We now attempt to make this estimate more precise. In general, the great majority of DNA is non-coding (so-called junk) DNA for which almost all mutations are neutral, that is, have no effect. Of non-neutral mutations, almost all are harmful and a few are beneficial. Many harmful mutations are fatal. We will assume that 90 percent of the DNA is non-coding and that mutations there are almost always neutral. For the remaining 10 percent, we will assume that half of the mutations are neutral, and of the rest, 9/10 are harmful and one is beneficial. We will assume that about half of the harmful mutations are fatal. So for a typical set of 200 mutations, 190 will be neutral, 5 will be fatal, 4 will be harmful but not fatal, and 1 will be beneficial. Of course, if the figures are different, our calculations can be modified accordingly. If anyone has better estimates, I would appreciate learning about them. One evolutionary source said that these ratios are unknown and variable. If this is so, when more information is gained, better calculations can be done. Another evolutionary source gave figures much as I have given them. Sir Julian Huxley estimated that perhaps less than one-tenth of one percent of all mutations could be advantageous to an organism. It is interesting that over 1000 mutations of the fruit fly have been studied and all are visible and none are beneficial. (A few are slightly beneficial under artificial conditions, but all appear to be disadvantageous in nature.) Since it is known that most visible mutations are fatal, this implies a ratio of fatal to beneficial mutations of at least 500 to 1, much more severe than I am using.
It is not really necessary to restrict attention to beneficial mutations. If we also consider visible mutations which are not harmful, the analysis is about the same. This permits us to include mutations to the organism which may be random, and may contribute to evolution. But for convenience, we use the term "beneficial" from now on.
Now, we consider the mutations that must have occurred to the coding DNA during its development. This would be about 3/10 billion base pairs, and we can assume that each would have changed several times during evolution in a beneficial way as the organism evolved. Thus we obtain about a billion beneficial mutations. In addition, there would be about 9 billion harmful mutations, 5 billion of them fatal (and selected out), 4 billion harmful but not fatal, and 190 billion neutral mutations. We can assume that the size of the genome has been increasing at a constant rate, meaning its average size was half of the present size. Thus we divide these figures by 2 to obtain half a billion beneficial mutations, 2.5 billion fatal mutations, 4.5 billion harmful ones, and 100 billion in all, or about 20 or 30 per year on the average. This would mean about 1 or 1.5 non-neutral (harmful) mutations per year, about one fatal mutation every one or two years, and a beneficial mutation every 7 to 10 years. If we assume 500 fatal mutations per beneficial mutation, which would be especially reasonable after the Cambrian era for multicellular organisms, this would be about 50 to 100 fatal mutations per year.
Some mutations can add many base pairs to the genome, such as copying of regions during recombination. Thus one could obtain 3 billion base pairs by fewer than 3 billion mutations. However, the evidence of such copyings should still be present in the genome for us to discover. Otherwise, each copy must have mutated enough to become significantly different, requiring again a number of mutations proportional to the length of the genome.
For organisms with sexual reproduction, beneficial mutations can accumulate faster than sequentially, since a child can inherit mutations from both parents and theoretically can have twice as many mutations as the parents. However, this is limited by the fact that certain regions of the genome are highly interrelated, and one cannot assume that the combination of two beneficial mutations there will be beneficial. In each such region, mutations can only accumulate sequentially, as we argued in the section about how population genetics limits evolution. However, different regions can evolve in parallel. The rate at which beneficial mutations can accumulate, therefore, depends on the number of regions of the genome that are highly interrelated.
Now, mutations will have to accumulate sequentially within each Si region. That is, if we have a crossover (recombination) within an Si region, and part of the child's Si region comes from the father and part from the mother, both having mutated separately, the likelihood is that the resulting Si region in the child will be less beneficial than that of the parents. Thus each Si region will pass on from parent to child essentially independently. So instead of considering each base pair independently in population genetics, it makes more sense to consider each Si region independently.
First we do the analysis under the assumption that the rate of accumulation of beneficial mutations in a typical individual is at most the same as the rate at which beneficial mutations occur to that individual. Later we will correct the analysis to allow a greater rate of evolution than this and explain why this is necessary.
