1. Ecology
  2. Neuroscience
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Burst muscle performance predicts the speed, acceleration, and turning performance of Anna’s hummingbirds

  1. Paolo S Segre
  2. Roslyn Dakin
  3. Victor B Zordan
  4. Michael H Dickinson
  5. Andrew D Straw
  6. Douglas L Altshuler Is a corresponding author
  1. University of British Columbia, Canada
  2. University of California, Riverside, United States
  3. California Institute of Technology, United States
  4. Institute of Molecular Pathology, Austria
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Cite as: eLife 2015;4:e11159 doi: 10.7554/eLife.11159
7 figures, 1 video, 5 tables, 1 data set and 1 additional file

Figures

Figure 1 with 1 supplement
A multi-camera, automated tracking system extracted hummingbird body position (blue circle) and orientation (red line) from solo and competitive flights.

The trajectory shown for one bird (a) is also shown in Video 1 (see Figure 1—figure supplement 1 for time series of position, velocity, and acceleration values). Stereotyped maneuvers were classified in each trajectory (b) and between one and five performance metrics were calculated from each maneuver. Maneuvers within a trajectory may be overlapping (e.g. #4,5,6). The trajectory presented in b is a top down (x-y projection) view of the trajectory shown in a. Body position and orientation were smoothed with an extended Kalman filter (c,d). The effects of four different sets of smoothing parameters are presented for an arcing turn (maneuver #9 in b) and an upward acceleration (maneuver #1 in b). Shown here are the unsmoothed position and orientation (black trace and text), the chosen levels of smoothing (blue), a lower level of smoothing (green; 0.1 x Rpos; 0.1 x Rori), and a higher level of smoothing (red; 10 x Rpos; 10 x Rori). The chosen smoothing parameters for body position were determined by tracking multiple dropped objects and calibrating the Z-axis acceleration to gravity. The chosen smoothing parameters for body orientation were determined by re-projecting the body axis vector onto the video. The higher and lower levels of smoothing for body position presented in this figure were both deemed too extreme, when re-projected onto the video. However, the level of smoothing for body orientation had minimal effect on the average yaw velocity.

https://doi.org/10.7554/eLife.11159.004
Figure 1—figure supplement 1
The representative trajectory from Figure 1 and Video 1 displayed through time.

The upper three panels provide the position, velocity, and acceleration values. The lower three panels provide the orientation vector, orientation angle and rotation velocity values. The maneuvers extracted for this sequence are given by thick black lines below the traces.

https://doi.org/10.7554/eLife.11159.005
Figure 2 with 1 supplement
Distributions of mean performance metric values for n = 52 bird-trial combinations.

Only PRTdeg has statistically significant outliers. See Figure 2—figure supplement 1 for distributions of residuals from the best-fit model in each case. Note that two statistical outliers were omitted from the analysis of PRTdeg.

https://doi.org/10.7554/eLife.11159.009
Figure 2—figure supplement 1
Distributions of residuals from the best-fit model for each performance metric.

Note that two statistical outliers were omitted from the analysis of PRTdeg.

https://doi.org/10.7554/eLife.11159.010
Most maneuvering performance metrics are highly repeatable.

Values > 70% are considered to have high repeatability, 40–70% moderate repeatability, and < 40% low repeatability. A metric is considered not repeatable if its 95% confidence intervals overlap zero.

https://doi.org/10.7554/eLife.11159.011
Burst muscle capacity was associated with most maneuvering performance metrics.

Each panel shows partial residuals for a performance metric (y-axis) in relation to burst muscle capacity (x-axis) for the most supported candidate model with burst capacity as a predictor. Partial residual values (y-axis) account for the other fixed effects in that model. Lines show model predictions assuming the median value of continuous predictors, and averaging across experiments and levels of competitor presence. Prediction lines are dashed for metrics where burst performance was not present in any of the supported models. Color is used to denote data points from the same bird (online version only).

https://doi.org/10.7554/eLife.11159.013
Aspect ratio was associated with two maneuvering performance metrics.

Each panel shows partial residual performance (y-axis) in relation to wing aspect ratio (x-axis) from a best-fit model that identified aspect ratio as an important predictor. Note that the partial residuals for PRT% in (b) go above 1 because PRT% was modeled as a normally-distributed (Gaussian) variable. All other features as in Figure 4.

https://doi.org/10.7554/eLife.11159.014
Competitor presence was associated with four maneuvering performance metrics.

