In early spring, adult anchovies migrate from their offshore overwintering grounds to coastal waters to spawn (Fig. 1). Spawning occurs from April to October and peaks between May and June (Hao et al., 2003; Zhang et al., 2020b). Embryonic development requires approximately 42–72 h. Previous studies indicate that anchovy larvae begin to exhibit weak active swimming ability at a body length of 5–7 mm, with swimming capacity gradually increasing between 10 and 20 mm, and reaching a more developed stage at 20–25 mm (Masuda, 2011). Given that the present study focuses on larvae ≤ 20 mm in length (approximately within 30 d post-hatching), active swimming behaviour was neglected following previous approaches, and larvae were treated as passive particles (Takeshige et al., 2015; Xing et al., 2020).

Seven Japanese anchovy spawning grounds (located in the Bohai, Yellow, and East China Seas) were selected for this study (Fig. 1), including: Zhuanghe Bay (ZH; Ye and Zhang, 1965); northeast of Bohai Bay and in Laizhou Bay (BHB and LZB, respectively; Yu et al., 2020); Yantai (YT; Ye and Zhang, 1965); south of the Shandong Peninsula and in Haizhou Bay (SDI and HZB, respectively; Zhang et al., 2020b); and the Changjiang Estuary (CJ; Iseki and Kiyomoto, 1997). Lagrangian particles were released and tracked from these sites. Additionally, two spawning grounds for Japanese stocks were included to study connectivity: northwest of Kyushu (TWC; Takeshige et al., 2015) and south of Kyushu (PS; Zenitani and Kimura, 2007). Notably, no particles were released from these two sites.

Lagrangian particle tracking simulation outputs from Xing et al. (2020) and Xing et al. (2021), which investigated larval retention of Japanese anchovy during 1987–2004, respectively, were applied in this study. In those simulations, passive particles representing larvae were released in surface waters throughout the Yellow Sea (YS) and the Bohai Sea (BS). From these datasets, we extracted and analyzed the trajectories of particles released from the larval release locations defined in the present study. The hydrodynamic model and Lagrangian particle tracking model were described as follows.

The particle trajectories analyzed here were taken from Xing et al. (2021) for 1987–2004. Details of the corresponding hydrodynamic-model configurations and validation are provided in those studies. Briefly, the Finite Volume Coastal Ocean Model (FVCOM) was used to simulate the hydrodynamic fields for larval dispersal. This model has been successfully applied to study larval retention of Japanese anchovy in the YS (Xing et al., 2020, 2021). The model configuration features a horizontal resolution of 6.5 km (41 sigma layers vertically), with a mesh of 44 682 nodes and 86 107 grids. The time step was 40 s and hourly current data from the published simulations were used to drive the particle tracking model. Over 4 months in 2012 and 2013 the model reproduced subtidal current velocities with root-mean-square errors of 0.70 to 3.24 cm s⁻¹.

Given the weak swimming ability of Japanese anchovy below 20 mm in length, a 2D Lagrangian particle tracking model was developed to simulate the passive transport of fish larvae, with active swimming behavior neglected (Takeshige et al., 2015; Xing et al., 2020). In this algorithm, a fourth-order Runge-Kutta scheme was used to prevent excessively large truncation errors. Random walk was also considered to resolve sub-grid scale phenomenon, such as horizontal turbulent flow (Willis, 2011; Choi et al., 2018). The horizontal diffusivity coefficient was based on the Smagorinsky diffusivity scheme (Choi et al., 2018). The time step for this particle tracking model was set as 1 h. The hydrodynamic fields from the FVCOM simulation served as the driver for the particle movements. A comprehensive description of the algorithm is provided by Xing et al. (2020). Larval release was specified as follows.

Larval release location. Larval particles were released from the seven spawning grounds identified in China Seas in Fig. 1 (ZH, BHB, LZB, YT, SDI, HZB, CJ). Each site was divided into ∼ 150 grid cells, consistent with the FVCOM grid. All particles were released from the center of the grid; and they were released in the surface layer (the uppermost sigma layer of FVCOM model) as living eggs and larvae for Japanese Anchovy have typically been found near the surface (Iseki and Kiyomoto, 1997). Larval vertical migration and larval mortality were not considered in this study. To minimize the influence of release-area size, we used standardized rectangular release areas for each release location.

