Chapter twenty one â Simulation Modeling as a Tool

Chapter | twenty one

Simulation Modeling as a Tool for Synthesis of Stock Identification Information Lisa A. Kerr1, Daniel R. Goethel2 1

University of Massachusetts, School for Marine Science and Technology, New Bedford, MA, USA; Gulf of Maine Research Institute, Portland, ME, USA 2 School for Marine Science and Technology, University of Massachusetts-Dartmouth, Fairhaven, MA, USA

CHAPTER OUTLINE 21.1 Introduction ...................................................................................................................502 21.2 Simulation Modeling to Test Hypotheses Regarding Stock Structure and Movement of Fish..............................................................................................504 21.2.1 21.2.2 21.2.3 21.2.4 21.2.5 21.2.6

Definition of the System ........................................................................................... 506 Characterization of the System .............................................................................. 506 Model Verification ........................................................................................................ 507 Simulation and Measuring Response Variables................................................ 507 Model Validation ........................................................................................................... 507 Hypothesis Testing......................................................................................................508

21.3 Incorporating Spatial Structure and Connectivity in Population Dynamics Models ........................................................................................................509 21.3.1 Spatial Heterogeneity...................................................................................................511 21.3.2 Spawning Isolation........................................................................................................ 512 21.3.3 Movement......................................................................................................................... 512 21.3.3.1 Larval Dispersal............................................................................................ 513 21.3.3.2 Adult Movement from a Lagrangian Perspective ........................... 513 21.3.3.3 Adult Movement from a Eulerian Perspective................................. 514 21.3.3.4 Straying and Entrainment......................................................................... 515 21.3.3.5 Full Life History Models ........................................................................... 515

21.4 Case Studies .................................................................................................................. 516 21.4.1 Simulation Modeling to Test Alternative Stock Structure and Connectivity Hypotheses ................................................................................... 516 Stock Identification Methods. http://dx.doi.org/10.1016/B978-0-12-397003-9.00021-7 Copyright Ó 2014 Elsevier Inc. All rights reserved.

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502 Simulation Modeling as a Tool for Synthesis 21.4.2 Simulation Modeling to Examine Ecological Consequences of Stock Structure........................................................................................................................... 517 21.4.3 Simulation Modeling to Examine Implications of Stock Structure for Assessment..................................................................................................................... 520 21.4.4 Simulation Modeling to Examine Implications of Stock Structure for Fisheries Management ............................................................................................... 522

21.5 Opportunities and Limitations ................................................................................ 524 21.6 Conclusions .................................................................................................................... 526 Acknowledgments .................................................................................................................. 527 References ................................................................................................................................ 527

21.1 INTRODUCTION Simulation modeling provides a flexible approach that can be used to explore a wide range of questions relevant to our understanding of stock structure and connectivity. Models can serve as tools to synthesize information gained from multiple stock identification methods (e.g., genetics, electronic tagging, otolith chemistry, larval dispersal, and life history traits; Cadrin et al., 2005). The assimilation of information from many sources into a population dynamics model can provide a holistic view of stock structure, and, by simulating the model, we can explore the ecological, assessment, and management implications for the resource (ICES, 2011). Simulation models can also be used to test hypotheses regarding stock structure and connectivity (Secor et al., 2009; ICES, 2011). Thus, simulation models can enable us to gain further insight into stock structure and its implications while also identifying gaps in our knowledge where further stock identification work may be needed. Increased application of stock identification methods and technological advancement in various methodologies have led to improved recognition of complex population structure within fish stocks. Complex population structure, also referred to as biocomplexity, can play a vital role in the stability and resilience of a population and species and is recognized as an important feature contributing to persistence (Hilborn et al., 2003; Kerr et al., 2010a,b). Unique behavioral groups (i.e., contingents) or subpopulations can dampen variation in productivity at the population or metapopulation level, with each component experiencing optimal recruitment success and survival under a different set of environmental conditions (a phenomenon termed response diversity; Hanski, 1998; Hilborn et al., 2003; Secor, 2007; Kerr et al., 2010a,b). Additionally, components that exhibit greater productivity can be critical to speeding the recovery of a population or metapopulation after perturbation (Kerr et al., 2010b). When connectivity exists between population components or subpopulations, source-sink dynamics may emerge whereby highly productive populations (i.e., sources) contribute to the recovery of less productive populations (i.e., sinks) and reduce the risk of local population extirpation (Lipcius et al., 2008). Thus, loss of biocomplexity in a fish stock can be accompanied by

Introduction

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decreases in stability and resilience, which can increase the risk of stock collapse (Hilborn et al., 2003). The complex nature of population structure does not always align with the existing boundaries of fishery management units (Stephenson, 1999; Smedbol and Stephenson, 2001; Reiss et al., 2009; Lorenzen et al., 2010). The result can be a mismatch between the biological population structure and the spatially defined stock units that are used for assessing and managing the resource (Reiss et al., 2009; Lorenzen et al., 2010). Simulation modeling has demonstrated that this type of mismatch can compromise the accuracy of the assessment and lead to ineffective resource management (Smedbol and Stephenson, 2001; Punt, 2003; Hart and Cadrin, 2004; Hutchinson, 2008; Lorenzen et al., 2010; Cope and Punt, 2011; Al-Humaidhi et al., 2012; Berger et al., 2012). Specific negative impacts associated with the failure to acknowledge spatial population structure in assessment and management include bias in assessment results, overharvesting, and, in extreme cases, extirpation of local spawning components (Stephenson, 1999; Fu and Fanning, 2004; Field et al., 2006; Montenegro et al., 2009; Reiss et al., 2009; Steneck and Wilson, 2010; Ying et al., 2011). Inappropriate stock boundaries along with the failure to preserve complex spatial structure have been suggested as contributing factors to the failure of Atlantic cod (Gadus morhua) management in the northeast Atlantic (Hutchinson, 2008; Reiss et al., 2009) and within Canadian (Smedbol and Stephenson, 2001; Sterner, 2007) and United States waters (Kovach et al., 2010; Steneck and Wilson, 2010). Depletion of unique spawning contingents within the assumed unit stocks defined by management boundaries led to recruitment overfishing and eroded the resilience of the entire Canadian cod stock complex (Walters and Maguire, 1996; Smedbol and Stephenson, 2001; Wappel, 2005). Simulations of cod in the northwest Atlantic support these findings and demonstrate that ignoring sub-stock population structure in fisheries management threatens the sustainability of the fishery, leads to localized depletion of the more vulnerable population components, reduces rebuilding capacity, and ultimately decreases the stability of the stock complex (Frank and Brickman, 2000; Fu and Fanning, 2004; Reich and DeAlteris, 2009; Kerr et al., 2010a). Maintenance of biological population structure and connectivity pathways can play a critical role in achieving the main objectives of fisheries management, including: obtaining optimum sustainable yields; avoiding recruitment failure; rebuilding overfished stocks; and conserving endangered species (Cadrin et al., 2005; Ying et al., 2011). Understanding population structure and connectivity is also critical to accurately assessing stock status and forecasting how populations will respond to various management strategies or changes in climate (Fu and Fanning, 2004; Kerr et al., 2010a). In order to properly manage fishery resources, it is necessary to improve our knowledge of population structure and its ecological, assessment, and management implications (Reiss et al., 2009; Steneck and Wilson, 2010). Due to the difficulty in directly observing and scientifically manipulating natural populations (Peck, 2004),

504 Simulation Modeling as a Tool for Synthesis simulation models provide the easiest avenue for large-scale studies of population components. Simulation modeling is a powerful tool because it allows the combination of multiple stock identification data sources into a single model framework, which can then be used to illustrate the potential risks of ignoring fish population structure for stock assessment and management (e.g., Kell et al., 2009; Montenegro et al., 2009; Cope and Punt, 2011; Ying et al., 2011). In this chapter we aim to: 1. Summarize the simulation modeling framework and how it can be used to test hypotheses regarding stock structure and connectivity; 2. Review recent advances in modeling to represent population structure and connectivity; 3. Discuss seminal simulation case studies that have led to increased understanding of stock structure in fish populations.

