General methodological approach
To examine if larvae utilize external cues (i.e., oriented movement) to swim in a directional manner (i.e., significant mean vector length), we develop two complementary analyses that compare the empirically observed directional precision (i.e., mean vector length) with the null distribution expected under a strict use of internal cues (i.e., unoriented movement). The empirically observed directional precision is quantified as the mean vector length (R) of larval bearings (θ) (Fig. 2a), herein ({hat{R}}_{theta }). The angular differences between consecutive bearings, herein turning angles (Fig. 2a; Δθt = θt-θt-1), are used to generate two null distributions of Rθ expected under the unoriented movement of Correlated Random Walk (CRW; ({R}_{{theta }_{0}})), based on the two analyses: Correlated Random Walk-von Mises (CRW-vm) and Correlated Random Walk- resampling (CRW-r), described below. The first is theoretical and is based on a von Mises distribution of simulated Δθ (Fig. 2b, c); the second is empirical, and is based on resampling the Δθ within each trial (Fig. 2d, e). These two analyses are complementary because the first can generate an unlimited number of trajectories but is based on a theoretical distribution rather than on observations, whereas the second is based on a finite number of observations. In addition to these two main analyses, we apply a third analysis, the Correlated Random Walk-wrapped Cauchy, herein CRW-wc, which is similar to CRW-vm, with the only difference of using wrapped Cauchy distribution instead of von Mises. The reason for applying CRW-wc is that it was shown to represent well animal movement in some cases33. Notably, we consider the simple cases of undirected movement pattern with a turning angle distribution centered at 0 (CRW), testing if the mean vector length of the trial’s sequence is higher than that expected under CRW. If true, that would be an indication for a directed movement pattern (i.e., BRW or BCRW), or an indication for more complex behaviors (discussed in Supplementary note 4).
Statistics and reproducibility
Quantitative analyses are applied to directional trials, i.e., larval bearing sequences ((hat{theta })) that are significantly different from a uniform distribution based on the Rayleigh’s test8 (p < 0.05). We compute the quantiles in which the observed precision (({hat{R}}_{theta })) of each trial falls within the null distributions (({R}_{{theta }_{0}^{{vm}}})and ({R}_{{theta }_{0}^{r}}), computation explained below), and compare these quantile distributions with the null quantile distributions using a chi-square test, gauging the observed directional precision ({hat{R}}_{theta }) against the potential of autocorrelated precision (({R}_{{theta }_{0}})). We employ the simplifying assumptions that a strict use of internal cues is expressed in a CRW process, and that oriented movement patterns result in more directional (or straighter) paths compared to unoriented patterns. Under these assumptions we expect that the empirical ({hat{R}}_{theta }) will exceed the autocorrelated pattern ({R}_{{theta }_{0}}) for individuals that apply oriented movement, whereas for an unorienting individual, ({hat{R}}_{theta }) is expected to be closer to ({bar{R}}_{{theta }_{0}})6 (Fig. 2c). Note however, that it is often difficult to distinguish between oriented and unoriented movement over a short duration (Fig. 2c); the differences between these two types of movements are much more apparent over long time duration, with oriented movement achieving greater displacement compared to unoriented movement45. ({hat{R}}_{theta }) values less than ({R}_{{theta }_{0}})may result from complex behaviors such as one-sided bias (left or right), representing the utilization of internal cues (Fig. 2c, Supplementary Information section S1). In addition, our methodology is not appropriate when movement patterns are complex, e.g., CRW composite, in which there is more than a single CRW pattern per a given sequence, and zig zag patterns, in which consecutive turning angles are drawn from von mises distributions centered around positive and negative values, respectively (Supplementary note 4).
We apply our methods to a database of 835 in situ orientation trials gathered on larvae of 21 species from eight families of perciform fishes at various tropical and warm-water locations in East Asia14,15, Australia16,17,18, Mediterranean52 and Red Sea19, synthesized from eight previously published studies (Table 1). These studies examined the orientation behavior of settlement-stage17 and pre-settlement-stage18 larvae15 of reef-14, non-reef20, and pelagic15 fish species. In addition, some of these studies examine whether larval fish use directional information from the sun for oriented movement19,52, as well as the difference in orientation patterns between individuals versus groups of larvae16.
