Maximum vertical force production (F_vert) is an integral measure of flight performance that generally scales with size. Numerous methods of measuring F_vert and body size exist, but few studies have compared how these methods affect the conclusions of scaling analyses. We compared two common techniques for measuring F_vert in bumblebees (Bombus impatiens) and mason bees (Osmia lignaria), and examined F_vert scaling using five size metrics. F_vert results were similar with incremental or asymptotic load-lifting, but scaling analyses were sensitive to the size metric used. Analyses based on some size metrics indicated similar scaling exponents and coefficients between species, whereas other metrics indicated different coefficients. Furthermore, F_vert showed isometry with body lengths and fed and starved masses, but negative allometry with dry mass. We conclude that F_vert can be measured using either incremental or asymptotic loading but choosing a size metric for scaling studies requires careful consideration.

Cocoons of adult-wintering Osmia lignaria were purchased from a commercial supplier (Foothill Bee Ranch, Auburn, CA, USA) and maintained at 4°C. Individuals were moved to a flight cage for emergence, as needed for experiments. A mature colony of Bombus impatiens was purchased from a commercial supplier (Koppert Biological Systems, Romulus, MI, USA) and maintained in a separate flight cage. Individuals in each cage were fed sucrose solution ad libitum, with fresh pollen weekly. All flight cages and experimental areas were held at 22-25°C. Active females (n = 25 for O. lignaria, n = 28 for B. impatiens) of each species were selected randomly for flight trials.

Flight performance

F_vert was measured on each individual using both the incremental and asymptotic methods, to allow for direct comparison. The order of the methods was alternated between individuals, with both tests performed during the same day, and testing methodology generally followed the descriptions by Buchwald and Dudley (2010) and Mountcastle and Combes (2013). Briefly, bees were cold-anesthetized at 4°C and a polyester thread was tied around the petiole of each individual (Mountcastle and Combes, 2013), near their center of lift (Buchwald and Dudley, 2010; Dudley and Ellington, 1990; Ellington, 1984a), leaving a free end of thread approximately 6 cm long. Once tied, bees were allowed to recover at room temperature for 10-20 minutes before any flight trials.

Incremental method: Individual beads (either 0.0250 or 0.0050 g in mass) were tied to the free end of thread around a bee’s petiole. Prior to each flight trial, the mass of the bee, string, and beads were recorded. The bee was released into a flight arena and prompted to fly, using agitation with forceps if necessary (Fig. 1a). If the bee took off and sustained flight, additional beads were added, mass was recorded, and the flight trial was repeated until the bee was unable to fly with the weight applied. The maximum mass lifted by the bee was multiplied by gravitational acceleration to calculate the bee’s F_vert. 

Asymptotic method: Beads (either 0.0250 or 0.005 g in mass) were attached to a polyester string, approximately 30 cm in length, at intervals of 2 cm. Based on preliminary trials, the strings used in O. lignaria flight tests had beads with mass = 0.0050 g, and the strings used in B. impatiens flight tests had beads with mass = 0.0250 g. Before and after each flight trial, the mass of the bee, along with the 6-cm thread tied around its petiole, was measured. During a flight trial, the bee was tied to the beaded string and prompted to fly, using agitation with forceps if necessary (Fig. 1b). Flights were recorded with a video camera at 30-60 frames per second, and the maximum number of beads lifted during each sustained vertical flight was counted. Up to five successful flight trials were recorded per individual. F_vert was calculated as the sum of bee mass (averaged between the pre- and post-flight mass) and the lifted mass of the beaded string, multiplied by gravitational acceleration. The lifted mass of the beaded string was calculated as the maximum number of beads lifted during the flights, multiplied by the average mass per bead (total mass of string and bead, divided by the number of beads on the string).

In both incremental and asymptotic methods, we consider the maximum lifted mass to be the observed maximum lifted mass, following Mountcastle and Combes (2013). However, other studies have considered the maximum lifted mass to be the mean between the observed maximum lifted mass and the next-highest mass that the bee was unable to lift (Buchwald and Dudley, 2010; Marden, 1987). While this variation in methodology can impact comparisons of data between studies, it does not affect the conclusions of the present study because the same approach was used for all trials.

Body size

After all flight trials using both methods were completed for each bee, the string was removed from the petiole and body mass was measured to the nearest 0.0001 g with a digital balance (providing the fed mass). The bee was placed in a separate dish with only a wet paper towel and left for 24 h at room temperature to consume any nectar remaining in its body. After 24 h, body mass was measured again (providing the starved mass), and the bee was placed in a freezer until all experiments were completed.

Once all flight tests were completed, we removed bees from the freezer, photographed them, and measured their intertegular (IT) span and forewing length (hereafter wing length) to the nearest 0.01 mm using ImageJ (v 1.53f51) (Schneider et al., 2012). Following these geometric measurements, bees were placed in a drying oven at 45°C, following Cane (1987), and dried for several days until all bees were no longer losing mass (providing the dry mass).

Misssing values are indicated with 'NA'