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Journal of Experimental Biology partnership with Dryad

Failure by fatigue in the field: a model of fatigue breakage for the macroalga Mazzaella, with validation
Katharine J. Mach, Sarah K. Tepler, Anton V. Staaf, James C. Bohnhoff, Mark W. Denny

SUMMARY

Seaweeds inhabiting the extreme hydrodynamic environment of wave-swept shores break frequently. However, traditional biomechanical analyses, evaluating breakage due to the largest individual waves, have perennially underestimated rates of macroalgal breakage. Recent laboratory testing has established that some seaweeds fail by fatigue, accumulating damage over a series of force impositions. Failure by fatigue may thus account, in part, for the discrepancy between prior breakage predictions, based on individual not repeated wave forces, and reality. Nonetheless, the degree to which fatigue breaks seaweeds on wave-swept shores remains unknown. Here, we developed a model of fatigue breakage due to wave-induced forces for the macroalga Mazzaella flaccida. To test model performance, we made extensive measurements of M. flaccida breakage and of wave-induced velocities experienced by the macroalga. The fatigue-breakage model accounted for significantly more breakage than traditional prediction methods. For life history phases modeled most accurately, 105% (for female gametophytes) and 79% (for tetrasporophytes) of field-observed breakage was predicted, on average. When M. flaccida fronds displayed attributes such as temperature stress and substantial tattering, the fatigue-breakage model underestimated breakage, suggesting that these attributes weaken fronds and lead to more rapid breakage. Exposure to waves had the greatest influence on model performance. At the most wave-protected sites, the model underpredicted breakage, and at the most wave-exposed sites, it overpredicted breakage. Overall, our fatigue-breakage model strongly suggests that, in addition to occurring predictably in the laboratory, fatigue-induced breakage of M. flaccida occurs on wave-swept shores.

FOOTNOTES

  • This research was supported by a Stanford Interdisciplinary Graduate Fellowship to K.J.M., NSF grant IOS-0641068 to M.W.D., and by PISCO, the Partnership for Interdisciplinary Studies of Coastal Oceans, a consortium funded by the Gordon and Betty Moore Foundation and the David and Lucile Packard Foundation. This is contribution 390 of PISCO.

  • LIST OF SYMBOLS

    a
    fitted constant, Eqn 2
    A
    representative area (single-sided surface area for algal frond), Eqn 3
    Axs
    cross-sectional area of frond resisting drag, Eqn 4
    b
    fitted constant, Eqn 5
    CD
    drag coefficient, Eqn 3
    d
    sphere diameter, Eqn 9
    Dcy
    fatigue damage for loading cycle, Eqn 6
    Dtot
    total fatigue damage due to loadings, Eqn 7
    FD
    drag force, Eqn 3
    HK
    fitted constant, Eqn 1
    HS
    offshore significant wave height, Eqn 1
    m
    fitted constant, Eqn 5
    Nbr
    number of cycles to breakage, Eqn 5
    Nbr,cy
    number cycles to breakage at cycle's maximal stress, Eqn 6
    Re
    Reynolds number, Eqn 8
    sdR
    standard deviation of residuals
    SD
    stress due to drag, Eqn 4
    Smax
    maximal stress imposed in each loading cycle, Eqn 5
    u
    fluid velocity, Eqn 3
    uasym
    fitted constant, Eqn 1
    umax
    maximal wave-imposed velocity, Eqn 1
    up
    peak velocity, Eqn 10
    up,max
    day's maximal peak velocity, Eqn 10
    up,norm
    normalized peak velocity, Eqn 10
    ν
    kinematic viscosity, Eqn 9
    ρ
    fluid density, Eqn 3
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