Here's an interesting example with regards to the woolly mammoth.
Taken from
http://www.answersingenesis.org/Home/Area/AnswersBook/iceage16.asp
...
The remains of hundreds of thousands of woolly mammoths are found across northern Europe, Siberia and Alaska. There was a lucrative trade in mammoth ivory for many years. At least a million mammoths must have lived in Siberia and Alaska.24 But how could the frozen wastes of Siberia have ever produced enough food for the mammoths? Woolly rhinoceros, bison, horses and antelopes also lived there in abundance. Even if the animals migrated there in summer, there would not have been enough food for them.
Furthermore, what did animals such as wooly mammoths, rhinoceros, bison and horses drink during the frozen winters? Such animals need large quantities of liquid water.
Evolutionists, with their eons of time and multiple ice ages, believe that Siberia and Alaska are relatively warm at present,25 compared with the time when mammoths lived there. So, how could these large populations of animals have lived in these areas?
It is estimated that about 50,000 carcasses or partial carcasses may still exist.26 The vast majority show signs of substantial decay before they were buried and frozen, though about a half-dozen intact frozen carcasses have been found.
And from
http://www.answersingenesis.org/creation/v21/i4/mammoth.asp
Third, the large numbers are a problem for the sceptic only because he has not performed the simple calculations required. Consider that the African elephant reaches breeding age at about 14, and its gestation period averages 670 days, while the Indian elephant matures even earlier and has a shorter gestation time.23 disembarked from the Ark, since there was less competition around. It takes only 22 population doublings to exceed eight million, and this number could be reached in only 550 years. Thus it would not be unrealistic to assume that a single mammoth pair could have four offspring by the age of 25. So it is actually generous to the sceptic to assume that the population could double four times per century (even if the parents in each generation died soon after their offspring were weaned). The mammoths would probably have multiplied quite quickly after the single mammoth pair disembarked from the Ark, since there was less competition around. It takes only 22 population doublings to exceed eight million, and this number could be reached in only 550 years.
Alright. Let's put together the creationist scientific timeline.
1. At the end of the flood, the elephant pair walked off the Ark and the Ice Age began. Note, not a mammoth pair. To solve the problem of too many animals on the ark they postulate that only a pair of each
kind, and not
species, were on the ark. (I am not making this up. It is contained in a footnote at the bottom of the page from the second link.)
2. Woolly mammoths reproduced healthily over 550 years in Siberia as the Ice Age steadily worsened.
3. After that, towards the end of the Ice Age, the woolly mammoths couldn't adapt to the environment and started dying out. Throughout this period and the previous 550 is when the large "cemeteries" of woolly mammoths formed.
4. The Ice Age ended 700 years after the Flood with the woolly mammoths all but extinct.
Does this scenario match up with what we see?
Firstly. Exactly what kind of elephant was on the ark? We know there was only one pair. Was it more mammoth, or more modern elephant? Well, creationists assume that the global flood resulted in warm oceans. As water falls from the skies it loses potential energy and this loss of energy means a gain of heat energy for the oceans they fall in. So a global flood would have caused global heating of the oceans. A mammoth would have suffered heatshock in tropical temperatures. Therefore it was an elephant.
This immediately raises problems. No mammoth pair disembarked from the ark! It was an elephant pair! Where did the mammoths come from? They must have been elephants that adapted to the extreme cold of the polar regions, right?
But look carefully at this explanation of the post-Flood Ice Age:
Meteorologist Michael Oard22 has estimated that it would have taken only about 700 years to cool the polar oceans from a uniform temperature of 30°C at the end of the Flood to the temperatures observed today (average 4°C). This 700-year period represents the duration of the Ice Age. The ice would have started accumulating soon after the Flood. By about 500 years after the Flood, the average global ocean temperature would have cooled to about 10°C, and the resulting reduced evaporation would have caused much less cloud cover. This, combined with the clearing of the volcanic dust from the atmosphere, would have allowed more radiation to penetrate to the earth’s surface, progressively melting the ice sheets. Thus the glacial maximum would have been about 500 years after the Flood.
In other words, right after the Flood, the polar regions were actually experiencing
tropical climates! Now, how would the elephants have adapted to polar conditions to form mammoths
if there were no polar conditions for them to adapt to? Oops. To be more precise, though: they say that the glacial maximum was 500 years after the flood, and that the Ice Age ended 700 years after the flood to reach today's polar climactic conditions. Thus it took 200 years for the glacial maximum to shrink to today's conditions: assuming a linear trend, today's polar conditions would also have begun 200 years before the glacial maximum, meaning that from when polar conditions began to the end of the Ice Age was 400 years. That's not enough time, even by AiG's own estimate.
But let's be generous to the creation scientists and invoke one miracle. Let's say that the conditions in the polar regions were immediately polar climate conditions, giving them the maximum benefit of the doubt, and take their estimated rate of four doublings a century = 1 doubling in 25 years. Firstly, the mammoths had to
get to Siberia (and Alaska, too, but we'll kindly ignore that) and
then adapt to the cold (since there wouldn't have been polar conditions between Ararat and Siberia). Let's say, absurdly, that they got to Siberia in one year walking directly there doing nothing else whatsoever. Let's say, even more absurdly, that they adapted to the glacial cold in 200 years - or in eight doublings; that rate of adaptation would be akin to dropping a white couple in Africa and expecting the fifth or sixth generation to be completely African black. Even giving them far beyond the benefit of the doubt, they only have 500 years to reach the population required.
But wait. What were they adapted
to? They were certainly adapted to the conditions of glacial maximum. After all, we don't have woolly mammoths today (whatever we have in Nepal), so they died out because they weren't fully adapted to today's conditions. But the polar conditions
weren't optimum all through the Ice Age: they were mostly higher temperature than the conditions of glacial maximum (after all we're talking about glacial
maximum), which means that the doubling rate could not have been the optimistic rate AiG gives, since more mammoth young would have died, less mammoth reproduction would have taken place (since there wouldn't have been enough food), etc. Instead of 25 years' doubling time, let's take 30 years' doubling time. Reasonable?
Putting it all together:
1. Elephants got to Siberia a year after the flood,
2. The first pair of woolly mammoths appeared 200 years after,
3. They had 510 years to double their population at the rate of 30 years per doubling. (510 is easier for the calculations than 500. This gives creationists another window for hope.)
With this (only slightly) more reasonable model, the total population of all woolly mammoths, dead and alive, would be 2 + 4 + 8 + ... + 2^18 = 2(2^18-1) = 524286, far short of AiG's 8 million, and barely enough if every single one of them was fossilized (which would not have been the case) ... and this model already makes ridiculous concessions to the creation science position.
So how?