little effect on
458
model simulations. They argued that, at least during the time of their study, hydrodynamic
459
models could not easily simulate the instabilities in the Kuroshio path that were responsible for
460
the contrasting flow fields they observed.
461 462
Hao et al. (2003) conducted Lagrangian simulations in the nearby Yellow Sea using a regional
463
configuration of the HAMSOM (Hamburg Shelf Ocean Model) hydrodynamic model. This
464
configuration covered the Yellow Sea and the East China Sea from about 25 to 40°N and 120 to
465
130°W at a horizontal resolution of 1/12° and with 12 vertical layers. They showed that including
466
a tidal component in the hydrodynamic model affected the predicted transport pattern of
467
simulated particles, and discussed their results in relation to the high concentrations of anchovy
468
(Engraulis japonicus) eggs and larvae that are observed in tidal fronts.
469 470
Despite the preliminary Lagrangian experiments conducted in the California Current upwelling
471
system to investigate the effects of vertical migration on larval drift trajectories (Botsford et al.,
472
1994), there has not been much follow-up with more biologically-based models of the early life
473
stages of small pelagic species. Lagrangian experiments have been designed to study the transport
474
patterns of other taxa, including zooplankton (Carr et al., in press) and shrimp larvae (Marinone
475
et al., 2004). Carr et al. (in press) used a nested approach in ROMS with a parent grid covering
476
the entire California upwelling system (7.5 km resolution) and a child grid focusing on the
477
Monterey Bay region (2.5 km resolution), and with 32 terrain-following vertical levels. They
478
investigated the effects of diel vertical migration of planktonic organisms, and obtained results
17
479
suggesting that migration into subsurface onshore currents during the day would not compensate
480
for surface offshore transport during the night and thus retention would be low within the
481
Monterey Bay. Marinone et al. (2004) explored different scenarios for when advection of
482
particles occurred (only during the day, the night, or when the current flows northwards), and
483
discussed their results in relation to transport patterns of shrimp larvae to their nursery areas.
484
They used a configuration of HAMSOM, developed by Marinone (2003), that covered the Gulf
485
of California at a horizontal resolution of 1/24° (~4 km) and with 12 vertical layers.
486 487
2.3.3 Models of small pelagic fish in “non-SPACC” regions
488 489
In this section, we briefly mention several early life stage models for small pelagic species and
490
regions outside the main focus of SPACC. We mention these examples because the methods and
491
results may be of interest, and because they provide a broad view of early life stage biophysical
492
models.
493 494
Vaz et al. (submitted) used outputs from a western South Atlantic configuration of the Princeton
495
Ocean Model (POM) as input to a biophysical model of anchovy (Engraulis anchoita) eggs and
496
early larvae. They investigated the spatial and seasonal patterns in the levels of retention and
497
transport along the coast off northern Argentina, Uruguay, and southern Brazil.
498 499
Bartsch and colleagues (Bartsch et al., 1989; Bartsch, 1993; Bartsch and Knust, 1994a, 1994b)
500
used hydrodynamics derived from early versions of the HAMSOM model as input to biophysical
501
models of herring (Clupea harengus) and sprat (Sprattus sprattus) early life stages for the North
502
Sea. Their seminal studies incorporated transport and size-dependent vertical migration of larvae,
503
and focused on qualitative comparisons between observed and simulated distributions of larvae.
504
Sætre et al. (2002) used the NORWECOM model to assess the transport routes and retention
505
areas for herring along the Norwegian coast. They showed that herring tended to spawn in areas
506
where retention was enhanced by the presence of topographically-induced quasi-stationary
507
eddies. Hinrichsen et al. (2005) developed a model of sprat for the Baltic Sea and showed that the
508
degree of overlap between observed and simulated distributions of juveniles was higher when
18
509
individuals were constrained to remain close to the surface than when they were allowed to
510
migrate to deeper waters during the day. Baumann et al. (2006) proposed different empirical
511
models fitted to observed values of sprat recruitment, and obtained the best result when they
512
incorporated a drift index derived from the biophysical model simulations.
513 514
Bartsch and Coombs (2001) developed a mackerel (Scomber scombrus) early life stage
515
biophysical model using an eastern North Atlantic configuration of the HAMSOM model. They
516
used initial conditions for egg distribution and abundance that were based on field data, and
517
simulated the drift of eggs and larvae and their growth using a function dependent on temperature
518
and age. Bartsch and Coombs (2004) later introduced additional biological processes into their
519
model, including vertical migration, feeding, and mortality. They used size-dependent diel
520
vertical migration, and dynamic prey fields calculated from satellite-derived sea-surface
521
temperature and chlorophyll-a concentration. Like Allain (2004), Bartsch and Coombs (2004)
522
also used super-individuals, where every simulated entity initially represented 106 individuals
523
who experienced the same environment and who died according to growth-dependent and length-
524
dependent mortality rates. Using this model, Bartsch et al. (2004) derived indices of mackerel
525
early post-larvae survival that they then compared to juvenile catch data for different sub-areas
526
during 1998 to 2000. These simulations however all used the same initial conditions of egg
527
distribution and abundance (those observed for 1998). Bartsch (2005) showed that simulating
528
survival for 2001 using 1998 egg data as the initial conditions lead to a “wrong” 60% increase in
529
survival compared with using actual 2001 egg data.
530 531
3 Biophysical models that include adults
532 533
There are two major categories of models that include adult fish and physics. The first category is
534
models in which the key processes of growth, mortality, reproduction, or movement depends on
535
the physics or variables greatly influenced by the physics. The second category is models for
536
which the questions to be addressed require full life cycle simulations (i.e., include all life stages)
537
so that the long-term (multigenerational) effects of impacts or environmental changes can be
538
examined. These full life cycle models thus must deal with eggs, larvae, and adults in a single
19
539
model. Such models are relatively rare now but model development is headed in that direction.
540
We expect biophysical full life cycle models to be the focus of much effort during the next
541
decade, and anticipate that full life cycle biophysical models will be especially important for
542
addressing issues related to the effects of climate change on fish populations and fisheries.
543 544
In this section, we review biophysical models that include adult stages of fish. We focus our
545
review on those models that are spatially-explicit, and that use physics, or variables derived from
546
the physics, as inputs. We also include the NEMURO family of models because some versions of
547
the NEMURO models fit our criteria for inclusion, but also because this effort is ongoing and
548
provides an example of a spatially-explicit full life cycle approach. We do not include models
549
that use environmental variables as inputs (e.g., temperature) but only simulate a single spatial
550
box (e.g., Robinson and Ware, 1999; Clark et al., 2003), and also do not include other population
551
modelling approaches (e.g., spawner-recruit models, Fiksen and Slotte, 2002; surplus production
552
models, Jacobson et al., 2005). These other modelling approaches are likely useful for addressing
553
certain questions related to climate change effects on fish. Our focus in this chapter is on
554
biophysical spatially-explicit models that include adult fish.
