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First published online February 6, 2004
Journal of Experimental Biology 207, 993-1004 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00850

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Allometry of kinematics and energetics in carpenter bees (Xylocopa varipuncta) hovering in variable-density gases

Stephen P. Roberts^1,*, Jon F. Harrison² and Robert Dudley^3,4

¹ Department of Biological Sciences, University of Nevada, Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV 89154-4004, USA
² School of Life Sciences, Arizona State University, Tempe, AZ 85287-1501, USA
³ Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA
⁴ Smithsonian Tropical Research Institute, PO Box 2072, Balboa, Republic of Panama

View larger version (12K): [in a new window]   Fig. 1. Relative thoracic muscle mass (Mmuscle) vs body mass (Mb) for female Xylocopa varipuncta. Model II regression: Mmuscle=0.682–0.411Mb, r29=–0.78, P<0.001.

View larger version (13K): [in a new window]   Fig. 2. Minimal gas density (MGD) necessary for hovering flight vs relative thoracic muscle mass for female Xylocopa varipuncta. Model II regression: MGD=1.536–2.256Mmuscle, r28=–0.86, P<0.001.

View larger version (14K): [in a new window]   Fig. 3. Wingbeat frequency during hovering in normodense air (fnorm; open symbols) and during maximal hovering in hypodense air (fmax; filled symbols) vs body mass (Mb) for Xylocopa varipuncta females. Model II regression: fnorm=101.92+24.70Mb, r27=0.53, P<0.005 (broken line); fmax=141.33–20.09Mb, r26=–0.15, P=0.44.

View larger version (16K): [in a new window]   Fig. 4. Stroke amplitude during normal hovering (norm; open symbols) and maximal hovering (max; filled symbols) vs body mass (Mb) for Xylocopa varipuncta females. Model II regression: norm=88.22+35.58Mb, r29=0.84, P<0.001 (broken line); max=128.26+11.62Mb, r28=0.03, P=0.89.

View larger version (15K): [in a new window]   Fig. 5. Reserve capacity in wingbeat frequency (fres; filled symbols) and in stroke amplitude (res; open symbols) vs body mass (Mb) for hovering Xylocopa varipuncta females. Model II regression: fres=17.93–18.94Mb, r26=–0.73, P<0.001 (solid line); res=50.44–39.35Mb, r28=–0.78, P<0.001 (broken line).

View larger version (16K): [in a new window]   Fig. 6. Stroke plane angle during normal (ßnorm; open symbols) and maximal hovering (ßmax; filled symbols) vs body mass (Mb) for Xylocopa varipuncta females. Model II regression: ßnorm=14.28–9.23Mb, r29=–0.49, P<0.005 (broken line); ßmax=10.16–10.01Mb, r28=–0.26, P=0.17.

View larger version (12K): [in a new window]   Fig. 7. Log body mass (Mb)-specific power output during normal (Pbody,norm; open symbols) and maximal hovering flight (Pbody,max; filled symbols) vs log Mb for Xylocopa varipuncta females. Assumed drag coefficient (CD)=1 (bottom panel) and 3 (top panel). Model II regression for CD=1: log Pbody,norm=1.979+0.516(log Mb), r27=0.43, P<0.02 (solid line); log Pbody,max=2.004+0.405(log Mb), r26=0.32, P=0.11. Model II regression for CD=3: log Pbody,norm=2.380+0.633(log Mb), r27=0.29, P=0.13; log Pbody,max=2.662+3.890(log Mb), r26=0.02, P=0.89.

View larger version (13K): [in a new window]   Fig. 8. Log muscle mass-specific power output during normal (Pmuscle,norm; open symbols) and maximal hovering flight (Pmuscle,max; filled symbols) vs log body mass (Mb) for Xylocopa varipuncta females. Assumed drag coefficient (CD)=1 (bottom panel) and 3 (top panel). Model II regression for CD=1: log Pmuscle,norm=2.517+1.126(log Mb), r27=0.82, P<0.001 (broken line); log Pmuscle,max=2.538+1.007(log Mb), r26=0.81, P<0.001 (solid line). Model II regression for CD=3: log Pmuscle,norm=2.909+1.160(log Mb), r27=0.76, P<0.001 (broken line); log Pmuscle,max=3.210+4.762(log Mb), r26=0.17, P=0.38.

View larger version (9K): [in a new window]   Fig. 9. Reserve capacity (%) in muscle mass-specific power output (Pres) vs body mass (Mb) for hovering Xylocopa varipuncta females. Assumed drag coefficient (CD)=1 (bottom panel) and 3 (top panel). Model II regression for CD=1: Pres=47.70–47.85Mb, r26=–0.37, P=0.05 (solid line). Model II regression for CD=3: Pres=54.74–59.05Mb, r26=–0.11, P=0.59.

View larger version (12K): [in a new window]   Fig. 10. Mean lift coefficient during normal (CL,norm; open symbols) and maximal (CL,max; filled symbols) hovering flight vs body mass (Mb) for Xylocopa varipuncta females. Model II regression: CL,norm=0.645+0.994Mb, r27=0.25, P=0.20; CL,max=2.678–1.236Mb, r26=–0.26, P=0.18.

View larger version (14K): [in a new window]   Fig. 11. Body mass-specific metabolic rate during hovering flight (W kg–1) vs gas density. Numbers in parentheses indicate the sample sizes at each air density. Error bars represent ± 1 S.E.M.

View larger version (17K): [in a new window]   Fig. 12. Log body mass-specific metabolic rate during normal (Pmet,norm; open symbols) and maximal hovering flight (Pmet,max; filled symbols) vs log body mass (Mb) for Xylocopa varipuncta females. Model II regression: log Pmet,norm=2.483–0.883(log Mb), r22=–0.53, P<0.02 (broken line); log Pmet,max=2.556–1.216(log Mb), r22=–0.64, P<0.001 (solid line).

View larger version (11K): [in a new window]   Fig. 13. Flight muscle efficiency during normal (norm; open symbol) and maximal hovering flight (max; filled symbols) vs body mass (Mb) for Xylocopa varipuncta females. Assumed drag coefficient (CD)=1 (bottom panel) and 3 (top panel). Model II regression for CD=1: norm=–3.44+33.28Mb, r21=0.59, P<0.005 (broken line); max=–6.76+33.12Mb, r20=0.70, P<0.001 (solid line). Model II regression for CD=3: norm=–48.34+123.23Mb, r21=0.28, P=0.20; max=–53.73+117.15Mb, r20=0.39, P=0.07.