The methodology used for these in situ studies can be divided into two main categories. First, with direct observations through Scuba-Following, where a larva is released in the pelagic environment and tracked by scuba divers for 10 min, during which swimming direction is recorded every 30 s, resulting in 21 observations (Nobs = 21); for the full protocol, see23,53. Second, with observations using the Drifting In Situ Chamber (DISC54). For each DISC trial, a larva is placed into a circular chamber, and its position is recorded for 15–20 min with an upward-looking camera fixed circa 50 cm below the chamber. The first 3–5 minutes of each DISC trial are considered as acclimation time and are excluded from the analysis, whereas the residual 10–15 min are the actual observations used for the analysis.
The number of observations per DISC deployment (Nobs = 90, 180 or 300; see Table 1) varies with the recording frequency of larval positions, ranging from 2 to 10 seconds (Table 1). Some of the DISC trials had missing data due to the fact that the position of the larva is not always identified during the manual digitization of the DISC trials, due to the small size of the larva and due to unfavorable visibility conditions54. Trials that had Nobs smaller than the required number were not used for the analyses. For the DISC trials, Nobs that had to be larger than 90% of the maximal Nobs designated per group (i.e., Nobs > 81, 162, 270). Trials with Nobs higher than the maximal Nobs were trimmed to contain the maximal Nobs per species, retaining the later-in-time data. For the scuba-following trials, the number of observations had to be Nobs > 20 due to the sensitivity of the analysis to a low number of observations. In other words, a low number of observations limits the capacity of the quantitative analyses to distinguish between oriented and unoriented movement patterns (see Supplementary note 3, Supplementary Figure S3). Importantly, both methods were shown to be robust in terms of artifacts and biases55,56, and have been tested together demonstrating high consistency in larval orientation results16,48.
Each orientation trial includes a sequence of larval swimming directions, termed bearings (θ) (Fig. 2a). For the DISC trials, θ are the cardinal directions of larval positions within the DISC’s chamber55. The angular differences between θ of consecutive time steps (t) are defined as Δθ (Δθt = θt-θt-1), such that for every θ sequence of a given length (N), there is a respective Δθ sequence of length N-1 (Fig. 2a). Directional precision with respect to external and internal cues is computed as the mean vector length of bearings (Rθ) and of turning angles (RΔθ), respectively54. Values of mean vector length (R) range from 0 to 1, with 0 indicating a uniform distribution of angles and 1 indicating that all angles are the same.
We used two quantitative approaches to examine if larvae exhibit oriented movement: the Correlated Random Walk- von Mises and Correlated Random Walk- wrapped Cauchy (CRW-vm and CRW-wc) analyses and the CRW resampling (CRW-r) analysis. Both types of analyses are based on the assumption that trajectories of animals that strictly use internal cues for directional movement are characterized by a CRW pattern. Hence, their capacity for directional movement is exclusively dependent on the distribution of their turning angles (Δθ)57. In contrast, for an external-cues orienting animal, for which movement directions are correlated with an external fixed direction, the mean vector length of the observed bearings, ({hat{R}}_{theta }), is expected to exceed that of a CRW, ({R}_{{theta }_{0}})6. Both analyses compare ({hat{R}}_{theta }) against the expected ({R}_{{theta }_{0}}), but the first type computes ({R}_{{theta }_{0}^{{vm}}})and ({R}_{{theta }_{0}^{{wc}}})using theoretical von Mises and wrapped Cauchy distributions of Δθ, and the second type computes ({R}_{{theta }_{0}^{r}}) by producing 100 new θ sequences per individual trial (larva) by multiple resampling-without-replacement of the Δθ.
A key principle for both analyses types stems from the fact that the mean vector length of bearings (Rθ) is inherently dependent on the mean vector length of turning angles (RΔθ)28. In other words, an animal with a high capacity for unoriented directional movement, i.e., a narrow distribution of Δθ, is likely to yield a high Rθ, even if it makes absolutely no use of external cues for oriented movement. Hence, in both analyses ({hat{R}}_{theta }) is gauged against a distribution of ({R}_{{theta }_{0}}), given its respective mean vector length of turning angles ({hat{R}}_{triangle theta }). The open-source software R58 with the package circular59 is used for all analyses in this study.
