Advancements in Riverine Fish Movement Modeling: Bridging Environmental Complexity and Fish Behavior

Abstract

Understanding fish movement and response in relation to their environment near infrastructure and migratory barriers is crucial for developing sustainable fisheries management solutions. Intermediate-scale (time scales of minutes to days and spatial scales less than 2 km) movement models are a contemporary approach for understanding and predicting movement patterns of riverine fish in light of their changing environment, which is predominately water flow (i.e., flow direction, flow magnitude, and rates of change). These models can be complex and require interdisciplinary knowledge. For more than 60 years, different approaches have been developed for investigating, reproducing, and predicting the movement outcomes of fish decision making. Due to the breadth of model frameworks available, a systematic review is helpful to summarize the available knowledge including a description of general model properties, environment modeling, agent characteristics, and methods of data use, output, and validation. The analysis of 38 studies found a wide range of model frameworks and architectures. Despite the lack of consistency, each model imposed some combination of the following behaviors: response to flow direction (i.e., rheotaxis), response to flow velocity magnitude, response to turbulence, response to depth, and memory/experience of the individual. There is a clear need for more consistent modeling approaches, increased consideration of memory/experience, inclusion of a wider range of species, incorporation of more detailed environmental covariates, and use of time-dependent solutions in fish movement models.

Keywords:

• Fish movement
• agent-based model
• individual-based model
• fish behavior
• fish passage
• ethohydraulics

Introduction

Efforts to computationally model fish movement date back 60 years (Balchen 1979; DeAngelis 1978; Neill 1979; Saila and Shappy 1963; Patten 1964) and have resulted in multiple modeling approaches for understanding and predicting fish movement across a range of space and time scales (Jager and DeAngelis 2018; Willis 2011). Macro-habitat models simulate fish movement and changes to fish populations across large spatial domains (>2 km) and for long durations (days to years). In contrast, evaluation of fish swimming mechanics or how they detect ephemeral features of water flow requires models with exceptionally fine spatiotemporal resolution (e.g., ≪1 m, <1 s) (Herzog et al. 2017; Borazjani and Sotiropoulos 2009). Intermediate-scale models generally have similar goals of understanding fish movement, but within an applied and specific focus of brief time periods (e.g. minutes to days) and river-reach scales (<2 km). A common use of these models is to elucidate how management or mitigation actions impact fish near built infrastructure. As a result, intermediate-scale models must incorporate varying environmental information in addition to the behavioral decisions of fish (Benson et al. 2021; Silva et al. 2020; Goodwin et al. 2023). Given the range of applied and project-specific settings of past modeling and the long history of animal behavior study, it is perhaps surprising that predicting fish movement at intermediate-scales remains challenging.

Agent (or individual) based models (ABM) are widely used in ecology and other fields to study complex systems where variability among individuals, local interactions, and behaviors driven by changing internal and external environment are paramount (Grimm et al. 2006). Intermediate-scale ABMs commonly employ an Eulerian, Lagrangian, and agent method – sometimes referred to as an ELAM model – where fish movement is simulated through a discretized representation of an aquatic environment. While the ELAM terminology is used throughout the literature to describe both a modeling framework and a particular fish movement model (Goodwin et al. 2006; Tan et al. 2018), it is used here to describe a modeling framework. The Eulerian component represents the environment as a computational mesh (or grid), which typically comes from simulated descriptions of the water flow field. In the context of riverine fish movement, water flow is the predominant feature in aquatic environments that provides sensory input, in the form of flow direction, magnitude, and rate of spatiotemporal change (e.g., velocity gradients and acceleration). The Lagrangian component represents individual fish as particles that move through the 2-D or 3-D environmental domain, and the agent component represents individual responses to environmental stimuli data stored in the computational mesh. While the availability of more efficient computational resources has made ABMs more wide spread, there has been limited generic application of these models due to the highly variable and complex behavior patterns of fish and a multitude of environmental stimuli that can be included (Goodwin et al. 2023). An evaluation of the state-of-the-science of intermediate-scale fish movement models is needed to help identify best practices in architecture, integration of environmental data models, selection of stimuli, and resultant behaviors.

The Eulerian perspective is natural for describing fields that vary in space and time and are convenient for the mathematical solution of governing equations for fluid flow. Acquiring data on water quality (e.g., temperature, salinity, dissolved oxygen) or flow dynamics (e.g., velocity, turbulence) at spatiotemporal scales proportional to the scale of fish movement decisions usually requires complex computer modeling approaches (Tonina and Jorde 2013). Currently, limitations of traditional flow field measurements (e.g., acoustic Doppler velocimetry, acoustic Doppler current profiler, particle image velocimetry) or physical-scale modeling restricts their use to very small domains or for initial input and validation of computer simulations. In the realm of fluid dynamics, modelers have several options for simulating flow that range in spatial and temporal complexity, from time-averaged 2-D to unsteady 3-D hydrodynamic methodologies. The spatiotemporal resolution at which hydraulic patterns are characterized by computer models or in situ measurements is essential to assessing fish responses (Tullos et al. 2016). Computational fluid dynamics (CFD) modeling is the most common method used to model turbulent flows and provides a greater resolution and spatiotemporal correlation of flow dynamics that is not possible with discrete measurements (Goodwin et al. 2023). CFD solvers operate on a computational mesh whose resolution dictates the quality and accuracy of the hydraulic characteristics that can be simulated. CFD models may use an individual or mix of element topologies (e.g., hexahedrals and tetrahedrals), but there is an increasing use of n-faced polyhedra, time-varying (adaptive), and non-conforming meshes. While fine meshes require substantial computer time, they afford greater detail of the fluctuations in the water velocity and pressure fields that occur over short spatiotemporal scales; however, such refinement comes at the cost of greater computer resources. Alternatively, coarse meshes are used to describe much larger water domains with less computer time but with less spatial and temporal resolution than fine meshes. A survey of the different methods and tradeoffs within each environmental modeling approach used in intermediate-scale ABMs is needed to help identify guidelines for what and how environmental stimuli are incorporated in the ABM.

