Open access

Modelling the effects of currents and migratory behaviours on the dispersal of Atlantic salmon (Salmo salar) post-smolts in a coastal embayment

Publication: Canadian Journal of Fisheries and Aquatic Sciences
17 October 2022


The post-smolt phase is considered a critical period for Atlantic salmon (Salmo salar). Hence, identifying migration routes used by post-smolts is needed to protect the habitats they require to successfully complete their life cycle. We used a biophysical model coupled with output from a water circulation model (FVCOM) to simulate dispersal of Atlantic salmon post-smolts in a semi-enclosed bay: Passamaquoddy Bay, New Brunswick, Canada. The model was run with nine post-smolt behaviours and six swimming speeds, and then tested against acoustic telemetry data. While no modelled behaviour entirely captured observed salmon migration routes, we identified some behaviours that could allow salmon to successfully leave the bay and resulted in predictions that matched observations reasonably well (e.g., swimming southwest, negative, or tide-varying rheotaxis). We could also rule out several behaviours as unlikely to be used by Atlantic salmon post-smolts in this area (e.g., passive dispersal, orienting based on salinity or temperature, and positive rheotaxis). Hence, with suitable behaviours and models, this approach can provide estimates of the essential habitats and migration routes of wild post-smolts.


La phase post-saumoneau est considérée comme une période critique pour le saumon atlantique (Salmo salar). Par conséquent, l'identification des routes migratoires utilisées par les post-saumoneaux est nécessaire pour protéger les habitats dont ils ont besoin pour compléter leur cycle de vie. Nous avons utilisé un modèle biophysique couplé à un modèle océanographique physique (FVCOM) pour simuler la dispersion des post-saumoneaux du saumon atlantique dans une baie semi-fermée: la baie de Passamaquoddy, Nouveau-Brunswick, Canada. Le modèle a été exécuté avec neuf comportements et six vitesses de nage, puis testé par rapport aux données de télémétrie acoustique. Bien qu'aucun comportement modélisé ne capture entièrement les voies de migration du saumon observées, nous avons identifié certains comportements qui pourraient permettre au saumon de quitter la baie avec succès et ont abouti à des prédictions qui correspondent raisonnablement bien aux observations (p. ex., nage vers le sud-ouest, rhéotaxie négative ou variable selon la marée). Nous avons également exclus plusieurs comportements comme peu susceptibles d'être utilisés par les post-saumoneaux du saumon atlantique dans cette zone (p. ex., dispersion passive, orientation en fonction de la salinité ou de la température, rhéotaxie positive). Par conséquent, avec des comportements appropriés, ce modèle peut fournir des estimations des habitats essentiels et des routes migratoires des post-saumoneaux sauvages.


Atlantic salmon (Salmo salar) may be particularly vulnerable to anthropogenic stressors during their initial seaward outmigration from natal rivers, a period considered critical for salmon due to their small size at this stage and the physiological stress associated with the metamorphosis from freshwater smolt to marine post-smolt (Thorstad et al. 2011, 2012). As post-smolts, they must often traverse estuaries and coastal bays in which many potentially stressful human activities, such as coastal development, shipping, and sea-cage salmon aquaculture, occur (Magnuson and Hilborn 2003; Lacroix et al. 2004; Levings 2016). Therefore, an essential component of conservation planning for wild Atlantic salmon populations is information on the migration routes used by post-smolts so that critical rearing habitats can be identified, protected, and incorporated into spatial planning and ecosystem-based management efforts (Trzcinski et al. 2004; Marshall 2014).
Migration routes, residence times, and mortality rates of Atlantic salmon post-smolts can be determined in estuaries and coastal bays through tagging and tracking studies (e.g., Lacroix et al. 2004; Lacroix 2008, 2013; Kocik et al. 2009; Hawkes et al. 2017; Chaput et al. 2018). Acoustic telemetry is a method often used to track salmon with tags that transmit acoustic signals (i.e., ultrasonic pulses) and receiver arrays. Although such studies may be expensive and limited in spatial and temporal scopes (i.e., dependent on where receivers are deployed and when the fish are tagged), they can nonetheless provide empirical estimates of migration speeds, success, routes, and even survival over particular scales (Kocik et al. 2009; Byron and Burke 2014).
A complementary method to investigate salmon migrations is the use of individual-based biophysical models (IBBMs). By coupling physical ocean circulation models with particle tracking algorithms (van Sebille et al. 2018), IBBMs allow the potential migration routes of a massive number of particles (representing salmon) to be simulated over large spatial and temporal scales. However, such computer-intensive models are subject to the quality of data and model inputs, including the behavioural rule(s) assigned to salmon particles, and require validation against empirical data (Byron and Burke 2014). Combining tracking by acoustic telemetry and IBBMs, while testing different salmon behaviours, can be used to: identify behaviours that are or are not feasible for salmon; estimate the usage of different habitats during migration by an entire population of fish; and infer the potential migratory characteristics of post-smolts and their behaviours when migrating in different habitats, such as coastal and offshore areas (Byron and Burke 2014; Brosnan and Welch 2020; Newton et al. 2021).
Atlantic salmon post-smolts are strong swimmers (Peake 2008), and thus likely use active swimming behaviours during their migration rather than dispersing passively (Hedger et al. 2008; Mcilvenny et al. 2021; Newton et al. 2021). Post-smolts may use a range of migratory behaviours as they leave their natal rivers, including current-following, localized cue-based orientation, or directional swimming via compass navigation. Many salmon species are sensitive to magnetic fields or exhibit evidence of a compass or map sense that allows them to navigate in particular directions or towards particular locations (Burke et al. 2014; Byron and Burke 2014), for example during natal homing (Putnam 2015). At smaller scales, salmon potentially orient their direction of movement relative to prevailing currents. This is called rheotaxis, and it may be positive (the animal faces into the current and swims into it) or negative (the animal faces away from the current, swimming with it; Byron and Burke 2014; Olive et al. 2016). Negative rheotaxis can allow animals to increase dispersal by combining their swimming velocity with current velocity, although this dispersal may occur in a disadvantageous direction, such as towards land on a flood tide (Lacroix and McCurdy 1996; Telesh and Khelbovich 2010). Positive rheotaxis generally decreases dispersal and is often used for position maintenance, but may also help animals avoid dispersal in a disadvantageous direction (Olive et al. 2016). An animal may also switch the direction or strength of its rheotaxis in response to some stimulus or internal/external rhythms; for example, animals inhabiting surface waters can increase their dispersal away from coastal natal habitats by exhibiting negative or stronger rheotaxis on ebb tides (swimming with currents directed away from shore) and positive or weaker rheotaxis on flood tides (resisting currents directed back towards shore). Such changes in current-following behaviour have been suggested for Atlantic salmon post-smolts (Lacroix and McCurdy 1996; LaBar et al. 1978; Martin et al. 2009), which may sense tidal phases based on salinity, scent plumes, turbulence, etc., in coastal areas (McCleave 1978; Tytler et al. 1978; Johnstone et al. 2011) or in response to food availability in deeper waters (Muelbert et al. 1994; Cresci et al. 2017). In addition to currents, salmon are also sensitive to other localized environmental gradients in temperature, salinity, olfactory cues, etc., that could help them to orient (Hvidsten et al. 1998; Johnstone et al. 2011; Byron and Burke 2014). Indeed, a link between water temperature and post-smolt migration has previously been established, for instance in the control of river exiting time (Hvidsten et al. 1998). When moving from a riverine to an estuarine to a marine environment, water temperature should generally decrease, and water depth and salinity should increase (Telesh and Khelbovich 2010), so differences in such habitat characteristics may provide post-smolts with cues leading them out of coastal estuaries and bays.
Directed swimming towards some landmark was often the most successful migratory strategy in past dispersal modelling studies of Atlantic salmon post-smolts (Byron et al. 2014; Moriarty et al. 2016; Ounsley et al. 2020; Newton et al. 2021; Table 1). However, most previous studies have also tested some form of negative rheotaxis and concluded that this behaviour resulted in reasonable dispersal estimates. Negative rheotaxis varying based on other factors (e.g., temperature or salinity, Mork et al. 2012; direction towards the ultimate migratory destination, Newton et al. 2021) has also been included in past models, but none have directly tested tide-varying rheotaxis. Positive rheotaxis has generally not been used in such studies or has been concluded to not be a viable migration strategy for salmon in the ocean (Booker et al. 2008; Mork et al. 2012; Byron et al. 2014; Table 1). Previous models of Atlantic salmon post-smolt dispersal have tested behaviours in which salmon avoided swimming through water with unfavourable temperatures or low salinity, or swam towards preferred ranges of these variables (Booker et al. 2008; Mork et al. 2012; Ounsley et al. 2020; Table 1). Past modelling studies made some assumptions about what the preferred/unfavourable ranges of temperature/salinity are for salmon, and some simulations of thermotaxis have achieved reasonably realistic predictions (Booker et al. 2008), although the specific values used are by no means certain and likely vary among regions or populations.
Table 1.
Table 1. Review of models, behaviours, and swim speeds used in previous studies modelling dispersal of Atlantic salmon post-smolts.
The assumed optimal swimming speed of migrating post-smolts has also varied among modelling studies, ranging from half a body length per second (0.5 BL·s−1) (Friedland 2002) to 2.5 BL·s−1 (Mork et al. 2012), but a value of 1.2–2.0 BL·s−1 is most often used (Booker et al. 2008; Byron et al. 2014; Moriarty et al. 2016; Ounsley et al. 2020; Newton et al. 2021; Table 1). Recently, Hvas et al. (2021) demonstrated that Atlantic salmon post-smolts could sustain swimming speeds of up to 2.2 BL·s−1 for up to 72 h or 2.7 BL·s−1 for 2 h, so it is unlikely that migrating post-smolts in nature move much faster than 2–3 BL·s−1 continuously.
As outlined above, several studies have attempted to use IBBMs to assess the migration of Atlantic salmon post-smolts in the western (Byron et al. 2014; Moriarty et al. 2016) and eastern North Atlantic Ocean (Booker et al. 2008; Mork et al. 2012; Ounsley et al. 2020; Mcilvenny et al. 2021; Newton et al. 2021). However, to date, all these studies have focused on the migration of Atlantic salmon post-smolts along relatively open coastlines (Table 1) rather than in complex and semi-enclosed estuaries and coastal bays. The unique and complex circulation features (e.g., whirlpools and vortices in channels: Yang et al. 2020) of such coastal environments, particularly those with large tidal ranges (Brooks et al. 1999), pose challenges to oceanographic modelling efforts, requiring greatly increased computing power, finer bathymetry data resolution, and appropriate-scale spatiotemporal oceanographic data to validate them (Brooks 2004). Such environments may also pose challenges to migrating salmon (Hawkes et al. 2017), perhaps requiring unique behavioural adaptations. Hence, further effort is required to understand the migratory characteristics and behaviours of Atlantic salmon post-smolts during their transition from fresh water to the open ocean.
The objective of the present study was to determine the migratory behaviour of Atlantic salmon post-smolts in a semi-enclosed coastal bay. Using an IBMM, we modelled the dispersal of Atlantic salmon post-smolts using different combinations of behaviour and swimming speed. Model predictions were then compared to empirically derived migration routes and bay residence times of Atlantic salmon post-smolts to determine the most likely navigational cues and swimming speeds that were used during their transition from this coastal bay to the open ocean.