21.2 SIMULATION MODELING TO TEST HYPOTHESES REGARDING STOCK STRUCTURE AND MOVEMENT OF FISH The simulation approach can be used to gain insight into many aspects of spatial structure for marine species ranging from fine-scale (e.g., individual behavior) to basin-scale (e.g., population connectivity). The utility of simulation modeling lies in the ability to experiment with a model representing a natural system, which, due to cost, scale, or lack of system control, is too difficult to directly manipulate (Peck, 2004). Spatially explicit simulations use the operating model concept to represent the biological complexities of the natural world in as realistic a fashion as possible given the current state of scientific knowledge (Hilborn and Walters, 1992; ICES, 2011). For the purpose of investigating spatial structure, simulation models can be used to evaluate: model performance (e.g., test the performance of spatially structured assessment models); biological attributes (e.g., estimate dispersal rates given observed data); and population response (e.g., compare how different management actions affect population trajectories; ICES, 2011). In simulation studies, establishing a goal is a critical first step because the specific questions to be explored or hypotheses to be tested will determine the structure and data requirements of the model. Each model is “tailor-made,” so best practices relevant to all applications cannot be readily determined. However, general guidelines can be identified (Aumann, 2007). Table 21.1 summarizes some of the specific considerations associated with simulation modeling to represent complex spatial structure and movement of fish populations. The basic approach for constructing a simulation model requires: (1) definition of the system; (2) developing an operating model through characterization of the system; (3) verification of the model; (4) simulation of the system; (5) measurement of response variables; (6) validation of the model; and (7) hypothesis testing.

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Table 21.1 Important Considerations in Constructing a Simulation Model of Fish Populations to Represent Complex Population Structure and Movement Establish Goal of Simulation: l Purpose of simulation (i.e., exploratory, hypothesis testing) Definition of the system: l Appropriate scale: Number of relevant interacting population components, populations, or metapopulations to be included in the model (including geographic boundaries and the model domain) Characterization of the system: l Incorporation of spatially explicit differences in demography and dynamics l Life stages to be explicitly modeled l Spatial heterogeneity e Variation in vital rates across the model domain (i.e., habitat quality) l Recruitment dynamics e Form of recruitment (e.g., spatially explicit egg production or stockerecruit relation) e Synchrony or asynchrony in recruitment dynamics between biological units e Scale of recruitment and degree of spawning isolation e Larval drift l Inclusion of temporal differences (e.g., seasonality of spawning) l Representation of connectivity in the model l Life stage (age) at which connectivity occurs l Pattern of movement (i.e., spatial overlap or reproductive mixing) l Estimation of connectivity rates (e.g., from tagging, genetics, or otolith chemistry) l Mode of population connectivity (i.e., straying or entrainment) Model verification: l Model structure and equations are correctly translated from conceptual model l Data is correctly input l Accuracy of computer programming and debugging of code l Reliability of the model output Establish goal of simulation: l Incorporation of stochasticity (i.e., random, density dependent) l Definition of a baseline model l Different scenarios to be simulated (e.g., exploitation or climate scenarios) l Details of model runs l Number of model runs l Time to equilibrium l Initial conditions Measurement of relevant response variables: l Productivity (spawning stock biomass) l Yield/maximum sustainable yield l Fishing mortality at MSY l Stability (coefficient of variation of spawning stock biomass) l Resilience (number of years to rebuild population above certain threshold) l Extinction risk/probability of recolonization l Population richness and evenness Model validation: l Confirm theory and assumptions reflect biological knowledge l Comparison of output to independent data sets (field or experimental) l Sensitivity analysis of model to parameter values, initial conditions, and alternative equations Hypothesis testing: l Using scientific method to systematically test original hypotheses based on simulation metrics

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21.2.1 Definition of the System After the specific hypotheses to be tested have been identified, the next step in simulation model development is defining the system. This involves determining the biological units of interest (e.g., a single spawning contingent or an entire metapopulation) and delimiting the model domain (e.g., a single spawning ground or the entire species range). In defining the system to be modeled, it is useful to develop a conceptual model based on the current state of knowledge of the species being studied (Jackson et al., 2000). The conceptual model should synthesize existing studies on stock structure and movement of the fish resource and lead to a holistic view of stock structure or several probable constructs of stock structure to be tested (e.g., Stephenson, 1999; Cadrin et al., 2010).

21.2.2 Characterization of the System The conceptual model is then transformed to a quantitative “operating” model through characterization of the system (Jackson et al., 2000). The operating model should represent, to the greatest extent possible, how the “real” population or metapopulation behaves and is used to simulate the system of interest under various conditions (e.g., exploitation or climate scenarios; Hilborn and Walters, 1992). The operating model considers all empirical information and incorporates stochastic and time-varying population processes (Linhart and Zucchini, 1986). The flexibility of this approach allows use of all sources of information and knowledge of the given system and is not limited to only observed data (Hilborn and Walters, 1992). In the absence of data, expert opinion and other a priori information may be used to fill in possible data gaps (Kell et al., 2006). Realistic sources and levels of uncertainty should be incorporated into the model; these may include natural variation in dynamic processes, such as recruitment, growth, or mortality, or may include alternative model structure to represent uncertainty in the view of stock structure (Kell et al., 2006). Characterization of the system takes place by using the “best available science” to quantitatively describe the demographics and dynamics of system components (Kell et al., 2006; Aumann, 2007). When possible, mechanistic relationships should be incorporated in order to describe dynamic processes, such as the influence of environmental factors on recruitment variability, which improves the realism and flexibility of the model (DeAngelis and Mooij, 2003). Technical decisions must also be made regarding how spatial structure and connectivity are represented in the model, which is addressed in detail in Section 21.3. Multiple models may be constructed to explore how different hypotheses regarding population processes (e.g., the form of recruitment or connectivity sub-models) impact population attributes (e.g., productivity; Kell et al., 2006). When modeling complex population structure, the choices and assumptions made at each stage of model development are critically important to the outcome of a simulation (Jackson et al., 2000). Therefore,

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careful consideration and documentation of how one defines and characterizes the system of interest is imperative. One particular challenge in the specification of an operating model based on best available information is the consistency of input parameter values from different sources. For example, some processes (e.g., movement, fishing mortality, natural mortality, and selectivity) have interactive effects on fishery and resource observations. Therefore, estimates of mortality and selectivity are conditional on assumed movement patterns (e.g., conventional stock assessments assume no movement among stock areas). Similarly, many analyses of tagging data do not account for different mortality rates among areas. Therefore, movement and mortality rates from different sources may not be consistent. If simultaneous estimates of movement and mortality are not available, model verification and validation (discussed later) may reveal inconsistencies. For some species, other vital rates such as recruitment estimates and maturity schedules may also interact with mortality and movement rates (e.g., Kerr et al., 2012).