Correlated Random Walk-von Mises (CRW-vm)
In this analysis, we first generate the directional precision (R), expected for unoriented CRW movement using the theoretical von Mises distribution (({R}_{{theta }_{0}^{{vm}}})). The CRW bearings sequences (({theta }_{0}^{{vm}})) are generated by choosing a random initial bearing, followed by a series of Nobs-1 turning angles (({triangle theta }_{0}^{{vm}})) in bearing direction; drawn at random (with replacement) from a von Mises distribution (Nrep = 1000). The length of ({theta }_{0}^{{vm}}) sequence is according to the number of observations in our four types of experimental trials: Nobs = 21 for the scuba-following, and 90, 180 and 300 for the DISC (Table 1). The directional precision of the von Mises distribution is dependent on the concentration parameter, kappa. Kappa values ranging from 0 to 399 are applied at 1-unit increments to cover the entire range of directional precision from completely random (kappa = 0), to highly directional (kappa = 399). Next, the directional precision of the bearings (Rθ) and the turning angles (RΔθ) are computed for each simulated sequence of θ (Fig. 2a–c).
These respective pairs of values (RΔθ, Rθ) provide the basis for generating the expected relationship between ({R}_{{theta }_{0}^{{vm}}}) and ({R}_{{triangle theta }_{0}^{{vm}}}). Then, for any given kappa value, the following quantiles are computed: 5th, 10th, 20th,….,90th, and 95th (grey vertical distributions in Fig. 2c). Next, smooth spline functions are fitted through all respective quantiles, generating the ({R}_{{theta }_{0}^{{vm}}})quantile contours, which represent the null expectation under CRW. This expected (RΔθ, Rθ) correspondence creates a phase diagram (Fig. 2c), based on which the observed θ patterns are gauged. The procedure is repeated four times to match the among-study differences in the number of θ observations per trial (i.e., Nobs = 21, 90, 180, and 300; see Table 1).
To examine if the observed larval movement patterns differ from those expected for unoriented movement (CRW-vm), we compute RΔθ and Rθ for each individual trial (({hat{R}}_{triangle theta }) and ({hat{R}}_{theta })). We then place these values in the phase diagram and examine their positions with respect to ({R}_{{theta }_{0}^{{vm}}}) (Fig. 2c). Larvae with ({hat{R}}_{theta }) substantially higher than ({bar{R}}_{{theta }_{0}^{{vm}}}), are considered to have a higher tendency for a straighter movement than expected under CRW, suggesting oriented movement such as BRW and BCRW (Fig. 2b, c)6,28. Larvae with ({hat{R}}_{theta }) values substantially below ({bar{R}}_{{theta }_{0}^{{vm}}})indicate irregular patterns such as a one-sided drift (right or left). A larva is considered directional if the bearing sequence ((hat{theta })) is significantly different from a uniform distribution based on the Rayleigh’s test (p < 0.05)8. Non-directional larvae are characterized by low ({hat{R}}_{triangle theta }) and ({hat{R}}_{theta }), and thus will be situated at the bottom left area in the phase diagram (Fig. 2c). 95% confidence interval (CI) was computed for each species’ trials (({hat{R}}_{triangle theta }), ({hat{R}}_{theta })). The difference (∆R) between ({hat{R}}_{theta }) and ({bar{R}}_{{theta }_{0}^{{vm}}}) was computed per each trial and pooled by species to assess the tendency for a straight movement compared to that expected under CRW, as an indication for oriented movement.
The quantile (Q) of each trial is then computed based on the location of (({hat{R}}_{triangle theta }), ({hat{R}}_{theta })) within the null quantiles’ contours in the phase diagram (Fig. 2c), using a 2-D interpolation such that X = RΔθ, Y = Rθ, and Z = Q (Akima R package60; Fig. 1b). 2-D interpolation is used once more to overlay the (({hat{R}}_{triangle theta }), ({hat{R}}_{theta })) of two species with a different number of observations (Nobs = 300: Premnas biaculeatus, Nobs = 90 Chromis atripectoralis) on the DISC’s phase diagram (Nobs = 180), which represents most of the DISC trials.
Correlated Random Walk-wrapped Cauchy (CRW-wc)
Although von-Mises distribution is the most commonly used circular distribution for simulating CRW11, the wrapped Cauchy distribution well represents the underlying distributions in some cases33. To examine the sensitivity to the underlying distribution of our method, we repeated the exact same protocol of CRW-vm, only with a wrapped Cauchy distribution instead of von-Mises, and respectively, using the rho concentration parameter instead of kappa, with values (n = 400) ranging between 0 and 0.999, representing rho’s minimum and maximum values.