Study area

We modelled the dispersal of Atlantic salmon post-smolts exiting the Magaguadavic River (New Brunswick, Canada) estuary into Passamaquoddy Bay and surrounding waters (Fig. 1). Passamaquoddy Bay is a shallow (averaging 27–36 m, but with a maximum depth of 73 m in particular channels; Bumpus et al. 1959), weakly stratified, and semi-enclosed system with extreme tidal ranges (7–8 m; Trites and Garrett 1983). The mouth of Passamaquoddy Bay is largely blocked off from the Bay of Fundy by the Fundy Isles (Deer Island, Campobello Island, and several smaller islands) aside from two main exit passages (Western Passage and Big L'Etete Passage) and two minor exit passages (Little L'Etete Passage and Doyle's Passage; Fig. 1). Passamaquoddy Bay is also connected to Cobscook Bay, a semi-enclosed system in Maine (United States) (Fig. 1).
Fig. 1.
Fig. 1. Map of the study area in Passamaquoddy Bay (PB), including locations mentioned in the text and predominant regional circulation (a) and locations of receivers and salmon detections during acoustic telemetry work in 2018 (b). Particles and fish entered the bay from the Magaguadavic River estuary (MRE) and left through one of the following passages: Big L'Etete Passage (BLP), Doyle's Passage (DP), Little L'Etete Passage (LLP), and Western Passage (WP). Additional locations plotted in panel (a) include: part of the outer Bay of Fundy (BoF), Campobello Island (CI), Cobscook Bay (CB), Deer Island (DI), Fundy Isles (FI), Head Harbour Passage (HHP), PB, Quoddy Narrows (QN), St. Andrews (SA), and St. Croix River (SCR). Arrows in panel (a) plot the generalized surface circulation in Passamaquoddy Bay during the spring (roughly drawn based on results of Lacroix et al. 2004). In panel (b), white open circles indicate the locations of acoustic receivers deployed during acoustic telemetry work in 2018, while red filled circles represent locations where tagged Atlantic salmon post-smolts were detected during manual tracking. In both maps, the light grey contour line indicates the mean low tide water level, and the dashed red line represents the Canada–United States border. The base map comes from Greenlaw and McCurdy (2014), and the map was produced in QGIS using the EPSG:4326-WGS 84 global coordinate system. [Colour online.]
The ocean circulation of Passamaquoddy Bay is dominated by tidal exchange with the Bay of Fundy, freshwater discharge, and wind-driven surface currents (Trites and Garrett 1983). Tidal currents are strong at the exit passages, particularly at Big L'Etete Passage, where they can reach 2 m·s−1 (Bumpus et al. 1959). Freshwater discharge into the bay is nearly all accounted for by the St. Croix, Magaguadavic, Digdeguash, and Bocabec rivers (Trites and Garrett 1983), with the St. Croix dominating inputs with discharge rates of ca. 42.5–127.4 m3·s−1 (historical annual mean: 62.3 m3·s−1; Bumpus et al. 1959). The large volume of fresh water originating from these rivers, combined with the relatively small size of Passamaquoddy Bay (area of ca. 220 km2), result in a bulk flushing time (i.e., the time for one day's worth of river water input to leave the estuary) on the order of 11–17 days in spring and summer (Ketchum and Keen 1953; Bumpus et al. 1959). Wind speed and direction vary seasonally, predominantly blowing from the southwest in the summer and from the northwest in the winter (Trites and Garrett 1983). Residual currents (net currents after subtracting the linear tidal component of circulation) estimated from classical drift bottle experiments in the bay are dominated by an outward flow in Western Passage and through Head Harbour Passage, and an inward flow through Big L'Etete Passage (Chevrier and Trites 1960) (Fig. 1). The currents in Head Harbour Passage are also affected by the outflow of water originating from Cobscook Bay (Chevrier and Trites 1960; Brooks et al. 1999; Brooks 2004).
The Magaguadavic River wild Atlantic salmon population, like several other wild populations of this species in North America, has declined to very low levels in recent decades (COSEWIC 2010; Hindar et al. 2011; DFO 2014; ICES 2019). This population is part of the Outer Bay of Fundy salmon genetic conservation unit (DFO 2010), which contains highly migratory salmon populations (Lacroix 2008); post-smolts leave their natal rivers to travel northwest to the Labrador Sea (west Greenland), possibly via the North Atlantic Sub-Polar Gyre, where they then spend 1–2+ years feeding and growing at sea before returning to natal rivers as adults to spawn (Dadswell et al. 2010). The population unit here is considered Threatened by the Canadian Species at Risk Act (DFO 2010) but Endangered by COSEWIC (2010), while Atlantic salmon populations in the nearby Inner Bay of Fundy unit, which do not apparently leave the Bay of Fundy at all (Lacroix 2013), are considered Endangered by both (COSEWIC 2010; DFO 2014). This study area thus provides a glimpse into oceanographic conditions faced by wild Atlantic salmon populations in need of conservation (Hindar et al. 2011).
The dispersal of Atlantic salmon post-smolts from the Magaguadavic River has been investigated in Passamaquoddy Bay using acoustic telemetry (Lacroix et al. 2004), as well as in the neighbouring, connected, and oceanographically similar Cobscook Bay (Brooks et al. 1999; Hawkes et al. 2017). Lacroix et al. (2004) noted that the majority (61%–87%) of post-smolts exited via Western Passage, although Big L'Etete Passage usage increased in the summer versus spring, especially for hatchery-reared smolts (84% usage for late migrants), which they argued was due to seasonal changes in the residual currents in Passamaquoddy Bay. A few post-smolts were detected in Head Harbour Passage between Campobello Island and Deer Island, suggesting that they turn northeast after leaving Western Passage and enter the Bay of Fundy via Head Harbour Passage, rather than going directly south through Lubec and the Quoddy Narrows (Lacroix et al. 2004;Fig. 1).

Materials and methods

Physical oceanographic model

We used physical oceanographic data produced by a new implementation of the Finite Volume Community Ocean Model (FVCOM) (Chen et al. 2011) to simulate Atlantic salmon post-smolt dispersal in Passamaquoddy Bay during May–June of 2018. FVCOM is a three-dimensional physical oceanographic model with an unstructured mesh comprising triangular “elements” defined by triplets of “nodes” that vary in size. Unstructured mesh models are ideal for coastal environments as they allow smaller triangles nearer the coast and in channels to better simulate fine-scale nearshore processes (Chen et al. 2011; van Sebille et al. 2018) and larger triangles further offshore for computational efficiency. Element size in the model we used ranged from 25 m nearshore to 11 km offshore (maximum size in Passamaquoddy Bay: ca. 1 km).
The full domain of the model mesh includes the Gulf of Maine, Bay of Fundy, and the Scotian Shelf, but with higher resolution in Passamaquoddy Bay and surrounding areas (in the Outer Bay of Fundy; Fig. 1). Each element/node contains 20 vertical layers, with higher resolution closer to the surface and near the seabed to resolve the surface mixed layer and the bottom boundary layer, respectively. At the air–sea interface, the model is driven by atmospheric forcing from Environment and Climate Change Canada's (ECCC's) High Resolution Deterministic Prediction System. At the lateral open boundaries, the model is forced with daily temperature and salinity from ECCC's Regional Ice Ocean Prediction System (RIOPS); sea-surface height is forced with tides (M2, S2, N2, K1, and O1) from the OSU tidal model and hourly residual sea surface heights from RIOPS. The model includes freshwater input from eight rivers with data from ECCC, NB Power, and JD Irving, and includes two rivers discharging into Passamaquoddy Bay: the St. Croix and Magaguadavic. Additionally, discharge from the Digdeguash River is included in the model, but since there are no data available for this river, its discharge is based on relative watershed areas of the Digdeguash and Lepreau rivers and the discharge of the Lepreau River (also included in the model). Although the Magaguadavic River is closer to the Digdeguash river, it was not used for this calculation as it has a dam which may impact the discharge rate. The model was initiated with temperature and salinity fields from RIOPS and ramped up from rest over an 18 h period with a total simulation period from 1 January 2018 to 30 September 2018. This project used a subset of the output from 25 May to 20 June 2018. The model allows wetting and drying of the nodes (i.e., elements becoming “dry” at low tide temporarily removed from the model flow field until they “wet” again at high tide) to account for the intertidal coastal regions that result from the large tides in the area (Greenberg et al. 1998). FVCOM has been widely used to simulate oceanography in various regions throughout the world (Chen et al. 2011), including in Passamaquoddy Bay and surrounding waters (e.g., Page et al. 2015; Yang et al. 2020), where its past outputs have been validated as reasonable representations of local currents and hydrography.
The FVCOM output contained values at each mesh element and node for each vertical layer at 1 h intervals. The following physical oceanographic variables were included in the model output: current velocities, with east–west, north–south, and vertical components; water temperature; salinity; sea-surface height (reflecting tidal changes in water depth); and element wet/dry status.

Physical model evaluation 1: model tide, current, temperature, and salinity fields

The modelled sea-surface elevation was compared against tide gauge data from Eastport, Maine (see Fig. S1), the nearest available sea-level recording station. The model reproduced the tidal variation of the sea surface height with no phase shift, but underestimated the magnitude of the tidal amplitude. The root mean square error in sea-surface height, defined as , where xm and xo are the modelled and observed sea-surface heights, respectively, was 37 cm and is approximately 10% of the maximum tidal amplitude.
Comparison of the modelled residual currents at 1 m below the surface (Fig. 2) qualitatively agree with the large-scale features of the region discussed in the literature (Fig. 1; Trites and Garrett 1983). Due to the difficulty of collecting current data near the surface using upward-facing bottom-mounted acoustic current meters, the near-surface model current field was validated by comparing simulated and observed surface drift tracks (see section “Physical model evaluation 2: Lagrangian comparisons to drifter tracks”). This comparison is appropriate as the model is being used for predicting Lagrangian drift.
Fig. 2.
Fig. 2. Model current fields interpolated to 1 m below the sea surface and averaged over the period of 25 May to 20 June 2018 to produce residual current fields. Map produced using the “coord_quickmap” function in the R package “ggplot” (Wickham 2009; R Core Team 2019) based on FVCOM model mesh coordinates (projection modified from NAD83; Chen et al. 2011). [Colour online.]
Within the Passamaquoddy Bay area, modelled mean near-surface temperature and salinity fields (see Fig. S2) indicate that horizontal variations are within a few degrees Celsius and a couple of practical salinity units (psu). This is qualitatively similar to historically observed patterns (Trites and Garrett 1983; Robinson et al. 1996). Direct comparisons between modelled and observed temperature and salinity were made at three locations (Figs. 3, S3, and S4). At all three locations, the modelled temperature and salinity at 1 m below the sea surface fall within the variability of the observed 2010 to 2020 seasonal cycles (Figs. 3 and S4). At Prince 7, the only station in the modelled salmon migration pathway (Fig. S3), the model underestimates near-surface temperature by 2 °C and overestimates near-surface salinity by 4 psu during May 2018 (Fig. 3). In June 2018, the modelled near-surface temperature agrees well with the observed value and the near-surface salinity is overestimated by less than 1 psu. In both months, the model underestimates near-surface stratification (Figs. 3 and S4).
Fig. 3.
Fig. 3. Comparison of temperature (a) and salinity (b) between model results (red) and observations in 2018 (blue) at Prince 7, located at 45.134°N, 67.010817°W (see Fig. S3), at 1 m below the sea surface. Prince 7 data collected from 2010 to 2020 (black) are also shown (see also Fig. S4). [Colour online.]