21.2.3 Model Verification Before simulations are carried out, model verification is required in order to ensure the reliability of the model and its outputs. A critical evaluation of the formulation of the model is necessary, which ensures that each model entity is consistent with the available data and the intended design specifications of the model (Aumann, 2007). The main component of model verification is determining if the intended system characterization has been logically translated into the proper mathematical equations and ultimately the computer programming language being used (Rykiel, 1996). Thus, model verification is a technical matter involving debugging computer code and certifying that input data have been correctly specified.

21.2.4 Simulation and Measuring Response Variables Once the model has been verified, the next step is to run the simulation and measure relevant response metrics. Common response variables for models studying population structure include: productivity (spawning stock biomass); yield (biomass of catch); stability (coefficient of variation of spawning stock biomass); resilience (number of years to rebuild a population above a certain threshold); and biological reference points (e.g., maximum sustainable yield [MSY] and fishing mortality at MSY). For spatially explicit models, response variables are commonly calculated on multiple spatial scales (e.g., by subpopulation and regionally). Tracking the outputs on both spatial scales allows comparison of regional and subpopulation dynamics simultaneously (Kerr et al., 2010a,b).

21.2.5 Model Validation Model validation is the process of determining whether the model accurately represents the behavior of the system (Aumann, 2007). Model validity should

508 Simulation Modeling as a Tool for Synthesis be evaluated both operationally (i.e., by determining if model output agrees with observed data) and conceptually (i.e., by determining whether the theory and assumptions underlying the model are justifiable; Sargent, 1984; Rykiel, 1996). Models can be validated by comparing output to independent field or experimental data sets that align with the simulated scenario. However, it is important to consider the quality of the data (e.g., the level of measurement error), whether it truly represents the system, and if it is the best test of the model (Rykiel, 1996; Aumann, 2007). Operational validation of the model using independent data may not be possible when the simulated scenario extends outside the realm of observed conditions (e.g., predicting responses to future climate change) or when using probabilistic forecasts (i.e., those that include uncertainty in system processes). In the latter case, the decision between using a deterministic or probabilistic framework comes at a trade-off between accuracy and precision. In general, deterministic models demonstrate higher precision but are less accurate than those that incorporate uncertainty (de Young et al., 2004). However, regardless of the type of simulation, conceptual validation is always feasible. Performing sensitivity analyses are another crucial part of the model validation process. The purpose of running a sensitivity analysis is to determine the relative influence of parameters, initial conditions, and alternative assumptions on model output. The process is iterative, providing feedback that can improve the model. A sensitivity analysis compares response variables from multiple model runs. In each of the comparison runs all parameters are held constant except for the parameter being examined. When a model parameter is observed to exert undue influence on the output of the simulation, which does not reflect reality, characterization of the model must be reevaluated. Conducting extensive sensitivity analyses to understand how each parameter influences the model’s behavior is an essential part of the simulation process (Peck, 2004). Ultimately, model validation strengthens support for the model and the reliability of its outputs (Jackson et al., 2000). Building a useful simulation requires the construction of a model that is a reasonably accurate representation of the biological phenomenon under consideration (Peck, 2004; Aumann, 2007). Although no model can be “proven correct,” validation is about testing the reliability and plausibility of model performance (Araujo et al., 2005). Due to the dynamic nature of natural systems, model validation should be a perpetually occurring process, especially when new data become available from the physical system.

21.2.6 Hypothesis Testing As with any scientific experiment, hypothesis testing within the simulation framework should follow the rigors of the scientific method. A null hypothesis and a competing set of alternative hypotheses should be laid out prior to simulation runs along with a framework for objectively determining whether or not a given hypothesis is supported by the calculated response metrics. Once the

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model has been verified and validated, the response metrics can then be used to test the hypotheses. Outputs from the various model runs can be contrasted to investigate how different population assumptions or management scenarios are expected to impact the response variables. More importantly for testing hypotheses of stock structure, simulation outputs can be compared to “observed” data from the physical system to determine which model best describes the real world. Using observed data in this way is similar to operational model validation, but once the model has been validated, the data can now be used to differentiate between the most likely hypotheses represented by different model runs or assumptions. Thus, the hypothesis corresponding to the model that best represents the physical world provides the best explanation of the stock structure and dynamics of the system being investigated. For example, simulations of Atlantic herring in the Celtic Sea and Irish Sea did not support the “entrainment” hypothesis (i.e., learned spawning migrations) when entire populations were subject to entrainment, because simulations incorporating the entrainment hypothesis of movement did not match the observed stock development and exploitation histories (Secor et al., 2009). Depending on the goal of the study, further steps may be taken after simulating the dynamics of the “true” system using the operating model. These include: application of an observation-error model that mimics the manner in which we observe fish populations with error (e.g., a tag observation model; Alade, 2008); a stock assessment model that estimates perceived status of the stock (e.g., NRC, 1998; Maunder, 2001); and harvest control rules that impose different management strategies on the system (e.g., Butterworth and Punt, 1999; Kell et al., 2006). See Hilborn and Walters (1992) for a detailed account of developing operating models; Kell et al. (2006) for a full description of management procedure evaluations; and ICES (1993) or NRC (1998) for examples of testing the performance of stock assessment models with simulated data.

21.3 INCORPORATING SPATIAL STRUCTURE AND CONNECTIVITY IN POPULATION DYNAMICS MODELS Development of operating models that accurately represent the biological complexity of a system is important to enable simulation of realistic population dynamics. Recognition of the impact that population structure can have on the ecology of a resource, and consequently the assessment, management, and fishery of the species, has led to advances in population modeling to represent spatially structured populations and connectivity between populations (Nielsen, 2004). Complex spatial structure can be incorporated in population models in the form of: (1) spatial heterogeneity, (2) the degree of spawning isolation, and (3) movement (Cadrin and Secor, 2009; Goethel et al., 2011). Assumptions regarding these three aspects of population structure are described in the form of population dynamics equations and determine the resultant structure of populations in the operating model.

