Revised Repost: What big teeth you have

i-eb062da3141e116d516a386390056c23-smildonknight.jpeg


One of Charles R. Knight's paintings of Smilodon fatalis, this one menacing a giant sloth stuck in tar (off panel).


There are few fossil mammals that are as impressive as the saber-toothed cat Smilodon fatalis, but despite it's fearsome dentition some recent reports have suggested it was more of a pussycat when it came to bite strength. This seems to be counter-intuitive; how could such a fearsome-looking animal be associated with the term "weak"? Incredulity aside, it has become apparent that the bite of Smilodon wasn't as strong as that of some other carnivores (extinct and extant), yet it also had a unique feeding ecology based upon its dentition. This issue goes far beyond just one genus or species, however, as Smilodon was only one of many genera that bore massive canines. In fact, huge "sabers" have evolved over-and-over again in the mammalian lineage, including the famous fangs of the machairodontine felids (saber-toothed cats) and their look-alike nimravid relatives.

i-893aebad72871a02a17cb7ae92ef0a7d-herbtusks.JPG


Lateral, anterior, and dorsal views of the herbivore Uintatherium (Note the prominent canines). From Marsh 1873.


Although this post will primarily be concerned with the great "sabercats," large, dagger-like canine teeth have evolved multiple times in many different lineages during the course of life on earth. In some herbivorous creatures, like the extinct Uintatherium (and even the extant Musk Deer), the fangs reflect sexual dimorphism and may be the result of sexual selection. Likewise, large canine teeth are present in living baboons (Papio sp.), and the sexual dimorphism exhibited between the dental equipment of the males and the smaller canines of the females has long been noted (males often yawn to show off their canines, the size of their teeth being very intimidating).

Do the same considerations of sexual selection and dimorphism hold true for the saber-toothed cats? Unfortunately, fossil evidence does not always allow comparisons of the two sexes, but extant big cats and some death-trap sites have provided some information to work with. According to Selesa et al. (2006), canine size among member of the Carnivora does differ between the sexes, more so than any other feature of the skull. As with baboons, the differences are greater between the sexes in species in which a male must defend a group of females (like lions) than in a species where males and females form monogamous pairs (like leopards).

i-893e2f5d114d02a9b8550a9185507644-eobasieuluscope.JPG


The skull of another member of the Dinocerata; "Loxolophodon cornutus" (known today as Eobasileus cornutus). Again, note the prominent canine. From Cope 1885.


Applying this to saber-toothed carnivorans of the past, body size and canine length may both reflect sexual dimorphism, and the degree to which a species is dimoprhic may allow researchers to make some inferences about breeding system. In the Salesa et al. (2006) paper, the researchers propose that the extinct sabercat Paramachairodus ogygia had a breeding system like modern jaguars based upon the low degree of sexual dimorphism in their sample. In such a system males would stake claim to non-overlapping territories with females moving between the territories, forming temporary pairs with males during mating. Young adult Paramachairodus would leave their mothers when they became mature, but (especially in the case of the males) they would have to find an empty spot to call their own. This may make them more "adventurous" and likely to take risks, and in the particular case being discussed, most of the bones found in the natural trap were from young adults that may have been looking for their own territory.

Determining the presence of sexual dimorphism and inferring life histories does not necessarily solve the problem of why saber-teeth evolved in the first place though, and the fact that they are present in so many extinct carnivores suggests that the lengthening of canines were of functional significance in killing and processing prey. Saber-teeth in a herbivorous species are easier to attribute to sexual selection, but in a carnivorous species the teeth must be functional even if they first began to lengthen as a result of reproductive pressures.

i-0c59046f8150ade09ab9fc6802284668-saberdiversity.JPG


Saber-Toothed Felid and Nimravid diversity (click for a larger image). From Emerson & Radinsky 1980.


Before proceeding further, however, it should be noted that there was not just one group of saber-toothed carnivorans. Nimravids were saber-tooth look-alikes that diverged from a common ancestral line earlier than the carnivores that would eventually give rise to Smilodon, but the two lines are were closely related and present a good example of parallel evolution (which I consider to be extreme convergence plus at least some temporal overlap). There is still some reshuffling of taxa going on and the true evolutionary history/affinities of many of the forms is still being worked out, but most saber-toothed carnivoran skulls you're likely to see grouped together at a museum fall into either the nimravid or felid camps. The focus of this essay, however, will be on felids, and although they are often discussed along with their nimravid cousins the larger amount of work has been done on the felids, particularly Smilodon.

