1

Chapter 6 1

2

Biophysical models of small pelagic fish 3

4

Christophe Letta, Kenneth A. Roseb, Bernard A. Megreyc 5

6 a Institut de Recherche pour le Développement, UR ECO-UP, University of Cape Town, 7

Oceanography Department, Rondebosch, 7701, South Africa, christophe.lett@ird.fr 8

9 b Coastal Fisheries Institute and Department of Oceanography and Coastal Sciences, 10

Louisiana State University, Baton Rouge, LA 70803, USA, karose@lsu.edu 11

12 c National Oceanic and Atmospheric Administration, National Marine Fisheries Service, 13

Alaska Fisheries Science Center, Seattle, WA 98115, USA, bern.megrey@noaa.gov 14

15

1 Introduction 16 17

Understanding and forecasting the effects of climate change on small pelagic fish involves 18

coupling the physics and lower trophic level dynamics to the growth, mortality, reproduction, 19

and movement processes of key life stages that govern fish recruitment and population 20

dynamics. Fish exhibit large changes in body weight, and often dramatic changes in body 21

form, habitat usage, and diet, with ontogenetic development through the egg, larval, juvenile, 22

and adult life stages. Early life stages (eggs and larvae) are heavily influenced by advective 23

processes, which determine where they go in the system and what environmental conditions 24

they are exposed to. There are many models that have coupled physics with eggs and larvae 25

dynamics, and examined how physical transport under different conditions can affect the 26

growth and mortality rate experienced by individuals during these early life stages (Werner et 27

al., 2001; Miller, submitted). The “Workshop on advancements in modeling physical-28

biological interactions in fish early-life history: recommended practices and future directions” 29

held on 3-5 April 2006 in Nantes, France (co-chairs: A. Gallego, E. North and P. Petitgas), 30

2

attracted more than 50 participants from 14 countries, an indication of the international 1

interest in the topic. 2

3

Many questions posed about climate effects on fish and fisheries can be only partially 4

answered by models that predict growth and survivorship to the larval or early juvenile life 5

stage. Recruitment for some species may not be determined until later in the life cycle than is 6

simulated with these early life stage models. Furthermore, some questions require simulating 7

the effects of climate on adults (e.g., how will climate affect migration and spatial 8

distributions), and other questions require multi-generational simulations that include all life 9

stages in order to forecast the long-term consequences of climate effects (e.g., climate effects 10

on sustainable harvest levels). The coupling of physics and the lower trophic levels to models 11

that include the adult life stages is much less common than models restricted to early life 12

stages. Biophysical models that include adult life stages are being increasingly considered and 13

their use, especially with the need to address climate change issues, will accelerate over the 14

next decade. 15

16

The objective of this chapter is to provide an overview of biophysical models of fish, with a 17

particular focus on those applied, or potentially applicable, for examining the consequences of 18

climate change on small pelagic species. We consider models of early life stages and models 19

that include adults. Our review is not intended to be comprehensive, and others have 20

previously reviewed biophysical models of early life stages (Werner et al., 2001; Miller, 21

submitted). We focus our review on models of fish that include physics and possibly lower 22

trophic level dynamics; inclusion of physics implies the models must be spatially-explicit. We 23

divided these models into two general categories: single-species individual-based models 24

(IBMs) of fish early life history and models of adult stages (either adults only, or full life 25

cycle that include all life stages). In the early life stage IBMs, the abiotic environment is 26

described with output from a hydrodynamic model, or by a hydrodynamic model coupled to a 27

biogeochemical (e.g., NPZ) model. Werner et al. (2001) classified IBMs in which the physics 28

is used for transport but the biotic (NPZ) environment is absent or represented by static prey 29

fields derived from field data as “hydrodynamics and simple behaviors” or “hydrodynamics 30

and static prey”. Building on the classification proposed by Werner et al., we also include in 31

our review IBMs that use the output of a biogeochemical model as a dynamic representation 32

of the prey for the fish, and these we term “hydrodynamics and dynamic prey”. The adult 33

models are much less common and, while we focus on models that are spatially explicit and 34

3

coupled to hydrodynamic and biogeochemical models, we also include models that do not 1

fulfil all of the criteria. We included some adult models because they could be adapted to 2

examine questions about climate change effects that require the inclusion of adult life stages. 3

4

This chapter is organized as follows. First, we give a brief overview of the methods used to 5

represent transport, growth, mortality, and behaviour of individuals in models of early life 6

stages. Second, we detail several case studies of such biophysical models of early life stages, 7

organized by models of anchovy and sardine in SPACC regions, anchovy and sardine in the 8

Benguela upwelling system and in other major upwelling systems, and for small pelagic fish 9

in general in “non-SPACC” regions. We then turn to models that include adults. We briefly 10

discuss methods used to represent movement, as advective transport only is no longer 11

sufficient, and detail several case studies of biophysical models that include adults that are 12

relevant, or potentially relevant, to small pelagic species and climate change. Finally, we 13

conclude with a discussion of the potential use of these biophysical models to investigate 14

some of the issues raised in the context of climate change. 15

16

2 Biophysical models of early life stages 17

18

2.1 Modelling the fish egg and larval environment 19

20

2.1.1 The abiotic environment 21

22

The abiotic environment for the fish eggs and larvae is usually provided by simulations of 23

hydrodynamic models. In some studies, field data were directly used to generate the needed 24

physics for model simulations (e.g., Heath et al., 1998; Rodríguez, 2001; Santos et al., 2004). 25

The hydrodynamic models were generally used to provide temporally dynamic, 3-26

dimensional fields for environmental variables such as water velocity, temperature, and 27

salinity. 28

29

4

2.1.2 The biotic environment 1

2

The use of biogeochemical models or field data to generate the biotic environment for the fish 3

eggs and larvae has received less consideration. Most applications focus on the prey field for 4

influencing the feeding and growth rates of the fish larvae. Prey fields have been generated as 5

input to the early life stage models using biogeochemical models (e.g., Hinckley, 1999; Koné, 6

2006), interpolated from field data (e.g., Hinrichsen et al., 2002; Lough et al., 2006), or 7

assessed using remotely-sensed data (e.g., Bartsch and Coombs, 2004). Use of models or data 8

to specify spatially and temporally varying predation on fish eggs and larvae is rare (but see 9

Suda and Kishida, 2003; Suda et al., 2005). Predation is usually considered part of the total 10

mortality rate, and the changing vulnerability of early life stages represented by mortality 11

rates being stage-specific or size-dependent. 12

13

2.2 Modelling the fish egg and larval dynamics 14

15

Most biophysical models of the early life stages are individual-based models (Lagrangian), 16

although a few models used an Eulerian approach (e.g., Zakardjian et al., 2003). There are a 17

variety of different methods for coupling a hydrodynamic model to an individual-based model 18

of eggs and larvae (Hermann et al., 2001). Most common is to run the hydrodynamic model, 19

store the outputs, and then use the outputs as inputs to the fish model (Figure 1). 20

21

Figure 1 22

23

2.2.1 Transport 24

25

Transport of individuals in biophysical models consists of updating the individuals’ position 26

x� using the following equation: 27

28

uudtxd ′+= ��� / (1)

29

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The deterministic advection term u� is typically derived from spatial and temporal 1

interpolations of the flow fields provided by the hydrodynamic model. A stochastic term u′� is 2

often added to take into account the small-scale fluctuations in the currents that are lost due to 3

the grid resolution of the hydrodynamic model and temporal averaging of the hydrodynamic 4

model outputs. The stochastic term is often represented using an ad-hoc diffusion term (i.e., 5

random walk process) or using a random displacement process if a spatially non-uniform 6

diffusivity is used (North et al., 2006). Recent theoretical results using the dispersal 7

characteristics of drifters show promise for objectively specifying the stochastic term (Haza et 8

al., in press). Equation (1) is numerically integrated using schemes such as a forward Euler or 9

a Runge-Kutta. Ådlandsvik (submitted) has recently proposed several standard test cases to 10

evaluate the advection scheme used in biophysical models. Some studies have specifically 11

attempted to “validate” the flow fields and the transport scheme used by comparing 12

trajectories of virtual and real drifters (Gutiérrez et al., 2004; Thorpe et al., 2004; Edwards et 13

al., 2006; Fach and Klinck, 2006). 14

15

2.2.2 Growth 16

17

A general relationship between the attributes of individuals (e.g., length L and age) and 18

environmental variables (e.g., temperature T and food biomass F ) was proposed by Heath 19

and Gallego (1997) to simulate growth: 20

21

dtFfTfagefLaget

tage )()()( 3

021∫

=

=

= (2)

22

In most biophysical models, the growth algorithm used various simplified versions of 23

equation (2) in which stage durations (e.g., Miller et al., 1998), length (e.g., Fox et al., 2006), 24

or weight (e.g., Vikebø et al., 2005) were functions of temperature only. When the effect of 25

prey fields on growth was considered, relatively more complex bioenergetics sub-models 26

were developed (e.g., Hinckley, 1999; Megrey and Hinckley, 2001; Hinrichsen et al., 2002; 27

Lough et al., 2005). These bioenergetics models allow for weight and temperature effects on 28

consumption and the lost terms (respiration, egestion, excretion), and use the prey field 29

information to determine the actual realized consumption rate. 30

6

1

2.2.3 Mortality 2

3

Mortality has been represented in early life stage models in a variety of ways, including as 4

constant rates (e.g., Brown et al., 2005; Tilburg et al., 2005), and depending on life stage 5