The 1D dispersal kernel has been long recognized as a useful approach to quantify dispersal patterns of plant seeds, insects and fish larvae (Cowen and Sponaugle, 2009; Ayata et al., 2010; D'Aloia et al., 2015; Almany et al., 2017; Shi et al., 2019; Shi et al., 2024). It represents the probability density function (PDF) of these dispersal distances, which is defined as the straight-line distance between a particle release location and its settlement location. In this study, dispersal distances from all 18 simulated years were aggregated for each spawning ground to compute a unique kernel for each ground. Additionally, a separate, combined kernel was calculated by pooling dispersal distances from all grounds, resulting in a total of eight dispersal kernels (seven for the individual grounds and one collective kernel).

The kernel can provide three important metrics characterizing larval dispersal: local retention, mean- (or median-) dispersal distance, and long-distance dispersal (Nickols et al., 2015). Local retention is the ratio of locally produced settlement to total local larval release, determining the self-persistence of a population (Botsford et al., 2009). The median-dispersal distance describes the distance within which half of larvae settle. Long-distance dispersal, usually defined as the 95th-percentile dispersal distance, is important for estimating population invasion, population spread, and genetic connectivity (Cowen and Sponaugle, 2009; Nathan, 2008; Nathan et al., 2008). Self-recruitment, which is related to but distinct from local retention (Botsford et al., 2009), was also computed. It represents the ratio of locally produced settlement to settlement from all origins at a site.

The kernel above is a function of distance only, and does not convey information on direction. It is thus referred to as a “one-dimensional (1D) dispersal distance kernel” (Siegel et al., 2003). Edwards et al. (2007) extended the 1D kernel into two dimensions (2D), as a “2D dispersal location kernel”, by computing a set of indices to describe the kernel in areas with strong anisotropy in circulation. Huret et al. (2010) further refined this approach by introducing spatial indices related to spatial occupation and aggregation. Several indices were defined to characterize the 2D larval dispersal location kernels, enabling statistical analysis of the particle distributions (Edwards et al., 2007; Ayata et al., 2010; Hinrichsen et al., 2012; Puckett et al., 2014).

The geographic position of the settlement locations, included the center of gravity, xm, ym, along with the associated variances and covariance, Sx, Sy, and Sxy.

We performed a multi-factor, multi-variable analysis of variance (MANOVA) to evaluate the impacts of spawning ground, travel duration, spawning year and spawning month on dispersal. Variables comprised seven metrics: (i) the geographic position of the center of gravity (xm, ym, Sx, Sy, and Sxy), (ii) the mean relative transport indices (mean distance and direction of the center of gravity from the release location, dm and θ), (iii) the ellipse characteristics (I, amaj, amin, iso, and θm), (iv) spatial and aggregation indices (PA, SA, EA and CV₀), (v) connectivity between each spawning ground (∑iCi,ZH, ∑iCi,BHB, ∑iCi,LZB, ∑iCi,YT, ∑iCi,SDI, ∑iCi,HZB, ∑iCi,CJ, ∑iCi,TWC, ∑iCi,PS), (vi) local retention, and (vii) self-recruitment. The MANOVA was performed using the 50-50 MANOVA Matlab^® code from Langsrud (2002), which is designed to handle multiple highly collinear response variables.

Japanese anchovy larvae were simulated to settle over a wide range, while were concentrated in the BS, the northern YS and along the southern coast of the Shandong Peninsula, with peak densities near 39° N, identifying these regions as major nursery grounds. From 1987–2004, larvae dispersed widely during their pelagic stage, encompassing the Bohai, Yellow, and East China seas, the Korea Strait, the Sea of Japan, and the northwestern Pacific (Fig. 2). Settlement density gradually decreased southward and offshore (except in the BS), consistent with a predominantly northward transport pattern driven by regional circulation (Xing et al., 2020).

We estimated the 1D dispersal kernel by fitting various PDFs to the modelled dispersal distances. The best-fitting 1D dispersal kernel was a Weibull function (Table S1 in the Supplement; Fig. 3): 11ρd=aλ(dλ)a-1⋅e-(d/λ)a where ρd is the probability density function, d is the dispersal distance (in kilometers). The scale parameter is λ=164.31, and the shape parameter is a=1.48. The modal dispersal distance was 73.31 km, the median-dispersal distance was 128.37 km, and the long-distance dispersal threshold was 344.03 km.

