Introduction

Recent computational advances have allowed us to extract knowledge from large-scale observed and simulated data to address key biological questions. As one of the most basic and essential scientific numerical technologies for a multidisciplinary approach, this review focuses on particle-tracking experiments (PTEs) for marine biology/marine ecosystems, usually in combination with a realistic ocean model. The words “ocean model” used throughout this article signify any circulation models for open-sea, shelf, coastal, and/or estuary waters, regardless of simulated target scales. Generally, the simplest particle-tracking model can trace the trajectory of particles (e.g., planktonic organisms with no active movement) that are virtually released in an ocean model and passively transported by ocean currents, and give an answer to the most basic question: where did an observed planktonic organism come from, or where will it go? In spite of this very basic simulation, however, there are still few particle-tracking models for marine biology that are adaptable to a variety of spatio–temporal scales and easily applicable by all scientists worldwide.

Similar methods are used to understand the transport and dispersion processes of things such as marine debris (Isobe et al. 2019), oil spills (Korotenko et al. 2004), and chemical pollutants [e.g., radioactive materials (Cetina et al. 2000)] by the inclusion of peculiar, material-dependent processes in virtual particles (e.g., windage, aggregation, decomposition, and sinking). Likewise, for marine biological simulations, species- or group-dependent biological processes are incorporated into virtual particles, such as active movement, growth, survival, and mortality. Some studies refer to this type of complicated particle-tracking model as an individual-based model (IBM) (Brochier et al. 2008; DeAngelis and Grimm 2014; Hinckley et al. 1996; Miller 2007).

As described throughout this review, marine biological simulations based on particle-tracking models with various levels of complexity have been essential tools for understanding and managing marine ecosystems for sustainable use and conservation. Nonetheless, there is little synthesized information about the multidisciplinary application of particle-tracking simulations for marine ecosystems around Japan; features of Japanese PTEs such as their weaknesses, advantages, and uniqueness are still not apparent. It is, therefore, unclear what kinds of studies with PTEs are needed to achieve sustainable ocean health and marine biodiversity around Japan, what currently used technologies associated with PTEs must be maintained beyond the coming decade, and what transformations of existing technologies can maximize the contribution of PTEs to ocean sciences. To answer these questions and obtain some perspectives in the coming decade, the present study reviews the history and current status of particle-tracking models, and to some degree tracer-tracking models, for marine biology around Japan, and summarizes the future vision. In other words, this paper aims to draw lessons from previous studies to most effectively design and apply PTEs that can precisely simulate marine organisms around Japan. Note that the present review seldom compares the current status in Japan with that in other countries because of the paucity of similar systematic reviews, which are beyond the scope of this article.

Materials and methods

To summarize the history of particle-tracking simulation around Japan, relevant articles in Japanese as well as English were collected from the fields of marine biology, fisheries science, and coastal/ecological/environmental engineering. First, the keywords “particle” and “model” were used to search the online databases Web of Science, CiNii, and J-STAGE, which are maintained by Clarivate Analytics Co. Ltd, the National Institute of Informatics, and the Japan Science and Technology Agency, respectively. Web of Science is a major international website that provides subscription-based access to multiple databases, CiNii is the largest academic information search service in Japan, and J-STAGE is an online platform for Japanese academic journals. This first search retrieved many papers unrelated to the focus of this review.

The results of the initial search were then narrowed down. To highlight studies around Japan and in the Japanese Exclusive Economic Zone, the same three databases were searched again after adding the keywords “Japan,” “Kuroshio,” or “Oyashio” to the search. Specific papers were selected that treated horizontal (two-dimensional) or three-dimensional transport of marine flora and fauna, including nutrients and organic substances. A small number of studies used grid-based tracer simulationFootnote 1 instead of particle-tracking; these were included as part of this review. The following criteria were used to further screen and reduce the number of relevant papers. Short abstracts and project reports were excluded if they did not have the format of a scientific paper, typically with several sections such as “Introduction,” “Material and methods,” “Results,” “Discussion,” and “Summary.” When some publications duplicated analyses and results, only a single representative paper was selected. In this selection, peer-reviewed English-language papers took the highest priority. Papers were also eliminated that focused only on non-biological materials such as seawater, sediments, and radioactive material. Lagrangian coherent structures in the ocean that were visualized by the finite-time Lyapunov exponent based on PTEsFootnote 2 were removed from consideration for this review (Prants et al. 2017). Moreover, studies with a particular focus on lower-trophic-level ecosystem modeling (e.g., Kishi et al. 2011) were excluded from this review, unless simulated results from the lower-trophic-level ecosystem models were combined with other biological or particle models.

Third, to avoid overlooking any relevant publications, an additional off-line (manual) search was performed of major journals, scientific reports, and science magazines in Japan that were not registered in the three on-line databases mentioned above. The combination of on- and off-line searches encompassed printed publications from major academic societies/communities of ocean science in Japan, i.e., the Japan Society of Civil Engineering, Oceanographic Society of Japan, Coastal Oceanography Research Committee, Japanese Society of Fisheries Oceanography, and Japanese-French Oceanographic Society. Details of the off-line search are summarized in Online Resource 1. Note that scientific magazines in Japanese such as Aquabiology and Monthly Kaiyo are not peer reviewed. Therefore, when there was an original article in a peer-reviewed publication that was introduced in the science magazines, only the original paper was included. In contrast, when the paper in the scientific magazine was original and had the format of a scientific paper, the magazine version was used.