510 Simulation Modeling as a Tool for Synthesis The main types of population structure that can be accounted for include: (1) populations that are spatially isolated or closed, (2) populations with heterogeneous spatial structure (i.e., patchy populations); (3) overlapping populations with natal homing (no reproductive exchange); and (4) metapopulations composed of subpopulations that exhibit some reproductive exchange (Figure 21.1). Spatially isolated populations have no spatial overlap with other populations and utilize a single, hydrodynamically isolated spawning area. Due to the lack of connectivity at any life stage, such populations exhibit independent dynamics that are not influenced by outside populations (Kritzer and Sale, 2004). Individuals in a spatially heterogeneous population are distributed in groups and may utilize more than one spawning area, but due to high rates of exchange between local spawning sites this is effectively a single population with synchronous dynamics. In the case of natal homing, individuals from multiple populations may overlap in their distribution

(a)

(b)

Unit populaon (with spaal structure)

(c)

Spaal isolaon

(d)

Natal homing

Metapopulaon

FIGURE 21.1 Schematic representations of the four types of spatially structured populations. Circles represent population components, straight arrows demonstrate movement between components, and curved arrows illustrate the scale of recruitment. The four population types are: (a) unit population with spatial structure: individuals of the species are unevenly distributed within a single reproductive population; (b) spatial isolation: organisms form a single, self-sustaining biological unit that does not overlap in space with other populations; (c) natal homing: individuals maintain self-sustaining populations through natal homing despite spatial overlap with other populations during certain time periods; (d) metapopulation: multiple, mainly self-sustaining, subpopulations are connected through migration between units, while organisms do not demonstrate spawning site fidelity. Adapted from Goethel et al. (2011).


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during certain periods but return to spawn with their natal population. In a metapopulation, there is a degree of reproductive exchange between subpopulations; however, the dynamics of individual subpopulations are distinct from each other and from the regional dynamics (i.e., the entire metapopulation; Goethel et al., 2011).

21.3.1 Spatial Heterogeneity The degree of spatial heterogeneity in a model is ultimately determined by the scale of the model and defined by the number, size, and demographics of the biological or spatial units modeled. Classic metapopulation models, such as the Levins patch-occupancy model, characterize spatial heterogeneity based on the size, location, and frequency of suitable habitat patches in the model domain. This approach, originating from terrestrial ecology, focuses on differences in the risk of extinction and probability of recolonization of populations in each patch (Levins, 1970). This classic form of the metapopulation model was the basis for modern marine metapopulation models, which tend to focus on modeling fishery dynamics rather than extinction risk (Kritzer and Sale, 2004). However, it is still relevant for modeling local extirpation and recolonization dynamics of populations or population components of marine species, such as Atlantic cod (G. morhua; Smedbol and Wroblewski, 2002). MacCall (1990) proposed another approach, termed the basin model, for modeling spatial heterogeneity of fish populations. This method incorporates the influence of density and habitat suitability on distribution and population growth. The underlying theory of the basin model postulates that fish inhabit their optimal habitat at low population size, and, as the population expands, individuals will increasingly utilize suboptimal habitat. Those suboptimal habitats inherently allow lower per capita population growth, but densitydependent effects in the best habitats reduce the demographic differences. An example of this application was the use of a generalized additive model to assess the spatial distribution of yellowtail flounder (Limanda ferruginea) as a function of environmental variables (i.e., depth, temperature, and sediment type; Simpson and Walsh, 2004). Spatial heterogeneity of a stock can be modeled more explicitly by dividing stock-specific data into smaller spatial (and/or temporal) units and modeling production of these units independently (Cadrin and Secor, 2009). These units may be scaled to represent biological entities, such as spawning populations that exhibit differences in their life history characteristics, or physical areas defined as fine-scale spatial units (usually represented as cells of fixed size) within a region. By selecting data from the appropriate spatial and temporal scale, spatially explicit vital rates (e.g., growth and maturity) and recruitment indices can be calculated to characterize the dynamics of unique spawning populations. This approach was applied to model Gulf of Maine Atlantic cod on a finer spatial scale (Kerr et al., 2010a). The model included three interconnected spawning groups, while the current management regime

512 Simulation Modeling as a Tool for Synthesis assumes a single homogeneous population. One caveat of this approach is that it requires larger amounts of data as the spatial scale decreases. When the data are lacking to estimate vital rates or inform dynamics on a finer spatial or temporal scale, a simpler approach, termed geographic apportionment, can be used (Quinn and Deriso, 1999). Applying this technique, the population is modeled using a single set of population parameters, and then the proportional abundance of the population is allocated to smaller areas based on an index of relative abundance (Quinn and Deriso, 1999). Heifetz et al. (1994) employed this approach to apportion exploitable biomass of Pacific ocean perch (Sebastes alutus) in the Gulf of Alaska to three smaller regions (western, central, and eastern Gulf of Alaska) using survey estimates of relative exploitable biomass.

21.3.2 Spawning Isolation The degree of spawning isolation assumed between populations plays an important role in determining model structure (Goethel et al., 2011). In an operating model, spawning isolation is specified in how recruitment is modeled. A spatially heterogeneous population can be modeled using a single stockerecruit function and geographic apportionment (e.g., Miller et al., 2008; Methot, 2009; Hulson et al., 2011) or spatially explicit egg production (e.g., Heifetz and Quinn, 1998; Bentley et al., 2004). The assumption of both approaches is that mixing during early life history is enough so that recruitment events cannot be distinguished between spawning locations, and thus all components are essentially homogeneous and not self-sustaining. In contrast, populations that exhibit complete spawning isolation, either through strict natal homing or hydrodynamic isolation of spawning grounds, assume that each reproductive unit is self-sustaining. The result is a lack of exchange of individuals with neighboring spawning populations. In this case, a single stockerecruit function for each reproductive unit is appropriate (e.g., Porch et al., 2001). Finally, metapopulation structure assumes that each spawning component is essentially self-sustaining, but a small degree of exchange may occur between spawning components of the metapopulation (Kritzer and Sale, 2004). Metapopulation models commonly use a single stockerecruit relationship for each subpopulation but may account for larval, juvenile, or adult exchange between adjacent subpopulations (e.g., Kritzer and Davies, 2005).

21.3.3 Movement Movement between populations is a complex process to model because it can occur across life stages (involving either passive drift or directed movement) with the potential for planktonic dispersal during the egg and larval stage, juvenile movement to and from nursery areas, and adult feeding, overwintering, and spawning migrations. Additionally, understanding the factors that motivate fish movement is difficult because it is a complex phenomenon that often results from interactions between numerous causal and reactionary mechanisms


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including physiology, behavior, environment, and life stage (Patterson et al., 2008). Modeling movement in population dynamics models has been approached from both a Lagrangian and Eulerian perspective (Berger et al., 2012). The Lagrangian approach tracks individual movement through time using individual-based models, while the Eulerian method calculates the number of fish per unit time that cross a point in space (i.e., flux; Lehodey et al., 2008).

21.3.3.1 LARVAL DISPERSAL In many cases the spatial aspects of recruitment processes are ignored in population models, even though factors such as spatial variation in the physical characteristics and environmental conditions of spawning habitats can be important drivers in year-class variation (Hjort, 1914). In recent decades, the development of individual-based models (IBMs) linked to hydrodynamic models have allowed scientists to simulate egg and larval drift and better understand how interannual variability in climate affects recruitment events (Werner et al., 2001; Dickey-Collas et al., 2009; Hinrichsen et al., 2011). In these models, egg and larval stage fish are often modeled as Lagrangian particles with biological traits where movement is driven by an ocean circulation model (Werner et al., 2001). Spatially explicit IBMs commonly include several modeling components including: a spatiotemporal flow field (i.e., hydrodynamics model), which determines the passive and current-oriented movement; a spatiotemporally resolved prey field; and a bioenergetics model (Grimm, 1999; Werner et al., 2001; Miller, 2007). In the simplest IBMs, the main spatial consideration is where particles are seeded in the model domain (i.e., the location of spawning grounds) and how flow fields, and thus modeled movement rates, vary depending on the location of particles (e.g., Bartsch et al., 1989). More complex biophysical IBMs account for spatial variation in larval growth and mortality due to factors such as prey density and water temperature (e.g., Hinckley et al., 1996; Werner et al., 1996; Hermann et al., 2001). Additionally, some IBM studies include vertical migration behavior of larvae, which necessitates accounting for the effect of environmental conditions in three dimensions (Vikebø et al., 2007; Dickey-Collas et al., 2009), an aspect currently ignored in most adult movement models. Vertical migration can have an important impact on the spatial distribution of newly settled larvae because positioning in the water column can greatly alter resulting horizontal dispersal due to ocean currents being vertically stratified (Churchill et al., 2011). For full reviews of the spatial complexities of larval IBMs, see Grimm (1999), Werner et al. (2001), and Miller (2007). 21.3.3.2 ADULT MOVEMENT FROM A LAGRANGIAN PERSPECTIVE Investigating how individual behavior leads to overall population structure also requires the use of individual-based models (IBMs). A common feature of adult movement is reaction to a spatially heterogeneous environment (i.e., kinesis and

514 Simulation Modeling as a Tool for Synthesis taxis; Humston et al., 2004). Kinesis involves a change in movement based on a response to a gradient stimulus (i.e., fish “follow” the gradient toward more preferred states based on a “reaction” to the state at a single point), whereas taxis behavior (also termed area search) implies behavioral reaction based on memory of past locations. In the latter, individuals actively assess habitat quality at their current location and compare it to previous locations leading to a constant movement toward the most suitable landscapes (Humston et al., 2004). Almost any stimulus can be responsible for causing a reactionary movement response (e.g., schooling behavior; Inada and Kawachi, 2002), but IBMs commonly assume that individuals follow increasing prey density or preferred abiotic conditions such as an optimal temperature or salinity range (Bertignac et al., 1998; Faugeras and Maury, 2005; Senina et al., 2008). Adult IBMs can be scaled to the population through the use of partial differential equations resulting in what is often termed advectionediffusion-reaction (ADR) models (see Schwarz, 2013 (Chapter 18) for details and Sibert et al., 1999 or Faugeras and Maury, 2007 for derivations). ADR models allow the estimation of population-level movement based on the individual behavioral elements used in IBMs, although an approximation must be incorporated to scale from the individual to the population (Faugeras and Maury, 2007).

21.3.3.3 ADULT MOVEMENT FROM A EULERIAN PERSPECTIVE Population-scale spatial simulations are useful for understanding the consequences of population structure and movement at a system level, which is more directly relevant to fishery management. The focus is shifted from individual responses to a heterogeneous environment toward the average impact of large-scale structure and movements. Although the Lagrangian approach is extremely useful, it can be computationally and data intensive (Goethel et al., 2011). The Eulerian approach, frequently termed box-transfer, models movement based on flux across a stock or geographic boundary (Beverton and Holt, 1957; Porch et al., 2001; Goethel et al., 2011) using transfer coefficients (Quinn and Deriso, 1999) to describe the probability of movement between (and fidelity within) stocks or spatial units. The distinction between the Lagrangian and Eulerian methodologies is blurred in simulations because Lagrangian larval IBMs are often nested within models that assume aggregate adult population dynamics using Eulerian movement (e.g., Rose et al., 1996; Heifetz and Quinn, 1998; Heath et al., 2008). Utilizing the Eulerian approach, we can model reproductive mixing wherein gene flow among fish from multiple spawning components occurs (also termed diffusion following Porch et al., 2001). Extensions of the original random diffusion box-transfer models have incorporated natal homing of fish, whereby fish move from one area to another but return to their natal area to spawn. Porch et al. (2001) refer to the latter scenario as the “overlap” model, due to the overlap of fish from different spawning populations that occurs in nonspawning areas. The process equations are essentially the same in modeling these two phenomena, but there is an important distinction in how fish are


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accounted for in each process (see Goethel et al., 2011). In the diffusion model fish take on the biological characteristics of whichever population they move into, while in the overlap model fish retain the characteristics of their natal population no matter where they move in the model domain. Additionally, in the overlap model fish only add to the spawning stock biomass of their natal population (Porch et al., 2001; Goethel et al., 2011).

21.3.3.4 STRAYING AND ENTRAINMENT Further subtleties, such as the mode of reproductive mixing, can be specified in movement models. There are two main types of mixing between spawning components to consider: straying and entrainment. Straying represents the movement of individuals away from their natal population (i.e., vagrancy; Sinclair, 1988), whereas entrainment involves the “capture” of individuals from one spawning group into another during a period of spatial overlap (Secor et al., 2009). These processes can be structured as unidirectional or bidirectional (in the case of straying) and as occurring randomly or in a densitydependent manner. Secor et al. (2009) explored the consequences of different types and magnitudes of reproductive connectivity between Atlantic herring populations on productivity, stability, and persistence of the local and regional populations. Overall, fish connectivity through straying had the effect of increasing the synchrony of local population dynamics, which decreased the stability of the metapopulation. On the other hand, entrainment had the effect of increasing asynchrony and increased metapopulation stability. 21.3.3.5 FULL LIFE HISTORY MODELS Many models have bridged the gap between larval and adult stages in an attempt to complete the life cycle of a given species. Possingham and Roughgarden (1990) investigated the spread of barnacles (Balanus glandula), which demonstrate a passive larval stage and a sessile adult stage, by combining an advectionediffusion model of larval drift with an adult population model. Other studies have coupled larval IBMs with age-structured matrix models of adult population abundance (e.g., winter flounder [Pseudopleuronectes americanus], Rose et al. (1996); sablefish [Anoplopoma fimbria], Heifetz and Quinn (1998)). Lehodey et al. (2008) developed an ecosystem simulation approach (SEAPODYM) that combined a biogeochemical ocean circulation model with a full life history population dynamics model. The SEAPODYM model was applied to multiple tuna species in the Pacific Ocean and allowed for larval drift and adult movement based on advectionediffusion as altered by habitat preference. Full life history metapopulation models represent the most sophisticated approach to modeling movement across life stages and between populations. Andrews et al. (2006) developed a spatially resolved population dynamics model of cod on the European continental shelf. Heath et al. (2008) took this approach further, developing a metapopulation model of 10 interlinked demes (genetic subunits) of cod that utilized the output from larval biophysical

516 Simulation Modeling as a Tool for Synthesis models (e.g., the proportion of successful recruits of a specific deme to a particular region) as input to the population model. It also incorporated spatial heterogeneity and movement across larval and adult life stages in order to examine the degree of natal fidelity of cod in the North Sea.

21.4 CASE STUDIES 21.4.1 Simulation Modeling to Test Alternative Stock Structure and Connectivity Hypotheses Simulation models can be used to test hypotheses about stock structure and connectivity by comparing multiple models with different underlying structure (e.g., Andrews et al., 2006; Heath et al., 2008) or a single model with a range of potential values for a specific attribute (e.g., connectivity rates between populations; Secor et al., 2009). By evaluating model outputs from a simulated range of possibilities, we can select, or at least narrow down, the most likely scenario of stock structure and mixing that coincides with our observations of the system. These models can be useful in identifying gaps in knowledge and informing researchers about data that needs to be collected. Information from several stock identification methods including genetics, tagging, microchemistry, and morphometrics suggests that cod in the North Sea and west of Scotland exhibit metapopulation structure. However, the mechanisms leading to population structure are not well understood. Heath et al. (2008) used a simulation framework and developed a spatially explicit model of cod in the region to examine the consequences of different assumptions about natal fidelity on population structuring and dynamics. The model was composed of 10 distinct demes (genetic subunits within a metapopulation, Figure 21.2) of cod and employed an age-structured discrete-time (monthly intervals) approach following Gurney et al. (2001) and Andrews et al. (2006). Fish movement was incorporated in the model as passive drift of eggs and larvae, first spawning migration, annual migration of mature fish, and straying. Passive transport of early life stages was driven by simulated patterns in ocean circulation. The location for the first spawning migration was determined by one of three scenarios: (1) natal homing, (2) oceanographic dispersal (i.e., the spawning area was equal to the fishes’ nursery area), and (3) diffusion (i.e., the spawning area could be any adjacent spawning ground; Figure 21.3). Annual migrations were structured so that fish spent a portion of their time on their spawning sites and the remainder of their time in feeding areas (Figure 21.3). Straying of fish from their spawning site occurred in accordance with data from tagging studies. The spatial and temporal distribution of fishing mortality was derived by disaggregating International Council for the Exploration of the Sea (ICES) regional fishing mortality rates using landings and survey data. The primary response variables were spawning stock biomass and recruitment for each natal population and spawning area. The natal origin of fish in each spawning area was also tracked to draw inferences about genetic structure, which was

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FIGURE 21.2 Maps outlining the 10 cod demes (genetic subunits within a metapopulation) in the North Sea and west of Scotland along with associated spawning (shaded squares, left panel) and nursery areas (shaded squares, right panel) used in the simulation of Heath et al. (2008). Thick black lines delineate demes: (1) Clyde; (2) West coast; (3) Minches and north coast; (4) Shetland; (5) Viking/Bergen Banks; (6) Moray Firth; (7) East coast; (8) Fisher; (9) Flamborough; (10) Dogger Bank and Southern Bight. Thick gray line indicates the 200 m contour, while the thin gray line represents the 50 m contour. Reprinted from Heath et al. (2008), Figure 1, p. 94; with permission from Elsevier.

compared to molecular genetics data. Simulated data from the three first migration scenarios were compared to stock status information from ICES regional stock assessments. Comparison of model output to observed data revealed that the key feature determining regional and finer-scale dynamics was the assumed mode of first spawning migration. For North Sea cod, simulations of spawning biomass from the natal homing and oceanographic dispersal scenarios both appeared to conform with regional observations. However, the diffusion scenario resulted in stock collapse. For cod west of Scotland, only the natal homing scenario reflected regional observations of spawning stock biomass with both the oceanography and the diffusion scenarios resulting in stock collapse. At a finer scale, comparison of the genetic structure suggested by model scenarios to molecular genetics data supported the oceanography rather than the natal homing scenario. Overall, modeling and data supported both natal homing and oceanographic dispersal as mechanisms for population structuring of cod from different spawning groups. Heath et al. (2008) concluded that recovery and recolonization of cod will require consideration of the mechanisms of population connectivity.

21.4.2 Simulation Modeling to Examine Ecological Consequences of Stock Structure Simulation models that are informed by empirical data and accurately represent the biological populations under consideration (i.e., observed rates of growth,


FIGURE 21.3 Representation of the three movement scenarios investigated by Heath et al.’s (2008) simulation of cod metapopulation dynamics in the North Sea and west of Scotland. The top panel illustrates example movement patterns between feeding, spawning, nursery, and sink areas for spawning migrations (solid lines) and larval drift (dashed lines). The bottom panel illustrates the differences between the connectivity assumptions in each of the three scenarios as defined by the behavior of first-time spawners (gray arrows) in their movement from nursery (open circles) to spawning grounds (shaded circles). In the “homing” framework individuals return to their natal spawning grounds to reproduce. In the “oceanography” scenario organisms spawn in the area closest to their nursery grounds. Finally, in the “diffusion” model first-time spawners are able to move to any adjacent spawning grounds to reproduce. Reprinted from Heath et al. (2008), Figure 2, p. 95; with permission from Elsevier.

maturity, mortality, recruitment, and connectivity) can provide insight into the ecological consequences of population structure and connectivity. Using simulation models can increase our understanding of the interaction between spatial heterogeneity in productivity and fishing mortality in a system. For example, in

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a metapopulation, overfishing of relatively unproductive sink populations can lead to extirpation (Ricker, 1958) and overfishing of productive source populations can lead to widespread declines throughout a regional population (Kritzer and Sale, 2004). Additionally, simulations can provide insight into the role that response diversity (i.e., asynchrony in response of unique components) plays in the stability and resilience of system dynamics (Hanski, 1998; Hilborn et al., 2003; Secor, 2007; Kerr et al., 2010a,b). Research on white perch (Morone americana) in a sub-estuary of the Chesapeake Bay (Patuxent River) identified complex population structure wherein a portion of the population remained resident in freshwater, while another portion exhibited a lifetime migration behavior moving into brackish water and returning to freshwater to spawn (Figure 21.4). Kerr et al. (2010b) used simulation modeling to explore the consequences of partial migration within the white perch population for productivity (spawning stock biomass), population stability (coefficient of variation of spawning stock biomass), and resilience (time to recover from disturbance). The focus of the study was to understand the role that contingents (i.e., portions of a population exhibiting divergent spatial life histories) play in mitigating population responses to unfavorable environmental conditions. Two contingent-specific, age-structured models were used to simulate population dynamics of resident and migratory white perch in the Patuxent River. The models were linked through a common stockerecruit relationship since empirical evidence suggests that resident and migratory contingents are behaviorally, but not genetically, distinct (Kerr et al., 2010b). The dynamics of

FIGURE 21.4 Map of the Patuxent River estuary, a sub-estuary of the Chesapeake Bay, Maryland (Kraus and Secor, 2004). The map illustrates the general domain of resident white perch in natal freshwater habitat (defined here as salinities 0e3 ppt, black box), and the brackish water habitat (salinities 3e15 ppt, hatched box) of the estuary, which the migratory contingent utilizes outside of the spawning period. The areal extent of boxes is based on the typical salinity structure of the river in summer months. Adapted from Kerr et al. (2010b).