The only possibility for achieving such rates of mutation during the Cambrian explosion is that many separate mutations in a population could combine in one individual to increase the rate of change by means of sexual reproduction. However, before the development of sexual reproduction, mutations could only accumulate sequentially, making the required speed of mutation inconceivable. In addition, many mutations would not make sense until after a multicellular organism had developed. Furthermore, we can bound the allowable generation times during the Cambrian explosion even for sexual reproduction, as explained above. But we consider this factor in more detail later, because it could conceivably permit evolution to occur faster than the rate of mutation in a single individual.
After the Cambrian explosion, and after the development of sexual reproduction, one can again conceive of mutations from many individuals combining in one individual, increasing the rate of mutation. But after the Cambrian explosion, the life spans of the organisms would have increased, again making such a rapid rate of mutation (one or two non-neutral mutations per year) implausible. This would mean that after a few years, an organism could not have viable offpsring due to the accumulation of nearly one fatal mutation per year. This would also mean that the number of surviving offspring would significantly decrease each year. In the highly constrained portion of the genome, I think that the ratio of fatal to beneficial mutations is more like 1000 to 1 or worse, and this part of the genome would also have had to evolve, leading to huge numbers of fatal mutations and impossibly short generation times. If there are 50 to 100 fatal mutations per year, then generation times could be at most a month or two, because there would be about 4 to 8 fatal mutations per month. Also, as explained in the article about how population genetics limits evolution and above, for a highly constrained portion of the organism, mutations must accumulate sequentially in any case. All of these effects make the traditionally accepted evolutionary scenario implausible. In addition, the article on how population genetics limits evolution argues that evolution cannot proceed very far in any case, because a large number of point mutations will invariably be detrimental.
Another point is that mutations from different individuals can only accumulate on one chromosome by recombinations. We discuss this in more depth below. However, this is less likely for mutations that are near one another on the chromosome. Such mutations tend to "repel" one another, making the accumulation of mutations from different individuals harder.
Suppose, then, that there are 50 to 100 fatal mutations per year. If an organism had offspring a year after birth, the offspring would have abou 50 fatal mutations on the average. What is the probability that a given fertilized egg would have no fatal mutations? Mathematically it is (1/e) 50 , that is, (1/2.718) raised to the 50th power. This is less than one in 5 times 10 21 , or one in a sextillion. Such an organism would need an astronomical number of fertilized eggs to get one living offspring. If the eggs were fertilized six months after birth, there would need to be at least 70 billion fertilized eggs per surviving offspring. If the eggs were fertilized three months after birth, there would need to be 150,000 fertilized eggs per offspring, still a huge number. For two months, it would be over 4,100 eggs per surviving offspring. So it is clear that two or three months is the upper limit on the fertile portion of lifespan for such an organism.
Now, we know that some fossil organisms such as dinosaurs and large animals and fish could not have had such short generation times. Thus one would have to say that the smaller organisms were mutating much faster for some reason. But this could not include much of the assumed evolutionary history of man, because many of the assumed ancestors had generation times much in excess of two months. One might get around this by saying that when the lifetimes of our ancestors were very short, their mutation rates were even higher so less evolution needed to occur later on. However, this would put even more severe constraints on their generation times (less than one month?). Also, this would mean that very little evolution could have occurred past a mouse-like ancestor of human beings. (Even mice generally have two or three month generation times.) There is plenty of change in the genetic material past the mouse stage that would have to be accounted for somewhere. So the whole scenario loses credibility. The only way out is to say that for some reason there were much less than 500 fatal mutations per beneficial (or non-neutral non-harmful) mutation in the past, but again there does not seem to be any reason why this should be so in organisms at least as complex as the fruit fly. One would expect that it would be more difficult to find beneficial mutations in a more complex organism.
Let us consider the unicellular phase in more detail. We first note that in the early stages of evolution, the copying of DNA would probably not be very accurate. This would lead to large mutation rates. This large mutation rate would lead to a degradation of the cell's genetic material before evolution really had a chance to get started. If there are as many as 200 mutations per generation, the genetic material will degrade since 9 of these will probably be harmful and one beneficial. And 200 mutations per cell division is not a large number for a newly evolving cell. In fact, 5 of these mutations will be fatal, so the offspring will die. Even if the number is 20 on the average, one of the two offpsring will die, and the genetic material should degrade due to the remaining harmful mutations. Instead of evolution, we would have had degeneration. Also, the size of the unicellular genome is very small compared to 3 billion base pairs, limiting the amount of evolution that can occur there in any case.
