Introduction to the Mathematics of Evolution

 

Chapter 16

 

Copy Genes and Evolution Genes

 

 

Mathematical Note

 

It was noted in the prior chapter on mathematics that 1 / 100 or 10‑2 was equal to .01.  .01 can also be written as 1%.  In other words, if we have a percentage, such as 14.65%, we can move the decimal over two places to the left and write it as .1465.

 

Likewise, if we have a number such as .0045, we can convert this to a percentage by moving the decimal point two places to the right.  Thus, .0045 is equal to: .45%.

 

In this chapter, sometimes a small number will be represented as a decimal (such as: .000004616) and sometimes this same exact number will be represented as a percentage (i.e. .0004616%).  They are the same thing.

 

 

The Different Kinds of Mutations

 

There are actually several different kinds of mutations.

 

For example, there are mutations where entire genes are copied more than once; which is called: duplication.  There are also mutations where entire chromosomes are copied more than once.  And so on.

 

When a gene is copied, the copy of the gene has no function.  It is felt that if one of these extra copies of a gene are bombarded with point mutations; that a new gene (actually a new gene complex is needed) may be able to be created by random mutations of nucleotides.

 

In other words, you start with a worthless, extra copy of a gene, mutate its nucleotides many times and end up with a new gene for a new species.

 

This is important to the theory of evolution because creating a gene from scratch is a very slow process and is riddled with statistical problems.

 

But let us consider the problems created by starting with a copy of a gene complex and trying to modify it; using numerous point mutations; to become a new functional gene complex for a new species.

 

In fact, this very thing had to have happened about 200 million times for the theory of evolution to be true (assuming each of the 10 million unique species has 20 unique gene complexes on average).  With 200 million unique gene complexes formed by evolution, it should be easy to convert a copy of a gene into a new gene with a new biological function.

 

For example, suppose a complex animal, such as a female chimpanzee, had an extra copy of a gene in one of her germ cells, as the result of a mutation.  Suppose the female chimpanzee mates.  We will ignore male and female issues.

 

Is it possible this second, useless copy of a gene can mutate to the point that it is a new, fully functional gene, which leads to a new species (a new species requires at least one new gene complex, but generally has dozens of unique gene complexes)?

 

Suppose we consider the potential evolution (via point mutations) of the extra copy of this chimpanzee gene.

 

Suppose, for example, that 50% of the nucleotides of this extra copy were identical to a gene which does not exist in chimpanzees, but which does exist in a more advanced primate.  Could the extra copy of a chimpanzee have been the source of a new gene complex for a more advanced primate?

 

Let us consider that "Gene A" is an extra copy of an existing gene, meaning it is a "copy gene" of a valid gene complex.

 

Let us say that the claim is made that "Gene A," in the old species, via random point mutations, becomes "Gene B" in the new species.

 

Remember, in this discussion 50% of the nucleotides of "Gene A" start out to be identical to the nucleotides in "Gene B," which does not yet exist.  "Gene A" is believed to "evolve" by random point mutations to become "Gene B."

 

Let us consider a nucleotide in a position of Gene A (say a 'T' is in nucleotide position 2,576).  Suppose a 'T' is also in position 2,576 of Gene B since B is a copy of A.  We will call this 2,576th nucleotide in Gene A a "right" nucleotide since it does not need to be changed to equal the 2,576th nucleotide in Gene B.

 

If a nucleotide in another position of Gene A is not equal to the same position of Gene B, we will call it a "wrong" nucleotide.

 

Thus, using this terminology, in our example 50% of the nucleotides in Gene A start out as "right" nucleotides and 50% of the nucleotides in Gene A start out as "wrong" nucleotides.

 

Let us study point mutations as they occur to Gene A.

 

 

How Point Mutations Affect "Wrong" and "Right" Nucleotides

 

First of all, any point mutations to this extra copy of the gene could affect any of the nucleotides, not just the "wrong" nucleotides.  Thus, a mutation would be just as likely to affect a "right" nucleotide as it would a "wrong" nucleotide.

 

Thus, you would have a never-ending battle trying to preserve the "right" nucleotides from mutating into "wrong" nucleotides while you are simultaneously trying to "fix" wrong nucleotides.