Each panel shows residual performance (y-axis) in relation to competitor presence from a best-fit model where competitor presence had a detected effect. All other features as in Figure 4.

https://doi.org/10.7554/eLife.11159.015
Arcing and pitch-roll turns are two classes of complex maneuver that differ in turn magnitude and duration.

Representative examples of arcing (a) and pitch-roll (b) turns are depicted from the above perspective. Arcing turns (Arc; orange) and pitch-roll turns (PRT; green) differed in the degrees turned (c) and elapsed time (d). Circles represent bird-trial means (n = 52) with grand means indicated with black lines. Histograms for the pooled dataset of all maneuvers are given on the right. The outliers for degrees turned in pitch-roll turns were included when calculating the grand means but not in the model analyses (Table 4).

https://doi.org/10.7554/eLife.11159.016

Videos

Video 1
The multi-camera, automated tracking system filming two hummingbirds in the flight arena at 200 frames per second.

Continuously tracked sequences are assigned an object number (from 0 to 4 over this sequence). Body position and orientation are calculated and reprojected onto the video of four cameras. The videos are saved using a compression algorithm that only records the sections of the image that are moving (Straw et al. 2011). Thus, birds disappear from the video when they land and stop moving. The trajectory shown in Figure 1 is taken from the bird labeled #2 and begins at 5.1 seconds and ends at 8.05 seconds.

https://doi.org/10.7554/eLife.11159.003

Tables

Table 1

Search parameters for the ten maneuvers analyzed in the study. The definitions, units, and symbols for the 14 related performance metrics are also provided.

https://doi.org/10.7554/eLife.11159.006
ManeuverSearch parametersPerformance metricUnitsSymbol
3D accelerationStart: velocity xyz minimum
End: velocity xyz maximum
Distance xyz > 25 cm
Maximum velocitym/sVelmax
Horizontal accelerationStart: velocity xy minimum
End: velocity xy maximum
Distance xy > 25 cm
Distance z < 10 cm
Maximum acceleration xym/s2AccHormax
Horizontal decelerationStart: velocity xy maximum
End: velocity xy minimum
Distance xy > 25 cm
Distance z < 10 cm
Maximum deceleration xym/s2AccDecmax
Vertical upwards accelerationStart: velocity z minimum
End: velocity z maximum
Distance z > 25 cm
Maximum acceleration zm/s2AccVUmax
Vertical downwards accelerationStart: velocity z maximum
End: velocity z minimum
Distance z > 25 cm
Maximum acceleration zm/s2AccVDmax
Pitch-up rotationStart: pitch minimum
End: pitch maximum
Degrees rotated > 45 deg
Distance xyz < 10 cm
Average pitch velocityrev/sPitchUvel,avg
Pitch-down rotationStart: pitch maximum
End: pitch minimum
Degrees rotated > 45 deg
Distance xyz < 10 cm
Average pitch velocityrev/sPitchDvel,avg
Yaw turnStart: velocity yaw = 0 deg/s
End: velocity yaw = 0 deg/s
Degrees rotated > 90 deg
Pitch maximum < 75 deg
Distance xyz < 10 cm
Average yaw velocityrev/sYawvel,avg
Arcing turnStart: Δ heading velocity > 0.25 rev/s
End Δ heading velocity < 0.25 rev/s
Velocity xy min > 50 cm/s
Distance xy > 25 cm
Distance z < 10 cm
Average xy velocity*
radius*
Centripetal acceleration*
m/s
m
m/s2
Arcvel, avg
Arcrad
Arccent, max
Pitch roll turnStart: velocity maximum
End: velocity maximum
Pitch maximum > 75 deg
Distance xy before velocityMin > 12.5 cm
Distance xy after velocity Min < 12.5 cm
Distance z < 10 cm
time
degrees turned
s
deg
PRTtime
PRTdeg
  1. *for a 25 cm segment centered at the sharpest point of the turn

  2. for a 25 cm segment centered at the minimum velocity xyz

Table 2

Wing morphology and load lifting performance of male Anna’s hummingbirds (n = 20 individuals).