Finally, the reference list of assembled papers was examined to check for any omissions. As a result, 178 papers were identified, of which 158 (88.8%) were from peer-reviewed publications, as of April 22 2021. Information about the specific papers and the features of their studies are summarized in Online Resource 2.

Results

Species studied by PTEs around Japan

The relevant papers involving PTEs around Japan can be divided into two groups. One includes those published by the Japan Society of Civil Engineering primarily as peer-reviewed proceedings of coastal/ecological engineering conferences and referred to as “E-field” studies in this review. The other group includes the remaining papers from other sources referred to as “O-field” studies. When the title of a journal or proceedings included the word “engineering,” the paper was categorized as an E-field study. Although the definition to discriminate the two studies is applicable only to PTEs around Japan and may not be somewhat strict, this definition will shed light on contrasting features of PTEs that have been developed almost independently by the two groups. Of the total number of papers, 73 (41.0%) were classified as E-field. Of these, 72 were in Japanese and 1 was in English. The remaining 105 papers (59.0% of the total) were classified as O-field studies. The O-field papers included 77 in English and 28 in Japanese. As described below, the PTEs differed markedly between the two fields in terms of species and spatio–temporal scale. These differences can be interpreted primarily as reflecting differences in viewpoint between the engineering community and the other scientific communities.

PTEs focused on marine biology, fisheries science, and coastal/ecological engineering around Japan were first implemented in the 1980s (Fig. 1). At this time, particle-tracking models were driven by velocity data that were either simulated by simplified ocean models with realistic topography but homogeneous density, or measured at the sea surface by geomagnetic electro-kinetograph (Kobayashi 1987; Naganuma 1982). A few PTEs in the 1980s already had practical applications; for example, for understanding distributions of plankton and ichthyoplankton around the cooling water intake of an electric power plant (Kadoyu et al. 1982), or migration patterns after the release of juvenile red sea bream Pagrus major (Yanagi et al. 1989). In a surprisingly advanced use of PTEs for this early date, Naganuma (1982) already performed PTEs that included mortality and growth of juvenile red sea bream. Incidentally, before the 1980s, there were some studies around Japan that considered the effects of ocean currents on the transport and dispersion of eggs and larvae under an idealized configuration, e.g., using theoretical one-dimensional coordinates (e.g., Hirano 1965).

Fig. 1
figure 1

The number of studies with PTEs over time intervals of about 5 years. Filled and open bars indicate E- and O-field studies, respectively

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The number of studies with PTEs increased after the 1980s (Fig. 1). Specifically, the number of E-field studies with PTEs increased after the early 1990s and became nearly constant after the late 2000s (filled bars in Fig. 1). In contrast, the number of O-field studies with PTEs increased dramatically in the mid-2000s (open bars in Fig. 1). As explained later, the decadal increase of PTEs in O-field studies can be attributed principally to the appearance of eddy-resolving ocean models and operational ocean forecast systems around Japan after the mid-2000s, the outputs of which have been publicly shared among scientists.

In total, there were 198 studies of a species or a group of species using PTEs (Fig. 2). Because some studies investigated two or three species, as later described, the 198 is larger than the total number of studies (178) in Online Resource 2. The PTEs covered a wide range of organisms including fish, squid, octopus, shellfish, marine snails, coral reefs, starfish, shrimp, lobster, marine and terrestrial crabs, seagrass, nutrients, harmful algal blooms (HAB), jellyfish, zooplankton, seaweed, and turtles. The rank of marine organisms that were the most frequently examined by PTEs is also listed in Online Resource 3. For some species, there were four or more studies (Fig. 3): red sea bream, chum salmon Oncorhynchus keta, Japanese sardine Sarninops melanostictus, jack mackerel Trachurus japonicus, Japanese anchovy Engraulis japonicus, Japanese eel Anguilla japonica, conger eel Conger myriaster, brown sole Pleuronectes herzensteini, marbled sole Pseudopleuronectes yokohamae, short-necked clam Ruditapes philippinarum, Japanese basket clam Corbicula japonica, Japanese scallop Patinopecten yessoensis, fiddler crabs Uca lactea lactea and Uca arcuata, eelgrass Zostera marina, giant jellyfish Nemopilema nomurai, and loggerhead turtle Caretta caretta. For coral reefs, multiple, unspecified species were examined, except for one study (Taninaka et al. 2019) that focused on Heliopora spp.

Fig. 2
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Classification of biological studies based on PTEs. Numerals in parenthesis show the number of studies for each category. # denotes an organism harmful to human activities

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Fig. 3
figure 3

Biological studies based on PTEs by individual species (except for most coral reef studies). Species in red were in more than four studies

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Most of the studies using PTEs (160) focused on a single species or on unidentified multiple species (i.e., a coral reef), but the 18 remaining studies investigated two or three species simultaneously (Online Resource 2). Note, however, that these totals do not account for PTE studies of different life stages of the same species, for example, different migration patterns in juvenile and immature chum salmon (Azumaya and Ishida 2004; Azumaya et al. 2018) or different reproductive strategies [e.g., different dispersion strategies for fruits and seeds of the seagrass Enhalus acoroides (Murakami et al. 2015a; b)].

