Since January 2020, the World has become accustomed to the idea that a deadly virus could have been transferred to the human species by another animal species. The chief suspects have been, since the beginning, some families of small “horseshoe” bats living in a large part of South-East Asia, such as Rhinolophus affinis or Rhinolophus pusillus, the “lesser horseshoe” bat. Apparently, such animals are part of a varied dietary regime that includes also pangolins, ferrets, minks, which by some cunning biological pathway seemingly have transferred the SARS-CoV-2 virus to humans (although this is only one among the possible origins of the virus currently being under investigation). I am not going to delve into the possible relations between such poor animals turned into human food, and the spreading of the Covid-19 disease (are they the villains or the victims?), since I think this has not much to do with physics. Today I am mainly interested in some biophysics of these small, distant relatives of ours, because of their incredibly small size that makes you wonder how such a tiny animal could exploit the typical mammalian physiological functions.
A size of 3-4 centimeters and weight of 5 to 9 grams make the pusillus one of the smallest mammals on Earth. But not the smallest. Chiroptera, the only mammals to have evolved true flight capabilities, count about 900 different species. Like us, they trace their ancestry back to the insectivores. They have been around for 50 million years already, therefore they had quite a lot of time to develop and adjust. For example, there are two suborders of bats that may have evolved independently, even if from a common bat-like insectivore ancestor. These two clans sense the environment very differently, as one is visually oriented and the other uses echolocation, or sonar. The value of the latter for a nocturnal animal is easy to understand. The record of the smallest mammalian probably belongs to the Tylonycteris pachypus meyeri: its large wingspan of about 12cm should not be overestimated, for it weighs an amazingly small 1,5 grams, and if we throw away the wings, its body alone must not be above 1 gram net. Since the average human body weight is about 70 kg, this tiny relative weighs 1/70,000 the weight of a human. If we apply dimensional scaling, a gland that weighs 10 g in the human body scales to 150 mg in Tylonycteris. At average cell weight of 3-4 nanograms, this makes for about 50-60,000 cells, so scaling should be still applicable.
For such small mammals, energy and heat management must be a real burden. In warm-blooded animals, a variety of physiological systems provide automatic feedback to maintain the reference temperature. Temperature sensors throughout the body respond to the central nervous controller, situated in the medial anterior hypothalamic region of the brainstem, which then adjusts heat production and loss accordingly. In humans, skin represents about 15 % of the body mass (the “largest organ” of the body), while muscles take up about 40%. For external temperatures far from 37C, the skin temperature is usually 2 to 4 degrees below that of the body. Under conditions of warming, as much as 30 % of the blood flow can go to the skin, to increase the cooling rate. A human has about 5 liters of blood, which take about 1 min to completely circulate in the body, therefore one can estimate that about 1.5 L/min flow to the skin under normal conditions. In medical physiology, the blood circulation rate is called the cardiac index: it originates from the heart pumping rate, which in humans is about 65 mL/beat at 1.15Hz (i.e., about 70 beats/min), resulting in a cardiac index of about 80 mL/(min kg). By reducing the size of the animal, the amount of blood decreases, the heartbeat frequency increases and so does the cardiac index. By applying scaling, in our minuscule Tylonycteris bat the heart mass should be about 10 milligrams (note that their heart contains four full chambers like ours), and the blood volume about 100 microliters; their cardiac index is estimated at 850 mL/(min kg). By scaling blood volume with the human/bat body mass ratio, the pumping rate of bat’s heart should be about 0.6 mL per beat, from which a heartbeat frequency of about 23 Hz (1400 beats/min) can be guessed. This value is not far from the experimentally measured values which give the cardiac index (see e.g. C.M. Bishop, Heart mass and the maximum cardiac output of birds and mammals, Phil. Trans. Roy. Soc. 352 (1997) 477).
These animals spend most of their life sleeping in groups of 20-40 inside the cavity of bamboo sticks. However, they must also feed by hunting small insects. Their only predatory activity starts early at sunset and consists of two raids of about 20 minutes each. The flight is slow, maneuvered, at an average measured speed of approximately 4.3 m/s, and can also remain suspended in the air hovering in front of the bamboo stalks. Given their proportionally smaller heart volume, small bats generally have lower mass-specific aerobic capacities, compared to birds of a similar body mass. Measurements of flight speeds and times in a wind tunnel (R. Carpenter, Flight physiology of intermediate sized fruit bats, J. Exp. Biol. 120 (1986) 79) show that small bats have a very limited range of speeds over which they are capable of prolonged continuous flight. In addition, small bats appear to have a relatively smaller flight muscle mass than birds, and should therefore require relatively less cardiovascular support, which maybe explains their smaller heart/body mass ratio.
However, on the short time scale, their flight dynamics seems to be more efficient than that of birds of similar mass and wingspan. Hovering flight is notoriously energy-consuming. Measurements of expended metabolic power show that at the same given power level, a small bat can generate enough lift to support a body mass about twice that of a hovering hummingbird, or a nocturnal moth. As far as direct horizontal flight, bats are again more economical than birds (Y. Winter & O. von Helversen, The energy cost of flight, J. Comp. Physiol. B168 (1998) 105); the metabolic flight power scales as P=50 M0.77 in a mass range of 5 to 30 g, that is about 25% lower than the typical values measured for birds of similar mass. Attempts at explaining such differences vary, among which a typical one invokes the absence of feathers on the wings, which could make for slicker aerodynamics. However, naked wings could also have a flip side of the coin.
Recent studies suggest that bats became nocturnal because of overheating when flying in daylight. This should be because – in contrast to the feathered wings of birds – the dark and naked wing membranes of bats efficiently absorb short-wave solar radiation. Accurate measurements of metabolic rates (C. Voigt & D. Lewanzik, Thermal and energetic constraints of daylight flight in bats, Proc. Biol. Sci. 278 (2011) 2311) report that core body temperature of flying bats differs by no more than 2 degrees between night and daytime flights, whereas mass-specific CO2 production rates are higher by up to 15 per cent during daytime. Such an increased flight costs only render diurnal bat flights profitable when the relative energy gain during daytime is high, and the risk of predation is low. This suggests that ancestral bats could possibly have evolved dark-skinned wing membranes to reduce nocturnal predation, but the low degree of reflectance of wing membranes made them also prone to overheating, and elevated energy costs during daylight flights. In consequence, bats might have become trapped in the darkness of the night, once their dark-skinned wing membranes had evolved.
And yes, any discussion of bats seems inevitably to lead to vampires and thoughts about who came first, the human or chiropterous variety. Linguistically, the word vampire derives from a very ancient Slavic term describing a supernatural malignant being supposed to seek nourishment by sucking the blood of sleeping humans. Actual bloodsucking bats do exist, the Desmodontidae confined to Central-South America, and their feeding habits were first described by English explorers in 1774. Therefore, it appears that the idea of human vampire long predated the zoological one, in our culture. A fascinating adaptation (one that, indeed, I never spotted in Dracula-themed novels) is that their saliva contains an anticoagulant, so that the blood of their victims does not clog as they sip. A good idea for the next Dracula movie.