(Miller et al., 1998), length (Hinckley, 1999), weight (Brickman et al., 2001), temperature 6

(e.g., Mullon et al., 2003), and slow growth (e.g., Hinrichsen et al., 2002; Bartsch and 7

Coombs, 2004). Suda and colleagues (Suda and Kishida 2003; Suda et al., 2005) is one of the 8

few examples that included inter-specific effects and density dependent effects on mortality. 9

The high mortality rates of early life stage IBMs can result in numerical problems because 10

many individuals need to be followed in order to obtain enough survivors to allow analysis of 11

the results. One method for dealing with the high mortality problem is to use the concept of 12

super-individuals (Scheffer et al., 1995), in which each simulated individual is assumed to 13

represent some number of identical population individuals (e.g., Hinckley, 1999; Megrey and 14

Hinckley, 2001; Allain, 2004; Bartsch and Coombs, 2004). Rather than mortality resulting in 15

the removal of model individuals, the worth of each super-individual is decreased based on 16

the mortality rate. Models can therefore use a constant, and a priori determined, number of 17

model individuals throughout their simulations. 18

19

2.2.4 Behaviour 20

21

Egg buoyancy schemes have been included in determining the vertical position of individuals. 22

Typically, a vertical velocity term is used that is assumed to be proportional to the difference 23

between egg density and water density. Egg densities have been assumed to be constant (e.g., 24

Parada et al., 2003; North et al., 2005), stage-dependent (e.g., Hinckley, 1999), and time-25

dependent (e.g., Brickman et al., 2001). Vertical migration of larvae has received a lot of 26

attention (Bartsch et al., 1989). Most studies use a diel vertical migration scheme (e.g., Rice 27

et al., 1999), but other vertical migration approaches include the use of a depth-by-age curve 28

(Ådlandsvik et al., 2004), stage-specific vertical velocities (Pedersen et al., 2006), and length-29

specific depth distributions (Bartsch and Coombs, 2004). Horizontal swimming of larvae has 30

also been considered in a few studies (Rodríguez et al., 2001; Yeung and Lee, 2002; Fox et 31

al., 2006). To our knowledge, schooling behaviour, which commonly appears in small pelagic 32

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fish larvae (Hunter and Coyne, 1982), has never been taken into account. However, there are 1

models of schooling that focus on how schools form and persist (e.g., Huth and Wissel, 1992). 2

3

2.3 Case studies 4

5

2.3.1 Models of anchovy and sardine in the Benguela upwelling system 6

7

Most biophysical models of early life stages developed for the Benguela Current upwelling 8

system have focused on anchovy (Engraulis encrasicolus) in the southern Benguela (Huggett 9

et al., 2003; Mullon et al., 2003; Parada, 2003; Parada et al., 2003; Skogen et al., 2003; Koné, 10

2006). Early life stage models have also been developed for sardine (Sardinops sagax) in the 11

southern Benguela (Miller, 2006; Miller et al., 2006) and in the northern Benguela (Stenevik 12

et al., 2003). All these models, except Koné (2006), fall into the “hydrodynamics and simple 13

behaviors” category; Koné’s (2006) model is an example of an “hydrodynamics and dynamic 14

prey” IBM. 15

16

Most of these Benguela Current models used the same regional PLUME configuration 17

(Penven, 2000; Penven et al., 2001) of the ROMS hydrodynamic model (Shchepetkin and 18

McWilliams, 2005). The PLUME configuration covers the southern Benguela from 28 to 19

40°S and from 10 to 24°E, at a horizontal resolution ranging from 9 km at the coast to 16 km 20

offshore and with 20 terrain-following vertical levels. Koné (2006) used the same PLUME 21

configuration of ROMS but coupled with a biogeochemical model (Koné et al., 2005). 22

Skogen et al. (2003) and Stenevik et al. (2003) used a different configuration and the 23

NORWECOM hydrodynamic model (Skogen, 1999). This configuration covered the whole 24

Benguela area, from 12 to 46°S and from 4 to 30°E, at a horizontal resolution of 20 km and 25

with 18 terrain-following vertical levels. 26

27

Recently, the ROMS model has been applied to the Benguela region using an embedding 28

procedure that places a high-resolution small-scale (child) grid nested into a low-resolution 29

large-scale (parent) grid (Penven et al., 2006a). The parent grid covers the whole southern 30

Africa from 5 to 46°S and from 2°W to 54°E, at a horizontal resolution of 0.25° ranging from 31

19 km in the south to 27 km in the north (Southern Africa Experiment or SAfE, Penven et al., 32

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2006b). The first child grid (SAfE south coast) was designed to study the interactions between 1

the Agulhas and Benguela systems and covers the area from 28 to 39ºS and 12 to 27ºE at a 2

horizontal resolution of about 8 km (N. Chang, personal communication). The second child 3

grid (SAfE west coast) was designed to encompass most of the Benguela from 18 to 35ºS and 4

10 to 20ºE, and also has a horizontal resolution of about 8 km (J. Veitch, personal 5

communication). The parent and child grids have 32 terrain-following vertical levels. 6

Hydrodynamics provided by SAfE west coast child grid was recently used in a Lagrangian 7

model (Lett et al., in press). 8

9

The development of anchovy early life stage models for the southern Benguela that used the 10

PLUME configuration of ROMS has followed a step-by-step progression from simple to more 11

complex models. The first model developed by Huggett et al. (2003) only tracked eggs and 12

larvae with transport completely determined passively by currents. Parada et al. (2003) 13

introduced a buoyancy scheme for the eggs, and Parada (2003) added temperature-dependent 14

and stage-dependent growth and mortality, and vertical swimming behaviour of larvae. A 15

synthesis of these simulation experiments can be found in Mullon et al. (2003). Koné (2006) 16

then added food-dependency to the temperature-dependent larval growth. 17

18

The progression of anchovy model development provides an opportunity for determining how 19

increasing biological complexity affected model results. All of these models used the same 20

configuration of the same hydrodynamic model (PLUME implementation of ROMS), and all 21

relied on the same method for designing simulations and analysing the results. Simulations 22

were performed using all combinations of pre-defined parameter values, and using 23

comparable graphical and statistical analysis to determine the effects of the parameters and 24

their interactions on the output variables. The main output variable used was the percentage of 25

larvae transported from the anchovy spawning grounds near the South African south coast to 26

nursery grounds off the west coast. This percentage was referred to as the simulated transport 27

success. The major results from the progression of models and analyses were: 28

1) Simulated transport success has a strong seasonal pattern, peaking in the austral spring 29

and summer time periods (October to March). 30

2) There is little chance for virtual eggs released on the eastern side of the spawning 31

grounds to be transported to the west coast. 32

3) Simulated transport success is highest for an egg density of 1.025 g.cm-3, and use of 33

this density generated results similar to those obtained using purely passive transport. 34

9

4) Simulated transport success increases with spawning depth within 0 to 75 m. 1

2

These modelling results corresponded reasonably well to the field observations of anchovy in 3

the southern Benguela. The main spawning season of anchovy is austral spring and summer, 4

with major spawning areas located in the western and central parts of the spawning grounds. 5

Measured egg density is about 1.025 g.cm-3. However, anchovy eggs are mainly found in the 6

upper 20 m and rarely deeper than 60 m (Dopolo et al., 2005). 7

8

While the early life stage models of the Benguela described above used hydrodynamics based 9

on seasonal forcing, other models (Skogen et al., 2003; Stenevik et al., 2003; Miller, 2006; 10

Miller et al., 2006) used hydrodynamics based on interannual forcing. Interannual indices of 11

retention or transport success derived from these models did not correlate well with time-12

series of sardine recruitment (Stenevik et al., 2003; Miller, 2006; Miller et al., 2006). 13

However, the main objective of these analyses was on investigating the factors that affected 14

retention and transport of sardine eggs and larvae, and not on deriving indicators of 15

recruitment success. Skogen et al. (2003) showed that different indices of transport to the 16

South African west coast were correlated to anchovy recruitment. The mixed results of 17

model-derived indices being correlated to recruitment was also found in other studies. Parada 18

et al. (in press) found that indices derived from their walleye pollock (Theragra 19

chalcogramma) model were not correlated with recruitment in the Gulf of Alaska, while 20

Baumann et al. (2006) found significant correlations for sprat (Sprattus sprattus) recruitment 21

in the Baltic Sea. The recent availability of interannual simulations covering the period 1957–22

2001 for the SAfE south coast and SAfE west coast implementations (N. Chang and J. Veitch, 23

personal communications), presents an opportunity for attempting to correlate model-24

generated indices to recruitment data for the Benguela region. 25

26

The numerical experiments performed by Mullon et al. (2002), Lett et al. (2006) and Lett et 27

al. (in press) provide some basic building blocks for analyses of anchovy and sardine early 28

life stage dynamics. Mullon et al. (2002) developed an evolutionary model that explored how 29

environmental constraints (e.g., avoiding offshore advection and cold water) to affect the 30

spatial and temporal patterns in spawning. Imposition of these relatively simple constraints 31

and then simulated for multiple generations lead to the selection of spawning patterns that 32

were in surprisingly good agreement with those observed for anchovy and sardine in the 33

southern Benguela. This approach of allowing the temporal and spatial patterns in spawning 34