Single studies involving multiple species could be roughly separated into three types: common habitat and similar survival/transport strategies [e.g., marine snails Haliotis discus discus, Haliotis gigantea, and Haliotis madaka during their larval stage in Sagami Bay (Miyake et al. 2009)], common habitat but different survival/transport strategies [e.g., Japanese basket clam and mudflat crab Chiromanters dehaani during their larval stage in the Tama River estuary (Mishima et al. 2018)], and different habitat but similar survival/transport strategies [e.g., interregional differences in passive transport during the hatchling stage between green turtle Chelonia mydas and loggerhead turtle from different nests (Kitagawa et al. 2002)]. It is worth noting that Tatebe et al. (2010) conducted a pioneering work that simulated the transport of three dominant Neocalanus copepods—N. flemingeri, N. cristatus, and N. plumchrus—with different strategies of ontogenetic vertical migration throughout their life cycle around the subarctic North Pacific Ocean. Note that, from a methodological perspective, PTEs do not easily treat multiple species, so collaboration among many scientists using PTEs with different species will be necessary to systematically understand the whole marine ecosystems in terms of biodiversity.

There was a marked difference between E-field and O-field PTE studies in their target species (Fig. 4a and b). PTEs in E-field studies dealt with species that inhabit shallow coastal and shelf waters during a partial life stage or throughout their life cycle. In contrast, O-field studies focused mainly on species that migrate extensively in offshore waters, although some stages of some species spend part of their lives in coastal and river waters (e.g., Japanese eel, chum salmon, and lobster) or on the land (turtle). Some exceptions included O-field studies of marine snails, harmful algae, and some types of jellyfish that inhabit coastal waters throughout their lifetime.

Fig. 4
figure 4

Biological studies based on PTEs, classified into a E-field studies and b O-field studies, and further classified into c E-field and d O-field studies targeting noncommercial fisheries species

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The species studied in the two fields were further classified into commercial and noncommercial species in terms of their value as fisheries resources (Fig. 4c and d). About 50% of the E-field studies (42 studies) targeted species unrelated to commercial fisheries. Of the O-field studies, 28.7% (33 studies) were accounted for by noncommercial species. When harmful organisms such as harmful algae and jellyfish were excluded, about 20% of the O-field studies involved noncommercial species. Hence, to properly understand and manage ecosystems with rich biodiversity around Japan, it would be desirable to more aggressively study noncommercial species in the offshore waters, which are typically associated with O-field studies. This gap between the two study fields could be filled by effectively combining PTEs with already-existing biological data for the offshore waters, as discussed in section “Biological data for interannual variations.”

Note that about 50% of E-field studies involving noncommercial species focused on rare or endangered species for conservation: horseshoe crab Tachypleus tridentatus (Seino et al. 2000), fiddler crabs Uca arcuata and U. lactea lactea (Nakano et al. 1997; Nakano and Uno 2001; Uno et al. 2007), terrestrial hermit crab Coenobita brevimanus (Murakami et al. 2014), and coral reefs suffering from massive destruction attributed to coral bleaching and feeding damage following outbreaks of crown-of-thorns starfish Acanthaster planci (Nadaoka et al. 2001; 2006a; 2006b). These types of studies contributed to the design of marine protected areas (Tamura et al. 2005).

Ocean models for PTEs around Japan

PTEs in offshore waters around Japan were conducted using gridded data from numerical simulations or from in situ and satellite measurements (e.g., Heath et al. 1998; Kim and Sugimoto 2002). Some studies employed altimetry-derived geostrophic velocity at the sea surface superimposed with climatological mean velocity, instead of using the output from a mesoscale eddy-resolving model (Iwahashi et al. 2006; Kon et al. 2006; Okunishi et al. 2012; Oozeki et al. 2015). In contrast, PTEs for coastal and shelf waters were combined mostly with numerical simulations.

The grid size of numerical ocean models can be shown separately for O-field (Fig. 5a) and E-field studies (Fig. 5b). The models with grid sizes ≤ 1 km correspond roughly to E-field studies and those ≥ 1 km to O-field studies. The models with grid sizes between a few hundred meters and a few kilometers overlapped both fields (Fig. 5c). Moreover, the model grid sizes for E-field studies tended to decrease decadally (right panel in Fig. 5b), whereas those for O-field studies had less of a tendency to decrease (right panel in Fig. 5a). For O-field studies, the mode of the model grid size was apparent around 10 km after the mid-2000s, when the mean grid size was also comparable to the 10 km. These features for O-field studies were mainly attributed to the fact that the grid size was regulated by the horizontal resolution (~ 10 km) of mesoscale eddy-resolving models (Sasaki et al. 2008) and ocean forecast systems with data assimilation (Hirose et al. 2007; Kuroda et al. 2017; Miyazawa et al. 2009; Usui et al. 2006), the outputs of which began to be shared among scientists in and after the mid-2000s. In addition, for O-field studies, the second mode of the model grid size appeared around 1–3 km in and after the 2010s, when next-generation ocean forecast systems with higher resolution (1–3 km) started to be implemented by some scientific groups in Japan (Hirose et al. 2016, 2019; Kuroda et al. 2021; Miyazawa et al. 2021).