Salmon tracking, observed residence time, and migration routes

An acoustic telemetry project was conducted in Passamaquoddy Bay in 2018 to provide empirical data to evaluate the IBBM's predictions. Detailed methods and results of this telemetry work will be published separately in the future (B.M. Wilson, Fisheries and Oceans Canada, unpublished data), but are briefly described here (see also Wilson et al. 2022). A total of sixty Atlantic salmon smolts from the Tobique River (a tributary of the Saint John River, New Brunswick, Canada) reared at the Mactaquac Biodiversity Facility were surgically implanted with Vemco V8 acoustic tags and released at the head of tide in the Magaguadavic River estuary on 25 May (n = 30) and 6 June (n = 30) of 2018 at low tide during daylight hours. Mean ± SD size of the tagged post-smolts was 16.7 ± 6.4 cm fork length (FL) and 42.1 ± 4.9 g mass. Tags transmitted at a random interval of 20–40 s (averaging 30 s) for 20 days, and subsequently were set to transmit at 60–120 s (averaging 90 s) for the remainder of their battery life. For these tags, the expected detection range of the receivers was approximately 400–500 m under calm sea conditions (wind speed <6 knots). Acoustic receivers (n = 29) were deployed in Passamaquoddy Bay during the spring of 2018, including at the mouth of the Magaguadavic River estuary and at each of the bay's four exit routes—Big L'Etete Passage, Doyle's Passage, Little L'Etete Passage, and Western Passage—as well as at other points in the river and bay (Fig. 1). Manual tracking elsewhere was also conducted over the course of the study to locate fish at intermediate points in the bay (Wilson et al. 2022). Two acoustic gates were deployed at each exit route of Passamaquoddy Bay to increase the likelihood of detecting fish leaving the bay and to determine their direction of travel. Fish were considered to have left Passamaquoddy Bay if they were last detected on the outermost gate in any exit route, and the exit route of each post-smolt was determined by the location of the outer gate at which it was last detected. Residence time in Passamaquoddy Bay was estimated as the difference between the last detection time at the exit route and the last detection time at the mouth of the Magaguadavic River estuary. Detections of the 53 tagged fish that left the estuary were used as empirical (observed) data, against which modelled particle trajectories were then compared. The remaining seven fish were not detected at the mouth of the estuary and were presumed to have died in the estuary of the Magaguadavic River prior to reaching Passamaquoddy Bay.

Individual-based biophysical (particle tracking) model

Atlantic salmon post-smolts were treated as particles advected by currents from the FVCOM simulation using a semi-Lagrangian IBBM with an offline particle tracking code (PTrack) developed for use with FVCOM (available online at, with some modifications (described below). The code was written in FORTRAN and runs in a Linux environment.
Particles (i.e., Atlantic salmon post-smolts) were released at the mouth of the Magaguadavic River estuary (Fig. 1) at random locations within 500 m of the receiver placed there during the acoustic telemetry work done in the area in 2018 (see above and Wilson et al. 2022). The number of particles released (n = 53) corresponded to the number of Atlantic salmon post-smolts that successfully reached the mouth of the estuary during the 2018 acoustic telemetry project. The particles were released at times these fish had last been detected at the Magaguadavic River estuary receiver (i.e., when they “left” the estuary) (ranges: 04:02 on 26 May to 19:21 on 27 May and 23:57 on 6 June to 04:39 on 9 June, 2018, all times in Atlantic Daylight Time (ADT, UTC − 3 h)). All particles were then tracked for 10 days, as telemetry work in 2018 (Wilson et al. 2022) indicated that the residence time of Atlantic salmon post-smolts in the area was less than 10 days. For simplicity, no mortality of particles was included in simulations, as our objective was to estimate the migration patterns of Atlantic salmon post-smolts based on oceans currents and different behaviours alone.
Particle positions were updated every 5 min (300 s) based on calculated advection with currents, horizontal diffusion (random walk), and then programmed behaviour. First, particle advection as a result of currents was calculated using a fourth-order Runge–Kutta discretization scheme to solve differential equations of particle velocity by iteration. Values of physical variables (e.g., currents) in the element and depth in which a particle resided at each 5 min time step were linearly interpolated between 1 h FVCOM time steps and vertical layers. Although the FVCOM simulation provides three-dimensional current fields, most previous studies that tracked the vertical positions of migrating Atlantic salmon post-smolts showed that they spent most or all of their time within the upper 1–2 m of the water column at this life stage (but with some evidence of short-term deeper dives (Davidsen et al. 2008; Manel-La et al. 2009; Renkawitz et al. 2012; Guðjónsson et al. 2015)). Thus, most modelling studies have also limited salmon to the surface layer during dispersal simulations (Table 1, and references therein), so particles in simulations herein were likewise forced to remain in the surface layer (depth = 1.0 m below the surface) and did not undergo vertical migration. Second, a random walk algorithm was applied, which gives particles an extra “kick” to randomly shift their trajectory beyond current-based advection at each time step to account for the influence of oceanographic processes occurring at scales smaller than the model elements (e.g., coastal eddies, diffusion, prey capture; van Sebille et al. 2018) on particle dispersion. A horizontal diffusivity value of 0.100 m2·s−1 was used in the random walk to determine the extent of trajectory slurring that it could calculate, as this value was previously found to be reasonable for the studied region (Page et al. 2015). To account for stochasticity introduced by the random walk term, we carried out 1000 identical runs of each simulation (i.e., of each behaviour–swim speed combination), in which particles corresponding to each of the 53 tagged fish were released. Model outputs analyzed were thus the averages of 1000 replicate simulations of 53 particles/fish. Lastly, particle positions were further modified based on the programmed salmon behaviour under consideration, as outlined in a later section.
During all simulations, a “no-slip” condition was applied to stop particles from moving (freeze them for the current time step) if their trajectory in a given time step would put them out of the model domain (i.e., on land; van Sebille et al. 2018). In addition, when particles were programmed to exhibit particular migratory behaviours (potentially continuously directing them landward and getting them “stuck” along the shore), a “free-slip” condition was applied to make their trajectory shift away from land and let them continue moving when they were located close to shore. Many different approaches have been used to simulate active land avoidance by Atlantic salmon in previous studies, including shifting trajectories to be parallel to the coast or weighted away from the coast if close to land (Mork et al. 2012; Byron et al. 2014; Moriarty et al. 2016). Given the abundance of land and narrow channels partially enclosing the mouth of Passamaquoddy Bay, these approaches did not work very well here (results not shown). Hence, an alternative approach was developed herein that avoided land with reasonable success in this system. Specifically, when a particle was located in an element with a depth of 10 m or less (representing most near-land water depths in Passamaquoddy Bay; Trites and Garrett 1983), that particle was set to “search” the elements immediately surrounding the one in which it resided during that time step and shift its trajectory towards the element with the greatest depth. This behaviour was essentially identical to the depth orientation behaviour tested below, but was only enacted in elements ≤10 m in depth, while otherwise different behaviours could be used by particles. Preliminary tests were performed using shallower depth limits in this free-slip condition (e.g., 0, 2.5, and 5 m; results not shown). These shallower depths did not work for all behaviours and swim speeds tested (i.e., particles could still “jump” onto land in such cases), but when they did work they did not result in categorically different overall results for particle residence times, exit success, and exit usage (B.K. Quinn and M. Trudel, unpublished data). Results for the 10 m limit, which did work for all tested behaviours, were thus analyzed and presented herein.

Physical model evaluation 2: Lagrangian comparisons to drifter tracks

To test the physical oceanographic model (FVCOM) output for the Passamaquoddy Bay area used herein, 10 experimental surface drifters equipped with SPOT Trace© GPS tracking devices (SPOT LLC, 2018) were released in the study area. GPS units transmitted their position every 5 min (300 s), provided they were in motion. In 2018, five drifters were released on 26 May (from ca. 13:42 to 13:45 ADT), and five more were released on 7 June (from ca. 09:50 to 10:16 ADT) (Table S2), at the mouth of the Magaguadavic River estuary. The mean ± SD drift duration of the 10 drifters was 1.7 ± 1.0 days overall (range: 0.2–3.9 days; Table S2). We used the particle dispersal model to predict the trajectories of virtual particles with deployment dates, times, release locations, and drift durations corresponding to those of these 10 drifters. Particles remained at 1.0 m below the surface of the water column and drifted passively in these model simulations. Two set of simulations were run: one with the random walk term turned off (deterministic) to assess dispersal based solely on modelled currents, with 10 particles tracked (each representing one drifter); and another with the random walk turned on (variable) to assess the potential variability in model trajectories, with 10 sets of 10 replicate particles tracked (each set representing one of the drifters, 100 particles in total). Modelled particle tracks were then extracted and plotted alongside observed drifter tracks for comparison. The final position of each particle and its corresponding drifter relative to their release location was also compared through the calculation of model error (Err) values (Chassé and Miller 2010, their eq. 10) as follows:
where Ao and Am are the amplitude of displacement (distance in km, from start to end position) of the observed drifter and modelled particle, respectively, and φo and φm are the observed and modelled direction (angle) of displacement, calculated to the initial position relative to the end position. The Err values represent the combined deviation of modelled drift end points from observed ones, accounting for both the magnitude and directionality of differences; lower values imply greater agreement between modelled and observed dispersal. Values calculated were normalized relative to 24 h of drift, to control for differences in overall drift times among drifters. The overall distribution of Err values was compared to zero and increasing test values (1, 2, 3, and 4 km) for “deterministic” and “variable” model outputs (n = 10 per test) using one-sample t-tests in IBM SPSS Statistics 22.

Salmon behaviours

In the present study, we tested several relatively simple behaviours that may help Atlantic salmon post-smolts travel from the Magaguadavic River estuary seaward towards the exits of Passamaquoddy Bay (Table 2). First, we ran a simulation in which particles underwent passive dispersal (i.e., no behaviours other than “no-slip” land avoidance when close to shore) with a swim speed of 0 cm·s−1; this was included as a “null hypothesis” to demonstrate how Atlantic salmon dispersed without using any particular behaviour. Then, we tested three kinds each of current-following (rheotaxis), cue-based orientation, and directed swimming (Table 2). We tested three behaviours that included rheotaxis, in which particles either exhibited (i) negative or (ii) positive rheotaxis at all times or (iii) switched from negative to positive rheotaxis on the ebb and flood phases of the tidal cycle, respectively. The last of these was chosen as a simple example of how rheotaxis may vary with tidal phase, although other, more complex options would be reasonable to test (e.g., post-smolts may follow currents but swim slower on flood than ebb tides; LaBar et al. 1978; Lacroix and McCurdy 1996) and could be considered in future studies. For orientation based on other localized cues, we focused on the possibility that post-smolts follow gradients in water depth, salinity, or temperature to guide them out of Passamaquoddy Bay. Because Passamaquoddy Bay is relatively small, cool, and well-mixed for much of the year due to its large tidal range, local spatial horizontal gradients in temperature and salinity are somewhat weak (Trites and Garrett 1983; Robinson et al. 1996; Lacroix et al. 2004; Fig. S2). This meant that scenarios directing post-smolts to swim towards a preferred thermal, salinity, etc. “zone” like in past studies (Table 1) would not work very well in this region (Fig. S2). Therefore, we examined behaviours in which particles oriented their trajectories at each time step based on (iv) water column depth, (v) salinity, or (vi) temperature. We included depth here even though, in reality, fish likely do not sense water depth. However, migrating salmon have been observed to remain within particular depth contour zones in the Pacific (Siwicke et al. 2019) or in deeper-water parts of the Bay of Fundy system (Lacroix 2013). In these cases, fish may use other cues correlated with depth to navigate from the coast to offshore feeding grounds, including a magnetic compass sense or following prey. In these simulations, each particle “searched” the ≤12 elements surrounding and sharing vertices (nodes) with the one in which it resided, and then oriented its trajectory towards the element with either the highest (depth or salinity) or lowest (temperature) value of the cue in question. Lastly, we tested scenarios in which particles moved in a particular compass direction. We first tested the possibility that (vii) salmon swim without any particular directionality (randomly, as in Booker et al. 2008); in this scenario, particles swam in a random (but non-landward) direction at a specified speed at each time step. After this, we tested swimming by Atlantic salmon post-smolts in all cardinal (N, S, E, and W) and primary intercardinal (NE, SE, SW, and NW) directions. However, we only analyzed, present, and discuss results for two of these directions—(viii) south and (ix) southwest—since these were the only directions that allowed particles to leave Passamaquoddy Bay within 10 days.
Table 2.
Table 2. Overview of the different types of behaviours and swimming speeds tested in the model in this study (x = tested, dash (—) = not tested); see “Materials and methods” for details.

Swimming speed

For each of the nine types of behaviours described above, we conducted simulations in which particles swam at different speeds (BL·s−1; Table 2). As the mean size of the tagged post-smolts (in 2018) that these particles represented was 16.7 cm FL, a speed of 1 BL·s−1 corresponded to 16.7 cm·s−1. Given the short duration of these simulations (10 days), fish growth would be minimal (<1 cm based on their length at ocean entry; Jonsson and Jonsson 2007); hence, we did not account for fish growth and its effects on swimming speeds like some previous studies over longer time periods have done (Mork et al. 2012; Byron et al. 2014). Previous studies modelling the dispersal of Atlantic salmon post-smolts have generally tested speeds of up to 2.5–3.0 BL·s−1, and most concluded that a realistic speed was approximately 1.2–2.0 BL·s−1 (Table 1). Some laboratory studies have suggested that salmon post-smolts are capable of swimming at higher speeds (Peake 2008), although it is unclear whether these can be sustained over long periods (Hvas and Oppedal 2017; Hvas et al. 2021). Estimates of optimal cruising speed and how it is impacted by temperature, body mass, and salinity, exist for a few other salmon species (Trudel and Welch 2005), but not for Atlantic salmon post-smolts of the tested size; hence, we tested a range of different, but seemingly reasonable, swimming speeds. Since speeds exceeding 3.0 BL·s−1 may approach or exceed the critical swimming speeds of Atlantic salmon (e.g., 75–92 cm·s−1, or 2.1–2.7 BL·s−1 for a 35–36 cm FL fish, Hvas et al. 2017; 2.2 BL·s−1 sustained for 72 h or 2.7 BL·s−1 for 2 h, Hvas et al. 2021) and have not been used or considered effective in past modelling studies (Table 1), we tested swimming speeds ranging from 0.5 to 3.0 BL·s−1, at 0.5 BL·s−1 increments. This resulted in six different speeds per behaviour, for a total of 55 different simulations (9 behaviours × 6 speeds, +1 passive simulation; Table 2). We also tested higher speeds of 3.0–6.0 BL·s−1, although these generally did not improve the ability of particles to leave Passamaquoddy Bay, and in many cases actually decreased particles’ exit success by trapping them in small bays, bypassing exit routes, or returning through exits after having temporarily left Passamaquoddy Bay (results not shown).

Biophysical model evaluation: comparisons to telemetry data

To determine the most realistic combination of behaviour and swimming speed (Table 2) that Atlantic salmon post-smolts likely use to transit Passamaquoddy Bay (i.e., exit the Magaguadavic River estuary to reach the Bay of Fundy), we compared a series of metrics from the model simulations to results obtained from an acoustic telemetry project conducted in that area in 2018. For each tracked and simulated fish (and in each behaviour + speed simulation), its residence time in Passamaquoddy Bay was calculated as the number of days elapsed from when it left the Magaguadavic River estuary to when it was last detected at one of the outer receiver arrays in one of the bay's four exit passages. Whether each fish or particle successfully left the bay (i.e., was last detected at one of the outer arrays rather than at an inner receiver or without having ever reached one of the outer arrays) and the route it used to leave Passamaquoddy Bay was also recorded. Because of the close proximately of the outer arrays at Big L'Etete, Little L'Etete, and Doyle's Passages, it was very common for a fish/particle that had actually left the bay through Big L'Etete Passage to be last detected at one of the other eastern passages, so at times these three exits (i.e., all but Western Passage) were grouped together under the name “L'Etete passages” herein. We then calculated the mean ± 95% confidence interval (CI) residence time of all observed fish or simulated particles (n = 53) in Passamaquoddy Bay (omitting all fish that failed to exit within 10 days from the calculation of the mean), as well as the mean ± 95% CI (across replicate simulations) percentage (%) that successfully exited Passamaquoddy Bay (exit success) and the percentage of exiting particles or fish that exited via Western Passage rather than one of the L'Etete passages (exit route used). We assessed whether modelled residence time, exit success, and Western Passage usage for each behaviour–swim speed combination significantly differed from empirical data by analysis of confidence intervals (Cumming et al. 2007): if the overall modelled mean was within the 95% CI of the observed mean, or vice versa, the modelled mean was not considered significantly different (P > 0.05) from the observed mean.
To select the overall most realistic behaviour–swim speed combination based on all three of the above endpoints (with different units—days vs. %), we developed a model performance index (PI, range from 0 to +∞) analogous to the chi-square distribution as follows:
where PR and OR are the overall mean predicted (from the model) and observed (from acoustic telemetry) residence time, PE and OE are the mean predicted and observed percentage exiting the bay, and PW and OW are the mean predicted and observed percentage exiting the bay through Western Passage. The best behaviour–speed combination was that which resulted in the minimum PI value (closest to 0), while higher values indicated poorer combinations, so PI values allowed model outputs to be ranked. If no simulated particles in a simulation left Passamaquoddy Bay in 10 days, there was no residence time value and thus no PI could be calculated, but this could be considered as the “worst” behaviour. The 95% CI of overall PI values were also calculated, which allowed comparisons among model outputs in overall performance. Dividing each of the three terms on the right-hand side of eq. 2 by the PI also allowed us to calculate the proportion of the PI due to deviations from observed residence time, exit success, and Western Passage use.
Representative maps of particle tracks using different modelled behaviours and swim speeds were generated by selecting a “typical” simulation from among the 1000 replicates for each behaviour–speed combination. This was one of the replicate model outputs that had performance endpoints (residence time, exit success, migration route usage, and PI value) equal or closest to the overall means for that behaviour–speed combination.


Validation of physical oceanographic model with GPS-equipped experimental drifters

Most (6/10) drifters released from the Magaguadavic River estuary were carried to end locations along the northeastern shore of Passamaquoddy Bay, between the Magaguadavic River estuary and the Digdeguash River estuary, while the remainder (4/10) ended up in southwestern Passamaquoddy Bay (Fig. 4). Drifters released in May tended to drift further and more to the southwest than those released in June (Fig. 4). Model-predicted dispersal of passive particles representing these drifters was generally similar to observed drifter dispersal, with some exceptions (Fig. 4). The random walk (“variable” simulations) caused particles released at the exact same place and time to fan out after their release, and within 1–2 days they could end up anywhere from the northeast to the southwest parts of Passamaquoddy Bay. Particles in “deterministic” (no random walk) simulations usually ended relatively close to observed drifters (2/5 in May and 4/5 in June) (Fig. 4). In general, the area of Passamaquoddy Bay spanned by “variable” modelled particles contained the observed drifter tracks (Fig. 4). The model tended to under- (3/5) or overestimate (2/5) total drifter displacement in May, whereas in June it mostly estimated comparable (low) displacement to observed (4/5), overestimating in only one case (Fig. 4). The calculated model error (Err) per 24 h for drifters ranged from 1.5 to 7.5 km (mean ± SD: 3.9 ± 2.3 km) for “deterministic” simulations and from 1.8 to 7.8 km (mean ± SD: 4.6 ± 1.7 km) for simulations with a random walk (“variable”, each value being the mean of 10 replicates per drifter) (see Fig. S5 for values per drifter/simulation). The overall distributions of model error values obtained differed significantly from zero (null model of no error) for both “deterministic” (t9 = 5.5, P < 0.001) and “variable” outputs (t9 = 8.5, P < 0.001). They were also significantly higher than test error values of 1–2 and 1–3 km, respectively, for these (“deterministic”: t9 ≥ 2.7, P ≤ 0.03; “variable”: t9 ≥ 2.9, P ≤ 0.02). However, overall errors were not significantly higher than values of 3 km (“deterministic”: t9 = 1.3, P > 0.2) and 4 km (“variable”: t9 = 1.0, P > 0.3). These overall model errors indicate that the physical model could predict observed dispersal endpoints with an error rate of ca. 3.9–4.6 km per 24 h; this was comparable to the mean 4.7 km per 24 h found by Chassé and Miller (2010) for their model of the southern Gulf of St. Lawrence.
Fig. 4.
Fig. 4. Observed (orange-red) and modelled dispersal tracks of experimental surface drifters released from the Magaguadavic River estuary (MRE) mouth (star) on 26 May and 7 June 2018. Modelled tracks include those produced from “deterministic” (no random walk) simulations (blue, 1 particle per drifter) and “variable” (with random walk) simulations (black, 10 replicate particles per drifter). Solid squares indicate the ends of drift tracks. Separate panels show tracks each representing May Drifters #1–5 (ae) and June Drifters #1–5 (fj), respectively (see Table S2 for deployment details). In four of the June releases (Drifters #1 and 3–5), no tracks left the immediate area northeast of the MRE (bottom left in these panels). Red text in the upper-left corner of each panel indicates the time (d = days) each drifter was tracked. Map produced in QGIS (base map from Greenlaw and McCurdy (2014); coordinate system: EPSG:4326-WGS 84).

Telemetry results

Tagged smolts released in the Magaguadavic River estuary resided in Passamaquoddy Bay on average for 4.6 days (range of 1.5–9.8 days; Figs. 5a–5i and Table S1). Similar to Lacroix et al. (2004), most post-smolts were initially detected along the north shore of Passamaquoddy Bay by manual tracking within the 5–10 m depth contour rather than along the shore to the south (Wilson et al. 2022), suggesting that the initial dispersal within Passamaquoddy Bay was counterclockwise. A total of 45 out of 53 Atlantic salmon post-smolts tracked in 2018 by acoustic telemetry successfully left Passamaquoddy Bay, so the mean observed exit success was 84.9%. Most post-smolts exited Passamaquoddy Bay through Western Passage (39/45 fish = 86.7%) rather than the eastern L'Etete passages. Model results were compared against these “observed” values (Figs. 5a5i).
Fig. 5.
Fig. 5. Performance of different modelled rheotaxis (ac), cue-based orientation (df), and compass directional swimming (gi) behaviours. Mean (±95% CI) residence times (days; a, d, g), exit success (%; b, e, h), and use of Western Passage as an exit route (%; c, f, i) of simulated (different colours and symbol types) and tagged fish (dashed horizontal lines) in/from Passamaquoddy Bay (total n = 53 for exit success, n = 53 × exit success for use of Western Passage). If a given behaviour resulted in no fish exiting the area, a residence time of 11 days is reported for illustrative purposes only. A white asterisk (*) inside a point indicates that results significantly differed from observed (analysis of 95% CI, P < 0.05); note that some significant and non-significant points overlap. The actual values and significance plotted in this figure can be found in the Supplementary material (Table S1). [Colour online.]