10

to emerge from a selective process and environmental conditions offers an alternative to the 1

usual approach of specifying the location and timing of egg deposition used in most 2

biophysical models. 3

4

Lett et al. (2006) used a Lagrangian approach to simulate and quantify enrichment and 5

retention processes in the southern Benguela. These two processes, along with the 6

concentration process, form a triad of processes that are fundamental for the survival and 7

recruitment of early life stages of pelagic fish (Bakun, 1996). The results of Lett et al. (2006) 8

reinforce the view of Cape Agulhas as a ‘dividing line’ in the southern Benguela pelagic fish 9

recruitment system, with a transport-based subsystem to the west and a retention-based 10

subsystem to the east. These two subsystems were considered by Miller (2006) and Miller et 11

al. (2006) in their sardine biophysical model. Lett et al. (in press) also used a Lagrangian 12

approach to investigate the processes responsible for the absence of anchovy and sardine 13

spawning in the central Benguela off the Lüderitz region. They examined the flow field and 14

temperature conditions that particles would experience in the Lüderitz region, and concluded 15

that the combination of a surface hydrodynamic and a subsurface thermal barrier could limit 16

the possibility for anchovy and sardine ichthyoplankton to be transported from the southern to 17

the northern Benguela. Recent remote sensing data also suggested a poor trophic environment 18

in the Lüderitz region (Bartholmae and Basson, submitted; Demarcq et al., submitted). 19

20

2.3.2 Models of anchovy and sardine in other upwelling systems 21

22

We are not aware of biophysical models of the early life stages of anchovy developed in 23

upwelling systems outside the Benguela. Models of sardine for the Kuroshio Current 24

(Sardinops melanostictus, Heath et al., 1998) and in the Iberian system (Sardina pilchardus, 25

Santos et al., 2004) used hydrodynamics derived from field data. However, three anchovy 26

(Engraulis ringens) biophysical models using hydrodynamics provided by ROMS are under 27

development for the Humboldt Current upwelling system (Brochier et al., abstract1; Soto-28

Mendoza et al., abstract2; Chai et al., abstract3), and there are anchovy models in the vicinity 29

1 T. Brochier, J. Tam, P. Ayón. 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. 2 S. Soto-Mendoza, L. Castro, C. Parada, F. Colas, D. Donoso, W. Schneider. Modeling the egg and early larval anchoveta (Engraulis ringens) transport/retention in the southern spawning area of the Humboldt Current.

11

of major upwelling systems. Models exist for European anchovy (Engraulis encrasicolus) for 1

the Bay of Biscay (Allain et al., 2003; Allain, 2004; Allain et al., submitted; A. Urtizberea, 2

personal communication) and for Japanese anchovy (Engraulis japonicus) in the Yellow Sea 3

(Hao et al., 2003). Models of the early life stages of taxa in upwelling systems besides small 4

pelagic fish include crab (Carcinus maenas) in the Iberian upwelling system (Marta-Almeida 5

et al., 2006), zooplankton in the California Current upwelling system (Carr et al., submitted), 6

and blue shrimp (Litopenaeus stylirostris) and brown shrimp (Farfantepenaeus californiensis) 7

in the Gulf of California (Marinone et al., 2004). 8

9

Santos et al. (2004) used a combination of measured and modelled velocities to estimate the 10

surface flow field experienced by particles during an upwelling event off Portugal, and 11

obtained qualitatively similar patterns of retention at the shelf-break for modelled particles 12

and for observed sardine eggs and larvae. In the same region, Marta-Almeida et al. (2006) 13

used the ROMS model on a domain extending from 37.5 to 44.3°N and 12.8 to 8.4°W and 14

simulated different vertical migration behaviours of crab larvae. They showed that migrating 15

larvae were retained within the inner shelf under a wider range of upwelling and downwelling 16

conditions than non-migrating larvae. We can anticipate a similar modelling study on sardine 17

as data on the vertical distribution and behaviour of sardine larvae have recently been 18

collected off Portugal (Santos et al., 2006). 19

20

Allain and colleagues (Allain et al., 2003; Allain 2004; Allain et al., submitted) used 21

hydrodynamics derived from the MARS 3D circulation model that covered the Bay of Biscay 22

south of 49°N and east of 8°W at a 5 km horizontal resolution with 30 terrain-following 23

vertical levels. Allain et al. (2003) used virtual passive buoys released in the simulated flow 24

fields to reconstruct the putative origins in time and space of collected anchovy larvae and 25

juveniles. Allain (2004) and Allain et al. (submitted) used a biophysical model of anchovy 26

that included transport, growth, and mortality. They used the super-individual approach 27

(Scheffer et al., 1995), with each simulated buoy representing a large number of eggs, larvae, 28

and juveniles. Every time step, each buoy was characterized by a distribution of growth rates 29

(function of age and the physical environment it experienced) and by a survival probability 30 International Conference on The Humboldt Current System: Climate, ocean dynamics, ecosystem processes, and fisheries. Lima, Peru, November 27 - December 1, 2006. 3 F. Chai, L. Shi, Y. Xu, Y. Chao, K. Rose, F. Chavez, R. T. Barber. 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.

12

(the probability that growth rates in the distribution were above a pre-defined age-specific and 1

stage-specific threshold). They used the simulations to form an index of recruitment (survival 2

rate multiplied by egg production, summed over the year and spatial domain) that correlated 3

remarkably well to a (short) time-series of anchovy recruitment data. 4

5

Rodríguez et al. (2001) released particles in a static two-dimensional flow field calculated 6

from observations to assess the potential for retention of organisms around the Canary Island 7

of Gran Canaria. They showed that particles released north of Gran Canaria would need 8

limited “swimming ability” (speeds of ~0.5 cm.s-1) in order for them to be retained, whereas 9

those particles released east or west of Gran Canaria would require a much stronger 10

swimming ability (>5 cm.s-1) in order to be retained. Hunter (1977) reported mean swimming 11

speeds of 0.3–0.45 cm.s-1 for early (5 mm) northern anchovy (Engraulis ringens) larvae at 17° 12

to 18°C. A configuration of ROMS for the northern Canary is under development (E. Machu, 13

personal communication). This configuration uses an embedding procedure with a parent grid 14

covering the area from 10 to 40°N and -5.5 to 30°W at a horizontal resolution of 1/4°, and a 15

child grid from 21 to 32.5°N and 9 to 20.5°W at a horizontal resolution of about 8 km. A 16

biophysical model will be developed in the near future to study sardine early life history in 17

this region (A. Ramzi, personal communication). 18

19

Lett et al. (2007) used a similar approach for the northern Humboldt upwelling system as Lett 20

et al. (2006) did in the southern Benguela. They derived indices of enrichment, concentration, 21

and retention based on Lagrangian simulations using hydrodynamics from a regional ROMS 22

configuration. This configuration covered the domain off Peru from 20°S to 3°N and 90 to 23

70°W at a horizontal resolution of 1/9° (~10 km) and with 32 terrain-following vertical levels 24

(Penven et al., 2005). Lett et al. (2007) analysed the spatial distribution and seasonal 25

variability in the simulated indices, and discussed their results in relation to the distributions 26

of anchovy (Engraulis ringens) eggs and larvae off Peru. A coastal area of enhanced 27

enrichment was identified between Punta Falsa and Pisco (6°S–14°S), which corresponds to 28

the zone where most anchovy eggs and early larvae are found. Preliminary modelling results 29

suggest that the early life stages of anchovy are found mainly in the northern part of this zone 30

(6°S–9°S) because this area provides high retention and concentration. Another striking 31

characteristic of anchovy spawning in the region is the bimodal seasonal pattern, with peaks 32

in January-March and August-October. A biophysical model of anchovy early life stages is 33

currently being developed to better understand the bimodal spawning pattern in this region (T. 34

13

Brochier, personal communication). Other biophysical models of the early life stages of 1

anchovy are under development for the northern Humboldt (Y. Xu, personal communication) 2

and southern Humboldt (S. Soto-Mendoza, personal communication) upwelling systems. 3

4

Heath et al. (1998) used static two- and three-dimensional flow fields calculated from 5

observations for two years to assess the dispersal of sardine (Sardinops melanostictus) eggs 6

and larvae in the Kuroshio Current upwelling system. They obtained very different results for 7

the two years, with most egg production being transported towards the Kuroshio Current 8

extension in the first year, while most of it was retained in the coastal areas in the second 9

year. In contrast, using different scenarios for transport (without and with diffusion) and for 10

behaviour (without and with vertical redistribution of individuals according to observed depth 11

distributions) had little effect on model simulations. They argued that, at least during the time 12

of their study, hydrodynamic models could not easily simulate the instabilities in the Kuroshio 13

path that were responsible for the contrasting flow fields they observed. 14

15

Hao et al. (2003) conducted Lagrangian simulations in the nearby Yellow Sea using a 16

regional configuration of the HAMSOM (Hamburg Shelf Ocean Model) hydrodynamic 17

model. This configuration covered the Yellow Sea and the East China Sea from about 25 to 18

40°N and from 120 to 130°W at a horizontal resolution of 1/12° and with 12 vertical layers. 19