Fig. 5
figure 5

Statistics for model grid sizes for a O-field and b E-field studies. For spherical coordinate models, the grid size was defined by the shorter length of the two grid dimensions at 35°N in the north–south and east–west directions. In addition, for unstructured finite-element models, the minimum grid size in the model domain was selected as the model grid size. The left panels in (a) and (b) denote frequency distributions for about 5-year intervals. The right-hand bar charts denote the mean grid sizes. Panel (c) shows the frequency distribution of the model grid sizes for E-field (filled bars) and O-field (open bars) studies

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Table 1 lists degree of dependence of PTEs on eddy-resolving ocean forecast systems. One-third of studies with PTEs (63 studies) used the six community systems. Community systems from the Japan Coastal Ocean Experiment group (JCOPE; Miyazawa et al. 2009; 2021) made the most significant contributions to biological studies with PTEs. The shared model outputs from the six systems were applied directly to 46 studies with PTEs and used in 17 studies as lateral boundary conditions of coastal ocean models. Hence, it is clear that eddy-resolving ocean forecast systems with a horizontal resolution of 1–10 km around the whole of Japan have resolved a bottleneck for marine biological studies with PTEs.

Table 1 The top six most frequently used ocean forecast systems for PTEs
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A variety of ocean models with a horizontal resolution < 1 km were employed for simulating coastal waters, particularly in E-field studies. Most of the fine-resolution coastal ocean models were prognostically implemented without data assimilation. For the fine grids (< 1 km), 45% of three-dimensional models were developed based on open-source code, such as the Finite-Volume Coastal Ocean Model (FVCOM; Chen et al. 2003), Princeton Ocean Model (POM; Blumberg and Mellor 1987), Delft3D (Delft Hydraulics 2008), Marine Environmental Committee (MEC; Yu and Kyozuka 2004), and Regional Ocean Modeling System (ROMS; Haidvogel et al. 2008). Meanwhile, the rest of the models (55%) were developed based on closed-source codes [e.g., Coastal Current Model (CCM; Murakami et al. 2014)]. The framework of coastal ocean models around Japan has been very diverse. In addition, some coastal ocean models have been coupled with lower trophic-level ecosystem, wave, and/or sediment models. Looking toward the future, therefore, it would be helpful to develop and publicly share a unified versatile package based on open-source code to allow easy and quick set-up and development of a regional coastal ocean model for PTEs by downscaling outputs from an ocean forecast system.

Configurations of particle-tracking models

Tracking direction in time

PTEs were classified into “forward” (159 studies), “backward” (8), “forward and backward” (5), and “two-way” (6) tracking (Online Resource 2). PTEs looking forward in time were the most frequently applied. In this study, “forward and backward” tracking means that the forward and backward tracking were applied independently; in two-way tracking, they were applied dependently. Two-way tracking was originally proposed by Isobe et al. (2009) to precisely specify the source area of marine debris, where tracking errors were statistically taken into account. In general, two-way tracking in marine biology has been used to specify a spawning ground through PTEs backward in time and estimate transport and survival processes from the inferred spawning area through PTEs forward in time, with tracking errors less carefully addressed [e.g., jack mackerel (Kasai et al. 2008), red sea bream (Sugimatsu et al. 2012), Japanese flying squid Todarodes pacificus (Kim et al. 2015), and marbled sole (Sugimatsu et al. 2016)].

Horizontal and vertical motions of particles

Most studies with PTEs around Japan attributed little swimming ability to early life stages of a species (e.g., egg, larva, and juvenile) or planktonic organisms [e.g., plankton, drifting eelgrass (including its flowering shoot and spadix), and seagrass Enhalus acoroides (including its seed and fruit)] (Online Resource 2). Therefore, passive transport was frequently assumed for the horizontal movement of particles. However, the period when this assumption was valid (i.e., the periods of the PTEs) was different among target species or life stages. Nevertheless, notably, the periods of PTEs and the grid sizes of ocean models were positively correlated with each other on common logarithmic scales (Fig. 6). The positive correlation is also clearer for PTEs with non-swimming ability (blue filled circles). This implied that the period of PTEs was regulated primarily by horizontal advection time for passive transport (roughly equivalent to a size of the model domain divided by a representative model velocity), which tended to be shorter as a higher-resolution model generally has smaller size of the model domain.

