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Index of Subjects Hi Paul, Derek, Andy, Dave and all, Quoting "Paul S. Boyer" <psboyer@eastlink.ca>: > We often hear this said about insects and how strong they are. > I suspect that the main reason insects seem so strong is merely the > scale factor. If ants are so mighty, why are there no really large > ants around? Clearly, there is a scale factor which limits their > size. It is not possible to build a viable ant larger than a > certain size. This scaling factor idea is a large subject with a venerable history in biology. The biggest insects are probably the formidable SE Asian bugs, genus Lethoceros, which can reach about 10 cm long. It would clearly be possible to build one much larger than this with the same exoskeletal materials -- crustaceans are similar in that regard and a big lobster can be ~50 cm long and way heavier (in air) than the biggest bug. The question then is, as Paul says, what is it that limits the achievable size for that body plan? In air-breathing vertebrates, oxygen is actively pumped into the lungs, where it combines with an efficient blood pigment which is actively pumped round the body by the heart, to release oxygen to the tissues. Insects also have hearts which circulate the blood, rather slowly, but oxygenation and removal of CO2 doesn't work that way at all. Instead, tiny air tubes (tracheae) originate at holes (spiracles) along the sides of the body and conduct the oxygen passively directly to the tissues, by simple diffusion (CO2 diffuses out similarly). As Paul points out, dimensional arguments (length L, L-squared, L-cubed] are very important determinants: in this case, gas diffusion gradients have the physical property that the rate of diffusion at the delivery end at the muscles is inversely proportional to the [length-squared] of the pathway, the tracheal tube. So if you double the width of the insect, you double the length of the tube pathway (*2), but the rate of movement of the gases O2 and CO2 will drop to one quarter of what it had been before, at the tissue end (1/(2 squared) = 1/4). This is believed to be one of the main factors that limits the ultimate size of insects, such that at large size they simply cannot supply O2 to the tissues fast enough by passive diffusion. The most energetically expensive tissue known is insect flight muscle, to give an idea of why this might be important. Crustaceans also have hearts and get round this limitation by having blood pigments that also do useful things with oxygen. In addition, they have a blood circulation with primitive capillaries that penetrate the body tissues directly, so they are a bit more analogous to vertebrates in this respect. These capillaries are not found in insects, which have a completely 'open' circulation. > I cannot find any reference proving that ant muscles are actually > stronger by weight than muscles in other creatures. Who knows? It > might be interesting to find out. But it seems to me that the > relative strength of a muscle is roughly proportional to its > cross-sectional area. As one scales up the size of a muscle, the > volume increases as the cube of the linear dimension, but the > cross-sectional area only as the square. So a bigger animal will > have trouble keeping up proportionate strength as it gets larger. The expectation is that all voluntary muscles will be fairly similar in their force-generating abilities, weight for weight. Since the 1960s it has become clear from the ultrastructure of voluntary muscles that all animals looked at use the same basic sliding-filament design, with two main sliding proteins actin and myosin, and a similar biochemistry powered ultimately by ATP. There are some differences, for instance some insect muscles are super-contracting where the filaments can slide even further along each other and cross into neighbouring sarcomeres. The sliding filaments are grouped into little modules arranged end to end each usually 2-5 micrometers long, called sarcomeres: each of these can exert its own mini-force. So it is expected that a muscle of twice the cross-sectional area will be able to generate twice the force, all other things being equal, as Paul says. But, in addition, a longer muscle fibre with 2000 sarcomeres in line will generate twice the force of a shorter fibre with only 1000, so the force generated by a muscle ought to be proportional to the volume of the muscle not its area, that is, vary as L-cubed. > We could see this in a jumping contest. I have seen a wild Norway > Rat leap laterally about 3 m, which is many times (perhaps x15) his > length. A human Olympic athlete can't jump proportionally so far; > and a bear (strong as he seems to us) is even a shorter jumper. And > they say that an elephant is totally unable to jump at all! A classical 'dimensional argument' like this is that the cross-sectional area of the legs (which varies as L-squared) has to be able to support the weight of the body without fracturing (body weight varies as L-cubed). As the animal gets a bit heavier (L-cubed), the cross-sectional area of the legs has to increase proportionally much more than that to keep up, until you end up with an elephant with almost unmanageably chunky legs with huge cross-sectional areas (or those on an even bigger Brontosaurus, which might have been helped by its buoyancy, living in water in a swamp). > Thus in a weight-lifting contest where the load is calculated as a > multiple of the contestant’s body weight, the small animals (other > things being equal) should win. Insects, of course, are not formed > at all like vertebrates, and in their size range an exoskeleton > could have many advantages. Exoskeletons do not work at all in our > size range, which is why there are not any really gigantic insects > (except in our nightmares, or in sci-fi movies). Not sure about this, depends what you mean by 'work at all'. While insect cuticle is impressive stuff, the breaking strain (under stress from a big powerful muscle contraction) for the best cuticle might be lower than that for a similar sized sample of bone; or, it might not be -- not sure without digging. > Similarly, we cannot scale humans down to ant size, and there are no > mammals with that tiny an adult size. Agreed, but there are certainly insects that are as large or larger than some very small mammals and birds, so there is some size overlap... > > Birds are another great example of scaling. Most birds are small. > Only a few get very large, and as they do, they have more and more > trouble taking off. The largest cannot fly at all. Analogous to the elephant story, the body mass to be lifted against gravity in flight varies as body volume or weight (proportional to Length-cubed), while the lift provided by