They showed that including a tidal component in the hydrodynamic model affected the 20

predicted transport pattern of simulated particles, and discussed their results in relation to the 21

high concentrations of anchovy (Engraulis japonicus) eggs and larvae that are observed in 22

tidal fronts. 23

24

Despite the preliminary Lagrangian experiments conducted in the California Current 25

upwelling system to investigate the effects of vertical migration on larval drift trajectories 26

(Botsford et al., 1994), there has not been much follow-up with more biologically-based 27

models of the early life stages of small pelagic species. Lagrangian experiments have been 28

designed to study the transport patterns of other taxa, including zooplankton (Carr et al., 29

submitted) and shrimp larvae (Marinone et al., 2004). Carr et al. (submitted) used a nested 30

approach in ROMS with a parent grid covering the entire California upwelling system 31

(7.5 km resolution) and a child grid focusing on the Monterey Bay region (2.5 km resolution), 32

and with 32 terrain-following vertical levels. They investigated the effects of diel vertical 33

migration of planktonic organisms, and obtained results suggesting that migration into 34

14

subsurface onshore currents during the day would not compensate for surface offshore 1

transport during the night and thus retention would be low within the Monterey Bay. 2

Marinone et al. (2004) explored different scenarios for when advection of particles occurred 3

(only during the day, the night, or when the current flows northwards), and discussed their 4

results in relation to transport patterns of shrimp larvae to their nursery areas. They used a 5

configuration of HAMSOM covering the Gulf of California at a horizontal resolution of 1/24° 6

(~4 km) and with 12 vertical layers, developed by Marinone (2003). 7

8

2.3.3 Models of small pelagic fish in “non-SPACC” regions 9

10

In this section, we briefly mention several early life stage models for small pelagic species 11

and regions outside the main focus of SPACC. We mention these examples because the 12

methods and results may be of interest, and because they provide a broad view of early life 13

stage biophysical models. 14

15

Vaz et al. (submitted) used outputs from a western South Atlantic configuration of the 16

Princeton Ocean Model (POM) as input to a biophysical model of anchovy (Engraulis 17

anchoita) eggs and early larvae. They investigated the spatial and seasonal patterns in the 18

levels of retention and transport along the coast off northern Argentina, Uruguay, and 19

southern Brazil. 20

21

Bartsch and colleagues (Bartsch et al., 1989; Bartsch, 1993; Bartsch and Knust, 1994a, 22

1994b) used hydrodynamics derived from early versions of the HAMSOM model as input to 23

biophysical models of herring (Clupea harengus) and sprat (Sprattus sprattus) early life 24

stages for the North Sea. Their seminal studies incorporated transport and size-dependent 25

vertical migration of larvae, and focused on qualitative comparisons between observed and 26

simulated distributions of larvae. Sætre et al. (2002) used the NORWECOM model to assess 27

the transport routes and retention areas for herring along the Norwegian coast. They showed 28

that herring tended to spawn in areas where retention was enhanced by the presence of 29

topographically-induced quasi-stationary eddies. Hinrichsen et al. (2005) developed a model 30

of sprat for the Baltic Sea and showed that the degree of overlap between observed and 31

simulated distributions of juveniles was higher when individuals were constrained to remain 32

close to the surface than when they were allowed to migrate to deeper waters during the day. 33

15

Baumann et al. (2006) proposed different empirical models fitted to observed values of sprat 1

recruitment, and obtained the best result when they incorporated an index derived from the 2

biophysical model simulations. 3

4

Bartsch and Coombs (2001) developed a mackerel (Scomber scombrus) early life stage 5

biophysical model using an eastern North Atlantic configuration of the HAMSOM model. 6

They used initial conditions for egg distribution and abundance that were based on field data, 7

and simulated the drift of eggs and larvae and their growth using a function dependent on 8

temperature and age. Bartsch and Coombs (2004) later introduced additional biological 9

processes into their model, including vertical migration, feeding, and mortality. They used 10

size-dependent diel vertical migration, and dynamic prey fields calculated from satellite-11

derived sea-surface temperature and chlorophyll-a concentration. Like Allain (2004), Bartsch 12

and Coombs (2004) also used super-individuals, where every simulated entity initially 13

represented 106 individuals who experienced the same environment and who died according 14

to growth-dependent and length-dependent mortality. Using this model, Bartsch et al. (2004) 15

derived indices of mackerel early post-larvae survival that they then compared to juvenile 16

catch data for different sub-areas during 1998 to 2000. These simulations however all used 17

the same initial conditions of egg distribution and abundance (those observed for 1998). 18

Bartsch (2005) completed these results for year 2001 and analysed the differences obtained in 19

the distributions and lengths of the simulated particles when using initial conditions based on 20

data of year 1998 or of year 2001. 21

22

3 Biophysical models that include adults 23

24

There are two major categories of models that include adult fish and physics. The first 25

category is models in which the key processes of growth, mortality, reproduction, or 26

movement depends on the physics or variables greatly influenced by the physics. The second 27

category is models for which the questions to be addressed require full life cycle simulations 28

(i.e., include all life stages) so that the long-term (multigenerational) effects of impacts or 29

environmental changes can be examined. These full life cycle models thus must deal with 30

eggs, larvae, and adults in a single model. Such models are relatively rare now but model 31

development is headed in that direction. We expect biophysical full life cycle models to be the 32

focus of much effort during the next decade, and anticipate that full life cycle biophysical 33

16

models will be especially important for addressing issues related to the effects of climate 1

change on fish populations and fisheries. 2

3

In this section, we review biophysical models that include adult stages of fish. We focus our 4

review on those models that are spatially-explicit, and that use physics, or variables derived 5

from the physics, as inputs. We also include the NEMURO family of models because some 6

versions of the NEMURO models fit our criteria for inclusion, but also because this effort is 7

ongoing and provides an example of a spatially-explicit full life cycle model. We did not 8

include models that use environmental variables as inputs (e.g., temperature) but only 9

simulate a single spatial box (e.g., Robinson and Ware, 1999; Clark et al., 2003), and also do 10

not include other population modelling approaches (e.g., spawner-recruit models – Fiksen and 11

Slotte, 2002; surplus production models – Jacobson et al., 2005). These other modelling 12

approaches are likely useful for addressing certain questions related to climate change effects 13

on fish. Our focus in this chapter is on biophysical spatially-explicit models that include adult 14

fish. 15

16

3.1 Abiotic and biotic environment, growth, and mortality 17

18

Models that include adults generally use similar information from the physics and lower 19

trophic models as used by the egg and larval models. These outputs include: water velocities 20

(advection), salinity, temperature, and prey fields. The growth and mortality formulations in 21

adult models are also similar to those by the early life stage models. Growth in weight is 22

generally either based on empirical relationships (e.g., von Bertalanffy equation – Shin and 23

Curry, 2004a) or bioenergetics-based (e.g., Megrey et al., 2007), and natural mortality rate is 24

often treated as a constant. There are also some predator-prey biophysical models that include 25

adults wherein mortality depends on fish encounters with other fish (Shin and Cury, 2004a; 26

Ault et al., 1999). With the inclusion of adult life stages, representing harvest rates and 27

fisheries can also become important. 28

29

3.2 Movement and behaviour 30

31

17

The process of movement is where models that include adults differ from early life stage 1

models. Unlike the egg and larval stages, movement of juvenile and adult fish no longer is 2

necessarily dominated by the physics. Movement of adults can be influenced by the physics, 3

neutral with respect to the physics, or even opposite to the physics. In many situations, the 4

physics (or variables directly derived from the physics – e.g., salinity, temperature, food) 5

influences some portion of the fish’s movement, while another component is due to other 6

factors dependent on behavioural decisions. An extreme example of movement of adult fish 7

opposite to the physics is migration upstream or counter to the prevailing currents. 8

9

How to represent the movement of adult fish in spatially-explicit biophysical models is 10

unclear and there are several approaches that have been proposed. Conceptually, movement of 11

adults adds terms to Equation 1 attributable to behaviour, and then there must be some 12

weighting of the relative contribution of the physics-based term and the behaviour-based 13

term. We highlight here two of the approaches for modelling movement to illustrate some of 14

the variety in how one can represent movement of adults in biophysical models. 15

16

Railsback et al. (1999) proposed an approach based on fitness considerations in which 17

individuals search neighbouring cells, and move towards cells that provide an optimal blend 18

of growth and survival. In our context, the physics would provide the temperatures and prey 19

fields, and possibly other variables, that are needed to compute growth and mortality in the 20

neighbouring cells. The growth and mortality in each neighbouring cell is then combined into 21

a fitness measure that is the projection of the likelihood of an individual surviving and 22

obtaining some target size at some time in the future (e.g., size at maturity next year), 23

assuming conditions in the cell remained constant into the future. Individuals moved towards 24

the cell in their neighbourhood that had the highest fitness. 25

26

Humston et al. (2004) implemented a different approach to modelling movement of fish that 27

does not require that the fish has knowledge of the conditions in neighbouring cells. Rather, 28

individuals evaluate the conditions in their present cell against some specified optimal value. 29

Movement had inertial and random components; inertial movement involved smaller angles 30

and shorter distances than the random component. They used a weighting scheme to combine 31

the inertial and random components into distances moved and the angle of movement. The 32

closer the conditions in the present cell were to optimal, the more the inertial movement 33

dominated and fish would make smaller moves going in about the same direction and 34

18

therefore tended to stay in the good areas. Poor conditions resulted in the random movement 1

being weighted more heavily and the appearance of individuals searching over relatively large 2

areas and in all directions. 3

4

The Railsback and Humston approaches illustrate a fundamental schism in movement 5

modelling approaches: whether organisms can sense the conditions in neighbouring cells 6

sufficiently to project how conditions there would affect their growth or mortality (Tyler and 7

Rose, 1994). With an appropriate weighting scheme, one can also add terms for the 8

contribution of advective transport to the mix in both approaches. Other approaches to 9

modelling movement include multi-step approaches that first determine the type of behaviour 10

from a list of discrete options and then implement the specifics of movement associated with 11

that behaviour (Anderson, 2002; Goodwin et al., 2006; Blackwell, 1997), and the use of 12

genetic algorithms to train neural networks (Huse and Giske, 1998). 13

14

Given the uncertainty in how to represent movement, it is important to note that some 15

biophysical models bypassed the issue. Heath et al. (1997) did not try to model movement but 16

rather simply assumed movement would occur and would result in the spatio-temporal 17

distributions derived from field data. Even more extreme is the growth potential approach 18

(Luo et al., 2001). They ignored movement and spatial distributions, and simply predicted 19

what would happen if fish were present in all locations. 20

21

3.3 Case studies 22

We have organized this section differently from the early life stage case studies section. There 23

are far fewer examples that include physics and adult fish, and not enough examples to divide 24

by species and geographic area as was done with the early life stage examples. Rather, we 25

have grouped the adult models together according to two general categories: models of adults 26

that use physics and full-life cycle models. We emphasize the methods used because of the 27

much wider diversity of approaches used with adult models than with the more standardized 28

approaches generally used with early life stage models. 29

30

3.3.1 Models of adults that use physics or physics-related variables 31

32

19

Luo et al. (2001) used the output of a 3-dimensional hydrodynamics coupled to a water 1

quality model as input to a fish feeding and bioenergetics model to determine the carrying 2

capacity of Chesapeake Bay for young-of-the-year juvenile menhaden (Brevoortia tyrannus). 3

The water quality model had over 4000 cells, arranged as a surface grid of 729 cells, with 4

vertical cells every 2 m. They averaged the 2-hour simulated values of temperature, dissolved 5

oxygen, and chlorophyll-a to obtain daily values for each cell for June through December in 6

an average freshwater inflow year. Temperature was used directly in the bioenergetics model, 7

and affected maximum consumption rate and respiration rate. Menhaden are filter feeders and 8

so chlorophyll-a concentrations were multiplied by the area of the mouth, swimming speed, 9

and an efficiency term to obtain realized consumption rate. Consumption, with the rest of the 10

bioenergetics model, enabled prediction of daily growth rate in each cell. Carrying capacity 11

for each cell was then computed based on the predicted consumption rate, prey production 12

rates, and prey biomass, and further adjusted for low dissolved oxygen, to obtain the biomass 13

of menhaden that could be supported in that cell on each day. 14

15

Luo et al. (2001) showed spatial maps and reported the percent of the bay volume able to 16

support different growth rates and carrying capacities. Their results showed that there was 17

large spatial and temporal variation in growth rate potential and biomass supportable due to 18

the nonlinear functional forms in the feeding and bioenergetics models and as a result of 19

combining the effects of the multiple factors of temperature, chlorophyll-a, and dissolved 20

oxygen. Menhaden must occupy cells with growth potential greater than 0.005 to 0.001 21

g/g/day during the June through December growing season in order to achieve their observed 22

weights in December, and the daily total volume of such good habitat in the bay varied 23

between practically zero and 80%. 24

25

There are many examples of the use of habitat suitability indices (HSI) that use spatially-26

explicit environmental variables estimated from field data or outputted from hydrodynamics 27

models. Most of these examples involve how changes in stream and river flows would affect 28

the habitat for specific species downstream because the HSI approach was initially developed 29

for evaluating how water releases from dams would affect fish downstream (Acreman and 30

Dunbar, 2004). Use of HSI avoids the issues of representing how adult fish move because an 31

endpoint can be simply the changes in the quantity and quality of the habitat. The HSI 32

approach has also been used as an intermediate variable that is then used to affect movement 33

(e.g., Lehodey et al., 2003). 34

20

1

Rubec et al. (2001) offers an example of HSI applied in an estuarine environment. We 2

summarize an estuarine example here even though it uses field data to derive the 3

environmental variables because the same analysis would be used with model-predicted 4

environmental variables. Others have computed HSI values from the output of hydrodynamics 5

and water quality models (e.g., Guay et al., 2000). Rubec et al. interpolated temperature and 6

salinity values to obtain seasonal values for 18.5 m2 cells in the surface and bottom layers for 7

Tampa Bay, Florida. Additional information on depth, bottom substrate type, and species 8

abundances were also used. Relationships between suitability (0 to 1) and each variable were 9

formulated from abundance data, and the product of the suitabilities in each cell (geometric 10

mean) was computed as the overall suitability of that cell for that life stage. They then 11

checked whether overall suitability was correlated to species abundances over the four 12

seasons, and swapped suitability functions with those developed for Charlotte Harbour to see 13

if the suitability function were transferable among locations. 14

15

Karim et al. (2003) coupled a hydrodynamic-NPZ model to a model of fish movement and 16

dissolved oxygen-related mortality. Their simulations were based on the Marbled Sale 17

(Pleuronectes yokohamae), a demersal species, in Hakata Bay. The spatial domain was a 18

horizontal grid of 300 m x 300 m cells with five vertical layers. The grid was selected to 19

correspond to the horizontal distance typically traveled by an individual fish in the 30 minute 20

time step. Movement could then be based on individuals moving to neighboring cells each 21

time step. The hydrodynamics-NPZ model was solved using its own time step, and 22

temperature and dissolved oxygen values were obtained for each grid cell for use with the fish 23

movement and mortality models. Karim et al. used a series of laboratory experiments and 24

field tracking data of individual fish to develop and calibrate the movement model. Movement 25

in the model was based on computing the preference of each neighboring cell in 3 dimensions 26

from functions that related temperature to preference level and dissolved oxygen 27

concentration to a preference level, and then a function that combined the preferences levels 28

into a single preference value for the cell. Individuals moved to the cells with the highest 29

preference. Horizontal position was updated every 30 minutes, while vertical position was 30

evaluated every 10 seconds. Exposure to low dissolved oxygen caused increased mortality. 31

32

After performing simulations that satisfactorily mimicked the laboratory and field tracking 33

results, Karim et al. (2003) performed 3-day simulations with individuals released in different 34

21

vertical layers (surface or bottom) and horizontal locations (whole grid or inner bay). They 1

computed the mortality rate of the cohort from exposure to low dissolved oxygen as mortality 2

accumulated over the three days. They concluded that hypoxic conditions in the inner portion 3

of the bay during the summer can cause significant mortality of demersal fish, and that future 4

extensions should include the simulation of hypoxia effects on pelagic species. 5

6

Ault et al. (1999) developed a predator-prey model of spotted seatrout (Cynoscion nebulosus) 7

and pink shrimp (Penaeus duorarum) that was imbedded in 2-dimensional hydrodynamic 8

model of Biscayne Bay, Florida. The hydrodynamics model consisted of 6346 triangular 9

elements and 3407 nodes, with grid spacing between nodes of about 500 m. The model was 10

driven with tide, winds, and freshwater discharge data for 1995. A 1 minute time step was 11

used to solve the hydrodynamics model, and currents and salinities were outputted at 10 12

minute intervals for use with the fish model. Shrimp and seatrout were followed as super-13

individuals (what Ault et al. termed “patches”). Patches were introduced monthly for shrimp, 14

and at night on incoming tides for seatrout. Patches were tracked using continuous x and y 15

positions; each time step the patch experienced the conditions of the cell it inhabited. 16

Circulation was used to move around the patches of egg and yolk-sac larval seatrout, 17

circulation and behavior together was used with pre-settlement shrimp, and active behavior 18

only was used for moving settled shrimp and juvenile and adult seatrout. Salinity affected the 19

angle and distance moved (based on swimming speed) of pre-settled shrimp, which was added 20

to the circulation-based movement. Horizontal movement only occurred at night; shrimp went 21

to bottom during the day. Once shrimp settled to the bottom, they were moved around based 22

on their body length and habitat quality. Seatrout movement was based on the growth rate in 23

cells within a specified distance (detection range) of their present location, and patches moved 24

towards cells with the highest growth potential. Shrimp grew based on the cumulative 25

temperature they were exposed to; seatrout grew based on bioenergetics with consumption 26

based on ingested shrimp co-located in their present cell. 27

28

Ault et al. (1999) reported the results of one year simulations that illustrated model behavior 29

and the usefulness of the model for examining how environmental and biological factors 30

affect predator-prey dynamics. They concluded that June-spawned seatrout were transported 31

more into the bay, settled over a wider range of habitats, and grew faster than August-32

spawned cohorts. They also showed that spatial variation in habitat quality can affect growth 33

22

rates of fish, even causing difference among individuals from within the same spawning 1

cohort. 2

3

3.3.2 Full life cycle models 4

5

The EcoPath with EcoSim (EwE) family of models (Walters et al., 1997) are biomass-based 6

compartment models and consist of a steady-state version (EcoPath), which is also used as 7

initial conditions for a one-box dynamic version (EcoSim). Walters et al. (1999) extended the 8