Fig. 6
figure 6

Scatter plots of model grid size versus particle-tracking period. Red (blue) filled circles indicate that horizontal swimming ability was (was not) taken into account. The size and contrasting density of filled circles denote the number of studies that share a particle-tracking period and a model grid size

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Roughly speaking, swimming ability tended to be considered when the period of PTEs exceeded 100 days (red-filled circles in Fig. 6). In these cases, which accounted for 14% of the total studies, the target period of PTEs included juvenile to adult stages of fish, mantis shrimp, jellyfish, and loggerhead turtle (Fig. 7a). A relatively large number of studies (≥ 5) incorporated swimming ability for conger eel and Japanese eel. Strictly speaking, the migration model for conger eel (e.g., Motomiya et al. 2015) was not a particle-based model but rather a grid-based tracer model (their differences are discussed in Miki et al. 2018), in which conger eel with multiple year classes was assumed to have a preference for specific water temperature, dissolved oxygen concentration, and sediment grain size. Similar migration models were applied to mantis shrimp Oratosquilla oratoria (Suzuki et al. 2017; Tabeta et al. 2017), marbled sole (Karim et al. 2003), and red sea bream (Hakuta and Tabeta 2013) in Japanese inner bays.

Fig. 7
figure 7

The number of studies for individual species, where a active horizontal swimming and/or b active vertical migration were taken into account. The height of each bar indicates the number of studies with PTEs for each species. Open bars denote studies where active swimming was not taken into account. The number to the upper-right in each panel indicates the total number of PTEs that took account of swimming behavior. The shaded bar in (a) signifies that active swimming in both the vertical and horizontal directions was incorporated into the PTEs

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Particle-based migration models were applied to fish that inhabit shelf and offshore waters. In general, most of these models were less complicated than the above-mentioned grid-based migration models for coastal waters. About half of the studies for larvae of the Japanese eel combined horizontal swimming with diel vertical migration (Fig. 7b) (e.g., Chang et al. 2015; Hsiung and Kimura 2019; Kim et al. 2007). Sea surface temperatures were used to determine the swimming direction of chum salmon (Azumaya and Ishida 2004) and skipjack tuna Katsuwonus pelamis age 0–2 (Aoki et al. 2017). Okunishi et al. (2012) developed an extended kinesis model to model the swimming direction and speed of age-0 Japanese sardine. These studies were limited to feeding migrations. Regarding spawning migrations, there have been a few studies: the spawning migration of Japanese eel from coastal habitats near the Japanese Islands to its spawning ground west of the Mariana Islands (Chang et al. 2016), the spawning migration of age-1 Pacific saury Cololabis saira from the Oyashio to the south area that began in summer (Kakehi et al. 2020), and a series of feeding and spawning migrations of Japanese sardine age 0–2 from the spawning grounds in shelf waters around the Kuroshio via the Oyashio and back to the spawning ground (Okunishi et al. 2009). This last study incorporated very complicated algorithms using an artificial neural network to allow the fish to learn a typical migration pattern. As noted above, PTEs have not been used to simulate the entire recruitment and life cycle beyond a single year class (i.e., one generation). Instead, PTEs are better suited for studies of physico–biological processes for specific stages of a target species assuming idealized conditions.

In contrast to the small number of PTEs incorporating horizontal swimming, more than one-third of the total number of studies (72 studies) incorporated vertical motion into their PTEs. These studies frequently used idealized diel vertical migration and Stokes’s terminal velocity based on the difference in density between particles and seawater [e.g., larvae of walleye pollock Gadus chalcogrammus (Kuroda et al. 2014) and juvenile Japanese grenadier anchovy Coilia Nasus (Fujimoto et al. 2019)]. Elaborate algorithms were developed for larvae of the short-necked clam and Japanese basket clam, where age-dependent ontogenetic vertical migration with a preference for experienced environmental conditions (temperature and/or salinity) were superimposed with Stoke’s terminal velocity (Fujiie et al. 2018; Otsuka et al. 2015; 2016; Yokoyama et al. 2014). For crustacean larvae in particular, it was essential to incorporate their vertical motion to successfully reproduce their observed horizontal distributions, because their megalopa larvae gradually sink to the sea bottom with age for settlement: swimming crab Portunus trituberculatus (Yanagi et al. 1993, 1995), snow crab Chionoecetes opilio (Mao et al. 2019a, b), brachyurans Mictyris brevidactylus and Scopimera globose (Kawachi et al. 2009), Deiratonotus japonicus (Kusuda et al. 2006), and callianassid shrimp Nihonotrypaea harmandi (Fujiie et al. 2004, 2006).

Most studies used simple settlement conditions; they assumed that settlement was completed at an integration time of PTEs (i.e., a specific age) as long as particles were transported to a specific area, which was determined by location of its representative habitat, water depth, and/or grain size on the sea bottom. In contrast, a few studies modeled settlement by using physical parameters: critical tractive force (Kawachi et al. 2009; Kawachi and Ishikawa 2008) or Shields number (Yamaki et al. 2006). For adult shellfish after larval settlement, it is worth pointing out that there is a unique transport model to dynamically explain their horizontal movement near the sea or lake bottom by wave-induced currents, i.e., where their horizontal transport is driven by wave action, not as suspended load but rather as bed load: Japanese scallop (Seto et al. 1998) and Japanese basket clam (Yajima et al. 2017).