Even within the felid sabercats, though, there was variation in tooth and skull form that was divided into three categories by Martin et al. (2000). The differences in the three types of skull shapes and dentitions hint at differing predatory tactics, prey, and habitat. Indeed, evolution did not create carbon copies of the same creature, barring life from becoming adapted to varying circumstances; there is more variety than would be first assumed if we based all our research on the presence of prominent canines. Instead, there seem to be three "ways of being a saber-toothed cat."

Members of the first group are called the scimitar-toothed cats, which have relatively short and coarsely-serrated canines but with a long-limbed body best suited for fast running. Homotherium is a good example of a scimitar-toothed cat. Species that fall into the second category are called dirk-toothed cats, which had longer, finely-serrated canines and short, powerful limbs. Smilodon is the epitome of a dirk-toothed cat. The third variety doesn't have a name but is represented by the genus Xenosmilus from the Early Pleistocene of Florida. Heavily built, almost like a bear, this cat had a stocky body but scimitar-like canines, and its habits likely differed from those of both the scimitar- and dirk-toothed cats.

i-78a095679892e2b8ed2547d4b31ee4ab-threekindsofcats.JPG


Xenosmilus hodsonae, Homotherium cf. crenatidens, and Homotherium serum. From Martin et al. 2000


The three different morphotypes (or even ecotypes) may represent different evolutionary trade-offs, the dirk-toothed cats perhaps dealing with larger, heavier prey than the scimitar-toothed cats. Clues as to how each group may have been making a living may be seen in the teeth. In the case of dirk-toothed cats, the canines would puncture the prey and have to travel a fairly long distance before the incisors would come in contact with the prey. The scimitar-toothed cats had shorter canines and longer incisors, closing the traveling distance and perhaps making it easier to rip off strips of flesh. This second sort of placement would have strengthened the tooth row and put less restrictions on where the cat could bite, and scimitar-toothed cats may have scooped large pieces of flesh out of their prey, causing it a great amount of trauma and blood loss. The scimitar-toothed cats had a smaller sagittal crest than the dirk-toothed cats, however, and since the size of the sagittal crest is proportional to the forces that can be achieved while biting, dirk-toothed cats probably had more powerful bites. Xenosmilus took this even further to the extreme and probably had an extremely strong bite.

In order to appreciate the differences in tooth structure and sagittal crest size, here are a few close-ups of carnivore skulls from the American Museum of Natural History that will help illustrate the point;

i-d98bea23730e70c89af4d601b5ba2b23-amphicodonbwclose.jpeg


The extinct "bear dog" Amphicyon. Note the size of the sagittal crest, the reduction of the bony enclosure around the eyes, and the large holes on the side of the skull for jaw muscle attachment.


i-47cb7d687160afaab775cdf1d6044c2e-hyenadonbw.jpeg


The extinct "saber-toothed" creodont Hyaenodon. Again, note the sagittal crest, reduction of bone enclosure around the eye, and the large canines.


i-b09abbf22f277f758870094b03d3c9b2-holophoneusskbw.jpeg


The skull of the nimravid Hoplophoneus. Note the size of the canines and sagittal crest in comparison with Hyaenodon and Amphicyon.


i-523c9309f0c2fb732bf6b5ec95560ced-smilocloseup.jpg


The skull of Smilodon on display at the AMNH. As observed in Martin et al (2000), the canines would have to pierce the prey for some distance before the incisors could come into play if the sabercat was driving its teeth fully into its prey.


i-fd44ea48bebb07364386bf8f47395690-thylacoleoamnhskull.jpg


The skull of the marsupial predator Thylacoleo. Note the large openings on either side of the skull for the jaw muscles and the cleaver-like premolars.


i-bcb925c8f72db7f2708c6d7df3b0f83b-thylacoskullcope.jpg



Ventral view of the skull of Thylacoleo. From Cope 1884. Note the large openings between the skull and the zygomatic arches that jaw muscles would have run through.