FIGURE 21.5 Results of the white perch simulation model of Kerr et al. (2010b), which provided insight regarding the role that migratory and resident contingents played in the overall white perch population in the Chesapeake Bay, Maryland. Simulations revealed that each contingent differed in its contribution to overall stock productivity (spawning stock biomass), stability (interannual variation in spawning stock biomass), and resilience (recovery time from perturbation). The migratory contingent contributed to higher productivity and resilience of the overall population but by itself was a relatively unstable population component. The resident contingent, although a minor contributor to population productivity and resilience, conferred greater stability to the overall population due to its consistent presence even in adverse drought conditions. Adapted from Kerr et al. (2010b).

contingents and the overall population were examined in scenarios that ranged in contingent representation (proportion of resident and migratory types within a year-class) and correlation in age-one abundance of contingents. Simulations revealed that the migratory contingent was more productive and exhibited more variability in recruitment than the resident contingent, which was less productive but consistent in its low levels of recruitment. Increased representation of the migratory contingent within the population resulted in increased productivity and resilience but decreased stability (Figure 21.5). The resident contingent conferred a unique stabilizing influence on the overall dynamics of the population due to its consistent recruitment even in adverse environmental conditions (i.e., drought). Overall, the diverse spatial structure within this white perch population appeared to contribute to population stability and resilience by buffering population-level responses to unfavorable environmental conditions and preventing recruitment failure (Kerr et al., 2010b). Kerr et al. (2010b) concluded that spatial structuring is important to the persistence of this white perch population.

21.4.3 Simulation Modeling to Examine Implications of Stock Structure for Assessment Simulation models can provide a means for testing the appropriateness of assessment models by evaluating how well they characterize the system of interest (Hilborn and Walters, 1992). An operating model that represents the “true” population structure of a resource can be used to generate data for

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testing the accuracy of assessment models with varying statistical and biological complexity (e.g., one vs. multiple stocks; Porch et al., 1998; Ying et al., 2011). This approach can be useful in examining potential adverse consequences (i.e., inaccurate and nonconservative biological reference points) of aggregating data across spawning components in assessments (Frank and Brickman, 2000; Hart, 2001; Kell et al., 2009; Cope and Punt, 2011). Simulations can be used to explore whether a more spatially explicit assessment is possible given the data available and, if not, what data will need to be collected in the future (Maunder, 2001; Carruthers et al., 2011; Hulson et al., 2011). Kell et al. (2009) used simulation modeling to explore the consequences of accounting for or ignoring complex population structure in the stock assessment and resultant scientific advice of Atlantic herring. A European Union project (WESTHER) studied stock structure of Atlantic herring in the region west of the British Isles and identified complex population structure that is not always aligned with the assessment and management units (Hatfield et al., 2007). Fish from these stocks are known to mix on the summer feeding grounds on the Malin Shelf and in the Celtic Sea, and fisheries target these mixed-stock aggregations (Figure 21.6). The model framework of Kell et al. (2009) was designed to emulate four herring stocks to the west of the British Isles, specifically the stocks: (1) west of Scotland, (2) west of Ireland, (3) in the Irish Sea, and (4) in the Celtic Sea (Figures 21.6 and 21.7). Four fisheries were simulated to operate in areas that roughly coincided with stock areas, and the catch was assigned to stock area based on management unit boundaries (Figure 21.7). In this study, the operating model was developed to generate data, data were sampled using an observation-error model, a stock assessment model (virtual population analysis) was applied, and management advice was derived from the assessment. The main hypothesis being tested was whether assessment bias, due to stock mis identification, would lead to inappropriate management of the regional herring resource. This hypothesis was tested by comparing estimates of stock status and exploitation rate from the assessment to the “true” values derived from the operating model. The impact of lumping data for two or three populations was explored under several scenarios designed to represent changes in the fishery as well as in the productivity of the population west of Scotland. Although lumped assessments were able to track the general trends of individual populations, the absolute estimates of stock status differed and, most importantly, the extirpation of population 1 (west of Scotland) was not detected in lumped assessments. Kell et al. (2009) determined that lumping catches from mixed stocks resulted in biased estimates of stock status and overexploitation of individual stocks. It also led to a tendency to underestimate the risk of stock collapse and overestimate the recovery of the stock. In further study on this topic, an ICES study group (SGHERWAY) was formed to evaluate the implications of results from WESTHER (ICES, 2010). A simulation that modeled the perceived herring metapopulation including the complexities in survey sampling and mixed-stock fisheries was


FIGURE 21.6 Model domain (light shaded areas) for the west of the British Isles Atlantic herring metapopulation simulations of Kell et al. (2009). Four stocks were included in the model based on International Council for the Exploration of the Seas (ICES) assessment and management boundaries: west of Scotland (area VIaN); west of Ireland (areas VIaS); Irish Sea (VIIaN); and Celtic Sea (areas VIIaS, VIIg, VIIh, VIIj, VIIk). Dark shaded areas represent the two summer feeding grounds (Malin Shelf and Celtic Sea), which are also the main target of the fishery. Catches on the feeding grounds consist of mixed-stock assemblages, but sampling assumes all fish belong to the stock from which they were caught and reported. Reprinted from Kell et al. (2009), Figure 1, p. 1777; by permission of Oxford University Press.

developed and used to evaluate alternative management procedures. The scenarios that were evaluated were not sustainable under all conditions, and it was determined that explicit management of metapopulations was only possible with better fisheries-independent data.

21.4.4 Simulation Modeling to Examine Implications of Stock Structure for Fisheries Management Simulation models can provide the operating models for management strategy evaluation (MSE), which can test the impact of different harvest strategies for a range of assumptions about stock structure and connectivity (Kell et al., 2006). For instance, employing a management strategy that does not account for the contribution of another stock to a local fishery may have unintended

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FIGURE 21.7 Schematic illustrating the assumed connectivity between stocks during summer feeding and fishing seasons for the Atlantic herring simulation of Kell et al. (2009). The model includes four spawning populations (dark circles), which mix during the feeding season (extent of distribution represented by light gray circles) but are assessed and managed on spatial scales ignorant of transboundary mixing (management borders given by black lines, fish within each region are managed according to an individual TAC (total allowable catch)). Reprinted from Kell et al. (2009), Figure 2, p. 1778; by permission of Oxford University Press.

consequences of unsustainable exploitation rates and depletion of the source stock (Fu and Fanning, 2004). Because rebuilding capacity may be linked to connectivity between populations, failure to account for mixing of populations can jeopardize the realization of rebuilding expectations. Therefore, it is important to document differences in vital rates, recruitment dynamics, and connectivity of populations with respect to the distribution of fishing effort and the management of a fishery. Ying et al. (2011) illustrated how ignoring spatial structure of fish populations can impact management results through simulation of a metapopulation of small yellow croaker (Larimichthys polyactis) off of China. The model was comprised of three subpopulations: (1) China Sea, (2) South Yellow Sea, and (3) North Yellow Sea and Gulf of Bohai (Figure 21.8). The operating model was a surplus production model that represented the “true” structure and dynamics of the metapopulation (Figure 21.9). Random variability was added to the output of the operating model to emulate observation of the system with error. Population parameters were estimated from the “observed” data using surplus production models with different assumed population structures. Three different assessment-management scenarios were tested: metapopulation structure (i.e., the assumed spatial structure matched the “true” simulated structure); three independent subpopulations with no connectivity; and a single


FIGURE 21.8 Population structure of small yellow croaker off the Chinese coast as defined by the simulations of Ying et al. (2011). Horizontal dashed lines divide the three populations in the model domain: (1) East China Sea (subpopulation 1); (2) South Yellow Sea (subpopulation 2); (3) North Yellow Sea and Gulf of Bohai (subpopulation 3). Each subpopulation has unique spawning (shaded circles) and overwintering (double circles) grounds but shares feeding grounds (dotted circle). Migration (solid arrows) rates were based on the speed and direction of the coastal current (dotted arrows). Reproduced with permission from Ying et al. (2011), Figure 1, p. 2102; copyright 2008 Canadian Science Publishing or its licensors.

homogeneous population (i.e., no spatial structure; Figure 21.9). The system was managed according to harvest control rules developed from each of the three different assessments. The results demonstrated that ignoring spatial structure can result in biased estimation of population parameters and stock status indicators, which led to inappropriate management and harvest targets. Similarly, localized depletion was possible when spatial structure was completely ignored, while overfishing was probable when connectivity among subpopulations was ignored.