 

Furthermore, even when there is a mutation to a "wrong" nucleotide, there is still a 67% chance that the new mutation will still be a "wrong" nucleotide.  To understand this, suppose there is a nucleotide in position 3,000 which is an 'A' (which is a "wrong" nucleotide).  Let us assume the "right" nucleotide is a 'G'.

 

There are three possible mutations of this 'A' nucleotide.  It can mutate into a 'C' a 'G' or a 'T'.  Note that two of these three mutations are still "wrong" (i.e. the 'C' and 'T' are still wrong).  Thus, 2 out of the 3 possible mutations (i.e. 67%) are still "wrong" even if there is a mutation to a "wrong" nucleotide.

 

There are thus three categories of mutations:

 

First, if the mutation changes a "wrong" nucleotide into a "right" nucleotide, we will call it a "good" mutation.

 

If the mutation simply changes one "wrong" nucleotide into a different "wrong" nucleotide, we will call it a "neutral" mutation (because it does not change the overall number of "right" nucleotides).

 

If the mutation changes a "right" nucleotide into a "wrong" nucleotide, we will call it a "bad" mutation.

 

Law #1: When there is a mutation to a "wrong" nucleotide, there is only a 33% chance the mutation will lead to a "right" nucleotide.

 

Law #2: When there is a mutation to a "right" nucleotide, there is a 100% chance it is replaced by a "wrong" nucleotide because any nucleotide other than the "right" nucleotide will be a "wrong" nucleotide (Note: a "mutation" implies the nucleotide is changed).

 

Since 50% of the nucleotides in the "copy gene" are correct, and because 50% of the nucleotides in the "copy gene" are wrong; there is a 50% chance a "wrong" nucleotide is changed.  But only 33% of these changes create a "right" nucleotide.  Thus, only 16.67% of the early point mutations (i.e. 50% times 33%) will convert a "wrong" nucleotide into a "right" nucleotide.

 

The other 33.33% of the early mutations of a "wrong" nucleotide will convert a "wrong" nucleotide into a different "wrong" nucleotide.  This is the "neutral" mutation.

 

Thus, only 16.67% of the early mutations will be beneficial.

 

On the other hand, 50% of the early mutations will convert a "right" nucleotide into a "wrong" nucleotide.  Every time you change a "right" nucleotide, it will become a "wrong" nucleotide.

 

Thus, 50% of the early mutations will be detrimental.

 

Do you see what is happening?  16.67% of the early mutations are "good" mutations.  33.33% of the early mutations are "neutral" mutations and do not affect the total number of "right" nucleotides, thus they can be ignored.  But 50% of the early mutations are "bad" mutations.

 

Thus, computer simulations would show a deterioration of the nucleotide sequence (i.e. a deterioration of the percentage of "right" nucleotides) as time passed.  No matter what percentage of "right" nucleotides you start with; a stable 25% "good" mutation level (i.e. only 25% of the nucleotides would be "right" nucleotides) will eventually result.

 

Let us analyze why the DNA will deteriorate until 25% of the nucleotides are "right" nucleotides.

 

Assuming 25% of the nucleotides are correct, all of the "right" nucleotides (25%) in this sequence, if they are changed by a mutation, will represent a "bad" mutation.  Thus, 25% of the mutations are "bad" mutations, which convert a "right" nucleotide into a "wrong" nucleotide.

 

25% of the "wrong" nucleotides (75% "wrong" nucleotides times a 33.33% chance the new nucleotide is a "right" nucleotide) are "good" mutations.

 

50% of the "wrong" nucleotides (75% "wrong" nucleotides times a 66.67% chance the new nucleotide is also a "wrong" nucleotide) are "neutral" mutations.

 

Thus the 25% "right" nucleotides will be a very stable percentage of "right" nucleotides once it is achieved.

 

You would eventually end up with 25% "right" nucleotides whether Gene A started out with 95% of its nucleotides identical to Gene B or if Gene A started out with 10% of its nucleotides identical to Gene B.

 

The bottom line is that regardless of the beginning percentage of "right" nucleotides, as more and more nucleotides were randomly mutated, the percentage of "right" nucleotides would slowly adjust up or down to 25%.

 

Of course, a gene complex which is only 25% "right," will perform no function and will be useless.

 

Even if you started out with no nucleotides, and simply added nucleotides, the 25% "right" nucleotides will be a very consistent percentage right from the beginning.

 

Let us understand why all of this is true by looking at computer simulations.