The Lagrangian perspective is a natural way to describe the motion of objects. In general, agent movement is permitted in ABMs through spatially-discrete or -continuous approaches. Spatially-discrete approaches rely on the original mesh of the environmental data to simplify the possible range of movement, and thus offer a reduction in computational complexity. Alternatively, spatially-continuous approaches tend to be more computationally expensive because agents can move in any direction and occupy any point in space and Eulerian environmental data must be interpolated at each point in space for every agent at every time step. Mesh dependency also influences options for agents to ‘sense’ their environment. Common approaches for an agent to sense their surroundings include incorporation of environmental data (1) solely at its location (e.g., Benson et al. 2021; Kerr et al. 2023), (2) within neighboring mesh cells (e.g., Padgett et al. 2020b), or (3) at multiple points a set distance from the agent (e.g., Goodwin et al. 2006, 2014, 2023; Gao et al. 2016; Tan et al. 2018). The programming architecture of how agents move about the environmental domain and incorporate simulated environmental data influences how movement behaviors are implemented and what movement patterns might emerge. A survey of the different methods and tradeoffs can help identify best practices for movement in ABM.

Identifying individual responses (or behaviors) that govern fish movement is fundamental to formulate an exploratory or predictive model capable of replicating movement patterns observed in the field. There is significant variability in the literature regarding the environmental features that elicit a response and what, as well as how, fish behavior is included in ABMs. For example, several models use simple hierarchical movement frameworks prioritizing movement toward the lowest velocity (Blank 2008; Plymesser 2014; Padgett 2020a) while others use multiple distinct swimming behaviors, dependent on complex factors such as tidal state (e.g., Benson et al. 2021), salinity (Brosnan and Welch 2020), and prior experience to features of the water flow field (e.g., Goodwin et al. 2006, 2014, 2023). While the specificity of most ABM can restrict the ability to develop strict guidelines on what behaviors and environmental stimuli are important for governing the movement patterns of all species and scenarios, a systematic review can help identify generalities and inform what factors should be considered in model development.

There are a range of model choices when it comes to understanding and predicting fish behavior as a function of the environment. Models are approximations of reality, with a range of specific tradeoffs compared to real-life contexts. Tradeoffs such as model resolution or agent movement dependencies induce different types, as well as ranges, of uncertainties for the applied use of the ABM that may or may not be acceptable for case-specific management goals. Despite the value of ABM utility to interpret fish behaviors in riverine environments, their computational complexity and cost can detract from broader application (Mawer et al. 2023). While Mawer et al. (2023) identified a list of strengths and weaknesses for a sub-set of ABM, there are more intermediate-scale ABMs that have been applied to a broader range of species and movement scenarios. A fulsome review of applied methods will help future modeling efforts to discern general behavior patterns and identify when and where different types of existing approaches are best applied, and how to advance the field of mechanistic interpretation forward.

This review summarizes the available knowledge on intermediate-scale fish movement models. Due to the variety of modeling techniques and scenarios, model details are generally summarized within broad categories of model properties (e.g., scenarios, fish species), environmental modeling, agent characteristics (e.g., movement, environmental sensing, behaviors), and methods of data use, output, and validation. Themes amongst the included models within each broad category are identified and basic information regarding the modeling scenario, fish species, computer language (when available), environmental stimuli, and numerical modeling approach are collected and the distributions across the field quantified. Specific themes, unsettled questions, and potential directions of future research are also highlighted.

Overview of literature review

Of the 38 texts included in the final analysis, 27 original model frameworks have been published, with 19 models reported once to date, and 7 ‘baseline’ models collectively resulting in 11 further publications. Search results are presented diagrammatically in Supplementary Data and additional details extracted from the literature are provided in Appendix A. Except one cellular automata approach (Padgett et al. 2020b) and three statistical inference approaches (Silva et al. 2020; Szabo-Meszaros et al. 2021; Arenas et al. 2015), all remaining studies detail an ABM. Only one model (Powalla et al. 2022) included a bi-directional Newtonian link in which the agent and hydrodynamic environment influenced each other. All remaining ABMs included an one way Newtonian link where the agent was influenced by hydrodynamics but the agent did not influence water flow fields. Responses to environmental variables were governed using one or more of the following frameworks: random-walk, rules-based, behavioral-state, statistical inference, and computer learning (see Table 1 for description of each framework).

Table 1. Summary and description of agent movement rules.

Response approach	Description
Random-walk	Movement is primarily based on random, biased, or correlated random walk dynamics. Movement in response to environmental variables are incorporated as parameters of the random walk.
Rules-based	Movement is determined based on comparatively simple responses to environmental conditions. Adjustments to swimming speed relative to local flow conditions, or selection of pathways of lowest velocity or energy consumption are examples of this approach.
Behavioral-state	Different behavioral-states are defined and individuals switch between states based on internal and external states. Each behavioral-state has unique movement rules in response to environmental variables.
Statistical inference	Movement rules are based on direct statistical analysis of observed fish trajectories as functions of the environment. Statistical inference facilitates variation in the orientation/speed response rooted in the spatial patterning of the nearby environment at the moment of decision.
Computer learning	Recurrent neural network model is used to relate environmental conditions to locomotion behavior of fish.

The intended use of each model differs, but may be loosely defined as primarily for hindcast or forecast. Model intent often dictates different input data and the models may be “tuned” for different objectives. Further complicating whether a model is categorized as hindcast or forecast is a lack of standardization in model validation techniques, which results in models being parameterized and compared to the same datasets. In cases where the same dataset is being used for parameterization and validation, a forecasting model is not truly predicting out-of-sample movement. For the purposes of this review, a model is categorized as hindcasting if the study focuses on model development to explore the underlying behaviors of observed fish movements or the past performance of a fish passage/exclusion devices. Alternatively, a model is considered to be forecasting if the study focuses on predicting future fish movements in response to changing environmental conditions or new or modified fish passage/exclusion devices. Of the reviewed literature, there was an even split between forecasting (predictive, n = 19) and hindcasting (exploratory, n = 19).

Model properties

Model language

Almost half (n = 18) of the studies did not report the computational language/software used for the ABM. For those that did, the most frequently used language/software was Fortran, followed by Matlab, and single occurrences of C++, ANSYS Fluent, Python, NetLogo, MIKE ECO Lab, TensorFlow and Star-CCM+.

Modeling scenarios

Out of the studies reviewed, most (n = 25) were applied to scenarios with natural/semi-natural domain (i.e., natural river channel, estuary and/or coastal region) whilst 13 modeled an enclosed artificial domain such as a fishway or experimental flume. Models were divided among components of dams, hydropower facilities (e.g., turbine intake channel or turbines), fishways, and sites without barriers.

Fish

Data from twenty-seven species and eleven families of fish were used for the movement models. The most prevalent families were Salmonidae, Cyprinidae, and Anguillidae, and the most prevalent species were Atlantic salmon (Salmo salar), Chinook salmon (Oncorhynchus tshawytscha), and European eel (Anguilla anguilla). Many species (n = 15) were only modeled once. Two studies simply stated data were from Pacific salmon (Oncorhynchus spp.), while one paper did not provide a species name.