555 556
3.1 Abiotic and biotic environment, growth, and mortality
557 558
Models that include adults generally use similar information from the physics and lower trophic
559
models as used by the egg and larval models. These outputs include: current velocities
560
(advection), salinity, temperature, and prey fields. The growth and mortality formulations in adult
561
models are also similar to those by the early life stage models. Growth in weight is generally
562
either based on empirical relationships (e.g., von Bertalanffy equation, Shin and Curry, 2004) or
563
bioenergetics-based (e.g., Megrey et al., 2007), and natural mortality rate is often treated as a
564
constant. There are also some predator-prey biophysical models that include adults wherein
565
mortality depends on fish encounters with other fish (Shin and Cury, 2004; Ault et al., 1999).
566
With the inclusion of adult life stages, representing harvest rates and fisheries can also become
567
important.
568
20
569
3.2 Movement and behaviour
570 571
The process of movement is where models that include adults differ from early life stage models.
572
Unlike the egg and larval stages, movement of juvenile and adult fish no longer is necessarily
573
dominated by the physics. Movement of adults can be influenced by the physics, neutral with
574
respect to the physics, or even opposite to the physics. In many situations, the physics (or
575
variables directly derived from the physics, e.g., salinity, temperature, food) influences some
576
portion of the fish’s movement, while another component is due to other factors dependent on
577
behavioural decisions. An extreme example of movement of adult fish opposite to the physics is
578
migration upstream or counter to the prevailing currents.
579 580
How to represent the movement of adult fish in spatially-explicit biophysical models is unclear
581
and there are several approaches that have been proposed. Conceptually, movement of adults
582
adds terms to equation 1 attributable to behaviour, and then there must be some weighting of the
583
relative contribution of the physics-based term and the behaviour-based term. We highlight here
584
two of the approaches for modelling movement to illustrate some of the variety in how one can
585
represent movement of adults in biophysical models.
586 587
Railsback et al. (1999) proposed an approach based on fitness considerations in which individuals
588
search neighbouring cells, and move towards cells that provide an optimal blend of growth and
589
survival. In our context, the physics would provide the temperature and prey fields, and possibly
590
other variables, that are needed to compute growth and mortality in the neighbouring cells. The
591
growth and mortality in each neighbouring cell is then combined into a fitness measure that is the
592
projection of the likelihood of an individual surviving and obtaining some target size at some
593
time in the future (e.g., size at maturity next year), assuming conditions in the cell remained
594
constant into the future. Individuals move towards the cell in their neighbourhood that has the
595
highest fitness.
596 597
Humston et al. (2004) implemented a different approach to modelling movement of fish based on
598
the concept of kinesis that does not require that the fish has knowledge of the conditions in
599
neighbouring cells. Rather, individuals evaluate the conditions in their present cell against some
21
600
specified optimal value. Movement has inertial and random components; inertial movement
601
involves smaller angles and shorter distances than the random component. They used a weighting
602
scheme to combine the inertial and random components into distances moved and the angle of
603
movement. The closer the conditions in the present cell were to optimal, the more the inertial
604
movement dominated and fish would make smaller moves going in about the same direction and
605
therefore tended to stay in the good areas. Poor conditions resulted in the random movement
606
being weighted more heavily and the appearance of individuals searching over relatively large
607
areas and in all directions.
608 609
The Railsback and Humston approaches illustrate a fundamental schism in movement modelling
610
approaches: whether organisms can sense the conditions in neighbouring cells sufficiently to
611
project how conditions there would affect their growth or mortality (Tyler and Rose, 1994). With
612
an appropriate weighting scheme, one can also add terms for the contribution of advective
613
transport to the mix in both approaches. Other approaches to modelling movement include multi-
614
step approaches that first determine the type of behaviour from a list of discrete options and then
615
implement the specifics of movement associated with that behaviour (Blackwell, 1997; Anderson,
616
2002; Goodwin et al., 2006), and the use of genetic algorithms to train neural networks (Huse and
617
Giske, 1998).
618 619
Given the uncertainty in how to represent movement, it is important to note that some biophysical
620
models bypassed the issue. Heath et al. (1997) did not try to model movement but rather simply
621
assumed movement would occur and would result in the spatio-temporal distributions derived
622
from field data. Even more extreme is the growth potential approach (Luo et al., 2001). They
623
ignored movement and spatial distributions, and simply predicted what would happen if fish were
624
present in all locations.
625 626
3.3 Case studies
627 628
We have organized this section differently from the early life stage case studies section. There are
629
far fewer examples that include physics and adult fish, and not enough examples to divide by
22
630
species and geographic area as was done with the early life stage examples. Rather, we have
631
grouped the adult models together according to two general categories: models of adults that use
632
physics and full life cycle models. We emphasize the methods used because of the much wider
633
diversity of approaches used with adult models than with the more standardized approaches
634
generally used with early life stage models.
635 636
3.3.1 Models of adults that use physics or physics-related variables
637 638
Luo et al. (2001) used the output of a 3-dimensional hydrodynamic model coupled to a water
639
quality model as input to a fish feeding and bioenergetics model to determine the carrying
640
capacity of Chesapeake Bay for young-of-the-year juvenile menhaden (Brevoortia tyrannus). The
641
water quality model had over 4000 cells, arranged as a surface grid of 729 cells, with vertical
642
cells every 2 m. They averaged the 2-hour simulated values of temperature, dissolved oxygen,
643
and chlorophyll-a to obtain daily values for each cell for June through December in an average
644
freshwater inflow year. Temperature was used directly in the bioenergetics model, and affected
645
maximum consumption rate and respiration rate. Menhaden are filter feeders and so chlorophyll-a
646
concentrations were multiplied by the area of the mouth, swimming speed, and an efficiency term
647
to obtain realized consumption rate. Consumption, with the rest of the bioenergetics model,
648
enabled prediction of daily growth rate in each cell. Carrying capacity for each cell was then
649
computed based on the predicted consumption rate, prey production rates, and prey biomass, and
650
further adjusted for low dissolved oxygen, to obtain the biomass of menhaden that could be
651
supported in that cell on each day.