 

 

Understanding Point Mutations to Gene Copies

 

Let us suppose that Gene A is a medium-sized gene complex with 20,000 nucleotides.  Let us further suppose that when this gene complex is copied, an extra copy of the gene complex is created.  This extra copy has no function.

 

Let us further suppose that 95% of the nucleotides of the extra copy of Gene A are identical to Gene B, which does not exist yet, but is the goal of evolution (i.e. via random point mutations).

 

We will call the extra copy of Gene A the "copy gene," and we will call the goal of mutations by evolution the "evolution gene."  The "copy gene" starts out, in this example, with 95% "right" nucleotides.  The goal is for the "copy gene" to become the "evolution gene" by random point mutations, which has 100% "right" nucleotides by definition.

 

First of all, only 5% of the nucleotides (meaning 1,000 of them) start out to be "wrong" nucleotides.  This means that only 5% of the "first mutation" (i.e. the very first point mutation we are considering) will affect a "bad" mutation.  5% of 20,000 nucleotides is 1,000 nucleotides (this is the number of nucleotides which start out as "wrong" nucleotides, which is 5% of 20,000).

 

However, as mentioned above, 66.67% of any "first mutation" on a "wrong" nucleotide would also be a "wrong" nucleotide.  This would be a "neutral" mutation.

 

This means only 33.33% of the mutations, on the 5% of "wrong" nucleotides, would yield an improvement in the total number of "right" nucleotides.

 

Multiplying .05 times .33333... yields a .01666... probability; meaning a 1.666...% probability, that the "first mutation" will convert a "wrong" nucleotide into a "right" nucleotide.

 

In other words, since we started out with 1,000 "wrong" nucleotides (i.e. 5% of 20,000 nucleotides), there is only a 1.666...% probability that the first mutation will increase the total number of "right" nucleotides to 19,001.

 

On the other hand, we know immediately that there is a 95% probability that the first mutation will be a "bad" mutation because 95% of the initial nucleotides are "right" nucleotides, and if one of these is mutated, it will automatically be a "bad" mutation.

 

We can summarize these probabilities thusly:

1st mutation is a "bad" mutation:   95%

  (i.e. a "right" nucleotide is changed into a "wrong" nucleotide)

1st mutation is a "neutral" mutation:   3.333...%

  (i.e. a "wrong" nucleotide is affected, but it is still a "wrong" nucleotide)

1st mutation is a "good" mutation:     1.666...%

  (i.e. a "wrong" nucleotide is changed into a "right" nucleotide)

 

 

First Simulated Point Mutation

 

Let us consider 500,000 computer simulations.  A "computer simulation" is a situation where a computer randomly picks a number and applies this number to the beginning condition (i.e. the simulation starts with 19,000 out of 20,000 nucleotides are "right" nucleotides).

 

Out of 500,000 cases where a "copy gene" is attempting to become an "evolution gene (i.e. 500,000 simulations) where a Gene A started out as 95% equal to Gene B, we would only expect 8,333 cases (i.e. 500,000 times .01666...%) where there were 19,001 "right" nucleotides after the first mutation (i.e. there was one additional "right" nucleotide added to the initial 19,000 "right" nucleotides).

 

Here is the calculation of how many "good" mutations we could expect in the very first mutation:

 

1) 1,000 "wrong" nucleotides at beginning of simulation

 

2) 1,000 / 20,000 = .05 or 5% of the initial nucleotides start as "wrong" nucleotides (these are the nucleotides we are hoping to change into "right" nucleotides)

 

3) However, even when a "wrong" nucleotide is affected, in only 33.333...% of the cases is a "wrong" nucleotide actually converted into a "right" nucleotide.

 

4) Thus in .05 times .3333... = 1.666...% of the initial mutations is a "wrong" nucleotide changed into a "right" nucleotide

 

5) Thus, in 500,000 simulations of the first point mutation, we would expect:

500,000 times .01666... = 8,333.33 instances where the number of "right" nucleotides increased.

 

Thus, 8,333 of the 500,000 simulations would be expected to be "good" mutations.  In other words, after 1 point mutation, in 8,333 of the 500,000 simulations there will be 19,001 "right" nucleotides.

 

 

The Second Simulated Point Mutation

 

What is the probability that both the first and second mutations will be "good" mutations and there will be 19,002 "right" nucleotides after the second point mutation?

