Research ArticleORGANISMAL BIOLOGY

Kinematic flexibility allows bumblebees to increase energetic efficiency when carrying heavy loads

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Science Advances  05 Feb 2020:
Vol. 6, no. 6, eaay3115
DOI: 10.1126/sciadv.aay3115
  • Fig. 1 Forces produced by loaded bees can be estimated from wing velocity, derived from measured stroke amplitude and flapping frequency.

    Variables related to force production by bees carrying loads are shown, with measured variables used in statistical analyses shaded in gray. Total force (F) produced by a flying bee to support the mass of its body (mbody) plus a load (mload) consists of forces produced at stroke reversal (not measured, indicated by dashed arrow) plus forces produced during wing translation, which are presumed to be larger in bumblebees than those produced at stroke reversal. Unsteady translational forces (Ft) can be estimated via quasi-steady modeling and are approximated in this study by the product of total wing area (S) and average wing velocity squared (Uw2), neglecting potential changes in the unsteady, translational force coefficient (CFt), which are unknown. Wing velocity is a function of flapping frequency (n) and stroke amplitude (Φ). Flapping frequency was measured from audio recordings and stroke amplitude from high-speed videos.

  • Fig. 2 Experimental loading treatments provided repeated measurements on individuals over a range of loading values.

    (A) Schematic of experimental protocol. External loads equivalent to 40% of bees’ initial mass (which included an unknown volume of nectar) were created and bees were randomly assigned to one of two treatment orders: heavy loading (H; with added external mass) first and light loading (L; internal load only) second, as shown in red, or light loading first and heavy loading second, as shown in blue. Bees varied in the amount of nectar (internal load) they initially carried, which affected the size of the external load created. The internal load also decreased slightly throughout both trials, as nectar was metabolized to fuel flight. After testing, bees were isolated without access to food until their honey crops were empty to determine body mass, mbody. (B) After obtaining body mass, loading was normalized for body size by determining the percent loading for each trial, calculated as the load mass (internal nectar load plus external load, if present) divided by body mass and multiplied by 100. Experimental values of percent loading versus body mass of bees (N = 30) are shown to illustrate the wide variability in bee size and loading conditions tested, with light (nectar only) loads ranging from 13 to 54% of body mass (open symbols) and heavy loads ranging from 57 to 109% of mass (filled symbols). For each bee, the first loading condition is indicated by a circle and the second condition is indicated by a triangle.

  • Fig. 3 Metabolic rate and a proxy for translational force production increased linearly with total mass supported during flight.

    (A) Measured metabolic rate as a function of total mass (body mass plus load) for bees in the heavy (filled circles, black line) and light (open circles, gray line) loading conditions. Metabolic rate increased with total mass for bees in both loading conditions (heavy, R2 = 0.7277; light, R2 = 0.7327), but the slope of this relationship was significantly lower for bees carrying heavy loads (interaction of mass and treatment χ21 = 7.17, P = 0.0074). (B) A proxy for translational force production (wing area × average wing velocity2; SUw2) increased with total mass of the bee plus load, as expected (heavy, R2 = 0.8496; light, R2 = 0.7921). The slope of this relationship was not significantly different for bees carrying light versus heavy loads. Average wing velocity2 was calculated from measurements of flapping frequency (n) and stroke amplitude (Φ).

  • Fig. 4 Changes in percent loading led to predictable changes in stroke amplitude, but not flapping frequency.

    (A) Change in stroke amplitude (heavy − light loading) plotted against change in percent loading (R2 = 0.3559). A linear model shows that changes in percent loading led to predictable changes in amplitude (P = 0.0005), after removing nonsignificant predictors (table S2). (B) Change in flapping frequency (heavy − light loading) plotted against change in percent loading (R2 = 0.0236). A linear model shows that there was no predictable change in frequency associated with changes in percent loading (P = 0.067); only treatment order was a significant predictor of changes in frequency (P = 0.004; table S3). For each bee, change in percent loading (Δ % loading) was calculated as the total mass during heavy loading minus the mass during light loading (regardless of loading order), divided by body mass; changes in amplitude and frequency were calculated similarly as values measured during heavy loading minus those measured during light loading.

  • Fig. 5 Changes in flapping frequency led to predictable changes in metabolic rate, but changes in percent loading and stroke amplitude did not.

    (A) Change in metabolic rate (heavy − light) plotted against change in stroke amplitude (R2 = 0.051). A linear model shows that changes in metabolic rate could not be predicted by changes in percent loading (P = 0.98; table S4). (B) Change in metabolic rate (heavy − light loading) plotted against change in stroke amplitude (R2 = 0.0356). A linear model shows that changes in metabolic rate could not be predicted by changes in stroke amplitude (P = 0.3), after accounting for the estimated effects of change in percent loading, treatment order, and bee size (table S4). (C) Change in metabolic rate (heavy − light loading) plotted against change in flapping frequency (R2 = 0.6083). A linear model shows that changes in frequency significantly predicted changes in metabolic rate (P = 0.0000006), after accounting for estimated effects of change in percent loading, change in amplitude, treatment order, and bee size (table S4). Note that change in metabolic rate (Δ metabolic rate) was log-transformed (base e) to meet statistical assumptions. Other variables were calculated as in Fig. 4.

  • Fig. 6 Bees that were more heavily loaded displayed smaller increases in metabolic rate and flapping frequency to accommodate additional loading.

    (A) Bees more heavily loaded on average (average % loading over heavy and light trials) throughout the experiment displayed smaller increases in metabolic rate per 1% additional loading (R2 = 0.4028). Change in metabolic rate per 1% load was calculated as the change in metabolic rate divided by the change in percent loading between trials (Δ metabolic rate/Δ % loading). (B) In contrast, we found no relationship between a bee’s average loading state and the change in stroke amplitude per 1% additional load (R2 < 0.001). (C) Bees with higher average loading displayed smaller changes in flapping frequency for a given 1% additional load (R2 = 0.4568). Bees tested in the heavy-to-light treatment order are shown in red and those in the light-to-heavy order are shown in blue.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/6/eaay3115/DC1

    Fig. S1. There was no relationship between stroke amplitude and wingbeat frequency or between the change in amplitude and change in frequency between trials.

    Fig. S2. Change in loading between trials scaled with bee size, but change in % loading was independent of size.

    Table S1. Morphological, kinematic, and metabolic variables for all bees tested, grouped by treatment order (light to heavy, L-H; heavy to light, H-L).

    Table S2. Results of linear model investigating how Δ amplitude is affected by Δ % loading, treatment order, and bee size.

    Table S3. Results from linear model investigating how Δ frequency is affected by Δ % loading, treatment order, and bee size.

    Table S4. Results from linear model investigating how Δ metabolic rate is affected by Δ % loading, Δ amplitude, Δ frequency, treatment order, and bee size.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. There was no relationship between stroke amplitude and wingbeat frequency or between the change in amplitude and change in frequency between trials.
    • Fig. S2. Change in loading between trials scaled with bee size, but change in % loading was independent of size.
    • Table S1. Morphological, kinematic, and metabolic variables for all bees tested, grouped by treatment order (light to heavy, L-H; heavy to light, H-L).
    • Table S2. Results of linear model investigating how Δ amplitude is affected by Δ % loading, treatment order, and bee size.
    • Table S3. Results from linear model investigating how Δ frequency is affected by Δ % loading, treatment order, and bee size.
    • Table S4. Results from linear model investigating how Δ metabolic rate is affected by Δ % loading, Δ amplitude, Δ frequency, treatment order, and bee size.

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