Passive dispersal

Particles drifting passively with currents were predicted to require 7.6 days on average to leave Passamaquoddy Bay through any of the passages in the model simulations, which was significantly (analysis of confidence intervals, P < 0.05) longer than observed (mean: 4.7 days (95% CI: 4.0–4.9 days); Figs. 5a–5d, and 5g). Less than 30% (significantly fewer than observed, P < 0.05) were predicted to leave Passamaquoddy Bay within 10 days (Figs. 5b–5e, and 5h). Moreover, only 13% (significantly fewer than observed, P < 0.05) of the particles that left Passamaquoddy Bay by passive drift were predicted to do so via Western Passage (Figs. 5c–5i and 6).
Fig. 6.
Fig. 6. Tracks of modelled particles released from the Magaguadavic River estuary (MRE) in 2018 and drifting passively (n = 53), with dispersal tracked for ≤10 days. The star marks the location at which particles were released. Solid black squares indicate the positions of particles representing different tagged fish at the end of a simulation (i.e., after 10 days), while blue lines represent their positions at intermediate 5 min model time steps; a white number inside a square indicates that multiple particles ended up at that position. Locations are labelled as in Fig. 1a. Positions of particles that dispersed beyond the indicated spatial range are not shown, but can be found in Fig. S6. In this and subsequent map figures, the results of a single “typical” simulation (out of the 1000 replicate simulations performed) are shown as a representative example of model outputs. Map produced in QGIS (base map from Greenlaw and McCurdy (2014); coordinate system: EPSG:4326-WGS 84). [Colour online.]


Particles “swimming” with currents (i.e., moving in the same direction as currents, exhibiting negative rheotaxis) at all times were predicted to spend less time in Passamaquoddy Bay and have higher exit success relative to passive drift (Figs. 5a, 7a, and 7b). At all speeds (0.5–3.0 BL·s−1), residence times with this behaviour were comparable to and not significantly different from observations from acoustic telemetry (P > 0.05; Fig. 5a). At speeds of 2–3 BL·s−1, the number of particles that exited Passamaquoddy Bay did not significantly differ from the observed number (P > 0.05), although at lower speeds (0.5–1.5 BL·s−1) significantly fewer successfully left (P < 0.05; Figs. 5b, 7a, and 7b). However, only 16%–39% of the particles using negative rheotaxis were predicted to leave Passamaquoddy Bay via Western Passage, which was significantly less (P < 0.05) than the 87% (95% CI: 73%–95%) observed for acoustically tagged fish (Fig. 5c).
Fig. 7.
Fig. 7. Tracks of modelled particles released from the Magaguadavic River estuary (MRE) and tracked for 10 days while using current-following behaviours (rheotaxis) as follows: negative rheotaxis (swimming with current) (a, b); positive rheotaxis (swimming against current) (c, d); tide-varying rheotaxis (swimming with current on ebb tide, against current on flood tide) (e, f); with speed = 0.5 BL·s−1 (a, c, e) or speed = 2.0 BL·s−1 (b, d, f). Star, release point; squares, particle positions at end of simulation (numbers indicate overlap); blue lines, particle tracks. Positions of particles that dispersed beyond the indicated spatial range are not shown, but can be found in Fig. S7. Map produced in QGIS (base map from Greenlaw and McCurdy (2014); coordinate system: EPSG:4326-WGS 84). [Colour online.]
Conversely, particles moving against currents (i.e., using positive rheotaxis) at all times were predicted to spend more time in Passamaquoddy Bay and have lower exit success relative to passive drift, particularly at swimming speeds greater than 1 BL·s−1 (Figs. 5a–5b, 7c, and 7d). Indeed, few (1.9%) to none of the particles were predicted to leave Passamaquoddy Bay successfully at speeds of 2 BL·s−1 or higher using positive rheotaxis (Figs. 5b and 7d). Additionally, less than 6% of exiting particles using positive rheotaxis were predicted to leave Passamaquoddy Bay via Western Passage at a swimming speed of 0.5 BL·s−1, and none left by this route at speeds of 1 BL·s−1 or higher (Figs. 5c, 7c, and 7d).
Similar to results for negative rheotaxis, particles switching the direction of their rheotaxis based on the phase of the tide (i.e., negative/with currents on the ebb, positive/against currents on the flood) were also predicted to spend less time in Passamaquoddy Bay relative to passive drift (Fig. 5a). Residence time in Passamaquoddy Bay and exit success were predicted to be similar to and not significantly different from observed values at swimming speeds of 0.5–1.0 and 1.5–2.0 BL·s−1, respectively (P > 0.05), but significantly shorter and higher, respectively, at swimming speeds of 1.5–3.0 and 2.5–3.0 BL·s−1 (Figs. 5a–5b, 7e, and 7f). Exit success for 0.5 BL·s−1 was also significantly less than observed (P < 0.05; Fig. 5b and Table S1). However, less than 20% of the particles using tide-varying rheotaxis were predicted to leave Passamaquoddy Bay via Western Passage at all swimming speeds (all significantly lower than observed, P < 0.05), and none used this route at 3.0 BL·s−1 (Figs. 5c, 7e, and 7f).

Orientation based on depth, salinity, or temperature

Most particles orienting their direction of movement based on increasing depth at swimming speeds of 1.5 BL·s−1 or higher were either trapped within Passamaquoddy Bay or repeatedly left and re-entered Passamaquoddy Bay, as this behaviour did not provide sufficient directional information to help them leave Passamaquoddy Bay within 10 days (Figs. 5d–5f, and 8b). At low/intermediate speeds, this behaviour actually resulted in residence times and exit success close to those observed in telemetry data, and the difference for both variables was non-significant at 0.5 BL·s−1 (P > 0.05; Table S1; Figs. 5d–5e, and 8a). However, the proportion of particles leaving Passamaquoddy Bay via Western Passage in this case was still significantly less than observed by acoustic telemetry (<40% vs. 87%, respectively, P < 0.05; Figs. 5f, 8a, and 8b).
Fig. 8.
Fig. 8. Tracks of modelled particles released from the Magaguadavic River estuary (MRE) and tracked for 10 days while using orientation behaviours as follows: orientation towards increasing water depth (a, b); orientation towards increasing salinity (halotaxis) (c, d); orientation towards decreasing temperature (thermotaxis) (e, f); with speed = 0.5 BL·s−1 (a, c, e) or speed = 2.0 BL·s−1 (b, d, f). Star, release point; squares, particle positions at end of simulation (numbers indicate overlap); blue lines, particle tracks. Note: in panel (b), all particles remained within the MRE, as indicated by the inset. Positions of particles that dispersed beyond the indicated spatial range are not shown, but can be found in Fig. S8. Map produced in QGIS (base map from Greenlaw and McCurdy (2014); coordinate system: EPSG:4326-WGS 84). [Colour online.]
Particles orienting based on increasing salinity or decreasing temperature resulted in them having similar or slightly shorter residence times to those observed in telemetry data at 0.5–2.0 BL·s−1, although differences from observations were statistically significant (P < 0.05) at all but two cases: salinity orientation at 1.0 BL·s−1 and temperature orientation at 0.5 BL·s−1 (Figs. 5d, 8c–8f, and Table S1). Many particles swimming at high speeds towards higher salinity or lower temperature actually did temporarily (and repeatedly) exit Passamaquoddy Bay, mainly on ebb tides through Big L'Etete Passage, but then returned to the bay through this passage on the flood tide (Figs. 8c–8f). As a result, fewer fish successfully exited Passamaquoddy Bay than observed (Figs. 5e and 8c–8f), and those that successfully left Passamaquoddy Bay did so primarily from the L'Etete passages rather than Western Passage (Figs. 5f and 8c–8f). Exit success and Western Passage usage were thus significantly less than observed for both these behaviours at all speeds (P < 0.05; Figs. 5d and 5e).

Directional swimming

Residence time in Passamaquoddy Bay for particles moving in random directions was similar to that of passively drifting particles at all speeds (ca. 6–8 days), and either not significantly different from observed values (at 0.5–1.5 BL·s−1, P > 0.05) or significantly longer than observed (at 2–3 BL·s−1, P < 0.05; Fig. 5g). Slightly more particles exited the bay in this scenario than with passive drift, but the number of fish leaving the bay was about half (30%–50% exit success) of that observed (87%) at all speeds (Figs. 5h, 9a, and 9b). However, typically less than 30% of the particles that left Passamaquoddy Bay did so through Western Passage (Figs. 5i, 9a, and 9b). Exit success and Western Passage usage were thus again significantly less than observed for this behaviour at all speeds (P < 0.05; Figs. 5h and 5i).
Fig. 9.
Fig. 9. Tracks of modelled particles released from the Magaguadavic River estuary (MRE) and tracked for 10 days while using directional swimming behaviours as follows: swimming in random directions (a, b); swimming directly south (c, d); swimming southwest (e, f); with speed = 0.5 BL·s−1 (a, c, e) or speed = 2.0 BL·s−1 (b, d, f); results not shown for other swimming directions. Star, release point; squares, particle positions at end of simulation (#s indicate overlap); blue lines, particle tracks. Positions of particles that dispersed beyond the indicated spatial range (e.g., in panel (d), the majority of particles) are not shown, but can be found in Fig. S9. Map produced in QGIS (base map from Greenlaw and McCurdy (2014); coordinate system: EPSG:4326-WGS 84). [Colour online.]
Swimming in a southward direction at 0.5–2.5 BL·s−1 was the behaviour that best enabled particles to leave Passamaquoddy Bay in model simulations (Fig. 5h). Particles that swam south at these speeds as soon as they were released at the mouth of the Magaguadavic River estuary had an average residence time in Passamaquoddy Bay between 1.4 and 3.3 days, and all or nearly all (range: 47–53/53 fish = 88.7%–100%) of them successfully left the bay (Figs. 5g–5h, 9c, and 9d). Many of these particles could even cross the Bay of Fundy and reach southwest Nova Scotia within 10 days if they swam south (see Figs. S9c and S9d). However, these particles were predicted to have a significantly shorter residence time at all speeds than observed (P < 0.05; Fig. 5g). Exit success was not significantly different (P > 0.05) from observed with this behaviour at some speeds (1.0, 1.5, and 2.5 BL·s−1), but significantly (P < 0.05) higher (at 0.5 and 2.0 BL·s−1) or lower (at 3.0 BL·s−1) at others (Figs. 5h, 9c, and 9d). Almost none of the particles swimming south (<4% and often 0%) left via Western Passage—rather, most or all particles left through the L'Etete passages with this compass direction (mainly Big L'Etete Passage; Figs. 5i, 9c, and 9d).
Particles moving southwest had mean residence time and exit success similar to and not significantly different (P > 0.05) from those observed by telemetry at a swim speed of 0.5 BL·s−1 (Figs. 5g–5h, and 9e). Residence times were slightly and significantly (P < 0.05) shorter than observed values at 1.0–1.5 BL·s−1, and not significantly different from observations at 2.0 BL·s−1 (Fig. 5g). Exit success out of Passamaquoddy Bay was generally and significantly (P < 0.05) lower than observed for particles moving southwest at all speeds of 1–3 BL·s−1 (Figs. 5f–5h, and 9e). At high speeds (2–3 BL·s−1), all particles moving southwest failed to exit Passamaquoddy Bay (Fig. 5i and Table S1) because they were trapped along the western shore of Passamaquoddy Bay or inner Western Passage or Cobscook Bay, Maine (Fig. 9f). Interestingly, the majority of particles that exited Passamaquoddy Bay while swimming southwest at 0.5, 1.5, or 2.0 BL·s−1 were predicted to leave through Western Passage rather than the L'Etete passages (mean 51%, 71%, and 100% of exiting particles, respectively), although the actual number of particles leaving Passamaquoddy Bay in the latter two cases was extremely low (10 and 3, respectively; Figs. 5i, 9e, and 9f).