Growth and mortality in PTEs

Growth was ignored in 107 studies (Online Resource 2). The remaining 35 studies estimated only the stage (e.g., eggs, larvae, and juveniles) from the age of tracked particles. Body length (or weight) of individual particles was estimated in 23 studies from prior age–body length, age–body length–season, or age–body length–experienced temperature. To sequentially estimate body length during the particle-tracking period, some studies used growth rates that were a function of water temperature, derived from rearing experiments [e.g., juvenile chum salmon (Azumaya et al. 2018)] or field data [juvenile Pacific saury (Oozeki et al. 2015), juvenile Japanese anchovy (Kasamo et al. 2016), and short-necked clam (Fujiie et al. 2018)]. A complicated biogenetic model (Kishi et al. 2009) was sometimes employed to estimate growth: Japanese sardine (Okunishi et al. 2009, 2012) and Japanese flying squid (Ji et al. 2020). Aoki et al. (2017) also applied a dynamic energy budget model to estimate the growth of skipjack tuna.

Mortality was ignored in 137 studies (Online Resource 2). In general, in the remaining studies, simplified natural mortality was applied; a constant mortality rate during a life stage was used in three studies, and particles were assumed to be non-living in 12 studies when the particles continuously experienced temperatures beyond a survival range during a certain period (e.g., > 1 day) or were transported to waters where survival was unrealistic. Some studies estimated a spatio–temporally variable natural mortality rate (i.e., survival rate) as a function of environmental variables: satellite-derived chlorophyll concentrations [crown-of-thorns starfish (Okaji et al. 2019)], temperature [mudflat crab Chiromanters dehaani (Mishima et al. 2018)], salinity [Japanese grenadier anchovy (Fujimoto et al. 2019)], temperature and satellite-derived chlorophyll concentrations [jack mackerel (Komatsu and Kasai 2007)], and predation by Aurelia and Noctiluca [short-necked clam (Hinata and Fukuwaka 2006)]. Under different configurations, natural mortality was estimated on the basis of body length and/or the age/life stage of tracked particles in addition to environmental variables, e.g., jack mackerel (Kasai et al. 2008), chub mackerel Scomber japonicus (Li et al. 2014), Japanese anchovy (Kasamo et al. 2016), and Japanese flying squid (Ji et al. 2020; Kim et al. 2015). Moreover, a general population-dynamics model was applied in some cases to predict the variability of fish population size, in which both natural and fishing mortality were taken into account: red sea bream (Hakuta and Tabeta 2013), and conger eel and mantis shrimp (Tabeta et al. 2017).

Timescale of PTEs

In considering the timescales of interest for PTEs around Japan, it is instructive to examine the time interval covered by the oceanographic, mostly simulated, data that were applied to PTEs (Fig. 8). Climatology and 1-year data were used in 97 studies (54.4% of the total). Interannual variations including year-to-year, multi-year, decadal, and climate timescales under global warming, were highlighted by a mere 14.0% of all studies (filled bars in Fig. 8). Accordingly, PTEs around Japan were most frequently conducted to develop a specific IBM, understand the climatological features of transport/dispersion/migration including their controlling factors, or explain biological features, especially biological distributions that were observed over a few years. Instead of using climatological and short-term (< 1–3 years) oceanographic data, a few studies used long-term ocean model outputs (≥ 10 years) to account for variance of horizontal dispersion and precisely understand the climatological features of transport and dispersion: Pacific bluefin tuna Thunnus orientalis (Kitagawa et al. 2010), Japanese spiny lobster Panulirus japonicus (Miyake et al. 2015), and Japanese eel (Kasai et al. 2021). For climatological and short-term viewpoints, important keywords were “connectivity” or “network,” e.g., short-necked clam in Tokyo Bay (Hinata and Furukawa 2006) and the Ariake Sea (Fujiie et al. 2018), callianassid shrimp around the Ariake Sea (Fujiie et al. 2006), fiddler crab Uca lacteal in the Seto Inland Sea (Uno et al. 2007), Ezo abalone Haliotis discus hanna in Pacific coastal waters of northern Japan (Miyake et al. 2011), marbled sole in the Seto Inland Sea (Sugimatsu et al. 2016; Uchiyama et al. 2014), coral reefs (Taninaka et al. 2019; Uchiyama et al. 2018), and crown-of-thorns starfish around the Ryukyu Islands (Nadaoka et al. 2006a).

Fig. 8
figure 8

Frequency distribution for the period of model outputs that were applied to PTEs. “Clim.” means climatology. Filled bars indicate studies with PTEs that focused on interannual variations such as year-to-year, multi-year, decadal, or climate timescales (e.g., projection of global warming)

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Biological data combined PTEs

Biological data for interannual variations

Note that 20 studies with PTEs examined long-term interannual variations (≥ 10 years) in combination with observed biological data (Fig. 8). Of these, 19 were O-field studies. This shows that interannual biological variations in Japanese coastal waters, which are associated with E-field studies, have been less frequently examined using PTEs. Except for five studies [i.e., turtle, starfish, coral reef, and snow crab (two studies)], the remaining 15 studies were related to interannual variability of pelagic fish and Japanese eel. The key elements for studying the biological interannual variability were fish data combined with PTEs. The biological data could be classified into three types: (1) fishery-independent surveysFootnote 3 for eggs, larvae, and juveniles, or from immature to adult stages, the main targets of which are commercial fisheries resources; (2) fisheries data (e.g., fishing grounds and catch); and (3) estimates by stock assessment for commercial fisheries resources, which were associated with virtual population analysis (VPA).