https://doi.org/10.7554/eLife.11159.007
TraitMeanRange
Wing length50.97 mm[45.76, 55.45]
Wing area 1355 mm2[1051, 1653]
Wing aspect ratio7.73[7.13, 8.46]
Body mass4.64 g[4.09, 5.61]
Mass of weights lifted5.93 g[4.00, 7.24]
Table 3

Descriptive statistics and sample sizes for maneuvering performance. Grand mean values were calculated by first taking the mean of each bird’s trial averages (i.e., the bird means), and then taking the mean of the bird means (n = 20 birds in 20 solo trials and 16 paired competition trials).

https://doi.org/10.7554/eLife.11159.008
ManeuverabilityPerformance metric# TrajectoriesGrand mean[Range of means]
Linear accelerationsVelmax71,0072.22 m/s[1.20, 2.94]
AccHormax47,2876.30 m/s2[2.96, 8.83]
DecHormax51,2456.67 m/s2[9.03, 3.45]
AccVUmax6,9353.78 m/s2[2.98, 4.67]
AccVDmax9,2843.58 m/s2[4.69, 2.68]
Rotational velocitiesPitchUvel, avg6,0851.13 rev/s[0.91, 1.34]
PitchDvel, avg14,8071.00 rev/s[1.19, 0.78]
Yawvel, avg12,6601.52 rev/s[1.32, 1.75]
Complex turns
Pitch-rollPRTdeg17,133133.3 º[34.9, 162.7]
PRTtime17,1330.47 s[0.38, 0.60]
ArcingArcrad6.9450.48 m[0.14, 0.70]
Arcvel, avg6,9451.57 m/s[0.80, 2.26]
Arccent, max6,9456.59 m/s2[3.42, 10.80]
Use of turnsPRT% 24,0780.69[0.39, 0.87]
Table 4

Maneuvering performance in relation to burst performance, wing morphology, and competitor presence (n = 20 birds in 20 solo trials and 16 paired competition trials). Standardized beta coefficients and R2GLMM(m) values are reported for either the best-fit model, or, if there was support for more than one model, the average of supported models. The standardized beta coefficient is a measure of effect size that can be compared among predictors in the same model. Relative importance is a measure of the weight of evidence in favor of a predictor on a scale from 0–1, and is reported for burst capacity and wing morphology variables as these alone were subject to model selection. Marginal R2GLMM(m) provides a measure of the combined explanatory power of fixed effects of interest (competitor presence, burst muscle capacity, and wing morphology effects combined). Details of all candidate models are provided in Supplementary file 1.

https://doi.org/10.7554/eLife.11159.012
ModelSupport forFixed effectsStd beta coef [95% CI]Relative importanceR2GLMM(m)
Burst
+ morphology
+ competitor
Velmaxburstcompetitor presence
mass
burst
wing length
wing aspect ratio
experiment (CA1)
experiment (CA2)
days post-capture
–0.04 [–0.18, 0.10]
0.10 [–0.01, 0.22]
0.09 [0.00, 0.18]
–0.08 [–0.22, 0.06]
0.10 [–0.07, 0.28]
1.01 [0.59, 1.42]
1.06 [0.68, 1.43]
–0.07 [–0.24, 0.11]
--
--
1.00
0.25
0.26
--
--
--
0.28
AccHormaxburst + competitioncompetitor presence
mass
burst
experiment(CA1)
experiment(CA2)
days post-capture
–0.46 [–0.82, –0.11]
0.20 [–0.28, 0.69]
0.39 [0.00, 0.77]
4.01 [2.46, 5.56]
3.68 [2.72, 4.64]
–0.39 [–1.09, 0.32]
--
--
1.00
--
--
--
0.18
DecHormaxburst + competitioncompetitor presence
mass
burst
experiment(CA1)
experiment(CA2)
days post-capture
–0.47 [–0.78, –0.16]
0.31 [–0.13, 0.74]
0.41 [0.06, 0.76]
3.86 [2.47, 5.25]
3.64 [2.76, 4.51]
–0.24 [–0.88, 0.39]
--
--
1.00
--
--
--
0.19
AccVUmaxintercept-onlyNANANA0 (NA)
AccVDmaxintercept-onlyNANANA0 (NA)
PitchUvel, avgburstcompetitor presence
mass
burst
experiment(CA1)
experiment(CA2)
0.02 [–0.02, 0.06]
0.00 [–0.04, 0.04]
0.03 [–0.01, 0.07]
0.14 [0.06, 0.23]
0.13 [0.03, 0.23]
--
--
1.00
--
--
0.10
PitchDvel, avgcompetition
+ burst
competitor presence
mass
burst
wing length
wing aspect ratio
experiment(CA1)
experiment(CA2)
0.06 [0.01, 0.10]
0.01 [–0.04, 0.05]
0.03 [–0.01, 0.08]
0.04 [–0.03, 0.12]
–0.04 [–0.13, 0.05]
0.19 [0.03, 0.34]
0.22 [0.03, 0.41]
--
--
0.66
0.37
0.28
--
--
0.18
Yawvel, avgintercept-onlyNANANA0 (NA)
PRTdegintercept-onlyNANANA0 (NA)
PRTtimeburstcompetitor presence
mass
burst
wing length
wing aspect ratio
experiment(CA1)
experiment(CA2)
0.00 [–0.01, 0.01]
–0.01 [–0.03, 0.00]
–0.02 [–0.03, 0.00]
–0.01 [–0.03, 0.01]
0.01 [–0.01, 0.04]
–0.08 [–0.12, –0.03]
–0.11 [–0.16, –0.05]