The modeled larval dispersal patterns in the present study are generally consistent with the observations reported by Wan et al. (2002), partly consistent with those of Wan et al. (2008), and partly inconsistent with the patterns described by Zhang et al. (2025). In Wan et al. (2002), larval abundance decreased along a survey transect extending from approximately 120.6° E, 35.9° N to 125.8° E, 33.0° N, consistent with the density gradient shown in Fig. 2b. Furthermore, along the transect from 123.0° E, 31.0° N to 125.8° E, 33.0° N, larval abundance peaked near the midpoint of the transect (approximately 125.0° E, 32.5° N), corresponding closely to the high-density region simulated in the northern East China Sea (Fig. 2b). Wan et al. (2008) reported the presence of larvae in the vicinity of Haizhou Bay during 2000–2003, which is consistent with the simulated settlement patterns. In contrast, Zhang et al. (2025) found relatively few larvae around Haizhou Bay during 2016–2018, with most individuals occurring in nearshore waters around 34° N, south of Haizhou Bay. This discrepancy may reflect the existence of additional spawning grounds that were not considered in the present study to provide those larvae around 34° N, or the simplifying assumption of passive larval transport. Incorporating active larval behaviors, such as directional swimming or rheotaxis, may alter settlement distributions and help reconcile model predictions with observed patterns. These possibilities are quite interesting and warrant further investigation.

Spawning grounds played a critical role in shaping larval dispersal patterns in this study because they were located within three distinct marine systems, including the Bohai Sea (BS), Yellow Sea (YS), and East China Sea (ECS), spanning approximately 8° of latitude and experiencing contrasting circulation regimes. The spatial variability in larval dispersal among spawning grounds primarily reflects differences in the surrounding hydrodynamic environments and geographic settings. For example, the Changjiang Estuary (CJ) spawning ground in the ECS is influenced by a complex circulation system involving the Changjiang Diluted Water (CDW), coastal currents, the Taiwan Warm Current, the Kuroshio, and wind-driven circulation. The eastward transport of larvae from this region is therefore associated with the combined effects of these circulation processes rather than the CDW alone (Xing et al., 2020). In contrast, spawning grounds in the BS, such as the Bohai Bay (BHB) and Laizhou Bay (LZB), are located within semi-enclosed coastal systems dominated by basin-scale circulation and coastal currents, which constrain larval transport and enhance local retention (Liang and Sun, 2003). Therefore, the location of spawning grounds determines the initial hydrodynamic conditions experienced by larvae, thereby exerting a stronger influence on dispersal pathways, distances, and connectivity patterns than other factors.

Although travel duration, spawning month, and spawning year also affected larval dispersal, their effects were largely mediated by seasonal and interannual variations in circulation. The settlement center shifted eastward and northward from April to June but shifted westward and southward after July (Fig. 5, bottom right panel), consistent with seasonal transitions in regional circulation. During the spawning period considered in this study, the circulation system of the China seas was primarily characterized by the summer monsoon-driven circulation pattern, although local and interannual variability remained. These circulation variations altered larval transport pathways and consequently contributed to differences in settlement distributions among spawning months and years.

However, the relative importance of these factors varies across environments and species. For instance, Huret et al. (2010) applied a particle tracking approach to investigate larval dispersal patterns of Engraulis encrasicolus in the Bay of Biscay and applied MANOVA to evaluate impacts of the various factors on 2D dispersal kernel metrices, including release date, spawning date (week and year), spawning ground (five grounds spanning 3.5° of latitude), travel duration, and vertical behavior. Their results showed that spawning location explained most of the variance in geographic and relative positions, travel duration dominated the variance in ellipse, and vertical behaviour primarily influenced aggregation patterns.

