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First published online August 8, 2008
Journal of Experimental Biology 211, 2658-2668 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.018853
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Scaling of suction-induced flows in bluegill: morphological and kinematic predictors for the ontogeny of feeding performance

Roi Holzman1,*, David C. Collar1,2, Steven W. Day3, Kristin L. Bishop1 and Peter C. Wainwright1

1 Section of Evolution and Ecology, University of California, One Shields Avenue, Davis, CA 95616, USA
2 Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA
3 Department of Mechanical Engineering, Rochester Institute of Technology, 76 Lomb Memorial Drive, Rochester, NY 14623-5604, USA


Figure 1
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  		Fig. 1. (A) Sampling locations for flow speed. Flow speeds were averaged over 21 points (red crosses; for clarity only 11 points are shown) equally spaced on a radial transect with a diameter of 1/2 gape, ranging from +50 to –50 deg. from the imaginary line projecting at a right angle to the mouth. The measure of mean fluid velocity at 1/2 gape distance from the mouth is referred to throughout the paper as `flow speed'. Velocity profiles were calculated for points under the imaginary line (broken blue line) projecting at a right angle to the mouth. (B) Determination of time to peak gape (TTPG), linear speed of mouth opening ({Delta}G/{Delta}t) and of the acceleration of the flow in front of the fish's mouth, illustrated on kinematic and flow speed measurements from a typical strike of a 180 mm bluegill sunfish with TTPG=32 ms. For bluegill, the change in jaw angle is constant between strikes (jaw angle transforms from {phi}10 to {phi}180), and thus, the time it takes the fish to open its mouth (TTPG; measured from 20% to 95% peak gape; gray reference lines) is inversely proportional to the angular speed of mouth opening, {Delta}{phi}/{Delta}t. The linear speed of mouth opening was determined by regression of gape distance on time (dotted blue line) through at least two-thirds of the opening phase of the mouth (filled blue circles). The slope of that regression (400 mm s–1) describes the mean rate of change in gape distance, {Delta}G/{Delta}t, during mouth opening. Fluid acceleration was determined similarly, as the mean rate of change in flow speed over the duration of increasing flow speed (dotted red regression line through closed red circles; 6.67 in this case). We retained strikes for further analysis only if R2 for the above regression was higher than 0.9.

 

Figure 2
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  		Fig. 2. Scaling of Suction Index (SI) and its underlying morphological components in bluegill, Lepomis macrochirus. (A) SI is a morphology-based index that describes the fish's potential to create suction pressure [Carroll et al., 2004Go; image modified from Collar and Wainwright (Collar and Wainwright, 2006Go)]. SI (arbitrary units) increases proportionately with the fish's length (B), due to the positive allometry of the lever ratio (C), the positive allometry of the cross-sectional area of the epaxial muscle (mm2) (D),and isometry of the buccal area. Buccal area is calculated based on morphological gape (mm) (E) and buccal length (mm) (F). Morphological gape and buccal length are also used, together with gape kinematics, to predict peak flow speed based on the Expanding Cone model (eqn 3; Fig. 3C). Ae, cross-sectional area of the epaxial muscle; Lin, in-lever arm, Lout, out-lever arm, Barea, buccal area. In the inset for each panel (B–F) the components of SI contributing to the dependent variable (y-axis) are colored red. Data are for N=11 fish (open circles=8 experimental fish; closed circles=3 other specimens).

 

Figure 3
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  		Fig. 3. Scaling of jaw kinematics for suction feeding bluegill, Lepomis macrochirus. (A) The time to peak gape (TTPG), defined as the time it took the fish to fully open its mouth (ms), was not significantly correlated with fish length. (B) The linear speed of mouth opening ({Delta}G/{Delta}t) was significantly correlated with standard length, and its scaling exponent was not significantly different from 1. The observed scaling of morphology and kinematics (buccal length, gape size and speed of mouth opening) was used to generate predictions for the scaling of flow speed (C) based on the Expanding Cone model (see eqn 3). Data are means ± s.e.m. (blue circles) or value of fastest speed observed (red circles). Slopes are for the regression of log-transformed mean values and standard length. N=9 fish, 7–30 strikes per fish.

 

Figure 4
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  		Fig. 4. Mean profiles of scaled fluid speed along the centerline transect for each of the nine individuals (broken red lines), in addition to a polynomial fit for the pooled data set (blue line). The deviations of individual profiles from the mean profile (averaged over all individuals) were small (average residual=3% of the speed at 1/2 gape±0.7%) and not significantly correlated with size. Scaled fluid speed is fluid speed relative to flow speed at 1/2 gape distance from the mouth, whereas scaled distance is the distance in gape diameters.

 

Figure 5
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  		Fig. 5. Representative sequences of gape kinematics (filled circles; solid lines) and flow speed (open circles; dotted lines) as function of time (left column) and histograms of peak flow speeds observed during the experiments (right column). Data are for three individuals representing (from top to bottom) the smallest fish, an intermediate fish, and the largest fish used in this study. Note that the time axis (x-axis in left column) is identical for the three fish however, gape distance and flow speed (y-axes in left column, x-axis on right column) increase with increasing fish size. SL is standard length. TTPG is the time to peak gape.

 

Figure 6
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  		Fig. 6. The relative timing of peak flow speed as a function of standard length. The timing of peak flow speed is expressed in fractions of the time to peak gape (TTPG), such that, at time 0, the gape equals 20% of the maximal gape and, at time 1, gape equals 95% of the maximal gape. The mean (± s.e.m.) relative timing of peak flow speed was 0.92 (±0.05). Data are mean values ± s.e.m. for each fish. The horizontal line (± gray band) represents the mean (± s.d.) timing of peak flow speed reported previously for intermediate sized bluegill (Day et al., 2005Go).

 

Figure 7
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  		Fig. 7. (A) Peak flow speed at half gape distance from the mouth as a function of {Delta}G/{Delta}t, the linear speed of mouth opening, and (B) acceleration at half gape distance plotted against the ratio of peak flow speed to time to peak gape (TTPG). Different colors represent individual fish (N=9 fish; standard length=57–190 mm) and individual points represent strikes (7–30 strikes per fish). Blue line represents regression for the pooled data set. Insets are for individual means, with x- and y-axes identical to those of the main panels.

 

Figure 8
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  		Fig. 8. Scaling of peak flow speed and acceleration at 1/2 gape distance in bluegill. Peak flow speed increases with size whereas the relationship between acceleration and standard length is not statistically significant. Data are mean values ± s.e.m. (blue circles) or maximal performance strikes (red circles). N=9 fish, 7–30 strikes per fish. Slopes are for the regression of log-transformed mean values and standard length.

 

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© The Company of Biologists Ltd 2008