Research ArticleMarine Ecology

Fairy circle landscapes under the sea

See allHide authors and affiliations

Science Advances  02 Aug 2017:
Vol. 3, no. 8, e1603262
DOI: 10.1126/sciadv.1603262
  • Fig. 1 Examples of fairy circles and spatial patterns in Mediterranean seagrass meadows.

    (A) Side-scan image of a seagrass meadow in Pollença bay (Mallorca Island, Western Mediterranean) from LIFE Posidonia (31) showing different patterns in meadows of P. oceanica and C. nodosa. Other examples are shown in figs. S9 to S11. (B) Image of a fairy circle in a P. oceanica meadow in the Adriatic Sea as seen from the coast. Photography by Zvaqan is available in Google Street View and (C) the same fairy circle in a satellite image of Google maps (44°05′37.5″N, 14°55′37.6″E). Other fairy circles can be found at the following locations: 44°04′01.8″N, 14°57′53.3″E and 39°08′48.2″N, 2°56′07.1″E.

  • Fig. 2 Mean shoot density Embedded Image (that is, total number of shoots divided by the whole simulation area) as a function of normalized mortality ωd0b for five different solutions of the ABD model for homogeneous ωd0 and homogeneous b.

    Homogeneous populated and unpopulated states are shown in red, hexagonal arrangement of fairy circles in yellow, stripes in green, and hexagonal arrangement of spots in blue. Solid (dashed) lines indicate stable (unstable) solutions. The insets show the vegetation patterns in the inhomogeneous cases. Only the stable part of the pattern branches is shown, as obtained from direct numerical simulations of the model. MI corresponds to the modulational instability of the populated state, and T corresponds to the transcritical bifurcation of the bare soil. We take parameter values in a range that reproduce patterns seen in side scans using typical values for P. oceanica for the parameters already known [see the study by Sintes et al. (33) and references therein]: ωb = 0.06 year−1, ν = 6.11 cm year−1, ρ = 2.87 cm, φb = 45°, b = 1.25 cm4 year−1, κ = 0.048 year−1, σκ = 2851.4 cm, a = 27.38 cm2, σμ = 203.7 cm, μ = ωd0 (see the Supplementary Materials). The formation of the three patterned solutions (negative hexagons, stripes, and positive hexagons) is shown in movies S1, S2, and S3, respectively.

  • Fig. 3 Spatial distribution of the shoot density (high densities are represented in dark green and low ones in bright yellow) in a simulation of a P. oceanica meadow showing a stable fairy circle.

    The fairy circle, or dissipative soliton, is clear in the density profile (B) along the transverse cut shown in (A) by a dashed line. Here, ωd0 = 0.057 year−1. Other parameters are the same as in Fig. 2.

  • Fig. 4 Comparison of numerical simulations with patterns observed in seagrass meadows.

    (A) Final spatial density distribution of shoots from a numerical simulation of the ABD model that uses the mortality profile plotted in (B). (C) Observed coverage (31) of P. oceanica from LIFE Posidonia side-scan cartography in the Balearic coast area limited by the following coordinates: 39°45′54.1″N, 3°09′49.5″E; 39°47′25.6″N, 3°11′48.7″E; 39°47′48.6″N, 3°11′19.0″E; and 39°46′17.1″N, 3°09′19.9″E. (D) Depth in that region averaged along the y direction. (E to H) Comparison of a numerical simulation with field density measures: (E) Spatial density distribution of P. oceanica as obtained from numerical simulations with a custom spatially dependent mortality [orange line in (G), left scale] and a profile of the saturation strength b(x, y) [blue line in (G), right scale]. (F) Cut of (E) at y = 102. (H) Observed P. oceanica density measured by scuba divers (in blue, data file S1) as function of the depth for different locations spread over the coastline of the Balearic Islands and the density in random locations of the numerical simulation shown in (E) (gray). Parameters are same as in Fig. 2. The time evolutions of the simulations are shown in movies S4 and S5.

  • Fig. 5 Comparison of numerical simulation with patterns observed by side-scan sonar (31) for a region of coexistence between holes and patches in a meadow of C. nodosa in Mallorca Island (Fig. 1).

