Research ArticleANIMAL NAVIGATION

Asymmetry hidden in birds’ tracks reveals wind, heading, and orientation ability over the ocean

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Science Advances  27 Sep 2017:
Vol. 3, no. 9, e1700097
DOI: 10.1126/sciadv.1700097
  • Fig. 1 Conceptual framework of the inverse problem approach with biologging data.

    The black and red lines indicate the process by which the movement path (the line at the bottom right) of an animal is generated and how the inverse problem approach is applied, respectively. In general, the animal’s movement is affected by both external factors (for example, wind or currents) and internal factors (for example, the internal state, animal navigation capacity, and motion capacity). Here, we simultaneously estimated information relating to animal heading (internal factors) and ocean wind (external factors) by analyzing time series data recorded by bird-borne GPS loggers. (A to C) Patterns of animal response to flow. (A) Full drift. (B) Partial compensation. (C) Complete compensation. The red, blue, and black arrows indicate the heading, flow, and track vectors, respectively. The green arrow indicates the preferred direction of the animal (the direction of the destination).

  • Fig. 2 Heading and track vector distributions of model prediction.

    (A) Example of probability distributions of heading vector pH(uH, vH), distributed symmetrically along the mean heading vector (red arrow). The radius of the red dashed circle is equal to the mean air speed. (B) Example of a probability distribution of a track vector pT(uT, vT), gained by moving pH(uH, vH) to the wind vector (blue arrow). It is asymmetric along the mean track vector (black arrow). The radius of the white dashed circle is equal to the mean speed of the track vector.

  • Fig. 3 Tracks of streaked shearwaters.

    Tracks of streaked shearwaters (N = 33). In the tracks, the parts used for analysis, that is, those in which the bird is in the homing phase and not on land (the boundary is indicated by blue dashed lines), are indicated by the colored lines. The orange dot is the nesting colony on the study site (destination).

  • Fig. 4 Track vector distribution of real track.

    (A to C) The black lines, red arrows, blue arrows, and orange dots indicate the homing tracks, the estimated heading vectors, the estimated wind vectors, and the study site, respectively. (D to F) The track vectors calculated from the position data in the 51-min time window [the part of the track colored green in (A) to (C) is plotted (green dots)]. The radius of the black dashed circles are equal to the mean speed of the track vector. The black, red, and blue arrows represent the mean track vector, the model-estimated mean heading vector, and the wind vector, respectively. The light blue dashed arrow represents the reanalysis wind data. (F) The upper right panel is a magnification of the estimated and reanalysis wind vectors in the main panel. The track vectors are distributed asymmetrically along its mean vector when a crosswind exists and almost symmetrically when the wind is weak, as predicted by the model in Fig. 2B.

  • Fig. 5 Comparison between the wind vectors estimated by the model and by the reanalysis data set.

    (A) Comparison of the wind vector (N = 32). The first and second rows show the mean wind vector of reanalysis data (wind that is calculated by the atmospheric simulation model) and the mean estimated wind vector (wind that is estimated using bird tracks), respectively. The length of the line indicates the wind speed, and the direction indicates the direction in which the wind blows. (B) Comparison of the wind speed. The red solid line is the regression line (y = 0.37x + 1.7), and the red dashed line represents y = x. (C) Comparison of the wind direction. The red dashed line is where y = x.

  • Fig. 6 Orientation strategies of streaked shearwaters.

    (A) Definition of α. (B to D) Mean direction of the track vector plotted against α in three sections: NC (B), OS (C), and WC (D). The slope of the regression line corresponds to the degree of compensation, and the intercept (the value of the track direction at α = 0) corresponds to the preferred direction. The pink dashed line (slope, 1) corresponds to birds that do not compensate (full drift), and the gray dashed line (slope, 0) indicates a bird that completely compensated for wind drift. (E) (Left) Gray lines are homing tracks, and orange, light blue, and purple lines show the NC, OS, and WC sections, respectively. The orange, blue, and purple points are median locations (the location with median latitude and longitude of tracks in each section) of the NC, OS, and WC sections, respectively. Green arrows are the preferred direction, and the red point is the nesting colony (final goal). (Right) Preferred direction (green arrows) and nest direction from the median location (black dots) in each section. The green lines are 95% CI of the preferred direction. The patterns of wind response of birds in each section are shown. The red, blue, and black arrows indicate the heading, wind, and track vectors, respectively.

  • Table 1 Slope and intercept of the linear regression.

    The directions of the colony from each of the median locations (the median locations of the tracks in each of the sections) (see also Fig. 6E) are also shown. PD, preferred direction.

    SectionN (trip)Slope
    (95% CI)
    Intercept (PD)
    (95% CI)
    Direction of the colony from the median locationR2
    NC180.17
    (−0.15 to 0.50)
    203°
    (197–209°)
    201°0.07
    OS260.33
    (0.08 to 0.59)
    211°
    (204–217°)
    199°0.23
    WC240.24
    (−0.08 to 0.55)
    213°
    (206–220°)
    190°0.10

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/9/e1700097/DC1

    note S1. Detailed information regarding the model.

    note S2. Numerical simulation test for checking the effect of realistic sample size on model fitting.

    note S3. Numerical simulation test to assess the effect of variation of flow and track location quality on model fitting.

    fig. S1. Relation between wind speed and difference between estimated and reanalyzed wind direction.

    fig. S2. Probability distributions of heading vector.

    fig. S3. Combinations of mean heading vector, mean track vector, and flow vector used in the simulation.

    fig. S4. Histogram of difference between the value of the estimated and true heading.

    fig. S5. Histograms of results that comply with conditions 1 and 2.

    fig. S6. Dependence of model fitted ratio and estimation accuracy on flow fluctuation and location observation error.

    Sample_Track_Simulation.doc: R code that outputs simulated track data (Sample_Track_Simulation.R)

    Heading_Wind_Estimation.doc: R code for estimating the heading direction and wind from the track data (Heading_Wind_Estimation.R)

    Real_Track_Data.csv: Homing track data of streaked shearwaters (N = 33)

  • Supplementary Materials

    This PDF file includes:

    • note S1. Detailed information regarding the model.
    • note S2. Numerical simulation test for checking the effect of realistic sample size on model fitting.
    • note S3. Numerical simulation test to assess the effect of variation of flow and track location quality on model fitting.
    • fig. S1. Relation between wind speed and difference between estimated and reanalyzed wind direction.
    • fig. S2. Probability distributions of heading vector.
    • fig. S3. Combinations of mean heading vector, mean track vector, and flow vector used in the simulation.
    • fig. S4. Histogram of difference between the value of the estimated and true heading.
    • fig. S5. Histograms of results that comply with conditions 1 and 2.
    • fig. S6. Dependence of model fitted ratio and estimation accuracy on flow fluctuation and location observation error.

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    Other Supplementary Material for this manuscript includes the following:

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