Overall assessment of behaviour model realism

The three best behaviour–speed combinations tested, with the lowest PI values for the overall mean indicator variables, were swimming southwest at 0.5 BL·s−1, negative rheotaxis at 2.0 BL·s−1, and orienting based on increasing depth at 0.5 BL·s−1; these simulations all had a PI of < 0.5 (Fig. 10 and Table S3). The PI values of these top three behaviours were not significantly different from one another (P > 0.05), although the PI of the best (swimming southwest at 0.5 BL·s−1) one was significantly better (lower; P < 0.05) than that of everything else (see 95% CI in Table S3). A further 15 simulations had an overall PI between 0.5 and 1.0, and these mainly comprised cases in which particles exhibited negative rheotaxis (at all other speeds), swam southwest (at 1.0–2.0 BL·s−1), or used tide-varying rheotaxis (at 0.5–2.0 BL·s−1), plus a few in which particles swam in random directions (at 2.0 and 3.0 BL·s−1) or oriented based on increasing depth (at 1.0 BL·s−1; Fig. 10). All other swim speeds for these behaviours, or other behaviours at all speeds (passive drift, swimming south, orienting based on decreasing temperature or increasing salinity), had a higher (poorer) overall PI (range: 1.0–2.7 BL·s−1) than the best behaviour–speed combinations with lower PI (Fig. 10). In nearly all cases (excepting seven behaviour–speed combinations in which no particles exited the bay in 10 days, and two in which very few exited), deviation in western Passage usage contributed a greater proportion (mean ± SD: 65.4% ± 22.2%; range: 2.4%–98.6%) of the PI value than errors in residence time or exit success (Table S3). The overall best behaviours based on PI were the same as those with residence time and exit success non-significantly different from empirical values, and Western Passage usage closest to observed, as described above (Figs. 5a–5i).
Fig. 10.
Fig. 10. Overall performance index (PI) values (bluer shading = lower PI and better performance; redder shading = higher PI and poorer performance) and ranks (1 = best; 49 = worst) of different modelled behaviour and swim speed combinations. Combinations ranked #49 all failed to transit particles out of Passamaquoddy Bay within 10 days, and are shaded with an arbitrary PI value > 3. Actual PI values, their 95% CI, and contributions of different model endpoints to them are included in Table S3.


This study modelled the dispersal of Atlantic salmon post-smolts by combining an ocean circulation model with a particle tracking model in which we included various behaviours and swimming speeds. While no modelled behaviour achieved a perfect match with observed salmon migrations, we were able to identify some behaviours that could allow salmon to successfully leave Passamaquoddy Bay and resulted in predictions that matched observations reasonably well (swimming southwest, negative or tide-varying rheotaxis at most speeds, plus orienting based on depth at 0.5 BL·s−1). These behaviours are thus potentially useful for modelling Atlantic salmon post-smolt migration in the study region. We also ruled out several behaviours as unlikely to be used by Atlantic salmon post-smolts in this area (orienting based on salinity, temperature, or depth at ≥1 BL·s−1, swimming south or randomly, and positive rheotaxis).

Passive versus active dispersal

In part, this study was undertaken to assess whether Atlantic salmon post-smolts use or respond to ocean currents or other stimuli during their seaward migration through Passamaquoddy Bay. In model simulations, the percentage of passively drifting particles that successfully exited Passamaquoddy Bay in 10 days was quite low (28%). Passively drifting particles also took longer to transit this area (7.6 days) than particles using most of the behaviours tested and took 1.8 times longer on average than observed (4.7 days) to leave Passamaquoddy Bay. Based on these findings, it appears highly unlikely that Atlantic salmon post-smolts drift passively with currents during their seaward migration out of Passamaquoddy Bay. These results are consistent with previous modelling efforts that concluded that passive dispersal was inferior to tested salmon behaviours (Table 1, and references therein; Byron and Burke 2014). Hence, perfect knowledge of the ocean currents and their variation in an area alone is likely insufficient to identify migration routes and critical habitats of wild Atlantic salmon post-smolts, and thus to inform an assessment of their encounters with potential stressors.

Rheotaxis—using currents to migrate

Lacroix et al. (2004) suggested that Atlantic salmon post-smolts might use currents to help them migrate through Passamaquoddy Bay, and beyond. In theory, residual surface currents in the spring and summer could carry Atlantic salmon from the Magaguadavic River estuary to the west, then south through Western Passage and further out of the Fundy Isles northeast via Head Harbour Passage (Fig. 1). Most previous studies modelling Atlantic salmon post-smolt dispersal tested some form of rheotaxis, with negative rheotaxis (swimming in the same direction as currents) tested most often, and usually achieving far better success than positive rheotaxis (swimming against currents; Booker et al. 2008; Mork et al. 2012; Moriarty et al. 2016). Tide-varying rheotaxis has not previously been tested for Atlantic salmon post-smolts, but was suggested as a mechanism they could use to leave estuaries (LaBar et al. 1978; Lacroix and McCurdy 1996; Martin et al. 2009), and is implicated in the dispersal of other species like flounder and eel (e.g., Sentchev and Korotenko 2007; Cresci et al. 2017). Our study was the first to include tide-varying rheotaxis (which worked quite well) in a dispersal model for Atlantic salmon post-smolts.
As in past studies, simulations in which particles exhibited positive rheotaxis performed very poorly at all speeds, as particles using this behaviour dispersed very little, took a long time to leave Passamaquoddy Bay, and had very low exit success (0%–32%), worsening with increased salmon swimming speed. In contrast, both negative rheotaxis and tide-varying rheotaxis performed very well overall and at most speeds tested (0.5–3.0 BL·s−1), allowing particles to leave Passamaquoddy Bay relatively quickly, and with high and similar-to-observed (60%–100%) exit success. However, negative rheotaxis at all speeds resulted in the best overall performance among current-based behaviours within Passamaquoddy Bay (i.e., comprising 6 of the 10 best (lowest PI) behaviour–swimming speed combinations), which supports previous studies suggesting that negative rheotaxis was likely a behaviour used by migrating Atlantic salmon post-smolts (Byron et al. (2014) and other studies cited in Table 1). The fact that the second-best result overall was attained with negative rheotaxis at 2 BL·s−1 herein (Fig. 10) may even support the “optimal” swim speeds of ca. 1.5–2 BL·s−1 used in previous studies (e.g., Hvas and Oppedal 2017; but see Friedland (2002) and Peake (2008) for lower and higher values, respectively). However, in spite of the good agreement with observed residence time and success achieved with these behaviours, simulated particles were predicted to use the L'Etete passages to exit Passamaquoddy Bay rather than Western Passage significantly more often than observed. This was related to many particles experiencing strong ebb tidal currents (e.g., Fig. 2) when they were northeast of Big L'Etete Passage on the first few (1–3) ebb tide cycles after they left the Magaguadavic River estuary (which is much closer to Big L'Etete Passage than to Western Passage), inducing them to swim rapidly out of the bay via this passage. This discrepancy may signal that various and other types of rheotaxis should be included in this model. For example, Hedger et al. (2008) suggested that post-smolts may swim faster during the day and slower and night. Martin et al. (2009) inferred that tracked post-smolts exhibited negative rheotaxis on both ebb and flood tides, but apparently did so at lower speeds on flood than ebb tides. They related this reduced net movement speed on flood tides to feeding behaviour by post-smolts (Martin et al. 2009). This type of behaviour would still allow post-smolts to be dispersed less landward on flood tides than in our modelled negative rheotaxis scenario, but more than our tide-varying rheotaxis one, and thus could lead to distinct (and maybe more realistic) trajectories.

Orientation based on depth, salinity, or temperature

Gradients in water temperature and salinity can provide cues that organisms can use to orient themselves in relation to the coast, particularly in estuaries and bays that drain rivers (Telesh and Khlebovich 2010). It was thus assumed that Atlantic salmon post-smolts could use increasing salinity or decreasing temperature as indictors of movement away from their natal river and coast and that they could use these conditions to orient their swim direction during seaward migration. Similarly, orienting towards waters with greater depths could allow Atlantic salmon post-smolts to move away from the coast and towards more oceanic habitats. Indeed, Lacroix (2013) detected the majority of acoustically tracked salmon migrating in the Bay of Fundy in the deeper channels of the bay. However, the cues that fish inhabiting surface waters could use to determine whether they are over deeper water are unclear. More likely, apparently depth-oriented behaviour (like we modelled) acts as a proxy for some other navigational cue(s) salmon may use to leave the coast, such as productivity (food) or magnetic field variation. The effectiveness of environmental variables as cues for orientation depends on their spatial variation (Byron and Burke 2014) and whether it aligns with seaward migratory vectors. Tides can also alter spatial gradients in temperature and salinity considerably, especially in areas with large tidal ranges like Passamaquoddy Bay (Trites and Garrett 1983). For example, surface salinity can increase shoreward on flood tides, but seaward on ebb tides (Telesh and Khlebovich 2010), leading salinity-orienting post-smolts to move in different directions between tidal phases.
We found that the exit success of particles from Passamaquoddy Bay was always lower than observed when they oriented based on temperature, salinity, or depth, at any swim speed, except when they oriented towards increased depths at 0.5 BL·s−1, and exit success decreased with swim speed with all these behaviours. Depth orientation at 0.5 BL·s−1 actually achieved good performance overall (i.e., the third lowest PI), although whether post-smolts could orient in this way in nature is uncertain (but see Lacroix 2013). This immediately suggests that spatial gradients in depth, salinity, and temperature in Passamaquoddy Bay were not large enough or directed enough shore to seaward to enable fish to navigate out of inner Passamaquoddy Bay based on them. Further, although at low speeds particles using these behaviours achieved reasonable exit success, those that left Passamaquoddy Bay did not appear able to leave the Bay of Fundy and pass Nova Scotia as real post-smolts should within 10 days (Figs. S8a–S8f) or longer (45 days; results not shown). Particles orienting towards deeper waters at higher speeds (1.5–3.0 BL·s−1) often moved contrary to the prevailing current in one direction on one-time step, and then in a completely different direction on the next, without moving in any clear direction across time steps (Fig. 8b; see also Fig. S8b). Particles orienting based on temperature and salinity behaved similarly and achieved some directed movement over time. However, changes in the tidal phase usually caused the direction of their movement to reverse, with some escaping the bay on the ebb tide but returning on the flood tide (Figs. 8c–8f), and swimming faster exacerbated these issues. Tidal reversals were also observed among tagged post-smolts in 2018 (Wilson et al. 2022), in similar past studies (e.g., Lacroix et al. 2004; Hawkes et al. 2017), and in simulations of particles using other kinds of behaviours herein (rheotaxis and directional swimming), but in these cases reversal did not generally last as long or prevent fish from exiting.
Results thus suggest that Atlantic salmon post-smolts cannot leave Passamaquoddy Bay if they orient based solely on these cues. Combinations of these cues might be used, and this could be tested in future work. These cues may also become important later in the migration of Atlantic salmon towards their marine feeding grounds, particularly when temperature or salinity gradients are much more pronounced, such as along the Scotian Shelf and the shelf break due to the competing influences of the Gulf Stream and Labrador Current (Townsend et al. 2015). Further, previous studies simulated Atlantic salmon migration with some success over larger scales by impelling particles to remain within a presumed preferred range of temperature and salinity (4–8 °C in Booker et al. 2008; 8–12 °C and up to 35 psu in Mork et al. 2012; 8–15 °C in Moriarty et al. 2016; Table 1), where swim speeds increased in a direction towards preferred conditions if a particle was outside of its preferred range, but swam in random directions about a set speed within it. This was not possible in the present study because the range of temperature and salinity values in Passamaquoddy Bay within the simulated 10-day windows was relatively small (ca. 10–12 °C and 22–32 psu; Fig. S2), which would have limited the effectiveness of this approach and essentially resulted in random swimming throughout (as was also tested). This may be more important when longer-term and larger-scale simulations are attempted.