652 653
Luo et al. (2001) showed spatial maps and reported the percent of the bay volume able to support
654
different growth rates and carrying capacities. Their results showed that there was large spatial
655
and temporal variation in growth rate potential and biomass supportable due to the nonlinear
656
functional forms in the feeding and bioenergetics models and as a result of combining the effects
657
of the multiple factors of temperature, chlorophyll-a, and dissolved oxygen. Menhaden must
658
occupy cells with growth potential greater than 0.005 to 0.001 g/g/day during the June through
23
659
December growing season in order to achieve their observed weights in December, and the daily
660
total volume of such good habitat in the bay varied between practically zero and 80%.
661 662
There are many examples of the use of habitat suitability indices (HSI) that use spatially-explicit
663
environmental variables estimated from field data or outputted from hydrodynamic models. Most
664
of these examples involve how changes in stream and river flows would affect the habitat for
665
specific species downstream because the HSI approach was initially developed for evaluating
666
how water releases from dams would affect fish downstream (Acreman and Dunbar, 2004). Use
667
of HSI avoids the issues of representing how adult fish move because an endpoint can be simply
668
the changes in the quantity and quality of the habitat. The HSI approach has also been used as an
669
intermediate variable that is then used to affect movement of adult fish (e.g., Lehodey et al.,
670
2003).
671 672
Rubec et al. (2001) offers an example of HSI applied in an estuarine environment. We summarize
673
an estuarine example here even though it uses field data to derive the environmental variables
674
because the same analysis would be used with model-predicted environmental variables. Others
675
have computed HSI values from the output of hydrodynamic and water quality models (e.g.,
676
Guay et al., 2000). Rubec et al. interpolated temperature and salinity values to obtain seasonal
677
values for 18.5 m2 cells in the surface and bottom layers for Tampa Bay, Florida. Additional
678
information on depth, bottom substrate type, and species abundances were also used.
679
Relationships between suitability (0 to 1) and each variable were formulated from abundance
680
data, and the product of the suitabilities in each cell (geometric mean) was computed as the
681
overall suitability of that cell for that life stage. They then checked whether overall suitability was
682
correlated to species abundances over the four seasons, and swapped suitability functions with
683
those developed for Charlotte Harbour to see if suitability functions were transferable among
684
locations.
685 686
Karim et al. (2003) coupled a hydrodynamic-NPZ model to a model of fish movement and
687
dissolved oxygen-related mortality. Their simulations were based on the Marbled Sale
688
(Pleuronectes yokohamae), a demersal species, in Hakata Bay. The spatial domain was a
689
horizontal grid of 300 m x 300 m cells with five vertical layers. The grid was selected to
24
690
correspond to the horizontal distance typically traveled by an individual fish in the 30 minute
691
time step. Movement could then be based on individuals moving to neighboring cells each time
692
step. The hydrodynamic-NPZ model was solved using its own time step, and temperature and
693
dissolved oxygen values were obtained for each grid cell for use with the fish movement and
694
mortality models. Karim et al. used a series of laboratory experiments and field tracking data of
695
individual fish to develop and calibrate the movement model. Movement in the model was based
696
on computing the preference of each neighboring cell in 3 dimensions from functions that related
697
temperature to a preference level and dissolved oxygen concentration to a preference level, and
698
then a function that combined the preference levels into a single overall preference value for the
699
cell. Individuals moved to the cells with the highest overall preference. This approach to
700
modeling movement could be considered a simplified version of the more general Railsback et al.
701
(1999) fitness-based approach. Horizontal position was updated every 30 minutes, while vertical
702
position was evaluated every 10 seconds. Exposure to low dissolved oxygen caused increased
703
mortality.
704 705
After performing simulations that satisfactorily mimicked the laboratory and field tracking
706
results, Karim et al. (2003) performed 3-day simulations with individuals released in different
707
vertical layers (surface or bottom) and horizontal locations (whole grid or inner bay). They
708
computed the mortality rate of the cohort from exposure to low dissolved oxygen as mortality
709
accumulated over the three days. They concluded that hypoxic conditions in the inner portion of
710
the bay during the summer can cause significant mortality of demersal fish, and that future model
711
developments should include the simulation of hypoxia effects on pelagic species.
712 713
Ault et al. (1999) developed a predator-prey model of spotted seatrout (Cynoscion nebulosus) and
714
pink shrimp (Penaeus duorarum) that was imbedded in a 2-dimensional hydrodynamic model of
715
Biscayne Bay, Florida. The hydrodynamic model consisted of 6346 triangular elements and 3407
716
nodes, with grid spacing between nodes of about 500 m. The model was driven with tide, winds,
717
and freshwater discharge data for 1995. A 1 minute time step was used to solve the hydrodynamic
718
model, and currents and salinities were output at 10 minute intervals for use with the fish model.
719
Shrimp and seatrout were followed as super-individuals (what Ault et al. termed “patches”).
720
Patches were introduced monthly for shrimp, and at night on incoming tides for seatrout. Patches
25
721
were tracked using continuous x and y positions; each time step the patch experienced the
722
conditions of the cell it inhabited. Circulation was used to move around the patches of egg and
723
yolk-sac larval seatrout, circulation and behavior together was used with pre-settlement shrimp,
724
and active behavior only was used for moving settled shrimp and juvenile and adult seatrout.
725
Salinity affected the angle and distance moved (based on swimming speed) of pre-settled shrimp,
726
which was added to the circulation-based movement. Horizontal movement only occurred at
727
night; shrimp went to bottom during the day. Once shrimp settled to the bottom, they were moved
728
around based on their body length and habitat quality. Seatrout movement was based on the
729
growth rate in cells within a specified distance (detection range) of their present location, and
730
patches moved towards cells with the highest growth potential. Movement within the Ault et al.
731
model of the different life stages of shrimp and seatrout illustrates the diversity of movement
732
algorithm and approaches, including purely hydrodynamics-driven, an approach rooted in cellular
733
automation, an approach that was later generalized into the Humston et al. (2004) kinesis model,
734
and a hybrid mix of the kinesis and Railsback’s fitness-based approach. Shrimp grew based on
735
the cumulative temperature they were exposed to; seatrout grew based on bioenergetics with
736
consumption based on ingested shrimp co-located in their present cell.
737 738
Ault et al. (1999) reported the results of one year simulations that illustrated model behavior and
739
the usefulness of the model for examining how environmental and biological factors affect
740
predator-prey dynamics. They concluded that June-spawned seatrout were transported more into
741
the bay, settled over a wider range of habitats, and grew faster than August-spawned cohorts.
742
They also showed that spatial variation in habitat quality can affect growth rates of fish, even
743
causing difference among individuals from within the same spawning cohort.