All of the carnivores illustrated above show varying adaptations to killing and consuming prey. Nearly all of them possess a sagittal crest, a feature that increases the area for jaw muscle attachment and is often larger in omnivores or bone-crushing carnivores as they require greater bite forces to crack hard foods (although recent research by Wroe et al. [2005] suggest that bone-crushers like spotted hyena might not have the strongest bites). Likewise, the holes between the skull and cheek bones are often enlarged or widened (the extreme of this group being Thylacoleo), the more muscle that can pass from lower jaw to skull also contributing to bite strength. What is interesting about sabercats, when considering these factors, is that they seem to be in the middle. They don't exhibit adaptations of the skull to the extreme as in Amphicyon or Thylacoleo, but they still exhibit changes allowing for powerful bites (strong enough to kill and consume prey, obviously). The similar features of these and other predators led Emerson and Radinsky (1980) to ponder the question of carnivore convergence;

With enlargement of upper canines, skulls of paleofelid, neofelid, marsupial and, as far as the record shows, creodont sabertooths were remodeled in similar ways. This evolutionary convergence in cranial morphology is not surprising, since most of the modifications relate to allowing increased gape while retaining bite strength at the carnassial. Those are factors essential for all sabertooths, and the possible ways to achieve them, starting from a generalized mammalian cranial morphology, are limited...

Why did sabertooth specializations evolve so many times? Their multiple evolution, plus the fact that several species of sabertoothed felids existed for most of the history of the family (from about 35 Myr to about 15,000 yr BP) suggest that sabertooth canines provided an effective alternative to the modern carnivore mode of killing prey.

i-a325288090caaa0c6a8ec01061239ad5-kittyteeth.jpg


The skull of the saber-toothed cat Megantereon.


Sabercats and similarly-equipped carnivores were certainly catching and killing prey, but the question of how they did so has long been a contentious topic. Were the elongated canines of these animals used for stabbing, cutting, slicing, crushing, or some combination of these? It is clear that the canines of sabercats were relatively delicate, and it's unlikely that they used them for crush or stabbing prey (if they got stuck in a large animal they might get taken for a ride or have their teeth broken off). Indeed, it's unlikely that sabercats jumped onto the backs of their victims and bit full-force into the back of their prey's skull like many modern big cats, especially when it appears that sabercats like Smilodon were ill-equipped to handle the stresses of struggling prey. Saber-like canines seem to be better suited to slicing open soft tissues that would be found along the ventral side of a prey animal rather than piercing hides or bone, and sabercats likely had a way of taking down prey distinct from the techniques of living big cats.

i-be65822ff0a827861074aa703204aca6-sabreteeth.jpg


Skulls (mandibles not pictured) of 4 "saber-toothed" mammals from Simpson 1941. Pictured are A) Machairodus (felid), B) Hoplophoneus (nimravid), C) Smilodon (felid), and D) Thylacosmilus (marsupial).


If sabercats targeted soft parts of their victims to attack during a hunt (i.e. the throat and abdomen), they may have ignored smaller prey that had too much bone and not enough soft surface to bite (making it more likely that a tooth would be broken during an attack). Sabercats would have been biased towards larger prey animals, and this could have eventually played into their extinction during the Pleistocene. In places where large herbivores would have died out, the sabercats may not have been able to adapt to the smaller selection of prey, perhaps suffering tooth-breaks and subsequent infections more often. This is probably not the cause for their extinction, but it may have been a contributing factor.

i-8939abb0baa8fce884e655cc57d8d755-amurleopardyawn2.jpg


An Amur Leopard yawns. Note the relatively small (but still prominent) canines of the upper and lower jaw.


What, then, of a smaller living cat, the Clouded Leopard (Neofelis nebulosa and N. diardii)? This genus has sometimes been heralded as a modern analog of sabercats, having elongated upper and lower canines. As Christiansen (2006) notes, though, clouded leopards are a bit bizarre, and it is incorrect to call them "small" big cats or modern sabercats, the genus showing a number of convergences with extinct forms while remaining distinct from the famed genus Panthera;

The skull morphology of the clouded leopard sets it apart from other extant felids, and in a number of respects it approaches the morphology of primitive sabertooths. This indicates convergence of several characters in machairodontine felids and the clouded leopard, mainly as adaptations for attaining a large gape. This raises doubts about the characters hitherto considered as distinguishing sabertoothed from nonsabertoothed predators...