Correlated Random Walk- resampling (CRW-r)
In this analysis, we generate ({R}_{{theta }_{0}}) expected under a strict use of internal cues of CRW pattern using resampling of the turning angles (Δθ) per trial sequence (i.e., ({R}_{{theta }_{0}^{r}})). Specifically, for every trial sequence, ({R}_{{theta }_{0}^{r}}) is computed by generating 100 θ sequences from 100 resampled Δθ sequences (Nrep = 100, without replacement) from the empirical Δθ (Fig. 2d). The ({R}_{{theta }_{0}^{r}}) sequence length is equal to the number of observations in each trial (Nobs). Next, Rθ for each of the resampled sequences (({R}_{{theta }_{0}^{r}})) and the quantile in which ({hat{R}}_{theta }) falls within ({R}_{{theta }_{0}^{r}}), are computed (Fig. 2e). The quantile represents the proportion of ({R}_{{theta }_{0}^{r}}) which is smaller than ({hat{R}}_{theta }) for each trial.
Meta-analysis chi-square goodness-of-fit tests
To test if ({hat{R}}_{theta }) was significantly higher than what is expected under the null, we used chi-square tests to compare the ({hat{R}}_{theta }) quantile distributions (observed trial counts) with the null (({R}_{{theta }_{0}^{{vm}},},{R}_{{theta }_{0}^{{wc}}})and ({R}_{{theta }_{0}^{r}})) quantile distributions (simulated sequences counts). For applying chi-square tests on larvae of different species pooled together, we used the following quantile partitioning: 0–50%, 51–70%, 71–90%, and 91–100%. For applying chi-square tests on larvae pooled by species, we used the following quantile partitioning: 0–50%, 51–75%, 76–100%. The reason for the differences is the minimal number of samples limitation of the chi-square goodness-of-fit test, which is a minimum of 5 samples per expected bin61. This limitation allows a minimum of 20 samples in the species chi-square test, and 50 samples in the chi-square test for all larvae pooled together. Importantly, the analysis is done on counts of the individual trials’ values, thus there is no information loss due to pre-analysis pooling of data.
To test whether ({hat{R}}_{theta }) are significantly higher than what is expected under the null across species, we computed the effect size (Cohen’s W) of each chi-square test per species, and examined if the effect sizes distribution is significantly higher than 0.5 using a one-sided one-sample t-test, after ensuring normality of effect sizes distribution using Shapiro-Wilk test62. Effect size of Cohen’s W ≥ 0.5 represents a strong effect size for the chi-square goodness-of-fit test63. This analysis was applied to trials that contained single larva rather than groups, as grouped larvae were shown to orient differently than single larvae16.
To examine the correspondence between the ({hat{R}}_{theta }) quantiles of the two methods: CRW-vm and CRW-r, the quantiles (Q) data were binned at increments of 5% for the two analyses, creating a 20 × 20 cell matrix (M). Then, the matrix was filled based on the ({hat{R}}_{theta }) quantiles of the larvae, such that for example, a given larva with QCRW-vm = 99% and QCRW-r = 96%, will be counted in M20,20. Whereas, a given larva with QCRW-vm = 52% and QCRW-r = 46%, will be counted in M11,10. Based on this matrix, the corresponding heatmap contoured plot in Fig. 1e was produced, using the R package plot3D64.
If the two methods of analysis (CRW-vm and CRW-r) provide significant test results for a given species, this can be regarded as evidence for oriented movement under our simplifying assumptions. If both methods fail to reject the unoriented movement null hypothesis, it seems likely that external cues are not used for directional movement. However, if the two methods provide differing test results, no definitive conclusion about how directional movement is maintained can be reached.
Subsampling of the DISC trials was carried out, obtaining subsampled sequences with Nobs = 21. This was done to examine the effect of variation in Nobs on the analyses results (i.e., quantiles and △Rθ), and to compare between the DISC and the scuba-following trials under a similar Nobs. Subsampled trials underwent the same filtering scheme as the regular trials in terms of the mean vector significance (Rayleigh’s test) and the available number of observations.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
Source: Ecology - nature.com