744 745
3.3.2 Full life cycle models
746 747
The EcoPath with EcoSim (EwE) family of models (Walters et al., 1997) are biomass-based
748
compartment models and consist of a steady-state version (EcoPath), which is also used as initial
749
conditions for a single spatial box time-dynamic version (EcoSim). Walters et al. (1999) extended
750
the EwE models to be spatially-explicit (EcoSpace) by imbedding an EcoSim model on each cell
26
751
of a 2-dimensional grid of cells. Differential equations are constructed for each fish compartment
752
(species or functional group) in an analogous manner as the equations for phytoplankton and
753
zooplankton in NPZ models (net effect of gain and loss terms corresponding to growth and
754
mortality processes). In early versions of EwE, fish were represented as biomass, which was
755
recognized as inadequate because of the large ontogenetic changes in growth and mortality in
756
many fish species and because a single biomass compartment did not allow for explicit
757
representation of recruitment dynamics which is critical to understanding and forecasting fish
758
population dynamics. Thus, EcoSim was extended to allow for each fish compartment to be
759
subdivided into smaller compartments (e.g., juveniles versus adults) as a crude way to allow for
760
ontogenetic differences and to make recruitment dynamics semi-distinct from total biomass
761
(Walters et al., 2000). Recent versions of EcoSpace went further and allowed for monthly cohorts
762
(age-structure) of key species or groups. EcoSpace is presently undergoing modification to allow
763
for even more detailed representation (e.g., following individuals or packets) for selected taxa,
764
and for easy coupling to hydrodynamic and NPZ models. While there have been many
765
applications of EcoPath and quite a few applications of EcoSim (e.g., Shannon et al., 2004; Field
766
et al., 2006), the spatially-explicit EcoSpace version has not yet received much attention. We
767
mention EwE here because we anticipate increasing attention being paid to the EcoSpace
768
approach in the future.
769 770
One example of the use of the EwE models is that of Shannon et al. (2004), who applied EcoSim
771
to the Southern Benguela ecosystem. The model was comprised of about 30 species or groups,
772
and they adjusted previous parameter values and assumptions (e.g., see Shannon et al., 2003)
773
based on the model’s ability to replay the historical biomasses of selected species for the 1978 to
774
2002 period. Using the EwE fitting algorithm, Shannon et al. (2004) explored how changes to
775
historical fishing pressure patterns, prey vulnerabilities to predation of key prey-predator
776
combinations, and environmental forcing of primary production affected the model fit to the
777
observed biomass time series. The fit of modelled biomasses to the observed time series was
778
insensitive to alterations in the fishing pressure time series, and moderately sensitive to
779
interannual variation in environmental forcing of primary production. The model’s relatively high
780
sensitivity to prey-predator vulnerabilities was consistent with the idea of wasp-waist control
27
781
(Cury et al., 2000), in which small pelagic fish control their zooplankton prey while
782
simultaneously exerting bottom-up control on their predators.
783 784
The IGBEM and BM2 models (Fulton et al., 2004a, 2004b) are also biomass-based but they are
785
truly spatially-explicit, coupled to an elaborate water quality model, and separate each fish
786
species or group into age-classes and follow the average weight and numbers of individuals in
787
each age-class. BM2 was developed in an attempt to reduce the complexity and parameter
788
demands of its more complicated predecessor IGBEM (Fulton et al., 2004b). The application to
789
Port Phillip Bay, Australia, followed 29 living compartments, plus compartments related to
790
detritus, nutrients, sediment, and some physical variables in a 3-layer grid with about 59 cells in
791
each layer. Transport among cells was derived from the output of a hydrodynamic model. A daily
792
time step was used, although if rates were too fast, then a finer time step was adopted. Four fish
793
groups were followed, with each represented by means of an age-structured cohort approach.
794
Spawning occurred outside of the model domain and recruits were injected into the grid on a
795
specific day as the initial number of individuals in the first age-class and then the oldest age-class
796
was removed. The average body weight of an individual in each age-class was followed using
797
two separate weight variables (structural and reserve) based on simulated growth. Growth
798
depended on the summed prey biomass, whose vulnerability was sized-based, in the same cell as
799
the predator and adjusted for feeding efficiency and crowding. Consumed prey was imposed as
800
mortality on the appropriate prey compartments in the cell. Movement of fish age-classes was
801
simulated using fluxes among cells based on specified quarterly target densities in cells and how
802
many days were left in the quarter. Fulton et al. (2004b) acknowledged that the recruitment and
803
movement formulations of the model were likely the weakest aspects of their model, and they
804
have investigated using spawner-recruit relationships and forage-based and density-based
805
movement approaches. They stated that they used the constant recruitment and simple movement
806
because the results did not differ much between the simple and more complicated alternatives.
807 808
Fulton et al. (2004b) performed a variety of simulations of BM2 and compared the outputs to
809
field data for Prince Philip Bay, to field data for other estuaries, and to predictions from the more
810
complicated IGBEM version. Simulations repeated a 4-year time series of forcings as input and
811
they determined that 30-year simulations were sufficient because the model state after 30 years
28
812
was similar to that predicted after 100 years. Examples of model outputs compared to field data
813
or to IGBEM predictions included: averaged biomasses of key compartments, predicted
814
community composition, relationship between DIN and chlorophyll-a, predicted and expected
815
size-spectra features, system-wide indices such as P/B ratios and cycling indices, and the
816
temporal and spatial dynamics of key compartments.
817 818
Adamack (2007) and Adamack et al. (abstract 5 ) coupled a 3-dimensional hydrodynamic-water
819
quality model to an individual-based population model of bay anchovy (Anchoa mitchilli) in
820
Chesapeake Bay. The water quality model is a 3-dimensional model that simulated 24 state
821
variables, including dissolved oxygen, four forms of nitrogen, four forms of phosphorous, two
822
phytoplankton groups, and two zooplankton groups in a 4,073 (729 surface layer cells) cell grid.
823
Anchovy were introduced weekly during the summer spawning season as individual recruiting
824
juveniles and followed until they reached their end of third year when they were removed from
825
the model. Growth and mortality rates of individual bay anchovy within a water quality model
826
cell were calculated every 15 minutes. Growth depended on a bioenergetics model with the
827
predicted zooplankton densities from the water quality model providing the prey for bay anchovy
828
consumption. Anchovy consumption was summed by cell and, with the predicted diet, imposed
829
as an additional mortality term back onto the zooplankton. Anchovy excretion and egestion also
830
contributed to the nutrient recycling dynamics of the water quality model. Mortality rate of
831
anchovy was assumed to decrease with their length. Movement of individual anchovy was
832
simulated both vertically (hourly) and horizontally (daily) based upon temperature, salinity, and
833
prey densities using the kinesis approach of Humston et al. (2004).