Clearly, Neofelis and the sabertooths independently evolved a suite of the same specializations for the same overall purpose of attaining a large gape, a prerequisite for efficient jaw mechanics with large canines, but the reasons for evolving these characters need not have been similar. Based on analyses of lower jaw bending moments and inferred resistance to mechanical loadings, Therrien (2005) suggested that Neofelis could be at the beginning of a new sabertooth radiation. Such claims are difficult to test, however, since the extant sister taxon to Neofelis (Panthera) shares none of its sabertoothed characters, and the fossil record provides no clues of felids closer to Neofelis than Panthera. At present, however, there is little evidence to suggest that Neofelis can be regarded as an "extant sabertooth," although it clearly shares a number of characters with them that are absent in other extant felids. On the other hand, it cannot be regarded as simply an intermediate between large and small felids, as normally assumed. The presence to some extent of characters normally ascribed to sabertooths in Neofelis raises doubts about their functional and evolutionary significance in primitive machairodonts such as Nimravides or Paramachairodus, hitherto the only reasonably well-known primitive machairodont. Such animals need not have shared the presumed functional skull morphology of later, more derived sabertooths and are perhaps not to be regarded as "sabertoothed" at all, if by sabertoothed is implied animals functionally significantly different from extant felids.

Such realizations make it somewhat difficult to ascertain whether clouded leopards have any significance for understanding sabercat paleobiology. Neofelis shows some convergences but it also distinct, and the factors that caused it to grow longer canines (and hence open its jaws wider) may be different than for any of the extinct groups. How narrowed a predatory niche clouded leopards occupy due to their dentition is not going to be the same for the larger, fossil sabercats like Smilodon, a felid that has recently said to have had a weak bite. It is true that sabercats had weaker bite forces than modern lions and tigers, but they are on par with jaguars and leopards, and so the term "weak" can only be used in a relative (not absolute) sense. The force of a bite isn't all about the action of the jaws either, and the contribution of neck muscles and behavior have to be considered as well; Smilodon could have had a relatively "weak" bite but still be a highly effective predator. In fact, Christiansen (2007) proposed that a shearing bite to the throat would have resulted in a faster call than a "throttling throat bite" like many modern cats deliver, and we can't assume that living big cats always provide us with a proper model for sabercat killing methods.

Considerations of the killing method of sabercats brings us to another point mentioned in the discussion of scimitar-tooths vs. dirk tooths, namely that the famous dirk-toothed cats like Smilodon were more powerfully built. They may have worked in groups intent on bringing a large animal down to the ground and then delivering devastating bites once the stomach and neck were exposed (a process that may be similar to modern examples like lions bringing down giraffes or elephants).




A group of lions brings down a giraffe.





A group of lions brings down an elephant.


Hunting isn't the only aspect of sabercat predation that seems to have differed from modern carnivores; the way they ate may have differed from the way extant cats feed. As is apparent at this point, the contact of the canines with bones would have been avoided, and it seems that the hard parts of the skeleton would have been avoided when a sabercat was consuming it. This could vary among different groups (perhaps some of the shorter-toothed forms not being so finicky about bone), but research into microwear patterns on teeth of Smilodon don't seem to match with wear patterns of any living carnivores, suggesting a different dietary preference. It could be hypothesized, then, that creatures like Smilodon primarily consumed the soft parts of the carcass or what could be removed without too much damage to the teeth, and it should be remembered that living big cats often do not eat every part of the skeleton. Some, like cougars, have favored parts that they eat but end up leaving as much as 40% of the carcass behind. Other predators, especially bone-crushing ones, could take advantage of the leftovers, although the felids might have had to eat quickly as some of their osteophagus competitors may not have been patient (and, in fact, lions and hyenas often fight over kills and steal them from each other today).

To summarize, sabercats may have specialized in bringing down prey relatively larger than themselves quickly (some working in groups to do so), killing prey animals by slashing open their stomachs or slicing through the blood vessels of the neck. This would be a much messier, but quicker, method than employed by living big cats, although the limitation of food sources likely caused in the eventual downfall of sabercats. Hypercarnivory can be a dangerous adaptive path to go down, and cats are clearly the most meat-dependant of the Carnivora, and the sabercats may have been even more dependent on the soft parts of a carcass. The price paid for such adaptations ended up being extinction, but given how many times they have shown up in the history of life on this planet, someday there may again be a saber-toothed predator stalking the shadows.