EwE models to be spatially-explicit (EcoSpace) by imbedding EcoSim models on each cell of 9

a 2-dimensional grid of cells. Differential equations are constructed for each fish compartment 10

(species or functional group) in an analogous manner as the equations for phytoplankton and 11

zooplankton in NPZ models (net effect of gain and loss terms corresponding to growth and 12

mortality processes). Fish were represented as biomass in most versions, which was 13

recognized as inadequate because of the large ontogenetic changes in growth and mortality in 14

many fish species and because a single biomass compartment did not allow for explicit 15

representation of recruitment dynamics which is critical to understanding and forecasting fish 16

population dynamics. Thus EwE was extended to allow for each fish compartment to be 17

subdivided into smaller compartments as a crude way to allow for ontogenetic differences and 18

to make recruitment dynamics semi-distinct from total biomass (Walters et al., 2000). While 19

there have been many applications of EcoPath and quite a few applications of EcoSim (e.g., 20

Field et al., 2006), the spatially-explicit EcoSpace version has not yet received much 21

attention. EcoSpace is not designed to be directly coupled to a hydrodynamic or NPZ model, 22

but can use as inputs variables related to transport and prey availability. We mention EwE 23

here because we anticipate increasing attention being paid to the EcoSpace approach in the 24

future. 25

26

The IGBEM and BM2 models (Fulton et al., 2004a, 2004b) are also biomass-based but they 27

are truly spatially-explicit, coupled to an elaborate water quality model, and separate each fish 28

species or group into age-classes and follow the average weight and numbers of individuals in 29

each age-class. BM2 was developed in an attempt to reduce the complexity and parameter 30

demands of its more complicated predecessor IGBEM (Fulton et al., 2004b). The application 31

to Port Phillip Bay, Australia, followed 29 living compartments, plus compartments related to 32

detritus, nutrients, sediment, and some physical variables in a 3-layer grid with about 59 cells 33

23

in each layer. Transport among cells was derived from the output of a hydrodynamics model. 1

A daily time step was used, although if rates were too fast, then a finer time step was used. 2

Four fish groups were followed, with each represented with an age-structured cohort 3

approach. Spawning occurred outside of the model domain and recruits were injected into the 4

grid on a specific day as the initial number of individuals in the first age-class and then the 5

oldest age-class was removed. The average body weight of an individual in each age-class 6

was followed using two separate weight variables (structural and reserve) based on simulated 7

growth. Growth depended on the summed prey biomass, whose vulnerability was sized-based, 8

in the same cell as the predator and adjusted for feeding efficiency and crowding. Consumed 9

prey was imposed as mortality on the appropriate prey compartments in the cell. Movement 10

of fish age-classes was simulated using fluxes among cells based on specified quarterly target 11

densities in cells and how many days were left in the quarter. Fulton et al. (2004b) 12

acknowledged that the recruitment and movement formulations of the model were likely the 13

weakest aspects of their model, and they have investigated using spawner-recruit relationships 14

and forage-based and density-based movement approaches. They stated that they used the 15

constant recruitment and simple movement because the results did not differ much between 16

the simple and more complicated alternatives. 17

18

Fulton et al. (2004b) performed a variety of simulations of BM2 and compared the outputs to 19

field data for Prince Philip Bay, to field data for other estuaries, and to predictions from the 20

more complicated IGBEM version. Simulations repeated a 4-year time series of forcings as 21

input and they determined that 30-year simulations were sufficient because the model state 22

after 30 years was similar to that predicted after 100 years. Examples of model outputs 23

compared to field data or to IGBEM predictions included: averaged biomasses of key 24

compartments, predicted community composition, relationship between DIN and chlorophyll-25

a, predicted and expected size-spectra features, system-wide indices such as P/B ratios and 26

cycling indices, and the temporal and spatial dynamics of key compartments. 27

28

In an ongoing effort, Adamack et al. (abstract4) coupled a 3-dimensional hydrodynamics-29

water quality model to an individual-based population model of bay anchovy (Anchoa 30

mitchilli) in Chesapeake Bay. The water quality model is a three-dimensional model that 31 4 Adamack, A.T., Rose, K.A. and Cerco, CF. 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 15-20, 2006.

24

simulated 24 state variables, including dissolved oxygen, four forms of nitrogen, four forms 1

of phosphorous, two phytoplankton groups, and two zooplankton groups in a 4,073 (729 2

surface layer cells) cell grid. Anchovy were introduced weekly during the summer spawning 3

season as individual recruiting juveniles and followed until they reach their end of third year 4

when they were removed from the model. Growth and mortality rates of individual bay 5

anchovy within a water quality model cell were calculated every 15 minutes. Growth 6

depended on a bioenergetics model with the predicted zooplankton densities from the water 7

quality model providing the prey for bay anchovy consumption. Anchovy consumption was 8

summed by cell and, with the predicted diet, imposed as an additional mortality term back 9

onto the zooplankton. Anchovy excretion and egestion also contributed to the nutrient 10

recycling dynamics of the water quality model. Mortality rate was assumed to decrease with 11

length. Movement of individual anchovy was simulated both vertically (hourly) and 12

horizontally (daily) using temperature, salinity, and prey densities using the approach of 13

Humston et al. (2004). 14

15

Preliminary simulations by Adamack et al. used the dynamically coupled models to predict 16

the effects of changes in nitrogen and phosphorous loadings on bay anchovy growth rates and 17

survival. Ten-year simulations using sequences of low, average, and high freshwater inflow 18

years were performed under baseline, increased, and reduced nutrient loadings. Results 19

showed that the anchovy response to changes in nutrient loadings was a complex function of 20

changes in high-quality habitat, prey densities, assumptions about movement, and the 21

magnitude and temporal pattern of the introduction of young-of-the-year recruits. This 22

analysis provides an example of biophysical model in which the physics is not used directly 23

because the egg and larval stages were bypassed and the adults did not need circulation 24

information, but the physics was needed to properly simulate the NPZ portion. 25

26

Lehodey et al. (2003) used the output of a 3-dimensional hydrodynamics and NPZ model of 27

the Pacific Ocean (45-65oN; 100oE-70oW) as input to an Eulerian-based tuna population 28

dynamics model (SEPODYM). The NPZ model used cells that were 2o in longitude by 2o in 29

latitude at the extreme north and south boundaries of the model domain and 0.5o square near 30

the equator. Forty vertical layers were represented with a layer every 10 meters within 31

euphotic zone and thicker below. Predicted currents were averaged over the 0-30 m surface 32

layer, primary production was integrated over the euphotic zone (1 to 120 m) and with SST, 33

were interpolated on 2-dimensional grid of 1-degree resolution. Lehodey et al. added 34

25

population models for the biomass of tuna forage and for tuna. The forage model simulated 1

tuna prey biomass in each cell using advection and diffusion, and assuming continuous 2

recruitment based on new primary production predicted by the NPZ model and a time lag to 3

account for the delay until the primary production would show up as new forage biomass. The 4

mortality rate and time lag of the forage were related to SST. Tuna were modelled by 5

following the numbers in age-classes. Length-at age were determined from a von Bertalanffy 6

relationship; length was then converted to weight. Two habitat indices (adult and spawning) 7

were computed for each cell based on SST in the cell. The spawning index was used to divide 8

up the annual recruitment among the individual cells. For larvae and juveniles (i.e., until 9

about 4 months of age), tuna movement was purely advection-diffusion. Movement of adult 10

tuna also used the advection terms but adjusted the advection and diffusion rate for tuna 11

length and by the adult habitat index. They assumed movement was proportional to the length 12

of the age-class and increased with poor habitat quality. Natural and fishing mortality was 13

applied to each age-class, with natural mortality rate increased when the habitat was poor 14

(spawning index used for first age-class; adult index used for the rest of the ages). Multiple 15

(six) fisheries with specific gear types and with effort varying by month and cell or subregion 16

were simulated to drive the fishing mortality rate. The SEAPOPDYM application shared 17

information and used outputs from a traditional fisheries stock assessment model called 18

MULTIFAN-CL (Fournier et al., 1998). Annual recruitment in SEAPOP was calibrated to 19

match the overall recruitment estimated by MULTIFAN-CL. 20

21

Lehodey et al. (2003) reported the results of a NPZ and SEPODYM simulation that spanned 22

1960 to1999. General features of the simulation were described, such as the effects of ENSO 23

events and the 1976-77 regime shift, to check the realism of the NPZ simulation. Tuna 24

recruitment and biomass simulated by SEPODYM qualitatively agreed with the estimates 25

from the MULTIFAN-CL model, and predicted catches by grid cell and month were well 26

correlated with observed catches. Most recruitment was predicted to occur in the western and 27

central Pacific region, with large variability caused by El Nino versus La Nina years. The out-28

of-phase dynamics of simulated primary production between the western and central Pacific 29

predicted by the NPZ model was also seen in the SEAPOP simulated tuna recruitment. They 30

emphasized the importance of a carefully constructed and evaluated NPZ model. The 31

26

SEAPOP model is now being applied to small pelagics such as sardine in the Humboldt 1

system (Gaspar and Lehodey, abstract5). 2

3

Shin and Cury (2004a) recently described a general simulator of fish communities 4