834 835
Adamack (2007) reported the results of simulations that used the dynamically coupled models to
836
predict the effects of changes in nitrogen and phosphorous loadings on bay anchovy growth rates
837
and survival. Ten-year simulations using historical sequences of low, average, and high
838
freshwater inflow years were performed under baseline, increased, and reduced nutrient loadings.
839
Results showed that the anchovy response to changes in nutrient loadings was a complex function
5
Adamack, A. T., Rose, K. A. and Cerco, C. F. Simulating the effects of nutrient loadings on bay anchovy population dynamics in Chesapeake Bay using coupled water quality and individual-based models. ECSA 41st International Conference - Measuring and Managing Changes in Estuaries and Lagoons, Venice, Italy, October 1520, 2006.
29
840
of changes in high-quality habitat, prey densities, assumptions about movement, and the
841
magnitude and temporal pattern of the introduction of young-of-the-year recruits. This analysis
842
provides an example of a biophysical model in which the physics is not used directly because the
843
egg and larval stages were bypassed and the adults did not need circulation information, but the
844
physics was needed to properly simulate the NPZ portion.
845 846
Lehodey et al. (2003) used the output of a 3-dimensional hydrodynamic and NPZ model of the
847
Pacific Ocean (45-65oN; 100oE-70oW) as input to an Eulerian-based tuna population dynamics
848
model (SEPODYM). The NPZ model used cells that were 2o in longitude by 2o in latitude at the
849
extreme north and south boundaries of the model domain and 0.5o square near the equator. Forty
850
vertical layers were represented with a layer every 10 meters within euphotic zone and thicker
851
below. Predicted currents were averaged over the 0-30 m surface layer, primary production was
852
integrated over the euphotic zone (1 to 120 m) and with SST, were interpolated on 2-dimensional
853
grid of 1-degree resolution. Lehodey et al. added separate population models for tuna and for
854
what they termed “tuna forage”. The forage model simulated the biomass of tuna prey in each cell
855
using advection and diffusion, and assuming continuous recruitment based on new primary
856
production predicted by the NPZ model and a time lag to account for the delay until the primary
857
production would show up as new forage biomass. The mortality rate and time lag of the forage
858
were related to SST. Tuna population dynamics were modelled by following the numbers in age-
859
classes. Length-at-age were determined from a von Bertalanffy relationship; length was then
860
converted to weight. Two habitat indices (adult and spawning) were computed for each cell based
861
on SST in the cell. The spawning index was used to divide up the annual recruitment among the
862
individual cells. For larvae and juveniles (i.e., until about 4 months of age), tuna movement was
863
purely advection-diffusion. Movement of adult tuna also used the advection terms but that were
864
adjusted by tuna length and by the adult habitat index. They assumed movement was proportional
865
to the length of the age-class and increased with poor habitat quality in the local cell. Natural and
866
fishing mortality was applied to each age-class, with natural mortality rate increased when the
867
habitat was poor (spawning index used for first age-class; adult index used for the rest of the
868
ages). Multiple (six) fisheries with specific gear types and with effort varying by month and by
869
cell or subregion were simulated to drive the fishing mortality rate. The SEAPOPDYM
870
application shared information and used outputs from a traditional fisheries stock assessment
30
871
model called MULTIFAN-CL (Fournier et al., 1998). Annual recruitment in SEAPOP was
872
calibrated to match the overall recruitment estimated by MULTIFAN-CL.
873 874
Lehodey et al. (2003) reported the results of a NPZ and SEPODYM simulation that spanned 1960
875
to1999. General features of the simulation were described, such as the effects of ENSO events
876
and the 1976-77 regime shift, to check the realism of the NPZ simulation. Tuna recruitment and
877
biomass simulated by SEPODYM qualitatively agreed with the estimates from the MULTIFAN-
878
CL model, and predicted catches by grid cell and month were well correlated with observed
879
catches. Most recruitment was predicted to occur in the western and central Pacific region, with
880
large variability caused by El Nino versus La Nina years. The out-of-phase dynamics of
881
simulated primary production between the western and central Pacific predicted by the NPZ
882
model was also seen in the SEAPOP-simulated tuna recruitment. They emphasized the
883
importance of a carefully constructed and evaluated NPZ model. The SEAPOP model is now
884
being applied to small pelagic species in the Humboldt system (Gaspar and Lehodey, abstract 6 ).
885 886
Shin and Cury (2004) described a general simulator of fish communities (OSMOSE) that uses an
887
individual-based size-based approach, and Shin et al. (2004) applied the model to the Benguela
888
Current system. They used the super-individual approach, with each super-individual assumed to
889
represent a school of identical fish. A distinction was made in the model between non-piscivorous
890
and piscivorous behaviour, with species assigned a behaviour based on stage or age. In the
891
Benguela application, 12 fish species were simulated on a 40 cell by 40 cell horizontal grid using
892
a 6-month time step. OSMOSE does not explicitly use the output of hydrodynamic or NPZ
893
models, but rather represents the prey field effects by specifying a system-wide carrying capacity
894
for non-piscivorous fish biomass. When total biomass of non-piscivorous species biomass
895
exceeded the carrying capacity, then mortality was imposed on all non-piscivorous individuals on
896
the grid, disproportionately on age-0 versus older individuals, until the total biomass fell below
897
the carrying capacity. Piscivorous stages consumed prey species if they co-occurred together in
898
the same spatial cell and if the prey were vulnerable based on predator to prey size ratios. All fish
6
Gaspar, P. and Lehodey, P. Application of a spatial Eulerian ecosystem and population dynamic model (SEAPODYM) to small pelagic fish: Modelling approach and preliminary tests. International Conference on The Humboldt Current System: Climate, ocean dynamics, ecosystem processes, and fisheries. Lima, Peru, November 27 December 1, 2006.
31
899
species grew in length according to von Bertalanffy equations, with the growth of piscivorous
900
species predicted by the von Bertalanffy equation affected by a predation efficiency computed for
901
each super-individual from its present consumption rate. Piscivorous super-individuals moved to
902
their neighbouring cell that had the highest prey biomass that was vulnerable to them. In addition
903
to predation, there were terms for starvation and harvesting mortality. Reproduction closed the
904
life cycle by initiating new super-individuals based on total egg production computed annually
905
from the mature female spawners; larval and juvenile survival determined subsequent
906
recruitment.
907 908
Shin et al. (2004) performed a series of 200-year simulations with increased fishing mortality
909
rates on selected species and compared predicted responses to those from a comparably
910
constructed EcoSim model. Predicted biomass of each species in OSMOSE was averaged over
911
the last 100 years of each simulation, and compared to the average biomass under the reference or
912
baseline simulation. Increased fishing morality on sardine (Sardinops sagax), anchovy (Engraulis
913
encrasicolus), and round herring (Etrumeus whiteheadi) showed that sardine would be the first to
914
collapse, anchovy would collapse second, and round herring were highly resistant because of the
915
small initial value of their fishing mortality rate. The biomass of some species, such as chub
916
mackerel (Scomber japonicus), increased due to relaxed competition. Increased fishing on Cape
917
hake (Merluccius capensis) also showed the expected decrease in hake biomass and a general
918
increase in the biomasses of hake’s competitors. Both sets of increased fishing mortality
919
simulations were compared to similar simulations preformed with an EcoSim version of the
920
Benguela Current system and, at the qualitative level (increase or decrease), both models
921
generated similar responses. While OSMOSE does not explicitly use the output of a NPZ model,
922
with some creativity, one could perhaps assume how climate change would affect prey and one
923
could adjust the carrying capacity appropriately. An ongoing effort is attempting to link an NPZ
924
model to OSMOSE so that the growth of non-piscivorous individuals can be modelled
925
dynamically (Y. Shin, personal communication).
926 927
The NEMURO (North Pacific Ecosystem Model for Understanding Regional Oceanography)
928
family of models was a milestone in an ongoing large international collaboration focused on the
929
development of standard NPZ model for application to the North Pacific, and the coupling of fish
32
930
growth and population dynamics models to this standard NPZ model. The biological food web
931
represented in NEMURO was fairly detailed with two groups of phytoplankton and three groups
932
of zooplankton, plus the usual nitrogen, silicate, and detrital recycling dynamics. Using this
933
common formulation for the NPZ, several models and applications were developed (Werner et
934
al., 2007). Of particular interest here are the spin-offs in which NEMURO was imbedded in a 3-
935
dimensional hydrodynamic model configured for the North Pacific, a version that coupled an age-
936
structured fish model to the NPZ (termed NEMURO.FISH), and the latest incarnation
937
(NEMURO.SAN) which is an individual-based, full life cycle, spatially-explicit model of sardine
938
and anchovy interactions.
939 940
NEMURO.FISH dynamically couples an adult fish bioenergetics-based population dynamics
941
model to the NEMURO NPZ model. The coupled models have been configured for Pacific
942
herring (Clupea harengus pallasii) on the west coast of Vancouver Island (Megrey et al., 2007)
943
and for Pacific saury (Cololabis saira) off Japan (Ito et al., 2007). The herring application uses an
944
age-structured approach, with bioenergetics used to describe the changes in the average body
945
weight of individuals in each age class and mortality rates used to describe the changes in the
946
numbers in each age class. Recruitment was knife-edge and computed from spawning biomass
947
and environmental variables (SST, air temperature, and North Pacific Pressure Index) using a
948
spawner-recruit relationship. New recruits become the new youngest age class. The dynamics of
949
the three zooplankton groups in the NEMURO model determine the consumption rate in the fish
950
bioenergetics model through a multispecies functional response formulation. Herring
951
consumption affects the zooplankton through predation mortality, and fish egestion and excretion
952
contribute to the nitrogen dynamics.
953 954
Using the NEMURO.FISH model of herring, Megrey et al. (2007) presented baseline simulations
955
of herring weight-at-age and population dynamics for Vancouver Island, Canada, and Rose et al.
956
(in press) used the model to examine how climate change could affect herring growth and
957
population dynamics. Rose et al. performed simulations that mimicked the conditions in each of
958
the four documented climate regimes in the North Pacific (1962-1976; 1977-1988; 1989-1997;
959
1998-2002). Climate regimes differed in the values assumed for environmental variables used in
960
the spawner-recruit relationship, and in the water temperature, mixed layer depth, and nutrient
33
961
influx rate used by the NPZ model. In agreement with general opinion and with the herring data
962
from West Coast Vancouver Island, model predicted estimates of weight-at-age, recruitment, and
963
spawning stock biomass were highest in regime 1 (1962-1976), intermediate in regime 2 (1977-
964
1988), and lowest in regime 3 (1989-1999). The regime effect on weights-at-age was a mix of
965
recruitment effects and lower trophic level effects that varied in direction and magnitude among
966
the four regimes.
967 968
Isolating the growth component of NEMURO.FISH, Rose et al. (2007) used the output of the 3-
969
dimensional NEMURO for the North Pacific and simulated weight-at-age (not population
970
dynamics) for the west coast Vancouver Island, Prince William Sound, and Bering Sea regions
971
for 1948-2002. The NEMURO application was a 3-D implementation for the Northern Pacific
972
(Aita et al., 2007). The NEMURO-3D simulation represented the NPZ dynamics for 1948 to
973
2002 using, as much possible, observed data for driving variables. The output of the NEMURO-
974
3D simulation at the three locations, averaged over cells in the top 50 m, was used as input to the
975
bioenergetics model and daily growth of herring was simulated for 1948 to 2000. Rose et al.
976
applied the sequential t-test analysis to detect regime shifts (STARS) algorithm (Rodionov and
977
Overland, 2005) to the simulated temperatures, zooplankton, and herring growth rate (annual
978
change in weight between ages 3 and 4) to identify statistical shifts in their average values. All
979
three locations showed shifts in simulated herring growth rate around the 1977 regime shift.
980
While the NEMURO-3D output showed warming temperatures at all three locations beginning in
981
the late 1970’s, herring growth was predicted to decrease in west coast Vancouver Island and
982
Prince William Sound, and to increase in the Bering Sea. Interannual variation in zooplankton
983
densities caused the time series response in herring growth for west coast Vancouver Island.
984
Temperature and zooplankton densities both played roles in Prince William Sound and the Bering
985
Sea herring growth responses, with zooplankton dominating the response for Prince William
986
Sound and temperature dominating the response for Bering Sea.
987 988
NEMURO.SAN is under development and extends the NEMURO approach to simulating sardine
989
and anchovy as individuals on a 2-dimensional spatial grid of cells (Rose et al., abstract 7 ). The
7
Rose, K. A., Agostini, V. N., Jacobson, L., van der Lingen, C., Lluch-Cota, S. E., Ito, S., Megrey, B. A., Kishi, M. J., Takasuka, A., Barange, M., Werner, F. E., Shin, Y., Cubillos, L., Yamanaka, Y. and Wei, H. Towards coupling
34
990
vertical dimension is represented as the volume of water in each cell based on the volume of the
991
water above the mixed layer depth. Each year, recruits are computed from spawning biomass at a
992
point in time and the recruits, after a suitable time delay, are slowly introduced over the next year
993
as new model individuals on the grid. Growth, mortality, and movement of individuals are
994
evaluated daily. Positions of individuals are tracked in continuous x and y space, and each day
995
their cell is determined and they experience the conditions in that cell. Alternative approaches to
996
movement, including the use of Railsback and Humston approaches, are being investigated. How
997
the spatial (among cells) and temporal (daily or monthly) variation in the mixed layer depth,
998
nutrient influx, and other inputs to NPZ portion are specified allows for flexibility in configuring
999
NEMURO.SAN to different locations. To date, 100-year simulations have been performed in an
1000
exploratory mode for a version configured to roughly resemble the California Current system.