Previous studies have reported conflicting results on using PLD as a proxy for dispersal distance. Our results help reconcile these findings by showing that PLD can capture broad-scale average patterns of dispersal potential, but is a poor predictor of realized dispersal distance at the individual level. Shanks et al. (2003) and Shanks (2009) compiled independent, direct estimates of dispersal distance and compared them to propagule duration (a broader term encompassing PLD). Both studies found that, at a coarse scale, propagule duration was moderately correlated (R2=0.6) with dispersal distance. Selkoe and Toonen (2011) further demonstrated a consistent, moderate fit between genetic proxies of dispersal (using either isolation-by-distance slope or global Wright's fixation index FST) and PLD. Similarly, Alvarez-Noriega et al. (2020) assumed that larval dispersal distance is proportional to PLD and thus computed the global latitudinal gradient in dispersal distance by multiplying PLD by local mean ocean current velocity. In contrast, D'Aloia et al. (2015) observed that individual PLDs were not correlated with dispersal distance based on genetic parentage analysis. More recently, Shi et al. (2024) reported a very strong linear correlation (R2=0.98) between PLD and travel distance (distance along transport trajectories), while only a moderate correlation (R2=0.85) between PLD and linear distance.

In this study, mean orthodromic distance from release location center to settlement center (dm) increased with increasing PLD (Fig. 7), indicating that PLD captures average dispersal trends. However, the correlation between individual dispersal distance and PLD was weak (Pearson correlation = 0.243, Spearman correlation = 0.238; Fig. S3). These suggest that, PLD captures broad, average trends in dispersal potential, but it is not a reliable predictor of dispersal distance at the individual level. This discrepancy arises because individual trajectories are strongly modulated by the spatial structure of the circulation field. When currents exhibit relatively persistent and unidirectional pathways, longer PLD may translate into greater displacement. In contrast, in regions characterized by curved streamlines, recirculation, or retention zones, larvae may remain within confined areas despite prolonged transport durations. Therefore, increasing PLD does not necessarily result in longer dispersal distances for individual larvae, because dispersal outcomes depend not only on the duration of transport but also on the connectivity and geometry of the underlying flow pathways.

The Weibull 1D dispersal kernel is consistent with previous Lagrangian particle tracking simulations, but differs from genetic parentage analyses, in which generalized Gaussian dispersal kernels were commonly used: 12ρk,d=exp[-(kd)c] where k is the scale parameter, and c is a shape parameter defining the form of the kernel. When c=1, the kernel reduces to the classical exponential decay model, also referred to as the Laplacian; c=2 gives the Gaussian (bell-shaped) distribution and c=3 yields a Ribbens function (Almany et al., 2013, 2017). Notably, this formulation is not explicitly normalized with a scale coefficient, as normalization is implicitly handled within likelihood-based connectivity models. In this kernel family, dispersal strength decreases monotonically with increasing dispersal distance, with the modal dispersal distance occurring at the source location.

Consistent with this property, genetic parentage analyses commonly infer kernels peaking at the natal reef (source location). For example, D'Aloia et al. (2015) and Almany et al. (2017) applied a Laplacian kernel to reef fish (Elacatinus lori; PLD: 15–42 d) on the Belize Barrier Reef, and clownfish (Amphiprion percula; PLD: 10–12 d) and butterflyfish (Chaetodon vagabundus; PLD: 28–45 d) in Papua New Guinea. Hamilton et al. (2021) fitted a Ribbens dispersal kernel for Bolbometopon muricatum (PLD: ∼ 25 d) larvae in Solomon Islands. Catalano et al. (2021) and Dedrick et al. (2021) applied generalized Gaussian kernels for Amphiprion clarkii (PLD: 7–10 d) along a 30 km Philippines coastline.

In contrast, Lagrangian particle-tracking studies often predict kernels with non-zero modal dispersal distances. Siegel et al. (2003) employed a Gaussian dispersal kernel to approximate the mechanisms of larval transport in turbulent coastal flows, with a modal dispersal distance of ∼ 208 km for long PLDs (0–56 d). Vaz et al. (2023) used a biophysical connectivity model (Connectivity Modeling System) to study larval dispersal of Lutjanus campechanus in the Gulf of Mexico, predicting a modal distance of ∼ 50 km (PLD: 26–30 d). Similarly, Nickols et al. (2015) found modal dispersal distances of 50–150 km using particle-tracking simulations with and without a coastal boundary layer (PLD: 2–30 d).

Consistent with these biophysical results, the best-fitting 1D dispersal kernel in the present study was a Weibull function, which predicts a non-zero modal dispersal distance (43–153 km) and broader dispersal, with 50 % of larvae settling 73–195 km from the source. The discrepancy between Weibull and Gaussian kernels may be attributed to several factors, including but not limited to two main aspects. First, parentage analyses rely on in situ observations and typically capture only a limited number of dispersal events within specific time windows and locations, potentially missing long-distance dispersal occurring farther from the source. Second, many simulations assume passive larvae and neglect active swimming behavior. In reality, larval behaviors such as oriented swimming toward the source, may reduce dispersal distances and alter the shape of the dispersal kernel. Further investigation that integrates parentage analysis with biophysical modeling is thus required to elucidate the mechanisms underlying these contrasting dispersal patterns.