Directional swimming

Salmon are sensitive to variations in the Earth's magnetic field, and thus could use these to navigate to/from/between marine feeding grounds and native spawning rivers (Byron and Burke 2014; Putnam 2015; Minkoff et al. 2020). The potential for salmon to navigate based on landmarks (map sense) or the sun or magnetic field (compass sense) has also been raised (Byron and Burke 2014; Burke et al. 2014). Some past studies have modelled salmon dispersal with an artificial navigational “goal” (e.g., the Ocean Tracking Network's “Halifax Line” offshore of Nova Scotia in Byron et al. 2014; Moriarty et al. 2016). However, this was not practical in the present study given the long distance between the release point and the ultimate destination of these highly migratory Outer Bay of Fundy stock fish (western Greenland), in addition to the complexity of the coast and intervening islands and peninsulas. As a first step, we tested if salmon swimming in any of the cardinal and primary intercardinal directions could successfully leave Passamaquoddy Bay. Swimming in several directions did not allow particles to leave Passamaquoddy Bay, including east and southeast, which led to particles becoming trapped in the Magaguadavic River estuary, and northeast, north, northwest, and west, which led to particles being trapped along the northern and western shores of inner Passamaquoddy Bay.
Nearly all of the particles that swam directly south were able to leave Passamaquoddy Bay over a relatively short period of time. However, almost all particles swimming south left Passamaquoddy Bay through the L'Etete passages, which are almost immediately south of the Magaguadavic River estuary and thus were encountered by particles very quickly, rather than mainly using Western Passage like real fish did. This concurs with the recent results of Newton et al. (2021) showing that Atlantic salmon post-smolts do not necessarily use the most direct and seemingly “best” route to migrate to their feeding grounds. Once our modelled south-directed particles left the Fundy Isles outside the bay, they could quickly move very far, especially those with higher swim speeds (see Figs. S9c and S9d in the Supplementary material). Swimming south also allowed particles to reach (and nearly pass) southwest Nova Scotia within 10 days (Fig. S9d), although the continued trajectories of these particles would most certainly have been further southward, rather than pivoting to move northeast along the Scotian Shelf as outer Bay of Fundy salmon are expected to do, unless they change their navigational cues or orientation at some point along their migration (Ritter 1989; Lacroix 2008,2013).
In contrast, the ability of particles swimming in a southwest direction to leave Passamaquoddy Bay was heavily dependent on their swim speeds. At speeds of 1.5 BL·s−1 or more, few to almost none of these particles left the bay, and were “stuck” along the Maine side of the bay or in Cobscook Bay, Maine. However, many particles swimming southwest at 0.5 BL·s−1 left the bay within a time frame comparable to observations of tagged fish, and with a high and realistic (>80%) exit success. Most importantly, the majority of fish swimming southwest at 0.5 BL·s−1 exited via Western Passage rather than the L'Etete passages, which was not seen for any other behaviour tested (other than a few with very low exit success); this behaviour–swim speed combination achieved the best performance overall (lowest PI). Although the percentage of fish using Western Passage with this behaviour (∼52%) was significantly lower than observed (∼87%), this still provides some support for this behaviour as the most realistic among those tested; indeed, the upper limit of the 95% CI of the mean Western Passage usage of simulations with this behaviour (67%) was relatively close to the lower limit of the 95% CI of observations (73%) (Fig. 5i and Table S1). Further, more of the particles released in May (65%) exited via Western Passage using this behaviour, while fewer of those released in June (41%) did so, which matches the general pattern observed for tagged wild post-smolts during telemetry studies (Lacroix et al. 2004; Wilson et al. 2022). Salmon post-smolts in nature were observed by Lacroix (2013) to initially migrate in a southwest direction from Big Salmon River, NB, population in the Inner Bay of Fundy. Swimming southwest allowed particles to exit Passamaquoddy Bay and the adjacent Fundy Isles quite quickly and with a high success rate. However, if particles continued to behave this way after leaving Passamaquoddy Bay, they would continue to transit southwest along the Maine coast, and thus fail to navigate east towards Nova Scotia and ultimately head northeast towards the Labrador Sea (Figs. S9e and S9f). Hence, while this behaviour was very successful at getting particles out of Passamaquoddy Bay and using realistic exit routes, it would not subsequently be useful for salmon to continue their migration to their feeding ground. This suggests that if this southwest orientation behaviour was actually used by Atlantic salmon post-smolts initially, they would need to switch to using a different behaviour (e.g., in response to an endogenous time- or ontogeny-dependent geomagnetic map sense) to continue their migration.
We also tested a scenario in which particles swam in random directions. As might be expected, this led to particle tracks being much more variable than any other scenario tested, essentially creating exaggerated versions of passive drift tracks. This extended particle residence times in Passamaquoddy Bay to values higher than observed at all swim speeds, although it did result in high exit success and a fair percentage of particles (up to 30%) using Western Passage. Subsequent exit success of particles through the Fundy Isles was fair with random swimming as well (Figs. S9a and S9b), although again with increased transit times. It thus seems that, while random swimming could allow fish to leave Passamaquoddy Bay successfully, the utility of this behaviour for longer-distance migrations is less clear. However, given the disparity between observed and modelled residence times, this behaviour is also unlikely to be realistic.

Swimming speed

Previous modelling studies have either inferred the optimal swimming speed of Atlantic salmon post-smolts based on other species, such as sockeye salmon (Oncorhynchus nerka; e.g., Smith et al. 2009; Byron et al. 2014), or simply assumed it was 0.5 BL·s−1 (Friedland 2002) or ∼2 BL·s−1 (Thorstad et al. 2011; Byron et al. 2014; Table 1). Given the uncertainty of the optimal swimming speed of Atlantic salmon post-smolts, we tested a range of swimming speeds (0.5–3.0 BL·s−1) rather than assuming an arbitrary value. Based on the recent laboratory study by Hvas et al. (2021), this range likely encompassed the range of speeds that migrating post-smolts would be able to continuously maintain. Exit success for particles swimming in a southwest direction at 0.5 BL·s−1 was close to that observed for tagged post-smolts. Moreover, a large proportion of these particles were predicted to leave Passamaquoddy Bay through Western Passage, though less than was observed by acoustic telemetry. Furthermore, particle dispersal tracks produced with this behaviour in Passamaquoddy Bay closely matched the inferred pathways obtained by manually tracking Atlantic salmon post-smolts in Passamaquoddy Bay (Lacroix et al. 2004; B.M. Wilson, unpublished data).
Although swimming southwest at 0.5 BL·s−1 produced realistic dispersal patterns for Atlantic salmon post-smolts in Passamaquoddy Bay, swimming at 2 BL·s−1 using either negative or tide-varying rheotaxis at 2 BL·s−1 produced residence times and exit success similar to that observed for tagged fish, though these behaviours underestimated the proportion of post-smolts exiting via Western Passage. Hence, it is difficult to give a general conclusion about the best or most likely swim speed used by Atlantic salmon post-smolts, particularly if they switch their behaviour and swim speed in different circumstances; indeed, past studies in this system (Lacroix and McCurdy 1996) and elsewhere (LaBar et al. 1978; Martin et al. 2009) suggested that fish swam slower with currents on flood than ebb tides, or at night (Hedger et al. 2008).
Definitive identification of the optimal swimming speeds of Atlantic salmon post-smolts would require estimating their standard and active metabolic rates at various swimming speeds for this range of body size and water temperature (Weihs 1973; Ware 1978; Trudel and Welch 2005). Although there is much information on standard metabolic rates of Atlantic salmon over a wide range of body sizes (Enders and Scruton 2005; Macnaughton et al. 2019), there is limited information on active metabolic rates for Atlantic salmon post-smolts with body masses ranging from ∼8 g (corresponding to ca. 10 cm FL) to 400 g (∼35 cm FL) (Hvas and Oppedal 2017; Hvas et al. 2017; and see studies cited by Macnaughton et al. 2019); this gap includes the ca. 42 g (16.7 cm FL) size of post-smolts tracked in the telemetry work referenced herein. Recent experimental work conducted on larger Atlantic salmon post-smolts (∼800 g, 42 cm FL) suggest that they can sustain swimming at 80% of their critical swimming speed (i.e., ∼1.8 BL·s−1) for 4 h (Hvas and Oppedal 2017), which would match speeds used in past studies and ours. However, it is unclear if this represents their optimal cruising swimming speed, and whether this holds for smaller post-smolts (16.7 cm FL; this study).