1001
Alternative hypotheses about climate conditions can be specified via changing the inputs to
1002
NEMURO, and then using the coupled models to predict the long-term responses of the anchovy
1003
and sardines in terms of their growth, survival, and spatial distributions.
1004 1005
4 Biophysical models and climate change
1006 1007
In this section we discuss the use of biophysical models of small pelagic fish in the context of
1008
predicting the effects of climate change. Harley et al. (2006) recently reviewed the potential
1009
impacts of climate change on coastal marine ecosystems. They discussed ecological responses to
1010
climate change at the individual, population, and community levels. We envision most analyses
1011
using biophysical models being single species analyses. The early life stage models focus on a
1012
single species, and while some of the full life cycle models include multiple species, there is still
1013
great uncertainty in how to represent the food web dynamics of the upper trophic level species
1014
(Rose and Sable, 2007). Despite the recognition of the importance of food web interactions and
1015
the push towards ecosystem-based fisheries management (Rose and Sable, 2007), community-
1016
level responses to climate change that require multi-species simulations will likely remain in the
1017
demonstration mode, rather than for management decision-making, for the foreseeable future. We
sardine and anchovy to the NEMURO lower trophic level model. North Pacific Marine Science Organization (PICES) 15th Annual Meeting, Yokohama, Japan, October 13-22, 2006.
35
1018
envision most analyses in the near term will focus mainly on the early life stages of key species,
1019
with some analysis using single-species full life cycle models for well-studied locations and
1020
theoretical-oriented analyses using the multispecies full life cycle models.
1021 1022
Among the factors reviewed by Harley et al. (2006), the ecological responses to changes in
1023
circulation, temperature, and productivity are relatively easy to investigate using biophysical
1024
models. Indeed, changes in circulation would induce changes in advective and dispersive
1025
transport, a process used directly in the early life stage models, and used directly or indirectly in
1026
the adult-based models. Some of the reviewed models used the direct effects of transport to at
1027
least influence the movement of adult fish, and many of the reviewed models used the effects of
1028
transport indirectly via transport’s effects on temperature, salinity, and prey fields that affected
1029
the growth, mortality, reproduction, and movement rates of adult fish. Harley et al. also discussed
1030
the potential shifts (vertical and horizontal) in species distributions that could occur under climate
1031
change. Initial conditions in early life stage models typically use data based on observed egg
1032
distributions. Shifts in egg distributions induced by climate change could be hypothesized and
1033
simulations performed to explore potential consequences on early life stage transport, growth,
1034
and survival.
1035 1036
To our knowledge, the only example of biophysical model used in the context of climate change
1037
comes from the recent study of Vikebø et al. (2007). In the Barents Sea off Norway, they used the
1038
ROMS hydrodynamic model forced by a global climate model in which the river runoff was
1039
increased by a factor three over the current value, causing the thermohaline circulation to slow
1040
down. Then they used a biophysical model of the early life stages of Arcto-Norwegian cod
1041
(Gadus morhua) to study the impact of the anomalous circulation and ocean temperature on
1042
transport and growth of cod larvae and juveniles. They showed clear differences between the drift
1043
and growth patterns obtained under the current and the reduced thermohaline circulation (Figure
1044
3).
1045 1046
Figure 3
1047
36
1048
We have more confidence in the early life stage models for simulating climate change scenarios
1049
because they are more tightly coupled to the physics and NPZ, and because early life stages of
1050
fish tend to be the focus of field and modelling studies in the marine ecosystems. Early life stages
1051
can be measured and they are often the focus as part of the search for recruitment indices
1052
(Kendall and Duker, 1998). Imposing climate change scenarios would seem to be possible almost
1053
from first principles because the early life stage models are tightly coupled to the hydrodynamic
1054
and NPZ models. Simulating climate change scenarios becomes more complicated for the adult
1055
models because many of the adult models used surrogates for the physics and prey outputs of the
1056
hydrodynamic and NPZ models as their inputs (e.g., carrying capacity). This implies another step
1057
is required to convert the hydrodynamics and NPZ outputs into the variables needed by the adult
1058
models.
1059 1060
Predicting responses of early life stages is necessary but not sufficient to address many but not all
1061
of the climate change issues. Many issues require that the predictions of early life stage models be
1062
related to population dynamics and health, and some questions require the simulation of the
1063
responses of the adult life stages. One challenge is to balance the use of early life stage, adult
1064
only, and full life cycle modelling approaches to ensure predicted responses are most relevant to
1065
the scientific questions and to management issues. There are also practical computing challenges.
1066
For example, the numerical considerations that arose with using super-individuals with early life
1067
stage models become more complicated with full life cycle models, as these models often include
1068
density-dependent effects and require new sets of individuals be introduced each year of their
1069
multi-year simulations. Also, full life cycle models typically simulate decades in order for the full
1070
effects of environmental and climate changes to be manifested in the population response. Yet,
1071
hydrodynamic and NPZ models typically simulate a few years. How one creates realistic long-
1072
term scenarios for use as input to the full life cycle model from the relatively limited number of
1073
hydrodynamic and NPZ results can affect predicted responses to climate change.
1074 1075
Perhaps the greatest challenge relates to the assumption that the predicted responses of the
1076
hydrodynamic and NPZ models under climate change scenarios are sufficiently accurate and
1077
precise, and on the correct spatial and temporal scales to be used as inputs to the fish models.
1078
There is still disagreement about how some important driving variables to the hydrodynamic and
37
1079
NPZ model (e.g., boundary conditions, precipitation, wind) will change under a given climate
1080
change scenario. Furthermore, climate change scenarios, even after agreed upon, can push the
1081
hydrodynamic and NPZ models beyond their calibrated and validated domain. Also, most climate
1082
change simulation experiments have been conducted at a large spatial scale (e.g., the entire
1083
Southern Ocean, Russell et al., 2006), whereas the early life stage and adult models tend to
1084
operate at smaller scales. Regional-level climate change simulation experiments should become
1085
increasingly available in the near future (e.g., for the California Current system, Auad et al.,
1086
2006). Meanwhile, creative use of long-term time series of historical hydrodynamic interannual
1087
simulations should be melded with climate change scenarios to ensure realistic outputs of the
1088
hydrodynamic and NPZ models that act as inputs to the fish models.
