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First published online May 21, 2007
Journal of Experimental Biology 210, 1868-1873 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.003772
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Morphological diversity of medusan lineages constrained by animal–fluid interactions

John O. Dabiri1,*, Sean P. Colin2 and John H. Costello3

1 Graduate Aeronautical Laboratories and Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA
2 Environmental Sciences, Roger Williams University, Bristol, RI 02809, USA
3 Biology, Providence College, Providence, RI 02918, USA


Figure 1
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  		Fig. 1. Visualizations of medusa flow currents. (A) Jet propulsion in juvenile Aequorea victoria. A vortex ring (CV) is formed in the water during the bell contraction phase, whereas no vortex is formed in the water during the bell relaxation phase. (B) Jet-paddling in Aurelia aurita. Vortex rings of opposing rotational orientation are formed in the water during bell contraction (CV) and relaxation (RV), respectively. The stopping vortex can be observed forming near the bell margin (RV). This vortex will interact with the subsequent contraction phase vortex, affecting swimming thrust and efficiency (see text).

 

Figure 2
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  		Fig. 2. Quantitative model of force balance between the force FM produced by medusan muscle contraction and the forces FJ or FL required for locomotion. Solid line, 0.5 Hz swimming frequency model; broken line, 1 Hz model; dotted line, 2 Hz model. The constraint on morphological diversity becomes more severe with increasing swimming frequency due to the increased flow accelerations and required locomotive forces. (A) Limiting curve corresponding to force balance FM=FJ, i.e. Eqn 11 plotted with the first term in parenthesis neglected. The model predicts that jet-propelled medusae are limited to the morphospace below this curve, i.e. medusae with bell shape and size combinations above the curve are not capable of swimming via jet propulsion. (B) Limiting curve corresponding to force balance FM=FL, i.e. Eqn 11. The new model predicts that all medusae are limited to the morphospace below this curve. At high fineness ratios the force constraints for jet-paddling and jet propulsion do not differ significantly because magnitude of the stopping vortex during the recovery stroke of jet-paddling is inversely related to fineness ratio. At low fineness ratios the stopping vortex sufficiently reduces FL such that it is never greater than FM; therefore, medusan sizes are not constrained below the critical fineness ratio fCRIT=Formula 13{approx}0.265. This is the key difference between A and B.

 

Figure 3
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  		Fig. 3. Medusan morphospace (fineness ratio, f, versus bell diameter, D) derived from morphological data of 660 extant species of medusae. The figure illustrates a non-random relationship between bell shape and size. The shaded area identifies shape and size combinations that do not exist among extant medusae.

 

Figure 4
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  		Fig. 4. Comparison of quantitative model of morphological diversity with data from 660 extant species of medusae. (A) Black circles, morphological data; solid blue curve, 0.5 Hz swimming frequency model; solid red curve, 1 Hz model; solid green curve, 2 Hz model. Broken red curve, model prediction in the absence of stopping vortex formation at 1 Hz. (B) Black circles, morphological data; solid blue curve, morphospace limit corresponding to an order of magnitude increase (10 times) in the physiologically available force FM for the model with 0.5 Hz swimming frequency; solid green curve, morphospace limit corresponding to an order of magnitude decrease (0.1 times) in the physiologically available force FM for the model with 2 Hz swimming frequency; red curve, 1 Hz model corresponding to average physiological data. fCRIT, critical fitness ratio.

 

Figure 5
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  		Fig. 5. Relationship between bell height H and the function of bell diameter D derived in Eqn 13 for 660 extant species of medusae. Black circles, morphological data; black line, model prediction with slope=0.5; grey line, least-squares fit with slope=0.37.

 




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