(OSMOSE) that used an individual-based approach, and Shin et al. (2004b) applied the model 5

to the Benguela Current system. They used the super-individual approach, with each super-6

individual assumed to represent a school of identical fish. A distinction was made in the 7

model between non-piscivorous and piscivorous behaviour, with species assigned a behaviour 8

based on stage or age. In the Benguela application, 12 fish species were simulated on a 40 cell 9

by 40 cell horizontal grid using a 6-month time step. OSMOSE does not explicitly use the 10

output of hydrodynamics or NPZ models, but rather represents the prey field effects by 11

specifying a system-wide carrying capacity for non-piscivorous fish biomass. When total 12

biomass of non-piscivorous species biomass exceeded the carrying capacity, then mortality 13

was imposed on all non-piscivorous individuals on the grid, disproportionately on age-0 14

versus older individuals, until the total biomass falls below the carrying capacity. Piscivorous 15

stages consumed prey species if they co-occurred together in the same spatial cell and if the 16

prey were vulnerable based on predator to prey size ratios. All fish species grew in length 17

according to von Bertalanffy equations, with the growth of piscivorous species predicted by 18

the von Bertalanffy equation affected by a predation efficiency computed for each super-19

individual from its present consumption rate. Piscivorous super-individuals moved to their 20

neighbouring cell that had the highest prey biomass that was vulnerable to them. In addition 21

to predation, there were terms for starvation and harvesting mortality. Reproduction closed 22

the life cycle by initiating new super-individuals based on total egg production computed 23

annually from the mature female spawners; larval and juvenile survival determined 24

subsequent recruitment. 25

26

Shin et al. (2004b) performed a series of 200-year simulations with increased fishing 27

mortality rates on selected species and compared predicted responses to those from a 28

comparably constructed EcoSim model. Predicted biomass of each species in OSMOSE was 29

averaged over the last 100 years of each simulation, and compared to the average biomass 30

under the reference or baseline simulation. Increased fishing morality on sardine (Sardinops 31 5 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.

27

sagax), anchovy (Engraulis encrasicolus), and round herring (Etrumeus whiteheadi) showed 1

that sardine would be the first to collapse, anchovy would collapse second, and round herring 2

were highly resistant because of small initial value of fishing mortality rate. The biomass of 3

some species, such as chub mackerel (Scomber japonicus), increased due to relaxed 4

competition. Increased fishing on Cape hake (Merluccius capensis) also showed the expected 5

decrease in hake biomass and the generally increased biomass in hake’s competitors. Both 6

sets of increased fishing mortality simulations were compared to similar simulations 7

preformed with an EcoSim version of the Benguela Current system and, at the qualitative 8

level (increase or decrease), both models generated similar responses. While OSMOSE does 9

not explicitly use the output of a NPZ model, with some creativity, one could perhaps assume 10

how climate change would affect prey and one could adjust the carrying capacity 11

appropriately. An ongoing effort is attempting to link an NPZ model to OSMOSE so that the 12

growth of non-piscivorous individuals can be modelled dynamically (Y. Shin, personal 13

communication). 14

15

The NEMURO (North Pacific Ecosystem Model for Understanding Regional Oceanography) 16

family of models was a milestone in an ongoing large international collaboration focused on 17

the development of standard NPZ model for application to the North Pacific, and the coupling 18

of fish growth and population dynamics models to this standard NPZ model. The biological 19

food web represented in NEMURO was fairly detailed with two groups of phytoplankton and 20

three groups of zooplankton, plus the usual nitrogen, silicate, and detrital recycling dynamics. 21

Using this common formulation for the NPZ, several models and applications were developed 22

(Werner et al., 2007). Of particular interest here are the spin-offs in which NEMURO was 23

imbedded in a 3-dimensional hydrodynamics model configured for the North Pacific, a 24

version that coupled an age-structured fish model to the NPZ (termed NEMURO.FISH), and 25

the latest incarnation (NEMURO.SAN) which is an individual-based, full life cycle, spatially-26

explicit model of sardine and anchovy interactions. 27

28

NEMURO.FISH dynamically couples an adult fish bioenergetics-based population dynamics 29

model to the NEMURO NPZ model. The coupled models have been configured for Pacific 30

herring (Clupea harengus pallasii) on the west coast of Vancouver Island (Megrey et al., 31

2007) and for Pacific saury (Cololabis saira) off Japan (Ito et al., 2007). The herring 32

application uses an age-structured approach, with bioenergetics used to describe the changes 33

in the average body weight of individuals in each age class and mortality rates used to 34

28

describe the changes in the numbers in each age class. Recruitment was knife-edge and 1

computed from spawning biomass and environmental variables (SST, air temperature, and 2

North Pacific Pressure Index) using a spawner-recruit relationship. New recruits become the 3

new youngest age class. The dynamics of the three zooplankton groups in the NEMURO 4

model determine the consumption rate in the fish bioenergetics model through a multispecies 5

functional response formulation. Herring consumption affects the zooplankton through 6

predation mortality, and fish egestion and excretion contribute to the nitrogen dynamics. 7

8

Using the NEMURO.FISH model of herring, Megrey et al. (2007) presented baseline 9

simulations of herring weight-at-age and population dynamics for Vancouver Island, Canada, 10

and Rose et al. (in press) used the model to examine how climate change could affect herring 11

growth and population dynamics. Rose et al. performed simulations that mimicked the 12

conditions in each of the four documented climate regimes in the North Pacific (1962-1976; 13

1977-1988; 1989-1997; 1998-2002). Climate regimes differed in the values assumed for 14

environmental variables used in the spawner-recruit relationship, and in the water 15

temperature, mixed layer depth, and nutrient influxing rate used by the NPZ model. In 16

agreement with general opinion and with the herring data from West Coast Vancouver Island, 17

model predicted estimates of weight-at-age, recruitment, and spawning stock biomass were 18

highest in regime 1 (1962-1976), intermediate in regime 2 (1977-1988), and lowest in regime 19

3 (1989-1999). The regime effect on weights-at-age was a mix of recruitment effects and 20

lower trophic level effects that varied in direction and magnitude among the four regimes. 21

22

Isolating the growth component of NEMURO.FISH, Rose et al. (2007) used the output of the 23

3-dimensional NEMURO for the North Pacific and simulated weight-at-age (not population 24

dynamics) for the west coast Vancouver Island, Prince William Sound, and Bering Sea 25

regions for 1948-2002. The NEMURO application was a 3-D implementation for the 26

Northern Pacific (Aita et al., 2007). The NEMURO-3D simulation represented the NPZ 27

dynamics for 1948 to 2002 using, as much possible, observed data for driving variables. The 28

output of the NEMURO-3D simulation at the three locations, averaged over cells in the top 50 29

m, was used as input to the bioenergetics model and daily growth of herring was simulated for 30

1948 to 2000. Rose et al. applied the sequential t-test analysis to detect regime shifts 31

(STARS) algorithm (Rodionov and Overland, 2005) to the simulated temperatures, 32

zooplankton, and herring growth rate (annual change in weight betweens ages 3 and 4) to 33

identify statistical shifts in their average values. All three locations showed shifts in simulated 34

29

herring growth rate around the 1977 regime shift. While the NEMURO-3D output showed 1

warming temperatures at all three locations beginning in the late 1970’s, herring growth was 2

predicted to decrease in west coast Vancouver Island and Prince William Sound, and to 3

increase in the Bering Sea. Interannual variation in zooplankton densities caused the time 4

series response in herring growth for west coast Vancouver Island. Temperature and 5

zooplankton densities both played roles in Prince William Sound and the Bering Sea herring 6

growth responses, with zooplankton dominating the response for Prince William Sound and 7

temperature dominating the response for Bering Sea. 8

9

NEMURO.SAN is under development and extends the NEMURO approach to simulating 10

sardine and anchovy as individuals on a 2-dimensional spatial grid of cells (Rose et al., 11

abstract6). The vertical dimension is represented as the volume of water in each cell based on 12

the volume of the water above the mixed layer depth. Each year, recruits are computed from 13

spawning biomass at a point in time and the recruits, after a suitable time delay, are slowly 14

introduced over the next year as new model individuals on the grid. Growth, mortality, and 15

movement of individuals are evaluated daily. Positions of individuals are tracked in 16

continuous x and y space, and each day their cell is determined and they experience the 17

conditions in that cell. Alternative approaches to movement, including the use of Railsback 18

and Humston approaches are being investigated. How the spatial (among cells) and temporal 19

(daily or monthly) variation in the mixed layer depth, nutrient influx, and other inputs to NPZ 20

portion are specified allows for flexibility in configuring NEMURO.SAN to different 21

locations. To date, 100-year simulations have been performed in an exploratory mode for a 22

version configured to roughly resemble the California Current system. Alternative hypotheses 23

about climate conditions can be specified via changing the inputs to NEMURO, and then 24

using the coupled models to predict the long-term responses of the anchovy and sardines in 25

terms of their growth, survival, and spatial distributions. 26

4 Biophysical models and climate change 27

28

In this section we discuss the use of biophysical models of small pelagic fish in the context of 29

predicting the effects of climate change. Harley et al. (2006) recently reviewed the potential 30 6 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 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.

