Fig 1.
Heat gain and loss mechanisms of a flying bee.
Incoming and outgoing short-wave radiation into the bee ( and
); long-wave radiation from the Earth and the atmosphere into the bee (
and
); thermal radiation out of the bee (
); convective cooling (
); movement of heat from the thorax to the head (
); metabolic heat production within the bee (
); cooling due to the interrupted countercurrent heat exchange between the thorax and abdomen (
); and evaporative cooling by tongue lashing with nectar (
). Direction of arrow indicates whether the bee is generally warmed or cooled via the indicated mechanism.
Table 1.
Key parameter values for an average temperate bumblebee (Bombus spp.)
Table 2.
Key parameter values for an average western honeybee (Apis mellifera).
Fig 2.
(A) Bumblebee, without cooling behaviour. (B) Bumblebee, with cooling behaviour. (C) Honeybee, without cooling behaviour. (D) Honeybee, without cooling behaviour. ∘C and all other parameters at default/fitted values. Solutions for a resting metabolic rate are in blue and flying metabolic rate in red.
Fig 3.
Equilibrium thorax temperature versus air temperature.
Left: an average temperate bumblebee. Right: an average western honeybee. Pink curves indicate flight and green indicate resting. Solid lines indicate no behavioural cooling via the abdomen or tongue-lashing, and dashed lines indicate that behavioural cooling is employed. The shaded regions indicate the limits on thorax temperature for flight.
Fig 4.
The range upper thermal limits for sustained flight depending on its thorax mass and flight speed.
The realistic range for the thorax mass of each bee group is indicated by the horizontal bars at the top of the plot. Variability due to flight speed is indicated by the shaded area. The middle curve is a flight speed of 4.5 m/s in both cases. The increasing trend seen in honeybees greater than thorax mass 0.08 g (outside of the realistic range) is due to convective cooling having a proportionally greater effect at these masses.