The species included in the literature were mainly anadromous fishes, as salmonids were modeled 24 times. Only one catadromous species was studied (Anguilla anguilla). The number of species included in a study, as well as their life history types, varied. Most of the studies used data from a single species. However, seven studies used data from two or more species. In some cases, multiple related species with comparable life histories were used (e.g., same genus or family; all potamodromous or all diadromous) (Scheibe and Richmond 2002; Zielinski et al. 2018). In other studies, species from different families and/or different life history types were used. For example, Haefner and Bowen (2002) included six species, each from a different family, of which four had anadromous life histories and two were potamodromous fishes.

Including information about life stage and body lengths is important, as these parameters impact the swimming ability and speed of fish. The life stages of the fish were included in 30 studies. Of these, 18 studies used data from juvenile fish (including salmonid smolt/parr and anguillid glass eels/elvers), ten studies used data from adult fish, and two studies included data from both adult and juvenile fish. Additionally, data on body length distributions were only supplied in 28 studies, typically included as a mean and +/- standard deviation, although in some cases it was included as a range of values or just a single, fixed value. Powalla et al. (2022) approximated fish as spherical particles with a diameter intended to be representative of an unspecified trout species.

Finally, fish data were collected in North America (19 from USA and Canada), Western Europe (11 from France, Germany, Norway, Sweden, or the UK), and East Asia (4 from China or Japan). There were four papers where the origin of the fish data was not described; they included Anguilla and species from Salmonidae. While the sampling locations for these data are not provided, they are all species native to North America, Europe, and/or Asia.

Environmental modeling

Descriptions of the fluid environment were accomplished almost entirely using CFD, while a single study (Lindberg et al. 2016) relied on direct mea­surements of water velocities and turbulence metrics using acoustic Doppler velocimeter (ADV). CFD simulations were obtained using commercially available (e.g., ANSYS Fluent, Flow-3D) or open-source (e.g., OpenFOAM) software. The majority of studies utilized three-dimensional simulations (n = 28); however, half of these reduced flow data to two-dimensions for agent modeling.

The CFD software used in modeling studies solved either the Reynolds-averaged Navier-Stokes (RANS) equations for three-dimensional flow or the De Saint-Venant shallow water equations for two-dimensional depth-averaged flows. No study employed an alternative turbulence model, like large-eddy simulation (LES) or detached-eddy simulation (DES), despite their ability to provide more information than RANS models and being better suited to describe unsteady, large-scale turbulent structures (Pope 2000). Solvers for the shallow water equations were selected for models of large spatial domains (e.g., estuaries or marine environments) where horizontal flow dynamics dominate.

Of the RANS solvers reviewed, most selected a two-equation turbulent closure model (n = 23), with the $k-\epsilon$, $k-\omega$, and Renormalization-Group (RNG) $k-\epsilon$ closure models being the most common. Closure models are required to solve turbulent flows because the RANS equations alone are undetermined (i.e., more unknowns than equations), but their selection imposes different approximations on how turbulence evolves. While the $k-\epsilon$ model is included in most software, it tends to lose accuracy near walls and in complex flows without recalibration. The $k-\omega$ and RNG closure models offer improved accuracy at low Reynold’s number and near wall flows (Pope 2000; Tonina and Jorde 2013). Despite the array of turbulence closure models, all RANS solvers were reported to have sufficient agreement with measured values.

The core hydraulic variables simulated by CFD were the flow velocity vector components ($u$, $v$, $w$) and hydrostatic water pressure (or water depth for two-dimensional models). Measures of turbulence are also intrinsically calculated in RANS models, but few models (n = 8) actually exported turbulent kinetic energy (TKE) or turbulent intensity (TI) as explanatory variables for fish movement. Following Reynolds decomposition, turbulent fluctuations are defined as (1) $$\begin{array}{c}{u}^{\prime }=\overline{u}-u\\ v^{\prime }=\overline{v}-v\\ w^{\prime }=\overline{w}-w\end{array}$$(1) where the overbar indicates time-averaged velocity. Additional hydrodynamic properties including spatial velocity gradient, $S$, and spatial acceleration gradient, $A$, were incorporated into select models (n = 8): (2) $$S=\hspace{0.17em}\parallel \nabla U\parallel {}_F=\sqrt{\begin{array}{l}{\left(\frac{\partial u}{\partial x}\right)}^2+{\left(\frac{\partial u}{\partial y}\right)}^2+{\left(\frac{\partial u}{\partial z}\right)}^2+{\left(\frac{\partial v}{\partial x}\right)}^2+{\left(\frac{\partial v}{\partial y}\right)}^2\\ +{\left(\frac{\partial v}{\partial z}\right)}^2+{\left(\frac{\partial w}{\partial x}\right)}^2+{\left(\frac{\partial w}{\partial y}\right)}^2+{\left(\frac{\partial w}{\partial z}\right)}^2\end{array}}$$(2) (3) $$A=\hspace{0.17em}\parallel U^T\nabla U\parallel {}_F=\sqrt{\begin{array}{l}{\left(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)}^2+{\left(u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)}^2\\ +{\left(u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)}^2\end{array}}$$(3) where $U$ is the velocity vector and $S$ and $A$ are Frobenius norms. The impetus for including $S$ and $A$ was driven by the models developed by Goodwin et al. (2000, 2006, 2014). The spatial velocity gradient is considered a pre-cursor to turbulence (Nestler et al. 2008; Goodwin et al. 2023), whereas TKE and TI are direct measures of turbulence. Some models (n = 4) also incorporated environmental variables such as salinity and turbidity via water quality models or scalar transport equations integrated within the RANS solver.