30

impacts of climate change on coastal marine ecosystems. They discussed ecological responses 1

to climate change at the individual, population, and community levels. We envision most 2

analyses using biophysical models being single species analyses. The early life stage models 3

focus on a single species, and while some of the full life cycle models include multiple 4

species, there is still great uncertainty in how to represent the food web dynamics of the upper 5

trophic level species (Rose and Sable, 2007). Despite the recognition of the importance of 6

food web interactions and the push towards ecosystem-based fisheries management (Rose and 7

Sable, 2007), community-level responses to climate change that require multi-species 8

simulations will likely remain in the demonstration mode for the foreseeable future. We 9

envision most analyses in the near term will focus mainly on the early life stages of key 10

species, with some analysis using single-species full life cycle models for well-studied 11

locations and theoretical-oriented analyses using the multispecies full life cycle models. 12

13

Among the factors reviewed by Harley et al. (2006), the ecological responses to changes in 14

circulation, temperature, and productivity are relatively easy to investigate using biophysical 15

models. Indeed, changes in circulation would induce changes in advective and dispersive 16

transport, a process used directly in the early life stage models and used directly or indirectly 17

in the adult-based models. In addition to changes in physics-based transport, changes in 18

temperature, salinity, and prey fields would lead to changes in growth, mortality, 19

reproduction, and movement rates because many of the reviewed models related these 20

processes to these and related environmental variables. 21

22

We have more confidence in the early life stage models for simulating climate change 23

scenarios because they are more tightly coupled to the physics and NPZ, and because early 24

life stages of fish tend to be the focus of studies in the marine ecosystems. Early life stages 25

can be measured and they are often the focus as part of the search for recruitment indices 26

(Kendall and Duker, 1998). Imposing climate change scenarios would seem to be possible 27

almost from first principles because the early life stage models are tightly coupled to the 28

hydrodynamics and NPZ models. Simulating climate change scenarios becomes more 29

complicated for the adult models because many of the adult models used surrogates for the 30

physics and prey outputs of the hydrodynamics and NPZ models as their inputs (e.g., carrying 31

capacity). This implies another step is required to convert the hydrodynamics and NPZ 32

outputs into the variables needed by the adult models. 33

34

31

Predicting responses of early life stages is necessary but not sufficient to address many but 1

not all of the climate change issues. Many issues require that the predictions of early life stage 2

models be related to population dynamics and health, and some questions require the 3

simulation of the responses of the adult life stages. One challenge is to balance the use of 4

early life stage, adult only, and full life cycle modelling approaches to ensure predicted 5

responses are most relevant to the scientific questions and to management issues. Another 6

challenge relates to the assumption that the predicted responses of the hydrodynamics and 7

NPZ models under climate change scenarios are sufficiently accurate and precise and on the 8

correct spatial and temporal scales to be used as inputs to the fish models. There is still 9

disagreement about how some important driving variables to the hydrodynamics and NPZ 10

model (e.g., boundary conditions, precipitation, wind) will change under a given climate 11

change scenario. 12

13

Furthermore, climate change scenarios, even after agreed upon, can push the hydrodynamics 14

and NPZ models beyond their calibrated and validated domain. Also, most climate change 15

information has mainly been conducted at a large-scale (e.g., the entire Southern Ocean, 16

Russell et al., 2006), whereas the early life stage and adult models tend to operate at much 17

shorter time scales and smaller spatial scales. Regional-level climate change results should 18

become increasingly available in the near future (e.g., the California Current system, Auad et 19

al., 2006). Meanwhile, creative use of long-term time series of historical hydrodynamic 20

interannual simulations should be melded with climate change scenarios to ensure realistic 21

outputs of the hydrodynamics and NPZ models that act as inputs to the fish models. 22

23

Harley et al. (2006) also discussed the potential shifts (vertical and horizontal) in species 24

distributions that could occur under climate change. Such shifts in spawning and early life 25

stages could be easily incorporated into most of the early life stage models. Initial conditions 26

in these models typically use data based on observed egg distributions. Initial egg (or larval 27

distributions) can be hypothesized and simulations performed to study potential consequences 28

of climate-driven changes in egg distributions on early life stage transport, growth, and 29

survival. 30

31

Models such as the Mullon et al. (2002) model could be used to derive expected egg 32

distributions under climate change. For example, simulation 4 of Mullon et al. (2002) was re-33

ran with hydrodynamic model outputs using weekly wind forcing from ERS satellites (run C 34

32

in Blanke et al., 2002) to study how simulated selected spawning patterns would change 1

according to evolutionary constraints that involve a lethal temperature threshold for the 2

transported particles. Two main spatio-temporal spawning patterns emerged depending on the 3

value of the temperature threshold. A cooler threshold selected spawning in the Central 4

Agulhas Bank in July–September (Figure 2a), while a warmer threshold resulted in the 5

selection of spawning in the Eastern Agulhas Bank in October–January (Figure 2c); an 6

intermediate temperature threshold resulted in a mix of both patterns (Figure 2b). Assuming 7

that the spawning pattern of Figure 2b corresponds to the current situation, and that climatic 8

change would only result in homogeneous increase (respectively decrease) of sea surface 9

temperature, one could infer that spawning would shift more towards the pattern shown in 10

Figure 2a (i.e., cooler threshold mimics warmer water). These results can then be used as 11

inputs to early life stage biophysical models. 12

13

Figure 2 14

15

Simulating geographic shifts in adult life stages will be more problematic with biophysical 16

adult models. The use of adult models for simulating geographic shifts is limited because the 17

distances that could be moved by adult fish in response to climate change would likely exceed 18

the spatial domain of most of the models. A few of the adult-based fish models used very 19

large spatial domains (e.g., Lehodey et al., 2003), but whether the biological aspects of these 20

models are sufficiently general to allow for prediction of geographic shifts needs to be tested. 21

This was partially addressed in the SEPODYM model because they had to deal with the 22

highly migratory tuna. Whether the current models of small pelagics are sufficiently robust to 23

simulate large-scale shifts in distribution remains to be determined. To date, more statistical-24

oriented empirical approaches have been used to predict geographic shifts in the distributions 25

of adult fish and other taxa in response to climate change (e.g., Rahel, 2002; Schmitz et al., 26

2003). Allowing for the capability for predicting geographic shifts should be considered as 27

present biophysical models are expanded and new models are developed. 28

29

Biophysical models of fish early life stages could likely be improved by using spawning and 30

nursery habitats defined by environmental variables rather than simply being geo-referenced 31

(P. Fréon, personal communication). Characterizations of spawning habitats based upon 32

environmental variables such as temperature and salinity have been performed for anchovy 33

and sardine in California (Lynn, 2003), the southern Benguela (Twatwa et al., 2005), the Bay 34

33

of Biscay (Planque et al., 2007), and elsewhere (Castro et al., 2005; van der Lingen et al., 1

2005). Relating spawning habitat to environmental conditions would allow for the simulation 2

of an “environmental homing” reproduction strategy as opposed to a “natal homing” strategy 3

(Cury, 1994), and allow investigation of climate-driven changes in the habitat and their 4

consequences on early life stages. Some caution is appropriate for such a “climate envelope” 5

approach (Davis et al., 1998) because habitats characterizations by environmental variables 6

may themselves change as the climate changes due to adaptation and acclimation and due to 7

changes in the food web. 8

9

Early life stage models are ready for species-specific and site-specific analysis of climate 10

change effects of small pelagics in upwelling systems. Some of the details of such 11

applications need careful attention, especially the matching of the spatial and temporal scales 12

of the hydrodynamics and NPZ models with the fish models, and how growth, mortality, and 13

behaviour-based movement are represented. We see increasingly movement from models of 14

“hydrodynamics and simple behaviors” to models of “hydrodynamics and dynamic prey.” It 15

may be possible to include invertebrate predators in the models, but it will remain difficult to 16

include fish predators of eggs and larvae. A large uncertainty may be getting agreement about 17

how climate change will affect hydrodynamic outputs that are used as inputs to the fish 18

models, and obtaining these output on the spatial and temporal scales needed by the 19

biophysical fish models. 20

21

Biophysical models that include the adult life stages of fish is an area of high research interest 22

but will likely be used for general analysis or application to a few, extremely well-studied 23

species and locations. The uncertainty in how to model movement will limit the development 24

of a generally agreed upon modelling approach that has helped advance the early life stage 25

models. New measurement methods are becoming available that should provide the empirical 26

basis for evaluating the alternative movement options (Cooke et al., 2004). Sugden and 27

Pennisi (2006) recently introduced a special section in Science on “movement ecology”. 28

Continued efforts on adult models is necessary in order to get to “end-to-end” (physics to 29

fish), full life cycle models capable of addressing the long-term consequences of climate 30

change on fish and fisheries. 31

34

1

Figures 2

3 Figure 1: A schematic view of the approach generally used for implementing biophysical 4

models of marine species early life history (modified from Hermann et al., 2001). An 5

hydrodynamic model provides three-dimensional dynamic fields of water velocity u� , 6

temperature T and other environmental variables, to an individual-based model that tracks 7

location x� , length L and other variables of interest for a collection of individuals i over 8

time. 9

10

(a) (b) (c)

Figure 2: Spatiotemporal spawning pattern obtained for 100 000 particles after 200 11

generations with a lethal temperature threshold of (a) 14°C (like simulation 4 in Mullon et al., 12

2002) (b) 15°C (c) 16°C. 13

35

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