1089 1090
Models such as the Mullon et al. (2002) model could be used to derive expected egg distributions
1091
under climate change. For example, simulation 4 of Mullon et al. (2002) was re-run with
1092
hydrodynamic model outputs using weekly wind forcing from ERS satellites (run C in Blanke et
1093
al., 2002) to study how simulated selected spawning patterns would change according to
1094
evolutionary constraints that involve a lethal temperature threshold for the transported particles.
1095
Two main spatio-temporal spawning patterns emerged depending on the value of the temperature
1096
threshold. A cooler threshold selected spawning in the Central Agulhas Bank in July–September
1097
(Figure 4a), while a warmer threshold resulted in the selection of spawning in the Eastern
1098
Agulhas Bank in October–January (Figure 4c); an intermediate temperature threshold resulted in
1099
a mix of both patterns (Figure 4b). Assuming that the spawning pattern of Figure 4b corresponds
1100
to the current situation, and that climatic change would only result in homogeneous increase of
1101
sea surface temperature, one could infer that spawning would shift more towards the pattern
1102
shown in Figure 2a (i.e., cooler threshold mimics warmer water). These results can then be used
1103
as inputs to early life stage biophysical models.
1104 1105
Figure 4
1106 1107
Simulating geographic shifts in adult life stages will be more problematic with biophysical adult
1108
models. The use of adult models for simulating geographic shifts is limited because the distances
1109
that could be moved by adult fish in response to climate change would likely exceed the spatial
38
1110
domain of most of the models. A few of the adult-based fish models used very large spatial
1111
domains (e.g., Lehodey et al., 2003), but whether the biological aspects of these models are
1112
sufficiently general to allow for prediction of geographic shifts needs to be tested. This was
1113
partially addressed in the SEPODYM model because they had to deal with the highly migratory
1114
tuna. Whether the current models of small pelagic fish are sufficiently robust to simulate large-
1115
scale shifts in distribution remains to be determined. To date, more statistically-oriented empirical
1116
approaches have been used to predict geographic shifts in the distributions of adult fish and other
1117
taxa in response to climate change (e.g., Rahel, 2002; Schmitz et al., 2003). Allowing for the
1118
capability for predicting geographic shifts should be considered as present biophysical models are
1119
expanded and new models are developed.
1120 1121
Biophysical models of fish early life stages could likely be improved by using spawning and
1122
nursery habitats defined by environmental variables rather than simply being geo-referenced (P.
1123
Fréon, personal communication). Characterizations of spawning habitats based upon
1124
environmental variables such as temperature and salinity have been performed for anchovy and
1125
sardine in California (Lynn, 2003), the southern Benguela (Twatwa et al., 2005), the Bay of
1126
Biscay (Planque et al., 2007), and elsewhere (Castro et al., 2005; van der Lingen et al., 2005).
1127
Relating spawning habitat to environmental conditions would allow for the simulation of an
1128
“environmental homing” reproduction strategy as opposed to a “natal homing” strategy (Cury,
1129
1994), and allow investigation of climate-driven changes in the habitat and their consequences on
1130
early life stages dynamics. Some caution is appropriate for such a “climate envelope” approach
1131
(Davis et al., 1998) because the characterizations by environmental variables may themselves
1132
change in response to climate change due to adaptation, acclimation, and changes in the food
1133
web.
1134 1135
Early life stage models are ready for species-specific and site-specific analysis of climate change
1136
effects of small pelagic fish in upwelling systems. Some of the details of such applications need
1137
careful attention, especially the matching of the spatial and temporal scales of the hydrodynamic
1138
and NPZ models with the fish models, and how growth, mortality, behaviour-based movement
1139
and trophic feedbacks are represented (Runge et al., 2005). We see an accelerating trend from
1140
models of “hydrodynamics and simple behaviors” to models of “hydrodynamics and dynamic
39
1141
prey”. It may be possible to include invertebrate predators in the models, but it will remain
1142
difficult to include fish predators of eggs and larvae. A large uncertainty may be getting
1143
agreement about how climate change will affect hydrodynamic outputs that are then used as
1144
inputs to the fish models, and obtaining these outputs on the spatial and temporal scales needed
1145
by the biophysical fish models.
1146 1147
Biophysical models that include the adult life stages of fish is an area of high research interest but
1148
will likely be used for general analysis or application to a few, extremely well-studied species and
1149
locations. The uncertainty in how to model the behavioural aspects of movement will limit the
1150
development of a generally agreed upon modelling approach (i.e., physics-based) that has helped
1151
advance the early life stage models. New measurement methods are becoming available that
1152
should provide the empirical basis for evaluating the alternative movement options (Cooke et al.,
1153
2004). Sugden and Pennisi (2006) recently introduced a special section in Science on “movement
1154
ecology”. Continued efforts on adult models is necessary in order to get to “end-to-end” (physics
1155
to fish), full life cycle models capable of addressing the long-term consequences of climate
1156
change on fish and fisheries.
1157
40
1157
Figures
1158
1159 1160
Figure 1: A schematic view of the approach generally used for implementing biophysical models
1161
of marine species early life history (modified from Hermann et al., 2001). An hydrodynamic
1162
1164
model (or an hydrodynamic-biogeochemical coupled model) provides three-dimensional dynamic r fields of current velocities u , temperature T , and other variables (e.g., phytoplankton biomass r P ), to an individual-based model that tracks location x , length L and other variables of interest
1165
for a collection of individuals i over time t .
1163
1166
41
1166
(a)
(b)
(c)
(d)
1167
Figure 2: Crab larvae concentrations (a) observed and (b–d) obtained from a biophysical model
1168
that included (b) diel vertical migration for larvae and river outflow (c) only diel vertical
1169
migration for larvae (d) only river outflow. Reproduced from Peliz et al. (in press).
1170
42
1170
(a)
(b)
1171
Figure 3: Simulated distribution and wet weight (colour scale, in mg) of 2-4 month old juvenile
1172
cod obtained from a biophysical model using hydrodynamics under (a) current conditions and (b)
1173
under reduced thermohaline circulation. Reproduced from Vikebø et al. (2007).
1174
43
1174
(a)
(b)
(c)
1175
Figure 4: Spatio-temporal spawning pattern after 200 generations obtained from a biophysical
1176
model that used 100 000 particles and a lethal temperature threshold of (a) 14°C (like simulation
1177
4 in Mullon et al., 2002) (b) 15°C (c) 16°C.
1178
44
1178
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