    The set of model parameters for C. nodosa is ωb = 2.3 year−1, ν = 160 cm year−1, ρ = 3.7 cm, φb = 45°, b = 112.71 cm4 year−1, κ = 2.76 year−1, σκ = 2226.1 cm, a = 21.0 cm2, σμ = 139.1 cm, and μ = ωd0, and the area modeled (a subset of that shown in Fig. 1A) is bounded by the coordinates 39°53′16.4″N, 3°05′12.7″E; 39°51′52.0″N, 3°06′15.7″E; 39°51′43.1″N, 3°05′55.6″E; and 39°53′07.5″N, 3°04′52.6″E (movie S6). (A) Final spatial density distribution of shoots from a numerical simulation of the ABD model using the mortality profile shown in (B). (C) Observed coverage (31) of C. Nodosa from LIFE Posidonia side-scan cartography in the Balearic coast.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/8/e1603262/DC1

    Materials and Methods

    fig. S1. Mean shoot density Formula (that is, total number of shoots divided by the whole simulation area) as a function of normalized mortality ωd0b for the supercritical case.

    fig. S2. Growth rate of perturbation with wave number (qx, qy = 0) close to the MI.

    fig. S3. Phase diagram of the ABD model for P. oceanica.

    fig. S4. Wavelength of the maximum growth rate as function of the competition range σκ for five different values of the intrinsic mortality ωd0.

    fig. S5. Shape of the kernel FormulaFormula in real space (left) and Fourier space (right).

    fig. S6. Comparison of numerical simulations with patterns in real meadows in the absence of noise in the profile corresponding to the same conditions as those in Fig. 4 (A to D).

    fig. S7. Example of noise distribution used in the numerical simulations.

    fig. S8. Fourier transform of a side-scan cartography image of a rectangular region of a meadow of P. oceanica.

    fig. S9. Side-scan cartography of Pollença and Alcúdia bays (Mallorca Island, Western Mediterranean).

    fig. S10. Side-scan cartography of Llevant coast (Mallorca Island, Western Mediterranean).

    fig. S11. Side-scan cartograhpy of Cap Enderrocat (Mallorca Island, Western Mediterranean).

    table S1. Coordinates of analyzed regions.

    table S2. Measured wavelength of the patterns.

    movie S1. Formation of negative hexagons.

    movie S2. Formation of stripes.

    movie S3. Formation of positive hexagons.

    movie S4. Temporal evolution of Fig. 4A.

    movie S5. Temporal evolution of Fig. 4 (E, F, and H).

    movie S6. Temporal evolution of Fig. 5A.

    data file S1. P. oceanica density as function of the depth for different locations spread over the coastline of the Balearic Islands.

    Reference (58)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Materials and Methods
    • fig. S1. Mean shoot density nt (that is, total number of shoots divided by the whole simulation area) as a function of normalized mortality ωd0b for the supercritical case.
    • fig. S2. Growth rate of perturbation with wave number (qx, qy = 0) close to the MI.
    • fig. S3. Phase diagram of the ABD model for P. oceanica.
    • fig. S4. Wavelength of the maximum growth rate as function of the competition range σκ for five different values of the intrinsic mortality ωd0.
    • fig. S5. Shape of the kernel K(r) in real space (left) and Fourier space (right).
    • fig. S6. Comparison of numerical simulations with patterns in real meadows in the absence of noise in the profile corresponding to the same conditions as those in Fig. 4 (A to D).
    • fig. S7. Example of noise distribution used in the numerical simulations.
    • fig. S8. Fourier transform of a side-scan cartography image of a rectangular
      region of a meadow of P. oceanica.
    • fig. S9. Side-scan cartography of Pollença and Alcúdia bays (Mallorca Island, Western Mediterranean).
    • fig. S10. Side-scan cartography of Llevant coast (Mallorca Island, Western Mediterranean).
    • fig. S11. Side-scan cartograhpy of Cap Enderrocat (Mallorca Island, Western Mediterranean).
    • table S1. Coordinates of analyzed regions.
    • table S2. Measured wavelength of the patterns.
    • Legends for movies S1 to S6
    • Reference (58)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mov format). Formation of negative hexagons.
    • movie S2 (.mov format). Formation of stripes.
    • movie S3 (.mov format). Formation of positive hexagons.
    • movie S4 (.mov format). Temporal evolution of Fig. 4A.
    • movie S5 (.mov format). Temporal evolution of Fig. 4 (E, F, and H).
    • movie S6 (.mov format). Temporal evolution of Fig. 5A.
    • data file S1 (Microsoft Excel format). P. oceanica density as function of the depth for different locations spread over the coastline of the Balearic Islands.

    Files in this Data Supplement: