FIGURE 1 (a) Map of the Karibetsu and Sarufutsu Rivers in Hokkaido, Japan. The grey rectangle denotes the area shown in (b). (b) Locations of fish sampling (L) and passive integrated transponder (PIT) detection systems (L and T1–T4) in the Karibetsu River.

We calculated Spearman’s rank correlation between migration timings in 2018 and 2019 for individuals that returned consecutively to the Karibetsu River. The calculation was made on both seasonal (date and time) and diel (time only) scales, separately for each sex at each of the following migration stages: arrival at Site L from the estuary (migration stage [MS]1), arrival at tributary sites from Site L (MS2), departure from tributary sites for Site L (MS3), and departure from Site L for the estuary (MS4). Seasonal-scale correlation was also calculated between MS1 and MS4 migration timings of the same individuals in 2019 (i.e. before and after spawning within a season). Circular statistical analyses were performed to test for the uniformity of the diel migration timing using the Rayleigh test, and for differences in the timing between sexes and between upstream and downstream migrations using the Watson–Wheeler test.

Seasonal migration timing was modeled with linear mixed-effects models (LMMs) separately for each migration stage. The PIT code was used as a random effect to account for between-year correlation of the same individuals. Sex, standardized FL, whether migration occurred during daytime (0420–1837 on 1 May, the approximate midpoint of the run, in Sarufutsu Village) or night-time (DN), and the first (First) and total number of tributaries (Tributary) each fish entered for spawning each year were included as candidate fixed effects. Sex and FL were unique to each fish across years and MS; First and Tributary could be different across years but constant across MS; and DN could be different across years and MS. To account for possible sex-related influences, we created a full model including interaction terms between Sex and the other fixed effects. The original response variable of timing in date and time was standardized to have mean 0 and standard deviation 1 for each year and MS. Water temperature and water level variables were not included in this modelling to avoid spurious correlations described earlier.

To determine whether Sakhalin taimen exhibited individual-specific responsiveness to environmental signals, and when the signals became critical, we used a sliding window approach. We defined a critical time window as a period when an environmental cue perceived by the same individuals between years yielded the highest correlation, based on the premise that the cue to initiate movement should be similar within individuals across years if responsiveness to the signal is idiosyncratic. As such, we calculated a series of Pearson correlations between 2018 and 2019 for each of the two variables (water temperature and water level), averaged over time windows relative to each spawner’s arrival timing at the first tributary each year (i.e. MS2). The window size was varied from 8 to 240 h at 4-h increments in both time lag (time to the window’s start) and duration (window width). The maximum correlation coefficient (r _obs) and the corresponding critical time window were recorded for each sex and variable. The significance ofr _obs was determined with a randomization test, in which Pearson correlations were calculated between randomly selected individuals from the two years by varying the window size to find a critical window with a maximum correlation (r _sim). This process was iterated 999 times, and the proportion of r _sim as large as or larger thanr _obs was considered a measure of significance by applying a one-sided test (van de Pol et al., 2016).

We evaluated whether Sakhalin taimen employed social navigation strategies that could lead to coordinated movements and repeatable migration timing by asking two questions: 1) did comigrating groups of pre-spawners ascending through Site L (MS1) tend to enter the same spawning tributaries, diverge into different tributaries, or enter tributaries at random, and 2) did comigrating groups of post-spawners descending through Site L (MS4) tend to consist of individuals that spawned in and departed from the same tributaries, different tributaries, or any tributary at random? If two or more tagged individuals passed Site L over an elapsed time of less than 1 h, the individuals were considered ‘comigrants’ according to a time-series analysis of fish passage in an earlier study (Rand & Fukushima, 2014). Given the disparity in migratory behavior between sexes (see Results), we considered sexes separately in this analysis.

To answer the questions above, we counted the observed total number of comigrating pairs during MS1 or MS4 that subsequently entered, or previously departed from, the same tributaries (n _obs) based on the 2019 dataset. Individual migrants were then randomly assigned to a spawning tributary while preserving their actual MS1 (and MS4) migration timings and the total numbers of migrants accommodated by each tributary. Comigrating pairs that were assigned the same tributaries during each randomization trial were counted (n _sim). This process was iterated 9999 times to generate a distribution of n _sim to compare with n _obs. If n _obswas found to be significantly high relative to the distribution ofn _sim, this would provide evidence that individuals exhibit conspecific attraction during the pre-spawn (i.e. transition from MS1 to MS2) or post-spawn (i.e. transition from MS3 to MS4) periods. Conversely, if n _obs was found to be lower than expected by chance, this provided evidence that individuals exhibit conspecific repulsion during the aforementioned migration stages. Thus, the social interaction hypothesis was tested with two-sided tests.

All statistical analyses were performed using R version 3.4.3 (R Development Core Team, 2017). The R package ‘lme4’ (Bates et al., 2015) was used to perform LMM, and ‘lmerTest’ (Kuznetsova et al., 2020) was used to select the best models via sequential backward elimination of non-significant effects, and to calculate P values based on Satterthwaite’s approximation. Circular statistical analyses used the R package ‘circular’ (Agostinelli & Lund, 2017). Statistical significance was defined at α= 0.05.