Output from the CFD models were generally time invariant (27 steady state vs. 11 transient solutions), meaning the flow field was static while agents transited the domain. Models stemming from Zielinski et al. (2018) used root mean square values of turbulent fluctuations ($\hspace{0.17em}u\prime ,\hspace{0.17em}v\prime ,w^{\prime }$) to randomly update instantaneous flow vectors, creating a quasi-unsteady, but uncorrelated, flow field. However, sensitivity analyses revealed that the quasi-unsteady conditions did not substantially change model results compared to a time-averaged solution. Of the models with transient solutions, the temporal resolution of the CFD model was proportional to the size of the spatial domain (i.e., large domains had large time steps), which is expected due to limits in computational resources. The time step of transient CFD output ranged from 1 s − 30 mins. Except for Olivetti et al. (2021) and Goodwin et al. (2023), all fish movement was modeled at longer time-steps than the CFD solution time step. The spatial resolution of CFD output was generally less than 1 m, except for models of larger spatial domains (Brosnan and Welch 2020; Morrice et al. 2020). The mesh size and quality dictate the scale and accuracy of flow dynamics that can be resolved. Typically, CFD model development includes an evaluation of mesh dependence where a single initial condition will be simulated using successively finer mesh resolutions. Once the solution differs less than 3-10% from the previous mesh size, the solution is considered mesh independent (Tonina and Jorde 2013). Regardless of mesh independence, the CFD solution cannot resolve flow structures (i.e., eddies) at scales smaller than the mesh resolution. Thus, it is critical to select a mesh size that considers the length scale of the boundaries (i.e., river bed roughness, physical boundaries) and targeted fish. When reported, the mesh resolution for half of the studies (n = 19) was equal to or finer than the average length scale of fish.

Agent characteristics

Movement

The freedom of movement that individual agents had within the domain varied. Agents were limited to discrete movements, usually to within a cell of a predefined mesh grid (spatially-discrete, n = 16) (Figure 1a, c). One of the discrete movement models was a cellular automata model, in which information transfer and agent movement was restricted to neighboring cells (Padgett et al. 2020b). For the remaining discrete models, agents could theoretically move to any cell within the environmental domain from one timestep to the next; however, movement was restricted at each timestep based on factors such as agent swim speed and turn angle. For example, in Zielinski et al. (2018), the size and shape of the cells between which agents could move corresponded with the mesh of the underlying hydrodynamic model and agents were only motivated to move upstream and swam at their distance-maximizing ground speed. Agents in other studies were limited to movements within a mesh grid that had a coarser resolution than the original mesh grid for environmental data (e.g., Plymesser 2014).

Figure 1. Examples of spatially discrete (either cell centered [a] or nodal [c]) and continuous (b, d) movement within either a simplified 2-D rectangular and triangular mesh grid. Examples of how agents within the models sensed their environment; (e) in adjacent upstream cells (e.g., Padgett et al. 2020b); (f) within cells that fell on the perimeter of a sensory circle (e.g., Tan et al. 2018); (g) at a fixed number of points (black crosses) that fell on the perimeter of a sensory ovoid (e.g., Goodwin et al. 2006, 2014, 2023); (h) at all nodes (black crosses) that fell within a sensory semi-circle oriented in line with the swim direction of the agent (e.g., Zielinski et al. 2018). Note, all examples show grid and sensory points in two dimensions for simplicity.

In the remaining studies (n = 22), agents could freely move within the domain to any point in space (spatially-continuous) (Figure 1b, d). These continuous movement models tended to include situations where agents were advected downstream with the flow. Movement patterns can be more complex within spatially-continuous models as agents can theoretically exhibit an infinite range of movement distances and turn angles at every movement time step. In practice, movement distances and turn angles are usually constrained to mimic those of the model organism. For example, in Kerr et al. (2023) agent swim speeds were linearly related to flow velocity magnitude, as this is how the model organism was observed to respond to flow velocity magnitude in situ.

Sensing

Further variability exists regarding how agents’ ‘sense’ their environment. For half of the studies, agent movement decisions were based on local environmental data (i.e., at the same location as the agent for each time step). Local sensing was not restricted to spatially-discrete models, as 13 studies using local sensing employed spatially-continuous movements. The remaining half permitted agents to sense environmental data in the region surrounding their location (Figure 1e, f, g, h). The five studies that restricted sensing of environmental data to cells adjacent to the agent’s position (Figure 1e) were limited to spatially-discrete movement approaches, while the rest permitted agents to sense their environment a set distance away from their body, typically 0.5-2 body lengths, at points that fell within (e.g., Zielinski et al. 2018) (Figure 1h) or on the boundary of a hypothetical sensory sphere (Gao et al. 2016; Tan et al. 2018) (Figure 1f) or ovoid (Goodwin et al. 2006, 2014, 2023) (Figure 1g). For the latter method, agent movement decisions typically involved either selecting a specific environmental value at one of its sensory points and moving toward it (Gao et al. 2016) or assessing the gradient of environmental change across multiple sensory points and using that information to guide its movement (Goodwin et al. 2006, 2014, 2023). The number of sensory points evaluated at each timestep also varied between models. For example, the model developed for Goodwin et al. (2006, 2014, 2023) used seven sensory points when operating in 3-D: one at the agents’ location, one ahead (0° in reference to the fish’s current trajectory), one behind (-180°), one to either side (-90°, 90°), and one each vertically above and below (in line with gravity) the agent. For other models, all the cells of the environmental model that fell on the circumference of the agents’ two-dimensional (x-y plane) sensory circle were used to inform movement decisions; approximately n = 60 cells for the model presented by Gao et al. (2016).

Behaviors

Once environmental data were incorporated by the agent, movement decisions were made over varying time-steps. The movement time-step represents the rate at which fish could sense the environment, make a movement decision, and move within the domain. The movement time-step was an explicitly defined model parameter for models using steady state environmental conditions, while models using transient environmental conditions generally set the movement time-step to be equal to the computational time-step forced by the model of the environmental data. Of those that reported the time-step (n = 27), step duration/period ranged from 0.01-3600s, with a mean and median time-step of 360 and 3 s, respectively. Models using time-steps over 30 s were generally associated with large spatial domains and estuarine environments.

While the mechanistic approach used to assign an agent’s response to environmental data was primarily dependent on modeling framework (Table 1), each model imposed some combination of the following behaviors: (1) response to flow direction (i.e., rheotaxis), (2) response to flow velocity magnitude, (3) response to turbulence, (4) response to hydrostatic pressure or water depth, and (5) memory/experience. The impact of water flow is conserved across studies, with the general description of agent movement vectors, ${\overrightarrow{U}}_{\mathit{\text{fish}}}$, as the resultant of advection due to flow, ${\overrightarrow{U}}_{\mathit{\text{flow}}}$, and displacement due to volitional swimming ${\overrightarrow{U}}_{\mathit{\text{swimming}}}$: (4) $${\overrightarrow{U}}_{\mathit{\text{fish}}}={\overrightarrow{U}}_{\mathit{\text{flow}}}+{\overrightarrow{U}}_{\mathit{\text{swimming}}}$$(4)

Response to flow direction

Rheotactic behaviors were included in every ABM model; however, the method in which positive (against the flow) or negative (with the flow) rheotaxis was applied differed across models. Rheotaxis was applied by (1) movement restriction, (2) waypoint, (3) local flow direction, or (4) response to non-hydraulic covariates. Movement restriction was implemented by limiting an agent’s movement to mesh cells up- or down-stream of its current position and was often limited to spatially-discrete approaches (Zielinski et al. 2018; Plymesser 2014; Zhu et al. 2021). Waypoints were user defined positions that agent movement was directed toward and were based on a global direction of movement (i.e., up- or down-stream) (Powalla et al. 2022) or specified habitat type (Willis and Teague 2014). Movement direction based on orientation to local flow direction was the most common approach (n = 12) and relied on agents orienting to or against local flow direction (Goodwin et al. 2006, 2014, 2023; Kerr et al. 2023). The remaining studies forced agents to orient with the flow direction based on other covariates like local salinity (Brosnan and Welch 2020), salinity gradient (Rossington and Benson 2020; Benson et al. 2021), or monotonic hormone concentration (Kulic et al. 2021).