References;

Anyonge, W. "Microwear on Canines and Killing Behavior in Large Carnivores: Saber Function in Smilodon fatalis" Journal of Mammalogy, Vol. 77, No. 4 (Nov., 1996), pp. 1059-1067

Christiansen, P. "Canine morphology in the larger Felidae: implications for feeding ecology." Biological Journal of the Linnean Society. Vol. 91, No. 4 (Aug., 2007), pp. 573-592

Christiansen, P. "Sabertooth characters in the clouded leopard (Neofelis nebulosa Griffiths 1821)." Journal of Morphology, Vol. 267, No. 10 (Jul., 2006), pp. 1186 - 1198

Christiansen, P. and Wroe, S. "Bite Forces and Evolutionary Adaptations to Feeding Ecology in Carnivores." Ecology, Vol. 88, No. 2 (Feb., 2007), pp. 347-358

Cope, E.D. "The Amblypoda (Continued)." The American Naturalist, Vol. 19, No. 1. (Jan., 1885), pp. 40-55.

Cope, E.D. "The Tertiary Marsupialia." The American Naturalist, Vol. 18, No. 7. (Jul., 1884), pp. 686-697.

Emerson, S.B., and Radinsky, L. "Functional Analysis of Sabertooth Cranial Morphology." Paleobiology, Vol. 6, No. 3. (Summer, 1980), pp. 295-312.

Leutenegger, W., and Kelly, J.T. "Relationship of sexual dimorphism in canine size and body size to social, behavioral, and ecological correlates in anthropoid primates." Primates, Vol. 18, No. 1 (Jan., 1977), pp. 117-136

Lucas, P.W., Corlett, R.T., and Luke, D.A. "Sexual dimorphism of tooth size in anthropoids." Human Evolution Vol. 1, No. 1 (Feb., 1986), pp. 23-39

Marsh, O.C. "The Fossil Mammals of the Order Dinocerata." The American Naturalist, Vol. 7, No. 3. (Mar., 1873), pp. 146-153

Martin, L.D., Babiarz, J.P., Naples, V.L., and Hearst, J. "Three Ways To Be a Saber-Toothed Cat." Naturwissenschaften, Vol. 87, No. 1 (Jan. 2000), pp. 41-44

McHenry, C.R., et al. "Supermodeled sabercat, predatory behavior in Smilodon fatalis revealed by high-resolution 3D computer simulation." PNAS, Published online before print October 2, 2007

Salesa, M.J., et al. "Aspects of the functional morphology in the cranial and cervical skeleton of the sabre-toothed cat Paramachairodus ogygia (Kaup, 1832) (Felidae, Machairodontinae) from the Late Miocene of Spain: implications for the origins of the machairodont killing bite." Zoological Journal of the Linnean Society, Vol. 144, No. 3, (Jul., 2005) pp. 363-377

Salesa, M.J., et al. "Inferred behaviour and ecology of the primitive sabre-toothed cat Paramachairodus ogygia (Felidae, Machairodontinae) from the Late Miocene of Spain" Journal of Zoology, Vol. 268, No. 3 (Mar., 2006), pp. 243-254

Simpson, G.G. "The Function of Saber-Like Canines in Carnivorous Mammals." American Museum Novitiates, August 4, 1941

Therrian, F. "Mandibular force profiles of extant carnivorans and implications for the feeding behaviour of extinct predators." Journal of Zoology, Vol. 276, No. 3 (Nov., 2005), pp. 249-270

Therrian, F. "Feeding behaviour and bite force of sabretoothed predators." Zoological Journal of the Linnean Society, Vol. 145, No. 3 (Nov., 2005), pp. 393-426

Van Valkenburgh, B., and Molnar, R.E. "Dinosaurian and mammalian predators compared." Paleobiology, Vol. 28, No. 4 (Dec., 2002), pp. 527-543

Walker, Alan. "Mechanisms of honing in the male baboon canine." American Journal of Physical Anthropology, Vol. 65, No. 1 (?, 1984), pp. 47 - 60

Wroe, S., McHenry, C., and Thomason, Jeffery. "Bite club: comparative bite force in big biting mammals and the prediction of predatory behaviour in fossil taxa." Proceedings of the Royal Society B, Vol. 272, No. 1563 (Mar., 2005), pp. 619-625

