Some evolutionists are saying that there wasn't enough time for animals to speciate to what they are now from what they were on the Ark. I read a good article called "Speciation and the animals on the Ark".
This is my attempt at supplementing the article with some estimates and numbers. I am only an amateur, who has some knowledge of Engineering math and a nice calculator that can solve equations.
This article has been updated and automated (once support for id's in MathML is supported). then you can put in stuff into the form fields and the equations and results will update as you type.
1. assume each pair of animal parents has *2* different species of offspring. Therefore I will be using powers of 2. It could be like dogs which have a litter in which all could be a different species. to make a better simulation you could substitute a different number here like 1.5. since not all offspring may be different species. Really, the Bible doesn't talk about Species anyway - it only talks about *kinds* which is is far different. you can have multiple species within a kind.
2. There are "millions of extant species on the earth today." I will assume around 50 million. let's get a nice power of 2: 50e6 since 2011. log (50e6;10)/log(2;10)=23.052,583,970,285,540,041,525,109 therefore 225.575424759098898782962555=50,000,000. fish that are included in this should not really be included in the list since they are not animals and were not on the Ark. I am not sure if that species number includes underwater.
3. There were 15000-30000 *kinds* of genetically viable *animals* on the ark, according to Dr. Criswell. Note that the fish did not need to be on the ark. let's assume worst-case 15000: log(15000;10)/log(2;10)=13.872,674,880,270,605,572,935,016,661
4. let's assume 15 years in a generation. 11.702,749,878,798,898,782,962,555 generations * 15 years/generation=175.541,248,181,983,481,744,438,325 years. I don't really know how long the average animal lasts, so I am using my guess at a dog lifespan.
IF the assumptions were correct, this is plenty of time after the flood for animals to speciate! This math does not take into account climate and environment. but my guess is the numbers in the assumptions are far off. I have no statistics to base this math on.
If you want to do curve fitting to today's estimates to fit the exact time that has passed, use 10^(15*(log(50e6;10)-log(15000;10))/(4357-1))=1.028,326,730,689,485,558,820,983,710,036,847,158,320,567 instead of 2 for the number of different species of offspring (note how small the number is). log(50e6;10)/log(1.028,326,730,689,485,558,820,983,710,036,847,158,320,567;10)=634.645,995,765,393,494,767,186,422 therefore 1.028,326,730,689,485,558,820,983,710,036,847,158,320,567^634.645,995,765,393,494,767,186,422=49,999,999.999,999,999,999,999,999,668, so 634.645,995,765,393,494,767,186,422-13.872,674,880,270,605,572,935,016,661=620.773,320,885,122,889,194,251,405,339 generations.
Assuming Archbishop Ussher's estimate for the time of the flood (2348BC) and 15 years/generation, we get 2011AD-2348BC=2011+2348-1=4,358 years (subtract 1 missing year 0) from today. Divide by 15 years/generation, we get approximately (2011+2348-1)/15=290.533,333,333,333 generations.
log(50e6;10)/log(1.028,326,730,689,485,558,820,983,710,036,847,158,320,567;10)=634.645,995,765,393,494,767,186 as before. log(15000;10)/log(1.028,326,730,689,485,558,820,983,710,036,847,158,320,567;10)=344.245,995,765,393,494,767,186,422,237 as before. 634.645,995,765,393,494,767,186-344.245,995,765,393,494,767,186,422,237=290.399,999,999,999,999,999,999,577,763 generations. 290.399,999,999,999,999,999,999,577,763generations*15years/generation=4,355.999 years
years(projected from current year)=0
There was ample time for speciation from the different kinds of animals on the ark.
References: Speciation and the animals on the Ark, April 2009 Acts & Facts pp.10-12, by Daniel Criswell, PH.D.