Response to flow velocity magnitude

Flow velocity magnitude influenced agent movement speed and/or direction in all studies. For the majority of ABMs, displacement due to volitional swimming ${\overrightarrow{U}}_{\mathit{\text{swimming}}}$ was determined by some function of flow velocity magnitude. The most direct example are models ascribing to energy conservation approaches, where agent movement was restricted to directions or mesh cells with the lowest available velocity magnitude (Plymesser 2014; Blank 2008; Abdelaziz 2013) or require the least energetic cost (Zielinski et al. 2018; Gilmanov et al. 2019). Velocity magnitude was also used to define suitable habitat that agents were attracted to (Han et al. 2013; Kopecki et al. 2022). Other studies permitted more nuanced responses to flow velocity magnitude, allowing for conditional responses (i.e., move toward comparatively higher or lower flow velocities) (Nestler et al. 2002; Goodwin et al. 2006, 2014, 2023; Ben Jebria 2021; Padgett 2020a). Even statistical inference models found fish swim speed and direction to be partially dependent on the magnitude of each flow velocity component (Silva et al. 2020; Szabo-Meszaros et al. 2021). While still including flow advection, four studies of downstream movement did not permit fish swimming responses to be a function of flow magnitude (Rossington and Benson 2020; Willis and Teague 2014; Gross et al. 2021b).

Response to turbulence

Agent responses to turbulence was less prevalent, but was included in 11 ABMs and all three statistical inference models. Both a direct measure of turbulence, TKE, and its precursor, the spatial velocity gradient, were the most common response variables. In general, agents responded to turbulence by seeking areas with lower (Abdelaziz 2013; Padgett 2020a; Kulic et al. 2021) or preferred level of turbulence (Zhu et al. 2021; Gao et al. 2016; Tan et al. 2018; Gisen et al. 2022). The premise behind turbulence avoidance was tied to its potential destabilizing effect on swimming efficiency (Smith et al. 2005), whereas preferred levels of turbulence were typically based on laboratory observations of fish movements (Gao et al. 2016; Tan et al. 2018). In contrast, Lindberg et al. (2016) incorporated a utilization parameter to simulate the potential energetic benefit or harm of eddies on swimming performance (Lacey et al. 2012). Goodwin et al. (2006) and later related models used a context dependent response to turbulence or its precursory features, with the latest iteration (Goodwin et al. 2023) permitting agent attraction to $S$ when water speed is decreasing and repulsion of areas of high $A$ when there is an abrupt change in flow acceleration/deceleration. Note, in the example of Goodwin et al. (2023), $A$ was not as tightly correlated to turbulence as $S$.

Response to hydrostatic pressure or water depth

Overall, 15 studies explicitly incorporated behaviors mediated by hydrostatic water pressure or water depth. The most common agent response (n = 11) was to bias movement toward a preferred depth or hydrostatic pressure. Alternatively, Padgett (2020a) limited vertical movements to 10° per time step and did not select a preferred value. Studies of downstream migrating eel (Rossington and Benson 2020; Benson et al. 2021), smelt (Gross et al. 2021b), and salmon smolt (Willis and Teague 2014) also prescribed tidal or diurnal vertical movements; however, these movements were directed toward specified positions in the water column or shallow/deep water and not in direct response to changes in depth or hydrostatic pressure. Finally, Kulic et al. (2021) and Gross et al. (2021a) included water depth responses to force agents to remain in the water column.

Memory/experience

In most models (n = 30), agent movement decisions were based on instantaneous environmental conditions and were not influenced by any ‘memory’ of previous movements or environment. Models that include some form of memory or longer-term conditioning (i.e., acclimatization, habituation) were rarer (n = 8) and mostly included the Goodwin et al. (2006) and later related models (see Supplementary Data Figure S1 for relation). The duration over which memory of past environmental conditions influenced movement ranged from 2 s to 4 hrs. Goodwin et al. (2006, 2014, 2023) and Gisen et al. (2022) each parameterized coefficients that determine the rate of depreciation of past conditions through calibration with known positional data, while Padgett (2020a) used a sensitivity analysis to determine an appropriate memory time-scale.

Data use, model outputs, and analysis

The number and type of parameters reported varied significantly across studies, due to factors such as the complexity of behavioral rules (e.g., multiple swimming behaviors as function of environmental factors) and how model outputs were quantified (e.g., passage index past dams or energy consumption for fishes). Some studies did not report the value or calculation of parameter estimates, but rather relied on estimates reported elsewhere. For a small portion of the studies (n = 8) that did not report any types of parameters directly, the model frameworks were described without mention of specific parameters, or models were described qualitatively (e.g., visual inspections of overlap between observed and predicted) rather than quantitatively.

Model validation and parameter estimation was generally informed using observed fish movement tracks generated from telemetry data (n = 15) or visual/camera observations (n = 7). Visual observations of fish movement behaviors were restricted to studies where simulated data was compared to laboratory data. Fish movement data collected from passive integrated transponder (PIT), acoustic, and radio telemetry allow for greater spatial range in the field, but the accuracy of positions is highly dependent on the technology and deployment conditions. While the spatial accuracy of telemetry data was rarely reported, the accuracy of fish positions expected from acoustic telemetry was ∼1-4 m (Ben Jebria 2021; Kerr et al. 2023; Leander et al. 2020). In lieu of quantifiable movement tracks, other models (n = 9) used trap catch or broad observations of passage to compare model results. The remaining models (n = 7) reported no use of direct laboratory or field observations to inform model validation or parameter estimation.