Here is a more explicit calculation to illustrate this. Assuming a survival advantage of .01, it would take about 70 generations for a mutation to double its frequency in the population. In each region of the genome, this mutation would probably have to reach at least a million individuals to have a reasonable chance for another beneficial mutation, which requires 20 doublings, or 1400 generations. Since there are 100 parts evolving in parallel, this means 14 generations per beneficial mutation. Beneficial mutations occur every 7 - 10 years on the average, leading to 1 - 2 generations per year. During the bursts of evolution, evolution would occur about 100 times this fast, which means 100 times as many beneficial mutations. This requires 100-200 generations per year. During the Cambrian explosion, we computed an average of 5 beneficial mutations per year, which by similar reasoning would lead to about 70 generations per year on the average, even without considering further bursts of evolution. Note that this analysis does not depend on the number of harmful mutations. Of course, these calculation have a lot of slack, because some beneficial mutations can propogate more rapidly, and beneficial mutations can be stored up gradually (although probably not more than 100 of them). On the other hand, the speed of evolution would be limited by the size of the largest region Si, which could make the scenario even much harder than we have indicated.
We now illustrate the speed with which evolution might occur, assuming that the number of parts of the organism that can evolve in parallel is very large. Suppose we have a population of a million individuals of some species. Suppose that beneficial mutations occur with a probability of 1/1000 per individual per year. Then there will be about 1000 beneficial mutations per year. These could eventually spread to the entire population. (Some of the beneficial mutations may only spread to a fraction of the population; these will have a lesser effect.) The harmful and fatal mutations will eventually disappear. So we can have evolution at the rate of 1000 beneficial mutations per year, or, a million beneficial mutations in a thousand years, a very rapid rate of evolution. With larger population sizes, evolution could occur even faster. A population of a billion could evolve at the rate of a million beneficial mutations per year, which would result in a billion beneficial mutations in a thousand years. This would be enough to construct just about any conceivable organism. Note that these mutations are very rare events, and probably largely unnoticeable when they occur. So evolution has a remarkable ability to take rare and unnoticeable events and transform them into bursts of evolution that are so fast that they do not even appear in the fossil record, all the while conveniently disposing of the millions of harmful mutations that occur.
Now, if a mutation has a fitness benefit of s, then its chance of being fixed (persisting) in the population is 2s. Also, a fitness benefit of one percent is considered reasonably high. So we would need to increase the above estimates by a factor of probably 50 to 100. That is, we would need more beneficial mutations, or a larger population.
We see that amounts of evolution (in the conventional theory) are influenced by population size, number of beneficial mutations, and time. Since the fossil record shows so few if any transitions between major groups of plants and animals, this implies either a much shorter time period than conventionally assumed or a great scarcity of beneficial mutations. Another possibility is that there are limits beyond which evolution cannot go in any length of time. All of these possibilities are favorable to the creation viewpoint except for the scarcity of beneficial mutations, which is neutral.
Let us assume for the sake of argument that beneficial mutations are very scarce and consider the fossil record. Evolution should be most rapid when the populations are very large and the environment is changing (which would make beneficial mutations more common). So we would expect that most transitions (if they exist) would be associated with large populations and long time periods. The rarity of beneificial mutations would make the requirement for long time periods and large populations even more stringent. Both of these factors would tend to make these transitions visible in the fossil record. A small population and stable environment could lead to low rates of evolution for long periods of time. A small population and a changing environment would lead to a small rate of evolution. A large population and a changing environment would lead to a large rate of evolution.
Punctuated equilibrium says that evolutionary transitions occurred rapidly and in small populations, and so were not preserved in the fossil record. It is possible that some of these transitions could have occurred in small populations, but hardly imaginable that all of them did, as essentially assumed by the theory of punctuated equilibrium. Large populations and long time periods would tend to make transitions visible, which they are not. But transitions are much less likely with small populations and short time periods. Thus we find that the theory of punctuated equilibrium is implausible and should be rejected. The consequence of this is that many of the transitions involved large populations and long time periods, and should be visible in the fossil record. Since they are not, we must conclude that transitions between the major groups of animals never occurred. This implies that many of the groups must have begun in essentially their current forms, and so must have been designed, since large life forms could not arise spontaneously and instantaneously by ordinary physical processes. So it follows that even the ability of evolution to explain rapid change results in a strong argument for creation.
