How Many Tyrannosaurs Were There?

Suppose you were transported back to the late Cretaceous, what is the probability that you would see a Tyrannosaurus? That depends on a large number of factors, and to simplify, I shall limit myself to T Rex. There were various Tyrannosaurs, but probably in different times and different places. As far as we know, T Rex was limited to what was effectively an island land mass known as Laramidia that has now survived as part of Western North America. In a recent edition of Science, a calculation was made, and it starts with the premise, known as “Damuth’s Law” that population density is negatively correlated with body mass through a power law that involves two assignable constants, plus the body mass. What does that mean? It is an empirical relationship that says the bigger the animal, the fewer will be found in a given area. The reason is obvious: the bigger the animal, the more it will eat, and a given area has only so much food. Apparently one of the empirical constants has been assigned a value of 0.75, more or less, so now we are down to one assignable constant.

If we concentrate on the food requirement, then it depends on what it eats, and what it does with it. To explain the last point, carnivores kill prey, so there has to be enough prey there to supply the food, AND to be able to reproduce. There has to be a stable population of prey, otherwise the food runs out and everyone dies. The bigger the animal, the more food it needs to generate body mass and to provide the energy to move, however mammals have a further requirement over animals like snakes: they burn food to provide body heat, so mammals need more food per unit mass. It also depends on how specialized the food is. Thus pandas, specializing on eating bamboo, depend on bamboo growth rates (which happens to be fast) and on something else not destroying the bamboo. For Tyrannosaurs, they presumably would concentrate on eating large animals. Anything that was a few centimeters high would probably be safe, apart from being accidentally stood on, because the Tyrannosaur could not get its head down low enough and keep it there long enough to catch it. The smaller raptors were also probably safe because they could run faster. So now the problem is, how many large animals, and was there a restriction? My guess is it would take on any large herbivore. In terms of the probability of meeting one, it also depends on how they hunt. If they hunted in packs, which is sometimes postulated, you are less likely to meet them, but you are in more trouble if you do.

That now gets back to how many large herbivores would be in a given area, and that in turn depends on the amount of vegetation, and its food value. We have to make guesses about that. We also have to decide whether the Tyrannosaur generated its own heat. We cannot tell exactly, but the evidence does seem to support the fact that it was concerned about heat as it probably had feathers. The article assumed that the dinosaur was about half-way between mammals and large lizards as far as heat generation goes. Provided the temperatures were warm, something as large as a Tyrannosaur would probably be able to retain much of its own heat as surface area is a smaller fraction of volume than for small animals.The next problem is assigning body mass, which is reasonably straightforward for a given skeleton, but each animal starts out as an egg.  How many juvenile ones were there? This is important because juvenile ones will have different food requirements; they eat smaller herbivores. The authors took a distribution that is somewhat similar to that for tigers. If so, an area the size of California could support 3,800 T. Rex. We now need the area over which they roamed, and with a considerable possible error range and limiting ourselves to land that is above sea level now, they settled on 2.3 + 0.88 million square kilometers, which, at any one time would support about 20,000 individuals. If we take a mid-estimate of how long they roamed, which is 2.4 million years, we get, with a very large error range, that the total number of T. Rex that ever lived was about 2.5 billion individuals. Currently, there are 32 individual fossils (essentially all are partial), which shows how difficult fossilization really is. Part of this, of course, arises because fossilization is dependent on appropriate geology and conditions. So there we are: more useless information, almost certainly erroneous, but fun to speculate on.

Free Will

You will see many discussions regarding free will. The question is, do you have it, or are we in some giant computer program. The problem is that classical physics is deterministic, and you will often see claims that Newtonian physics demands that the Universe works like some finely tuned machine, following precise laws of motion. And indeed, we can predict quite accurately when eclipses of the sun will occur, and where we should go to view them. The presence of eclipses in the future is determined now. Now let us extrapolate. If planets follow physical laws, and hence their behaviour can be determined, then so do snooker or pool balls, even if we cannot in practice calculate all that will happen on a given break. Let us take this further. Heat is merely random kinetic energy, but is it truly random? It seems that way, but the laws of motion are quite clear: we can calculate exactly what will happen in any collision and it is just in practice the calculations are too complicated to even consider doing it. You bring in chaos theory, but this does nothing for you; the calculations may be utterly impossible to carry out, but they are governed solely by deterministic physics, so ultimately what happens was determined and it is just that we do not know how to calculate it. Electrodynamics and quantum theory are deterministic, even if quantum theory has random probability distributions. Quantum behaviour always follows strict conservation laws and the Schrödinger equation is actually deterministic. If you know ψ and know the change of conditions, you know the new ψ. Further, all chemistry is deterministic. If I go into the lab, take some chemicals and mix them and if necessary heat them according to some procedure, every time I follow exactly the same procedures, I shall end up with the same result.

So far, so good. Every physical effect follows from a physical cause. Therefore, the argument goes, since our brain works on physical and chemical effects and these are deterministic, what our brains do is determined exactly by those conditions. But those conditions were determined by what went before, and those before that, and so on. Extrapolating, everything was predetermined at the time of the big bang! At this point the perceptive may feel that does not seem right, and it is not. Consider nuclear decay. We know that particles, say neutrons, are emitted with a certain probability over an extended period of time. They will be emitted, but we cannot say exactly, or even roughly, when. The nuclei have angular uncertainty, therefore it follows that you cannot know what direction it is emitted because according to the laws of physics that is not determined until it is emitted. You may say, so what? That is trivial. No, the so what is that when you find one exception, you falsify the overall premise that everythingwas determined at the big bang. Which means something else introduced causes. Also, the emitted neutron may now generate new causes that could not be predetermined.