In general, the parameters reported were context-dependent, and thus were considered applicable only to the specific scenario for the study. More precisely, the parameters or model concept were only tested and validated under specific environmental settings, making inference of the applicability of parameters under other situations difficult. However, Goodwin et al. (2023) is an exception to this observation where various forms of the movement model and its parameters were fit to an extensive data set of juvenile Pacific salmon from the tidal Sacramento River in the California Bay-Delta. Most studies (n = 28) report some type of validation of the model and/or parameter estimates, but the type of validation varied considerably. The most common validation approach (n = 14) was to compare broad metrics (e.g., passage efficiency or rate) of model outputs and field or laboratory observations. Other studies (n = 9) sought to quantitatively or qualitatively compare simulated fish swimming trajectories to trajectories acquired using acoustic telemetry or visual observation. The number of trajectories compared was also highly variable, with some studies comparing very few (n = 2; Gao et al. 2016) or an unspecified number of trajectories (Abdelaziz 2013). The remaining studies (n = 5) elected to validate model results using more comprehensive statistics (Silva et al. 2020; Szabo-Meszaros et al. 2021), pattern-oriented modeling (Gisen et al. 2022; Kerr et al. 2023), or comparison to other model types (Powalla et al. 2022). There were only a few studies that reported validation of parameters and/or model performance based on data that was not initially used to parameterize the model (Kerr et al. 2023; Szabo-Meszaros et al. 2021; Goodwin et al. 2023; Finger et al. 2020; Whitty et al. 2022).

Discussion

Intermediate-scale movement models are a contemporary approach for understanding and predicting riverine fish decision-making processes in light of their changing environment, which is predominately water flow (i.e., flow direction, flow magnitude, and rates of change). These models can also become quite complex, requiring interdisciplinary knowledge to effectively incorporate numerous movement decisions in response to ancillary environmental data through 3-D space and time. The result of more than a half century of development is an array of model framework/architectures, movement rules, and environmental stimuli considered, which are customized for a range of fish passage and movement situations. Despite the lack of consistency in modeling approaches, each model imposed some combination of the following behaviors: response to flow direction (i.e., rheotaxis), response to flow velocity magnitude, response to turbulence, response to depth, and memory/experience of the individual. There is also an evolving trend in the reviewed models toward spatially-continuous models of increasing complexity to incorporate multiple behavior states and agent memory/learning.

Across the literature, models generally employed rules-based or behavioral-state decision processes. Rules-based decision models could be considered a sub-set of the more complex behavioral-state models because behavioral-state decision models incorporated multiple rules-based movement decisions within an array of behavioral states. As a result, rules-based models were used primarily in broad evaluations of passage rate through specific structures like a spillway (Zielinski et al. 2018), culvert (Blank 2008), or fishway (Plymesser 2014). These models all relied on swimming performance to constrain movement/passage, but differed on how fish navigated the flow field based on flow direction and magnitude or magnitude alone. More nuanced behavioral-state models were primarily used for evaluations of passage routes and efficacies. Behavioral-state models were thus more fish-centric compared to rules-based approaches and were used to evaluate passage routes at complex hydroelectric dams (Goodwin et al. 2006, 2014), fish screens (Haefner and Bowen 2002; Lemasson et al. 2008), and diversion structures (Kerr et al. 2023; Goodwin et al. 2023). Random-walk models were limited to downstream drift scenarios across large spatial scales (Scheibe and Richmond 2002; Gross et al. 2021b). Most of the remaining approaches, including statistical inference (Silva et al. 2020; Szabo-Meszaros et al. 2021; Arenas et al. 2015) and computer learning (Olivetti et al. 2021) have been developed since 2020 and have produced promising results, but the sample size is too small to compare with more common approaches. Presently, it is difficult to provide a direct comparison between approaches because no evaluation using the same originating data set has been performed.

The diversity of species examined by fish movement models was proportionate to the number of unique modeling frameworks; however, fish species located outside of North America and Western Europe are underrepresented, with no species included from the Southern Hemisphere. The predominate species were all of special commercial, recreational, or ecological concern (i.e., threatened, endangered, or invasive). As there is a noted history of salmonid focus in fish passage research (Mallen-Cooper and Brand 2007), unsurprisingly, fish from the family Salmonidae were disproportionately represented. Although telemetry data, used for model validation and parametrization, can be limited for small fish sizes due to potential tag effects on swimming performance, growth, and survival (Klinard et al. 2018), both adult and smaller, sub-adult life stages were equally represented in models. Larval fish movement was excluded from this analysis due in part to their movement being dominated by active-passive downstream movement at flows exceeding their critical swim speed (Zens et al. 2018). Lechner et al. (2014) found that although larvae were capable of orienting to flow patterns, larvae primarily relied on bulk flow for transport. In the future, modelers should continue to examine movement behaviors of underrepresented species at various life stages, especially species from the Southern Hemisphere.

Environmental modeling

The hydraulic stimuli used in the models were very similar, with all models using the fundamental flow characteristics of water velocity magnitude and direction. Given the preponderance of RANS and shallow-water CFD solutions, the water velocity fields used in models were temporally averaged (i.e., not reflections of instantaneous conditions). Time-averaged velocity vectors are just one component of a complete representation of the flow field. In comparison, laboratory and in situ studies of fish movement (Webb and Cotel 2010; Liao 2007; Kemp et al. 2005) usually consider both time-averaged and turbulence characteristics. Based on a litany of experimental data, Lacey et al. (2012) suggests turbulence intensity, periodicity, orientation, and scale (IPOS) as critical features of turbulence relevant to fish movement. At the very least, the IPOS framework serves as a baseline for characteristics of turbulence that could be considered in fish movement models. Select models do quantify the intensity of turbulence using variables like TKE and spatial velocity gradient; however, ephemeral components of turbulence and their characteristics (e.g., orientation of an eddy, vorticity, and eddy size) are either not captured by RANS solvers due to the time-averaged values of the velocity field or not reported in the model. LES or DES solvers present a potential, albeit computationally expensive, option to resolve the period, orientation, and spatiotemporal scale of turbulence features that could be incorporated into movement decisions. Unfortunately, linking the temporal sequence from LES or DES solvers to a specific date-time in situ is not trivial (Goodwin et al. 2023).