Limitations and future prospects

The tendency for modelled particles in nearly all (including passive) simulations to exit primarily via the L'Etete Passages contributed the most to model performance loss, as tagged fish mainly used Western Passage to leave the bay (Figs. 5c–5i, and Table S3). Since we used a new FVCOM run (2018, Passamaquoddy Bay) as the source for oceanographic data in this study, some aspects of it may have led to this result. However, based on modelled particle tracks (Figs. 69) the issue was rather more that few particles reached Western Passage, instead being advected out of the L'Etete Passages; particles that managed to enter Western Passage were able to transit it (Figs. 69). Drifter comparisons suggested that this L'Etete Passages bias was not due to a problem with the physical model, at least not manifesting over a timescale of 1–2 days, as there was no overall tendency of modelled drifters to drift towards the L'Etete Passages more than real drifters (Fig. 4). Over a longer timescale of the full 10-day salmon simulations, the majority of particles drifting passively did leave via the L'Etete Passages, but there was no aspect of their overall dispersal tracks (Figs. 6 and S6) that appeared particularly anomalous relative to known circulation patterns in the region (i.e., mainly counterclockwise in the spring, etc.) (see Study Area section and Fig. 1 vs. Fig. 2; Bumpus et al. 1959; Trites and Garrett 1983; Lacroix et al. 2004). This reiterates that real fish must behave in some way to modify passive drift during their migration to preferentially leave via Western Passage. None of the behaviours (and speeds) tested herein captured this “real” behaviour completely on their own (e.g., swimming with currents led particles to rapidly exit via the L'Etete Passages), although swimming southwest at 0.5 BL·s−1 came closest. This suggests that fish must use multiple cues/behaviours and swim speeds to migrate out of Passamaquoddy Bay via Western Passage in reality, and further that some cue(s) bestowing a southwest direction of movement (e.g., compass/map sense), perhaps along with negative rheotaxis, should be a part of the suite of behaviours actually used. Behaviour by fish that delays their migration could also be considered, for example if fish deviate from physically “optimal” migration routes to spend time feeding (Newton et al. 2021). Future studies modelling migration using multiple cues would be useful, although to be tractable these should attempt to use some observations of actual migrating post-smolts in situ to guide the weighting or timing of different behavioural modes.
Additional aspects of the physical model may have contributed to differences between observed and modelled dispersal. For example, comparisons with observed surface temperature and salinity data indicated that the model may not have sufficient fresh water input (Figs. 3, S2, and S4), which could impact the surface circulation. Furthermore, particles were constrained to disperse within the surface layer of the modelled water columns (Renkawitz et al. 2012), and the top 2–5 m of most oceanographic models, even when they are otherwise well-validated, is still usually not well resolved due the difficulty of simulating the complex impacts of turbulence and wind forcing at the water's surface (van Sebille et al. 2018; Fox-Kemper et al. 2019). It can also be difficult to validate modelled surface circulation, since Acoustic Doppler Current Profilers cannot accurately measure currents in the upper few meters of the water column. Longshore currents, formation of water masses with differing densities, and seasonal changes in water column stratification also likely play a role in the dispersal of post-smolts in nature (Lacroix and McCurdy 1996; Thorstad et al. 2011, 2012), but such processes are difficult to capture in models, especially over short time scales (i.e., 10-day simulations; van Sebille et al. 2018). Some of the spread among modelled (vs. observed) trajectories may have been due to small-scale horizontal shears in the simulated velocity field (Page et al. 2005; Yang et al. 2020). Model trajectories are highly sensitive to the timing and location of release (Cantrell et al. 2018), so the results suggested that both the empirical and modelled drift tracks were very sensitive to spatial and temporal features in the flow fields and the times and locations of releases. Given this apparent impact of small-scale processes on particle tracking results, the frequency at which the flow fields are stored in the FVCOM output may be particularly important. The flow fields were stored at hourly intervals, which is typical and can be adequate for many applications (Chen et al. 2011). However, since the particle tracks suggest trajectories are sensitive to variations at finer temporal (and spatial) in the flow field, it would likely be better to store the flow fields at higher frequencies in the future. Otherwise, due to the nonlinear dynamics of oceanographic forces, this storage frequency is a potential source of uncertainty in the predicted drift tracks, which will be an issue regardless of whether the circulation model has been otherwise well validated. Storing flow fields at a higher temporal frequency might also have reduced the issues with particles jumping onto land in our simulations, and thus allowed us to capture more realistic nearshore migrations pathways. Another potential source of error is the sensitivity of the modelled particle tracks to the time step used in the particle tracking model, 5 min in this study. Therefore, additional work to determine the sensitivity of drift tracks to storage frequency of flow fields and the particle tracking time step could be beneficial. In spite of these potential limitations, validation exercises via comparison to experimental GPS-equipped drifters provided support of the physical model used. Drifters and model particles in each release period (May/June) were deployed within a short time period (minutes) and close together in space (tens of metres). Both drifter and particle tracks were qualitatively similar (Fig. 4), exhibited similar variability and spatial “spread” across the study area (Fig. 4), and ended at locations about 3–4 km apart after 24 h of drift (Fig. S5). The model was therefore considered useful to estimate potential dispersal of particles representing post-smolts under different assumptions and conditions (i.e., with different behaviours and swim speeds). Subsequent validation and refinement may increase the precision and accuracy of the results.
This study simulated the migration of Atlantic salmon post-smolts in a coastal embayment using different behaviours to assess whether modelled particle trajectories adequately matched the dispersal of acoustically tagged salmon. This is a challenging environment in which to conduct dispersal modelling work due to its inherent complexity. However, this is by no means unique in the Atlantic salmon's range, as there are many rivers with Atlantic salmon that drain into bays and fjords with similarly complex arrangements, such as Penobscot Bay, Maine, United States (Brooks et al. 1999; Renkawitz et al. 2012; Hawkes et al. 2017) and the Bras d'Or Lakes, Nova Scotia, Canada (Crossin et al. 2016). To prevent particles from being trapped on-shore in such an environment, a “free-slip” condition was applied to particles located in an element with a depth of 10 m or less. Particles thus avoided land with reasonable success but this 10 m threshold prevented particles from using the shallow waters located on the north shore of Passamaquoddy Bay, where acoustically tagged post-smolts have been previously observed (Lacroix et al. 2004). Importantly, most of the post-smolts tracked in 2018 initially migrated out of the Magaguadavic River estuary to the northeast along the northern coast of Passamaquoddy Bay, and during this time travelled within water shallower than 5 m (Wilson et al. 2022); such fish may have been using the longshore current to aid in their migration. Preventing particles from entering shallow areas may be a contributing factor to the differences between the observed and modelled fish trajectories. Nevertheless, for many particles tested in simulations using passive drift, rheotaxis (all types and speeds), orientation behaviours (at low speeds), and random swimming, but not directed swimming to the south or southwest, initial trajectories were still to the northeast, and thus within the correct general area of Passamaquoddy Bay (northern coastal zones; see Figs. 69). Lower depth thresholds for the “free-slip” condition were attempted (unpublished data), but this often trapped particles onshore. Hence, the depth threshold used in this study for the “free-slip” condition represents a compromise between achieving biological realism and allowing particles to leave Passamaquoddy Bay with a reasonable success.
Although no modelled behaviour achieved a perfect match with observed salmon migrations in this study, we were able to identify some behaviours that could allow salmon to successfully leave Passamaquoddy Bay. Some behaviours matched observations fairly well-swimming southwest, negative or tide-varying rheotaxis, and low-speed depth orientation. We also identified several behaviours as being unlikely (at least on their own)—orienting based on depth (at high speeds), salinity, or temperature, swimming south or randomly, and positive rheotaxis. While these results were produced using simulations in which salmon exhibited a single type of behaviour, salmon may navigate using multiple cues or behaviours or switch their behaviours (or swim speeds) over the course of their migration (Byron and Burke 2014). Hence, more complex combinations or different behaviours over longer time periods may need to be tested. Future work should also try to improve the match of modelled versus observed post-smolt migration trajectories. Comparisons of full movement tracks might be optimal for this, but will require information on fish locations at intermediate positions throughout their migration, not just at acoustic receiver gates or from irregular manual tracking detections. This may not be possible with existing technology and infrastructure, although current developments in satellite tracking using acoustics may enable widespread and detailed fish tracking in the future (Bernis 2022). However, tracking work using more receivers and arrays, as was done in this area in later years (2019+; Wilson et al. 2022), can provide more information for potential validation. Our PI index also provides a means by which multiple model performance versus observational endpoints could be compared in further studies.
In this study, a model was developed that simulates the dispersal of Atlantic salmon post-smolts tagged that were released at two times from a single location in Passamaquoddy Bay. This modelling approach can thus be used in the future to provide estimates of the essential habitats and migration routes of wild Atlantic salmon post-smolts, as well as their likelihood of encountering various stressors along their migration routes.


We thank Greg Cormier, Asghar Ghori, Peter Kraska, Tobias Spears, and the Microsoft Azure team for providing computing resources and support for this project. We also thank the following individuals for help during telemetry work: Shawn Robinson, Fred Whoriskey, Jack Fife, Becky Graham, Owen Jones, Ross Jones, Rob MacDougall, Alanna MacFarlane, Sarah Scouten Graham Chafe, Eric Brunsdon, John Kocik, and Tim Sheehan. Additional assistance and resources were provided by the Atlantic Canada Fish Farmers Association, the Atlantic Salmon Federation, the National Oceanic and Atmospheric Administration, and the Ocean Tracking Network. Funding for this project was provided to Fisheries and Oceans Canada by the Species At Risk Program (SARP) and the Aquaculture-Ecosystems Interactions Program (AEIP). We also thank the associate editor and two reviewers for comments that improved the manuscript. Reference to trade names does not imply endorsement by the US Government.


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Published In

cover image Canadian Journal of Fisheries and Aquatic Sciences
Canadian Journal of Fisheries and Aquatic Sciences
Volume 79Number 12December 2022
Pages: 2087 - 2111


Received: 15 November 2021
Accepted: 20 June 2022
Accepted manuscript online: 12 July 2022
Version of record online: 17 October 2022

Data Availability Statement

Data used in this study are available from the authors within Fisheries and Oceans Canada, Maritimes Region, upon request.

Key Words

  1. acoustic telemetry
  2. Atlantic salmon
  3. dispersal model
  4. migration route
  5. post-smolt


  1. télémétrie acoustique
  2. saumon atlantique
  3. modèle de dispersion
  4. voie de migration
  5. post-saumoneau



Fisheries and Oceans Canada, St. Andrews Biological Station, 125 Marine Science Drive, St. Andrews, NBE5B 0E4, Canada
Fisheries and Oceans Canada, St. Andrews Biological Station, 125 Marine Science Drive, St. Andrews, NBE5B 0E4, Canada
Brent M. Wilson
Fisheries and Oceans Canada, St. Andrews Biological Station, 125 Marine Science Drive, St. Andrews, NBE5B 0E4, Canada
Jonathan Carr
Atlantic Salmon Federation, 15 Rankine Mill Road, Chamcook, NBE5B 3A9, Canada
Jason Daniels
Atlantic Salmon Federation, 15 Rankine Mill Road, Chamcook, NBE5B 3A9, Canada
Susan Haigh
Fisheries and Oceans Canada, St. Andrews Biological Station, 125 Marine Science Drive, St. Andrews, NBE5B 0E4, Canada
David C. Hardie
Fisheries and Oceans Canada, Bedford Institute of Oceanography, 1 Challenger Drive, Dartmouth, NSB2Y 4A2, Canada
James P. Hawkes
NOAA Fisheries, Northeast Fisheries Science Center, Maine Field Station, 17 Godfrey Drive-Suite 1, Orono, ME04473, USA
Christopher W. McKindsey
Fisheries and Oceans Canada,Institut Maurice-Lamontagne, 850 Route de la Mer, Mont-Joli, QCG5H 3Z4, Canada
Mitchell O'Flaherty-Sproul
Fisheries and Oceans Canada, St. Andrews Biological Station, 125 Marine Science Drive, St. Andrews, NBE5B 0E4, Canada
Émilie Simard
Fisheries and Oceans Canada,Institut Maurice-Lamontagne, 850 Route de la Mer, Mont-Joli, QCG5H 3Z4, Canada
Fred Page
Fisheries and Oceans Canada, St. Andrews Biological Station, 125 Marine Science Drive, St. Andrews, NBE5B 0E4, Canada

Competing Interests

The authors declare that they have no competing interests related to this work.

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