--
1.00
0.21
0.23

--
0.29
Arcradburstcompetitor presence
mass
burst
wing aspect ratio
experiment(CA1)
experiment(CA2)
–0.02 [–0.07, 0.03]
0.01 [–0.03, 0.06]
0.06 [0.01, 0.10]
–0.06 [–0.15, 0.03]
0.25 [0.12, 0.37]
0.29 [0.06, 0.52]
--
--
1.00
0.44

--
0.22
Arcvel, avgburstcompetitor presence
mass
burst
experiment(CA1)
experiment(CA2)
days post-capture
–0.01 [–0.09, 0.08]
0.03 [–0.06, 0.12]
0.11 [0.04, 0.19]
0.89 [0.59, 1.19]
0.74 [0.56, 0.92]
–0.06 [–0.20, 0.08]


1.00

--
--
0.18
Acccent, maxwing shapecompetitor presence
mass
wing aspect ratio
experiment(CA1)
experiment(CA2)
days post-capture
0.29 [–0.37, 0.94]
–0.20 [–0.74, 0.34]
1.09 [0.19, 1.99]
5.93 [4.02, 7.84]
0.85 [–1.59, 3.28]
–1.76 [–2.62, –0.90]
--
--
1.00
--
--
--
0.36
PRT% wing shape + competition
+ burst + wing size
competitor presence
mass
burst
wing length
wing aspect ratio
experiment(CA1)
experiment(CA2)
–0.14 [–0.19, –0.09]
0.00 [–0.04, 0.05]
0.04 [0.00, 0.09]
–0.06 [–0.13, 0.01]
–0.16 [–0.24, –0.07]
0.17 [–0.03, 0.36]
0.44 [0.19, 0.69]
--
--
1.00
0.61
1.00
--
--
0.27
Table 5

Candidate models of maneuvering performance. All models include an intercept as well as a random effect of bird identity to account for repeated measures of individuals.

https://doi.org/10.7554/eLife.11159.017
ModelFixed effectsDescription
1.Solo/comp + experiment + body mass + wing lengthWing size
2.Solo/comp + experiment + body mass + wing aspect ratioWing shape
3.Solo/comp + experiment + body mass + wing length + wing aspect ratioWing size & shape
4.Solo/comp + experiment + body mass + weight liftedBurst power
5.Solo/comp + experiment + body mass + weight lifted + wing lengthBurst power & wing size
6.Solo/comp + experiment + body mass + weight lifted + wing aspect ratioBurst power & wing shape
7.Solo/comp + experiment + body mass + weight lifted + wing length + wing aspect ratioBurst power, wing size & shape
8.Intercept-only
  1. *Candidate models 1-7 also include a fixed effect of days post-capture for the following metrics: Velmax, AccHormax, DecHormax, Arcvel, avg, and Arccent, max

Data sets

The following data sets were generated
  1. 1

Additional files

Supplementary file 1

Details and ranking of candidate models of hummingbird maneuvering 788 performance, and unstandardized regression coefficients.

https://doi.org/10.7554/eLife.11159.018

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