In lieu of discrete modeling of turbulence structure, select models (Gisen et al. 2022; Zhu et al. 2021; Padgett 2020a; Goodwin et al. 2023, 2014, 2006; Abdelaziz 2013; Haefner and Bowen 2002) included some post-processed hydraulic characteristics like spatial velocity gradients and spatial acceleration gradients. The spatial velocity gradient serves as a logical approximation of turbulence orientation and scale as their numerical derivation incorporates metrics of turbulence stretching and rotation. While inclusion of more explicit turbulence measures should be considered in future models, they must be weighed against issues relating to additional model complexity, uncertainty of field resolution and time synchrony, and uncertainty in fish response. There are also limitations to the detail in which covariates other than hydraulic characteristics can be incorporated into the models. Localized habitat, prey, predators, and cohorts are all features that may have varying influence on fish movement at different scales that simply have not been widely incorporated into intermediate-scale models of riverine fish movement to date.

The majority of models reviewed did not employ time varying environmental data. Time-dependent solutions using RANS solvers are relevant in fish passage situations to deal with large-scale unsteadiness of flow (i.e., changes in discharge), and not necessarily smaller scale turbulent structures (e.g., eddies). While LES solvers produce inherently time-dependent solutions, the solutions are not locked in phase with real-time. Thus, averaging an LES solution over time yields a solution that would be analogous to RANS. The limitation on using time-dependent solutions is not typically caused by limitations of CFD or fish movement models, but rather limitations on the availability of computational resources.

Agent characteristics

Many of the reviewed models used similar measures to reduce computer time and resource requirements. Spatially-discrete movement is the first such computational cost savings approach. Using the mesh generated by the CFD model or overlaying a structured grid reduces movement complexity, but can bias movement direction and result in movement paths that are more tortuous compared to spatially-continuous paths (Gilmanov et al. 2019). The use of a coarser resolution movement meshes likely stems from a desire to have movement occur over a larger distance for a single movement iteration and to minimize computational resources (i.e., the size of the environmental data required to be stored and accessed is reduced and fewer iterations may be required to move the agent a set distance). With the prevalence of multiple particle tracking algorithms, spatially-continuous movement is less of a computational burden. However, selection of a particle tracing algorithm may restrict which software or computing language can be used (e.g., Tecplot, Star-CCM+, ANSYS-Fluent).

Reducing the dimensionality of the underlying CFD data is another common approach used by modelers to reduce computer resources. While fundamentally different from spatially-discrete movements, dimension reduction (i.e., restrict fish movement in two dimensions while flow data is generated in three dimensions) still restricts movement in one dimension, typically in the vertical direction, and restricts agents from accessing flow field heterogeneities that may be critical for movement past barriers. Simplifying models to operate in 2-D were attributed to either lower computational effort or analytical convenience (Gao et al. 2016; Blank 2008), lack of fish movement observations in the vertical dimension to parameterize the model (Szabo-Meszaros et al. 2021; Olivetti et al. 2021; Ben Jebria 2021), or vertical migration was not deemed to impact horizontal progress of fish (Brosnan and Welch 2020). Goodwin et al. (2023) found dimensional reduction (i.e., restricting agent movement to a horizontal plane with data from 3-D CFD) did not have an appreciable impact of model performance in a relatively shallow system compared to that of a deep dam forebay. Alternatively, fish passage output using 2-D depth-averaged CFD did differ from those generated with 3-D CFD (Goodwin et al. 2023). The potential tradeoffs for reduced computational effort from movement restrictions and reduced dimensionality must be considered on a case-by-case basis.

The general trend across studies is that fish largely align with flow magnitude and direction, and, depending on the model spatiotemporal scale, turbulence; however, overall movement rules vary to a large degree. One of the fundamental challenges of modeling fish responses to flowing water is centered around how to simulate their ability to sense their environment. In reality, fishes detect and perceive the hydrodynamic environment through their mechanosensory lateral line and inner ear (Webb 2014; Mogdans 2019). Models replicate the function of a fish’s lateral line system by permitting agents to sense their environment only at its location, in adjacent mesh cells, or at a limited number of locations a set distance from the agent (typical range: 0.5-2 body lengths). The choice of sensory points being located 0.5-2 body lengths from the agent stems from the idea that a fish can sense a vibrating sphere at approximately this distance (Coombs 1999), but the relevance of this distance for sensing spatially heterogenous hydrodynamics to inform navigation is unclear. No conclusions can be derived as to which method of modeling a fish’s sensory system (e.g., number of sensory points, sensory query distance, etc.) is most appropriate because the efficacy of existing methods have not been systematically compared.

Fish decisions were solely based on instantaneous environmental conditions for the majority of models, which is unlikely to match reality, where prior experience is known to influence movement decisions in most taxa (Fagan et al. 2013), including fish (Odling-Smee and Braithwaite 2003). For example, European eel will actively reject (swim away from) an accelerating velocity gradient whilst migrating downstream but after repeated exposure they become habituated and pass downstream (Piper et al. 2015). Fish can also optimize spatial movement decisions (i.e., efficiently locate food) by learning from previous experience (Long and Fu 2022). Goodwin et al. (2006) included a form of functional memory within an agent-based fish movement model by allowing perception of hydraulics, based on recent exposure to that variable, to trigger a behavioral response. In Padgett (2020a), the mean flow direction was averaged over a fixed number of previous timesteps to provide the agent with an indication of mean rather than just instantaneous velocity direction. In this case, the agents’ memory acts as a filter, allowing it to orient relative to the bulk flow rather than just the transient flow direction. Inclusion of memory effects in fish movement models other than in the Goodwin et al. (2006, 2014, 2023) applications and follow-on studies is rare. Modeling fish memory typically involves the addition of multiple parameters, increasing model complexity, and this is one reason why others have likely avoided including fish learning and memory to date. Additionally, there is very little context-specific information available to assist parameter estimation at the scale required for modeling. Despite these limitations, it is assumed that learning and memory will play an important part in fish movement models in the future.

In addition to resolving how fish sense their environment, it is important to consider how quickly fish can respond. In response to a threatening mechanical stimulus, fish can detect and initiate an escape response within 5 to 20 ms (Domenici and Hale 2019). Fish use special neural pathways to enable them to quickly initiate such responses (Domenici and Hale 2019) but these times indicate just how fast fish can respond to a hydraulic stimulus if needed. The median and range of the agent time-steps in the models reviewed in this manuscript was 3 s and 0.01-3600s, respectively. A shorter time-step results in the agent sensing its environment more frequently and having the opportunity to respond more often but it is computationally taxing, with a greater number of movement iterations required to move the agent a set distance. Hence, in certain situations, there is a potential for computational resource availability to influence model accuracy by limiting how frequently agent’s sense and respond to their environment. Both Padgett (2020a) and Gilmanov et al. (2019) examined the importance of timestep duration on agent movement trajectories, finding that trajectories appear ‘noisier’ with increasing duration. Such results were not compared against empirical data, so it is hard to ascertain whether the observed results for longer timesteps were due to a breakdown in realism or due to nuances of the underlying movement models.

There is also uncertainty regarding how different timestep durations may be used to replicate different scales of movement. In general, decision timesteps were equal to or smaller than the timestep of movement observations from telemetry data. Decisions made at a high temporal resolution (i.e., <1 s) may only be important for governing small-scale space use patterns (i.e., feeding, prey avoidance), whereas large-scale movement patterns (e.g., channel selection or space use in estuaries) may be reproducible using much longer movement timesteps (i.e., >30 s). Indeed, two of the large-scale estuarine migration models analyzed in this review showed good agreement between model results and empirical data for coarse resolution spatiotemporal movement patterns using long movement timesteps (e.g., 30 s: Benson et al. 2021; 90 s: Brosnan and Welch 2020). The influence of decision timestep on model output has not been systematically assessed under multiple scenarios or a range of spatial scales; therefore, future practitioners must make decisions on model sensitivity to timestep on a case-by-case basis.

Data use, model outputs, and analysis

The observed variation in model frameworks often reflects the context-specific cases for which each model was developed, which and how environmental variables were sampled, how validating/parameterizing data (e.g., fish trajectories) were sampled, and how stimuli were integrated into decision-making processes. The inconsistency in modeling decisions limits the potential opportunity to train or parameterize models across systems and species and to test the generality of the models under different situations. With the exception of a few studies (Kerr et al. 2023; Szabo-Meszaros et al. 2021; Goodwin et al. 2023; Finger et al. 2020; Whitty et al. 2022), it was difficult to assess the robustness of model results as validations tended to be optimistically biased to systematically overestimate the predictive performance of the model. In other words, as the models were parameterized to the same specific data that was used for validating the model, there is a higher probability that parameters of interest are systematically off, as the assumption of data being completely representative outside the training data is unlikely given generally small datasets available for parameter estimation. Thus, the question of whether models can perform well under different settings (i.e., using out-of-sample data) remains unanswered for most modeling frameworks.

The methodology used to compare simulations to observed fish movements, when done, was highly dependent on the modeling scenario, and thus situation specific. For example, models examining fish movement through an engineered structure or fishway relied on comparisons of broad statistics of passage efficiency (Plymesser 2014; Blank 2008; Lindberg et al. 2016; Goodwin et al. 2014) rather than comparisons to characteristics of fish trajectories (e.g., swim speed, tortuosity). Contemporary studies (Gisen et al. 2022; Kerr et al. 2023) have employed pattern-oriented modeling (Grimm and Railsback 2012) to facilitate model development with an appropriate level of complexity. Here, pattern-oriented modeling calls for organizing and evaluating model performance based on an observed set of patterns that span across multiple spatial and temporal scales. Ideally, a generic movement model that could be re-parameterized and rigorously and objectively tested across systems, and even species, would be preferred over case-specific models in many cases. The state of the science for this type of modeling is somewhat unsettled regarding many of the computational frameworks, agents and elements modeled, and how the data is validated and compared, if at all, to observed fish movements.

The manner in which biological data is collected also plays a role in how movement rules can be and are developed. Specifically, many of the studies use acoustic, radio, and PIT telemetry, which have been limited to positional data. Recent advances in tag development have allowed for integrated sensors with radio and acoustic telemetry that can monitor additional environmental (e.g., water temperature), physiological (e.g., muscle activity, heart rate, tail-beat frequency), and movement (e.g., acceleration) data (Jacoby and Piper 2023). These data could be used to improve development of fish decision-making processes that incorporate more covariates than only hydraulic characteristics. The spatiotemporal accuracy and, thus, the utility of radio and acoustic telemetry data to inform movement models can vary depending on environmental conditions and receiver deployments. When fine-scale trajectories are required, substantial post-processing of acoustic tag detections are required. Despite advances in detection processing, accurate positioning in noisy environments (i.e., regions of water with high air entrainment and are coincidentally associated with water discharge at engineered structures) can be challenging (Jacoby and Piper 2023). Similar to the limitations in using computationally-expensive CFD models, the cost of acoustic telemetry equipment and detection processing effort for 3D tracks can be prohibitive.

Conclusion

Intermediate-scale fish movement models have contributed to the understanding of how fish respond to changing environmental conditions, primarily water flow. The reviewed literature demonstrates a wide range of model frameworks and architectures, with an increasing trend toward spatially-continuous models of higher complexity. Models incorporating multiple behavioral states and agent memory/learning indicate a move toward more realistic representations of fish movement. Despite the lack of consistency in modeling approaches, each model imposed some combination of the following behaviors: response to flow direction (i.e., rheotaxis), response to flow velocity magnitude, response to turbulence, response to hydrostatic pressure or water depth, and memory/experience. There was also clear preference for rules-based decision-making for broad evaluations of passage, while behavioral-state decision-making processes were more suitable for evaluating fine-scale passage routes and efficacies.

With the continuous advances in computing power available, some of the tradeoffs between computational efficiency and model accuracy that were identified may be of lesser importance in future model development. Computational advancements may also permit further exploration of time-varying CFD solutions and incorporation of fish learning and memory into the models. Combined, integration of time-varying environmental data and memory/experience into models could provide a more comprehensive and realistic understanding of fish responses to changing environmental conditions.

Overall, intermediate-scale fish movement models have made significant progress in capturing the complexities of fish movement decision-making processes. Further research and collaboration are needed to standardize modeling approaches, incorporate a wider range of species and environmental factors, improve spatiotemporal synchrony between environmental models and agent movement, and improve the representation of fish sensory systems and learning abilities. By continuing to refine and develop these models, we can advance our understanding of fish movement and contribute to sustainable fisheries management.

Acknowledgements

This manuscript is contribution 15 of FishPass. FishPass is the capstone to the 20y restoration of the Boardman (Ottaway) River, Traverse City, Michigan. The mission of FishPass is to provide up- and down-stream passage of desirable fishes while simultaneously blocking or removing undesirable fishes, thereby addressing the connectivity conundrum. We are grateful to the primary project partners: Grand Traverse Band of Ottawa and Chippewa Indians, Michigan Department of Natural Resources; U.S. Army Corps of Engineers; U.S. Fish and Wildlife Service, U.S. Geological Survey. We also extend sincerest thanks to the primary partner, the City of Traverse City. Without the city’s support and the vision of the city commission, FishPass would not have been possible.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Funding for this contribution came from the Great Lakes Fishery Commission [award 2022_SIL_793013].