Fishery-independent surveys of eggs and larvae around Japan (e.g., Oozeki et al. 2007; Sassa et al. 2016) were used to initialize particle positions for Japanese sardine and Japanese anchovy (Itoh et al. 2009, 2011; Kasai et al. 1992, 1997; Nishikawa et al. 2013; Nishikawa 2019) and to compare with results of PTEs (Kasai et al. 1992; Takeshige et al. 2015). Fisheries data were used to estimate catch per unit effort (CPUE), which was compared with results of PTEs for neon flying squid Ommastrephes bartramii (Nishikawa et al. 2014). Commercial catch data were frequently used to validate results from PTEs for Japanese eel, CPUE for glass eels in Tanegashima (Zenimoto et al. 2009), commercial catches of glass eel in East Asian countries (Hsiung et al. 2018), glass eel recruitment in East Asia (Hsu et al. 2017), and glass eel catches in Japan and Taiwan (Chang et al. 2018). For both biological data types (1) and (2), Kakehi et al. (2020) developed an immigration model for age-1 Pacific saury to fishing grounds in the vicinity of Japan to predict changing fishing grounds in space and time. The particle positions in a given year were initialized by fishery-independent surveys a few months before the beginning of the commercial saury fishery, and the immigration model precisely predicted fishing grounds, the distribution of which was consistent with that of actual fishing fleets. Of the type (3) biological data, recruitment per spawning (RPS) estimated by VPA was frequently used as a proxy for mortality rate for virtual larvae, i.e., particles: Japanese sardine (Nishikawa et al. 2013; Nishikawa 2019), Japanese sardine and anchovy (Itoh et al. 2009), and chub mackerel (Keneko et al. 2019). Interannual variations of abundance based on stock assessment were also compared with PTEs for snow crab (Mao et al. 2019b).

These three types of fish data were a very valuable dataset for initialization and validation of PTEs in terms of interannual variability. In particular, fishery-independent surveys of eggs and larvae along the Pacific coast of Japan (Oozeki et al. 2007) have been conducted monthly since 1978. The surveys of eggs and larvae also provide information about basic biological conditions, which were also used in stock assessment by VPA to estimate year-to-year egg production (e.g., Furuichi et al. 2020; Kamimura et al. 2020; Takasuka et al. 2019). It should be remembered that O-field PTEs were less targeted at noncommercial species than E-field PTEs, regardless of the demands for understanding marine biodiversity in offshore waters. However, note also that fishery-independent biological data have already been collected. If the original egg-to-larva net samples are reanalyzed, the resulting datasets would potentially have great usefulness in understanding noncommercial species (e.g., Sassa and Konishi 2015) via initialization and validation of the PTEs.

Pioneering biological data for PTEs

Features of individual particles that were tracked by PTEs (e.g., trajectory, migration route, temperatures experienced, and growth) have been compared with those of individuals that were subsampled from an actual ocean. Itoh et al. (2011) sampled larvae of Japanese sardine and Japanese anchovy around the Kuroshio waters and conducted otolith microstructure analysis. The number and width of otoliths was used as an index of age and growth rate, respectively; the estimated age was used as the particle-tracking period, and the estimated growth rate was compared with the temperatures experienced by particle-based virtual larvae. In general, otolith analysis of larval fish is basic in fisheries science (e.g., Takasuka et al. 2007). Nevertheless, comparison and combination with PTEs is rare in Japan. This is a large gap in Japanese studies that could be immediately filled through collaboration of biological scientists with fisheries oceanographers and PTEs. Additionally, when one-by-one comparison of individual features between an observed sample and a simulated particle is feasible, Lagrangian estimation errors from PTEs are substantial and need to be meticulously discussed (e.g., Itoh et al. 2011).

To obtain biological history along the trajectory of fish migration, Sakamoto et al. (2019) sampled age-0 (about 6 months old) Japanese sardine in the western subarctic region of the North Pacific Ocean and conducted stable oxygen isotope ratio (δ18O) analysis of otoliths with a resolution of 10–30 days. They reproduced the migration history of the sampled age-0 sardines by combining otolith data with a migration model based on PTEs. Yamaguchi et al. (2018) also sampled statoliths of swordtip squid Uroteuthis edulis with an age of about 160 days and estimated micro-increment counts (i.e., the age of the sampled individuals) and Sr:Ca ratios, from which they estimated the temperatures experienced by each sampled squid. These biological data were compared with simulated experienced temperatures of particle-based virtual larvae to adults to reveal the transport process and history.

In some studies, DNA data for a species were analyzed, combined with PTEs, and used to interpret its group behavior, rather than individual behavior based on otolith and statolith data. In and around Sekisei Lagoon in southwestern Japan, Taninaka et al. (2019) extracted genomic DNA from brooding corals Heliopora spp., conducted population connectivity genetic analysis, and showed the validity of the genetic analysis by comparing their results with the results from PTEs for coral larvae. Kasai et al. (2021) sampled environmental DNA (eDNA) for Japanese eel from river waters across all of Japan. The distribution of Japanese eel was clarified by eDNA and accounted for by maritime larval transport based on PTEs. Takayama et al. (2018, 2019) also hypothesized that eDNA sampled at a fixed site over time can be utilized to monitor growth and decay of eelgrass (Zosteraceae) in coastal waters and tested this hypothesis using PTEs.