We consider in more detail the effect of a changing environment on evolution, since we do not know how much the environment changed. For the sake of argument, suppose that the environment during geologic time did not change, a highly implausible assumption. Evolution must have occurred (under the traditional scenario) because different fossils appear in different geologic strata, even though they do not change much in these appearances. This means that evolution must happen even in a constant environment. Thus there would be no reason for the fossil record to show organisms staying much the same for many millions of years, since there must have been a large population for them to appear in the fossil record. Suppose that the environment did change. Again, there would be no reason for the fossil record to show organisms staying much the same for many millions of years, because there would have been large populations and a changing environment. Either way, it seems that the traditional theory of large evolution is in difficulty.
We can also say something about the ratio of beneficial to harmful mutations. Suppose we have a population of over a million individuals (which seems reasonable) and one point mutation per year per individual. Then in a thousand years, over a billion point mutations would occur to some individual. This would be enough for every possible point mutation on the entire genome to occur. (Technically, the probability that a point mutation would not occur in this time would be less than 1/(2.718). Also, there are three different point mutations at every location.) But beneficial mutations are accumulating at the rate of one every 5 or 10 years, or 100 or 200 per thousand years, under the traditional scenario. Since all of the beneficial mutations would be preserved, this would mean that out of the entire genome, only 100 or 200 point mutations are beneficial. Actually, some beneficial mutations may not be preserved because the individuals having them may die out for other reasons. But if these beneficial mutations spread to a few individuals, they will probably spread to the whole population, and so we make this as a simplifying assumption. When these 100 or 200 beneficial point mutations have spread to the population, 100 or 200 new point mutations would be beneficial. We can assume a coding region of the genome of say at least 20 million base pairs (for humans it is possibly over 300 million). We can assume that over half of the point mutations to this region of the genome are fatal. This means that there are 10 million fatal point mutations and only 100 or 200 beneficial ones, for a ratio of about 50,000 to 100,000 fatal mutations for every beneficial one. This incidentally puts a bound on how fast evolution can occur regardless of population size, since there are only a small number of beneficial mutations that can occur. Also, if mutations occur at a much faster rate, then the number of fatal mutations per individual would be too large to tolerate. The only way that one could have bursts of evolution is for the ratio of beneficial to fatal mutations to increase. This would have to happen only at isolated intervals in the fossil record by some unexplained mechanism that otherwise does not operate. Even if a change in the environment is the driving force, we would expect this to operate gradually at least some of the time, and leave more traces of transitional forms in the fossil record. Again, this calls punctuated equilibrium into question.
Now it is easy to see how one could have rapid evolution after the flood. The animals saved on the ark would have reproduced quickly, since there would be no other animal life to compete with. Soon these animals would have populations in the millions or billions. There also would have been a changed environment. These factors would lead to tremendously rapid accumulations of mutations and very rapid evolution. Note that with a short history of life, we do not need to assume such low rates of beneficial mutations as for the traditional evolutionary view. By the same argument, a few marsupials that reached Australia would soon multiply to a population of millions or billions of individuals, which could rapidly evolve to the many unusual creatures found in Australia today. (Actually, marsupials are also found on many other continents.)
We also have not discussed how interacting proteins can evolve. If two proteins interact, they have to have shapes that are closely matched. If one of the proteins' shapes changes, then they cannot interact any more. So it is hard to see how sets of interacting proteins can evolve at all, in any length of time. This is even more of a problem because there are often sets of many proteins that interact with each other.
Thus we see that problems remain with the idea of large evolution, as we mentioned in another place. We also find problems with the origin of life by ordinary physical processes, problems with the early stages of life when copying of DNA is inaccurate, and problems with the fossil record. In addition, there are philosophical problems with the verifiability of a theory that can explain so much. There is little evidence for large evolution except the similarities between species, which can only be seen as evidence given certain philosophical presuppositions.
For some evidences against evolution having to do with fossils out of place and similar findings, see the chapter entitled "The Scientific Case for Creation: Life Sciences" of the on-line edition of the book "In the Beginning: Compelling Evidence for Creation and the Flood" by Dr. Walt Brown, This may be found at the URL http://www.creationscience.com/
These arguments are not conclusive, based on abstractions of reality. However, I believe that the burden of proof should be on the evolutionist to show how these problems could be overcome and how evolution could have occurred and did occur, and not on the creationist in proving rigorously that evolution could not have occurred or did not occur.