Categories

More like this

According to a news report released last night the first confirmed remains of a scimitar-toothed cat have been found in Venezula, a contemporary of the dirk-toothed cat Smilodon. The uncovered remains are said to represent six individual sabercats, called Homotherium, including a complete skull.…
A Smilodon fends off vultures at what would later be called the Rancho La Brea tar pits, situated in Los Angeles, California. Painting by Charles R. Knight. The feeding habits of saber-toothed cats have long perplexed scientists. How in the world did these cats kill prey with their almost…
A reconstruction of Smilodon, photographed at the American Museum of Natural History. When it comes to animals, encyclopedias often present us with generalized descriptions. Where a creature lives, what color it is, what it eats, and other tidbits of information are listed to distinguish one…
A very lion-like Smilodon, from Ernest Ingersoll's The Life of Animals (1907). For decades after its discovery the saber-toothed cat Smilodon fatalis was depicted as little more than a lion with a short tail and long fangs. Given its size and habits as a large carnivore the connection appeared…

The last two pictures aren't there.

Nice review, however! You only missed the gorgonopsians :-)

By David Marjanović (not verified) on 10 Apr 2008 #permalink

Great topic! I think saber teeth are fangscinating!

I'd like to take this opportunity to ask two questions, one of which is not entirely on-topic.

First, does anyone know off-hand where the remains of Eobasileus have been found? I haven't been able to discover this via Google. Uintatherium, yes (Wyoming). Eobasileus, no.

Second, as an amateur paleo-illustrator, I've acquired a sudden itch to depict an encounter between Andrewsarchus and a Uintatherium/Eobasileus-type dinoceratan. Something about a fight between two beasts that each sport both fangs and hooved toes, yet one herbivorous and one a flesh-eater, has suddenly come to fascinate me.

Question: Is there a chance in hell that anything like that could have happened? The two beasts lived at approximately the same time.

I know Andrewsarchus is known only from Mongolia -- we just have the one skull, right? But that doesn't tell us much about the extent of their range.

I also know (I think) that Uintatherium/Eobasileus-style dinoceratan fossils have been found only in North America -- but other members of the tribe aren't strangers to the Mongolia area. There's Gobiatherium, but it has a significantly different morphology from its American cousins (and therefore not as cool, IMO).

But there was also some kind of land-bridge between Asia and North America during the Eocene, no? So is it even possible that the ranges of an Andrewsarchus-like species and a Uintatherium-like species might have intersected?

Thanks for any opinions.

By Stevo Darkly (not verified) on 10 Apr 2008 #permalink

> Question: Is there a chance in hell that anything like that could
> have happened? The two beasts lived at approximately the same time.

*Uintatherium* and *Eobasileus* lived in the early- to mid Eocene, *Andrewsarchus* in the late Eocene, so they are separated by at least 5 million years. If *Andrewsarchus* clashed with graviportal megaherbivores, they were brontotheres, who btw were just as impressive and bizarre as dinoceratans, if lacking in the fang department. Still, a fight between *Andrewsarchus* and a big bronththere - or a fight between *Andrewsarchus* and *Sarkastodon* over a brontothere carcass - would have been an unforgettable sight!

> So is it even possible that the ranges of an Andrewsarchus-like
> species and a Uintatherium-like species might have intersected?

Smaller mesonychians like *Pachyena* or *Mesonyx* did indeed co-exist with large dinoceratans in NA, but I don't think there was much interaction between them - there is not much interaction between rhinos and hyaenas or canids, either. Perhaps a mother *Eobasileus* chased them away if it had a young calf to protect. On the other hand, if I watch those videos of the lions bringing down a giraffe or even an elephant, I have second thoughts about it. Perhaps hyena- or small bear-sized mesonychians might have been more than a nuisance for dinoceratans if they formed a large enough pack?

johannes -- Thank you. And, darn it.

I might do the sketch anyway, for fun, with a disclaimer.

I guess I tend to think of creatures separated in time by "only" 5 million years as more-or-less contemporaries.

I guess I also staked my hope on the fact that we only know Andrewsarchus from a single skull (and, I think I just read somewhere, some other minimal fragments) and therefore we only have one data-point that doesn't help us plot the extremes of Andrewsarchus' range of existence in either space or time.

I guess my thinking above isn't very ... parsimonious in its assumptions, but I hoped there was still some room for some speculation.

Oh well ... I'll probably do the sketch as an exercise in "what if?" alternate history, anyway.

By Stevo Darkly (not verified) on 11 Apr 2008 #permalink