Practical application of PTEs for environmental management

As described above, most PTEs were developed and applied to academically understand transport, dispersion, and/or migration processes, including connectivity and their controlling factors, as well as to clarify mechanisms of interannual variations in stock and/or recruitment. However, some studies used PTEs for practical purposes related to environmental management. Such studies, mostly E-field studies, focused on coastal species. Suenaga et al. (2001) carried out PTEs to evaluate the effect of habitat corruption attributed to sea-sand mining on recruitment of sand eel Ammodytes personatus in the Seto Inland Sea. Using information from PTEs, Amano et al. (2012) recommended an artificial restoration of riverine topography to recover a suitable habitat and stock of the Japanese basket clam. Suenaga et al. (2004) proposed an optimal deployment location for artificial reefs for Octopus sinensis on the basis of PTEs. Likewise, using PTEs, Shiomi et al. (2012) empirically showed plausible effects of an artificial tidal flat on the short-necked clam fishery. In addition, Yokoyama et al. (2019) evaluated the effects of discharged sewage-treatment water on seaweed aquaculture (i.e., Nori farms) in the Ariake Sea in terms of the artificial supply of dissolved inorganic nitrate. Moreover, Miyake et al. (2011) proposed a practical methodology based on PTEs for the suitable design of abalone refugia. Similarly, Tamura et al. (2005) applied PTEs to understand larval dispersion of reef corals and design marine protected areas.

PTEs have been used in combination with other models to simulate and manage commercial fisheries in Japanese coastal waters. For example, PTEs were combined with a population-dynamics model for juvenile sand eel in the Seto Inland Sea (Nakatani et al. 2013) and with a fish migration and a population-dynamics model for conger eel from fry to adult (Tabeta et al. 2015) and mantis shrimp (Tabeta et al. 2017) in Ise Bay. However, the focus of these fishery simulators was still limited to simulating the seasonality in climatology or a specific year; interannual simulation of these fisheries remains for future work.

Summary

PTEs were first applied around Japan in the 1980s. The history of the PTEs covers only the last 40 years, during which the technology for PTEs has been drastically developed and improved. The current status and perspectives of PTEs around Japanese waters are briefly summarized as follows.

  1. (1)

    Studies with PTEs around Japan can be divided into two groups: E-field and O-field studies. E-field studies deal mainly with species that inhabit coastal-shelf waters during part of a lifetime or the entire life cycle, whereas O-field studies focus primarily on species that migrate extensively in the offshore waters.

  2. (2)

    About 20% of O-field studies and 50% of E-field studies were targeted at noncommercial species, excluding studies of harmful organisms. About 50% of the E-field studies targeting noncommercial species were directed toward rare or endangered species for ecological conservation.

  3. (3)

    For conservation and management of biodiversity in offshore waters around Japan, fishery-independent biological net samples that have been collected for commercial fisheries resources have great potential for providing essential conditions to PTEs for noncommercial species and stimulating O-field studies in the near future.

  4. (4)

    The number of publications of O-field studies with PTEs increased dramatically in the mid-2000s in accordance with the appearance of eddy-resolving ocean models and operational ocean forecast systems. Reanalysis products from the ocean forecast systems were also used as lateral boundary conditions for dynamically downscaled coastal ocean models, mainly in E-field studies. It should again be stressed that the ocean forecast systems around Japan with a horizontal resolution of 1–10 km have resolved a bottleneck for marine biological studies with PTEs and need to be maintained for the sustainable conservation of marine ecosystem and diversity.

  5. (5)

    Many types of ocean model frameworks were used for developing regional coastal ocean models around Japan. It would therefore be helpful to develop and publicly share a unified, highly versatile modeling package based on open-source codes to allow easy, quick, and flexible set-up of coastal ocean models for PTEs.

  6. (6)

    There seem to be technical limitations of PTEs. In most cases a single species, and no more than three species, were treated in a single study with PTEs. In addition, most studies with PTEs in which swimming ability was taken into account successfully reproduced feeding migrations, and a few studies successfully reproduced spawning migrations. However, PTEs were restricted to within one life cycle of a species, so PTEs around Japan have not been used to continuously simulate year-to-year variations in recruitment beyond a single generation (i.e., a year class). Instead, PTEs are most effective for simulating Lagrangian processes in a partial lifetime of a specific species under idealized conditions. Interspecies studies through collaboration among multiple scientists using PTEs are desirable and necessary in the near future to systematically understand marine biodiversity.

  7. (7)

    In O-field studies, biological interannual variations were examined by combining PTEs with fishery-independent data, fisheries data, and stock assessment data. For E-field studies, there is less focus on interannual variations for coastal species using PTEs, although several sophisticated fish migration models coupled with population dynamics and fishery models could reasonably simulate biological seasonality in a few inner bays. A key factor for performing PTEs in coastal waters on an interannual timescale is how to determine lateral boundary conditions for marine biology between a bay mouth and the continental shelf. Active collaborations between the E-field and O-field are anticipated in near future.