Whether Japanese anchovy populations from the China Seas and the Japan Sea spawning grounds belong to a single stock or represent distinct stocks remains unresolved. Using genetic analyses, Yu et al. (2002) reported that the Japanese anchovy populations from spawning grounds near northeastern Taiwan, in the Pacific Ocean, and near southwestern Taiwan, in the Taiwan Strait, were indeed separate stocks. In contrast, Yu et al. (2005) and Zheng et al. (2015) found no significant genetic differentiation among populations from the YS and East China Sea. Furthermore, marginally significant genetic structure was detected between the BS and Japan Sea populations, as well as between the North YS and Japan Sea population (Zhang et al., 2020a).

Results from the present larval dispersal study suggest that the CJ spawning ground may provide a potential pathway for larval exchange among regional populations. Larvae originating from CJ were transported not only to the central YS, where they potentially overlap with larvae from other China Sea spawning grounds, but also to the northwest of Kyushu (TWC) and south of Kyushu (PS) in the Japan Sea. This is consistent with trajectories of satellite-tracked surface drifters deployed between the Changjiang River mouth and Jeju Island in summer from 1993–2003, some of which were transported to Jeju and Korea/Tsushima Strait (Matsuno et al., 2006; Moon et al., 2010). These results suggest the potential for larval exchange between the China Seas and Japan Sea regions. However, the arrival of CJ-derived larvae in TWC and PS alone is insufficient to demonstrate effective stock connectivity. Larvae spawned at TWC and PS may already have been transported elsewhere by the time CJ-derived larvae arrive, resulting in limited spatial and temporal overlap between the two groups. Consequently, the observed dispersal pathways indicate only the potential for connectivity, rather than direct evidence of population mixing or recruitment into a common stock. A more convincing demonstration of stock connectivity would require showing that larvae originating from CJ, TWC, and PS converge in the same or adjacent nursery habitats and overlap in space and time, thereby increasing opportunities for mixing and recruitment into a shared population.

Despite providing new insights into larval dispersal and connectivity of Japanese anchovy in the China Seas, several limitations should be acknowledged. First, the particle-tracking simulations assumed predominantly passive larval transport and did not explicitly incorporate active swimming behaviors (e.g., rheotaxis or directional swimming), which may influence realized dispersal distances and connectivity patterns. Second, although egg production and distribution are spatially and temporally heterogeneous in nature, particles were released uniformly in space and time in the present study. This simplification may affect estimates of dispersal rates and connectivity strength among spawning grounds. These standardized release areas should therefore be interpreted as experimental source regions for comparing dispersal potential, rather than as exact reconstructions of realized egg-production fields. Third, biological processes such as growth, mortality, predation, and habitat selection were not explicitly represented; for example, larvae released from different locations will experience different water temperature, thus affect larval growth rate and travel duration. Notably, this study focused on connectivity among spawning grounds rather than between spawning and nursery grounds, as the latter remain insufficiently characterized. Further research is therefore needed to identify nursery habitats and quantify spawning–nursery connectivity.

The findings of this study have several important implications for fisheries management and conservation of Japanese anchovy. First, the dominant role of spawning location in shaping dispersal and connectivity suggests that key spawning grounds, particularly the Changjiang (CJ) spawning ground, warrant further attention in future connectivity and management studies because this region may provide a potential transport pathway between the China Seas and the Sea of Japan. Second, the identification of the BS, northern YS, and southern Shandong Peninsula as major nursery areas suggests that these regions may warrant consideration in habitat conservation and management planning. Third, the strong seasonal variability in dispersal patterns indicates that management strategies should account for temporal dynamics. Fourth, the relatively minor contribution of interannual variability in these simulations suggests that persistent spatial structures may be important, although this result should be interpreted cautiously because interannual variability in spawning-ground location and egg production was not represented. Finally, the quantified dispersal kernels provide a useful framework for incorporating connectivity into stock assessment and spatial management models.