21.5 OPPORTUNITIES AND LIMITATIONS Advances in the representation of complex population structure in models have enabled the examination of questions critical to our understanding of fish

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FIGURE 21.9 Conceptual representation of the simulation design for Ying et al. (2011) illustrating the flow for the three spatial hypotheses tested: (1) three independent populations; (2) metapopulation; (3) single population. In each scenario the input data was provided to the model representing the assumed population structure, population parameters were estimated, and a management strategy was developed based on the assumed dynamics and parameters. The management strategy was then applied to the true operating model (i.e., the metapopulation scenario), and the resulting catch and biomass that resulted from each of the “mis-specified” (i.e., three independent populations and the single population) management strategy options were compared to those from the true population structure. Reproduced with permission from Ying et al. (2011), Figure 2, p. 2103; copyright 2008 Canadian Science Publishing or its licensors.

population dynamics and spatial structure. Currently, the major limitation in resolving population dynamics at a finer scale for simulations is not model sophistication but rather data and processing time. Biological data collected at a finer spatial scale is always useful. However, the cost of increasing the spatial and temporal resolution of sampling programs can be prohibitive. It is likely that current state-of-the-art spatial collection techniques, such as acoustic and satellite tagging, will become more common and less expensive in the near future. Such data, although costly to collect, have already proven invaluable in determining stock structure, migration pathways, mixing rates between populations, and abundance trajectories (Nielsen, 2004; Block et al., 2005; Gr€oger et al., 2007; DeCelles and Cadrin, 2010; Taylor et al., 2011). In the short term, however, the solution is not necessarily new or better data collection but better use of current data sets and novel application of alternative data forms. Ulltang (1996) argued that for European fisheries many available

526 Simulation Modeling as a Tool for Synthesis data sources were being underutilized. For instance, many fisheries and management agencies have numerous fine-scale data sets that have yet to be used to their full potential. In the United States and Europe, vessel monitoring systems (VMS) and electronic logbooks record catch locations on fine scales (Nolan, 1999; Palmer et al., 2007; Gerritsen and Lordan, 2011). This data could be incorporated into spatial simulations to inform spatially explicit catch estimates or used to delineate areas of high population abundance and critical spawning or feeding habitats. Other examples of underutilization of data sets exist, including qualitative information such as sediment type or habitat quality, which could be incorporated into simulation models to inform movement based on habitat attraction. Furthermore, many areas of biological research are often overlooked by modelers and could play an important role in informing population structure or movement estimates. Prime examples include analysis of otolith microchemistry and genetics to delineate natal populations and estimate rates of movement based on gene flow or chemical markers (e.g., Kerr et al., 2010b; Pita et al., 2011; Taylor et al., 2011). The design of new sampling schemes should include input from modelers to ensure that relevant information is collected. Continued interdisciplinary collaborations between biologists, geneticists, oceanographers, and modelers will help facilitate construction of more accurate full life history metapopulation models, which will help to broaden our knowledge of population structure and inform better management of important commercial species. Nevertheless, model verification, validation, and sensitivity analysis remain the key components in the development of accurate and useful simulations for fisheries management. New data sources may provide useful and novel insight into population processes, but continual model testing is the most critical step in maintaining model accuracy. Simulations that lack thorough validation, verification, and investigation of sensitivities remain severely limited in both their usefulness in the management process and in the amount that they can contribute to the general knowledge base for a given species. Construction of more biologically realistic operating models for use in simulation, application of sensitivity analyses, model verification, and validation of results with independent data will increase confidence in the use of these models to inform decision making regarding the appropriate scale of stock units used in assessment and management.

21.6 CONCLUSIONS Simulation models are valuable and flexible tools for the synthesis of stock identification information and for testing hypotheses of stock structure and connectivity and their implications. These models enable us to experiment with a system in a way that may not be feasible in the real world. However, it is important to note that these models represent abstract simplifications of biological systems and thus have their limitations. A robust simulation requires an

References 527 operating model that accurately portrays biological processes and is supported by the observed data. Additionally, the hypotheses to be tested should be carefully considered with respect to model limitations, and metrics should be selected that are useful in evaluating the outcome of a given model scenario with respect to the specific hypothesis being tested. Much remains to be learned about fish population structure, particularly with regard to the role that individual behavior, physical oceanography, movement, and spawning dynamics play in defining population structure. As computing power continues to advance and new data sources become available, simulation models are likely to become more advanced, and we predict that they will continue to gain popularity as predictive and explanatory tools. There has been considerable development in models that provide a Eulerian view of fish populations whereby we can assess the average impact of spatial structure and movements. However, further development of Lagrangian models is needed to better understand the impact that individual behavior across the life cycle plays in the structuring of fish populations (Humston et al., 2004). For example, determining the causal mechanisms for various forms of movement (e.g., permanent migration versus temporary ranging) would enable better characterization of fish distributions and improve management (Dingle and Drake, 2007). Overall, computer models do not represent a replacement for field studies, but they do provide a means for examining physical systems that cannot be directly manipulated with other experimental methods.

ACKNOWLEDGMENTS We acknowledge the contribution of participants in the ICES Workshop on Implications of Stock Structure (WKISS, April 5e7, 2011) to this book chapter, particularly work by Niels Hintzen. We also thank the participants in the 2012 ICES Annual Science Conference theme session N, entitled “Examining the Implications of Complex Population Structure on Fish Resources, Fisheries, Assessment and Management,” and the 2011 Northeast Consortium’s “Workshop on Reconciling Spatial Scales and Stock Structure for Fisheries Science and Management” for providing insight on this topic. We acknowledge Steve Cadrin for providing helpful comments on this chapter, and the influence of others in the field, including Doug Butterworth and Terry Quinn, on our thinking about incorporating spatial structure into simulation models.

REFERENCES Alade, O.A., 2008. A Simulation-Based Approach for Evaluating the Performance of a Yellowtail Flounder (Limanda ferruginea) Movement-Mortality Model, University of Maryland Eastern Shore. PhD: p. 316. Al-Humaidhi, A.W., Wilson, J.A., Young, T.H., 2012. The local management of migratory stocks: implications for sustainable fisheries management. Fish. Res. 141, 13e23. Andrews, J.M., Gurney, W.S.C., Heath, M.R., Gallego, A., O’Brien, C.M., Darby, C., Tyldesley, G., 2006. Modelling the spatial demography of Atlantic cod (Gadus morhua) on the European continental shelf. Can. J. Fish. Aquat. Sci. 63, 1027e1048. Araujo, M.B., Pearson, R.G., Thuillers, W., Erhard, M., 2005. Validation of species-climate impact models under climate change. Glob. Change Biol. 11, 1e10.

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