Now we start to see a way out. Every physical effect follows from a physical cause, but where do the causes come from? Consider stretching a wire with ever increasing force; eventually it breaks. It usually breaks at the weakest point, which in principle is predictable, but suppose we have a perfect wire with no point weaker than any other. It must still break, but where? At the instant of breaking some quantum effect, such as molecular vibration, will offer momentarily weaker and stronger spots. One with the greatest weakness will go, but due to the Uncertainty Principle that the given spot is unpredictable.

Take evolution. This proceeds by variation in the nucleic acids, but where in the chain is almost certainly random because each phosphate ester linkage that has to be broken is equivalent, just like the points in the “ideal wire”. Most resultant mutations die out. Some survive, and those that survive long enough to reproduce contribute to an evolutionary change. But again, which survives depends on where it is. Thus a change that provides better heat insulation at the expense of mobility may survive in polar regions, but it offers nothing in the equatorial rain forest. There is nothing that determines where what mutation will arise; it is a random event.Once you cannot determine everything, even in principle, it follows you must accept that not every cause is determined by previous events. Once you accept that, since we have no idea how the mind works, you cannot insist the way my mind works was determined at the time of the big bang. The Universe is mechanical and predictable in terms of properties obeying the conservation laws, but not necessarily anything else. I have free will, and so do you. Use it well.

The Hangenberg Extinction

One problem of applying the scientific method to past events is there is seldom enough information to reach a proper conclusion. An obvious example is the mass extinction that we know occurred at the end of the Devonian period, and in particular, something called the Hangenberg event, which is linked to the extrinction of 44% of high-level vertebrate clades and 97% of vertebrate species. Only smaller species survived, namely sharks smaller than a meter in length and general fish less than ten centimeters in length. This is the time when most ammonites and trilobites, which had been successful for such a long time, failed to survive. One family of trilobites survived, only to be extinguished in the Permian extinction, another  of those that wiped out 90% of all species. 

So why did this happen? First, it is most likely the ecosystems had been stressed. The Hangenberg event occurred about 358 My ago, but before that, at about 382 My BP most jawless fish disappeared, while from 372 – 359 My BP there were a series of extinctions or climate changes known as the Kellwasser event (although it was almost certainly a number of events.) So for about 30 million years leading up to the Hangenberg event, there had been severe difficulties for life. At this stage, leaving aside insects and plants that had left the oceans, most life were in marine or freshwater environments and it was this life that appears to have suffered the most. That conclusion, however, may more reflect a relative paucity of land-based fossils. Climate change was almost certainly involved because over this period there was a series of sea level rises while the water became more anoxic. The causes of this are less than clear and there have been a numper of suggestions.

One possibility is an asteroid collision, and while impact craters can be found they cannot be dated sufficiently closely to be associated with any specific event. A more likely effect questions why anoxic? The climate  should have no direct effect on this, although the reverse is possible. The question is really was it the seas only that became anoxic? One possibility is that on land the late Devonian saw a dramatic change in plant life. In the early Devonian, plants had made it to land, but they were small leafy plants like liverworts and mosses. In the late Devonian they developed stems that could move water and nutrients, and suddenly huge plants emerged. One argument is that this caused a flood of nutrients through the weathering of rocks caused by the extensive root systems to flow down into the sea, which caused algal blooms, which led to anoxic conditions. Meanwhile, the huge forests of the Devonian may have reduced carbon dioxide levels, which would lead to glaciation, and the sea level fall in the very late Devonian. However, it does not explain sea level rise earlier. That may have arisen from extensive volcanism that occurred around 372 My ago, which would enhance greehouse warming. You can take your pick from these explanations because even the experts in the field are unsure.

Accordingly, a new theory has just emerged, namely Earth was bombarded by cosmic rays from a nearby supernova (Fields, et al., arXiv:2007.01887v1, 3rd July, 2020). This has the advantage that we can see why it is global. The specific event would be a core-collapse supernova. If this occurred within 33 light years from Earth, it would probably extinguish all life on Earth, but one about twice as far away, 66 light years, would exterminate much life, but not all. The mechanism is in part ozone depletion, but there is the possibility of enhanced nitrogen fixation in the atmosphere, which might lead to algal blooms. One of the good things about such a proposition is it is testable. Such an event would bombard Earth with isotopes that would otherwise be difficult to obtain, and one would be plutonium 244. There is no naturally occurring plutonium on Earth, so if some atoms were found in the fossils or in accompanying rock, that would support the supernova event.

So, is that what happened? My personal view is that is unlikely, and the reason I say that is that most of the damage would be done to life on land, and as I gather, the insects expanded into the Carboniferous period. The seas would be relatively protected because the incoming flux would be protected by the water. The nitrate fixation might cause an algal bloom and while a lot of energy would be required to saturate the world’s oceans, maybe there was sufficient. The finding of plutonium in the associated deposits would be definitive, however. The typical deposits were black shales overlaid by sandstone, and are easy to locate, so if there is plutonium in them, there is the answer. If there is not, does that mean the proposition is wrong? That is more difficult to answer, but the more samples that are examined from widespread sources, the more trouble for the proposition.

My preferred explanation is the ecological one, namely the development of tree ferns, etc. The Devonian extinction was slow, taking 24 million years, and while most marine extinctions occurred during what is called the Hangenberg event, the word event may be misleading. That specific period took 100,000 – 300,000 years, which is plenty of time for an ecological disaster to kill off that which cannot adapt. To put it into perspective, Homo Sapiens has been around for only 30,000 years, and effective for only about 10,000 years. Look at the ecological change. Now, think what will happen if we let climate change get out of control. We are already causing serious extinction of many species, but the loss of habitat if the seas rise will dwarf what we have done so far because our booming population has to eat. We should learn from the late Devonian.