 

Here is the calculation:

 

1) We assume the first point mutation was a "good" mutation (i.e. one of the 1,000 initial "wrong" nucleotides was converted into a "right" nucleotide), leaving 999 "wrong" nucleotides after the first mutation (i.e. before the second mutation).

 

2) 999 / 20,000 = .04995 (probability one of the 999 "wrong" nucleotide is affected by a point mutation)

 

3) .04995 times .3333... (probability "wrong" is converted to "right) = .01665

 

4) Now we need to multiply the probability of the 1st "good" mutation with the probability of a 2nd "good' mutation:

.01666... times .016665 = .0002775

 

5) 500,000 times .0002775 = 139 cases out of 500,000 will have two consecutive "good" mutations in the first two attempts.

 

Thus, out of 500,000 cases where a Gene A started out as 95% equal to Gene B, we would only expect 139 of the 500,000 cases to create 19,002 "right" nucleotides after 2 mutations.

 

 

The Third Simulated Point Mutation

 

What is the probability that the first 3 mutations would all be "good" mutations?  Try to figure this out for yourself before looking at the answer.

 

For the third mutation, there are 19,002 "right" nucleotides and 998 "wrong" nucleotides to start with (i.e. after the second mutation).

 

Here is the calculation:

 

1) 998 "wrong" nucleotides at beginning (i.e. before the third mutation)

 

2) 998 / 20,000 = .0499 (probability a "wrong" nucleotide is affected)

 

3) .0499 times .3333... = .0166333... there is a "good" mutation applied to a "wrong" nucleotide

 

4) Now we need to multiply the probability of the 1st two "good" mutations with the probability of the 3nd consecutive "good' mutation:

.0166333... times .0166500 times .0166666... = .000004616

 

500,000 times .0000046156 = 2

 

In summary, out of 500,000 computer simulations of the first 3 point mutations, we would only expect 2 of them to have the first three consecutive mutations be "good" mutations, ending up with 19,003 "right" nucleotides.

 

 

Conclusions of First 3 Simulations

 

Thus we have these statistics for the first 3 mutations for 500,000 simulations:

1) Expected number with one "good" mutation: 8,333 (.01666...)

2) Expected number with two consecutive "good" mutations: 139 (.0002775)

3) Expected number with three consecutive "good" mutations: 2 (.000004616)

 

Do you see a trend?  The probability of getting consecutive "good" mutations drops very quickly and will continue to drop.

 

But even if there were three "good" mutations in the first three attempts, there would still be only 19,003 "right" nucleotides and 997 "wrong" nucleotides.  It would be ludicrous to think that the first 1,000 mutations would all be good mutations because the probability drops so quickly.

 

However, there are many different way to get to 19,003 "good" mutations.  Consider this scenario:

Start out with 19,000 "good" mutations,

First Mutation: a "neutral" mutation (still 19,000 "right" nucleotides)

Second Mutation: a "good" mutation (19,001 "right" nucleotides)

Third Mutation: a "bad" mutation (19,000 "right" nucleotides)

Fourth Mutation: a "good" mutation (19,001 "right" nucleotides)

Fifth Mutation: a "neutral" mutation (19,001 "right" nucleotides)

Sixth Mutation: a "good" mutation (19,002 "right" nucleotides)

Seventh Mutation: a "good" mutation (19,003 "right" nucleotides)

 

In this case it took seven mutations to get to the goal of 19,003 "good" mutations.  However, there are still 997 "bad" mutations to fix before getting to where evolution wants to get.

 

Rather than consider all of the possible paths to 20,000 "good" mutations, and the probability of each path, there is a much easier way to grasp the problems with converting a "copy gene" (i.e. a copy of an existing gene) into an "evolution gene" (i.e. a gene which has a nucleotide sequence which is the goal of evolution, meaning the goal of random mutations).

 

This far better method is called computer simulations.  Computer simulations have a great deal of advantages to highly complex statistical analysis in a situation like this one.

 

 

A Single Simulation

 

Let us consider the two kinds of genes we have been talking about (which will be simulated in a computer program):

"copy gene" is an accidental mutation copy of an entire "old gene,"

"evolution gene" is the gene which the "copy gene" is attempting to mutate into.

 

One theory of evolution is that new genetic material comes from mutations affecting copies of existing genes.  The "evolution gene" represents this new genetic material and is, by definition, a new "gene complex" of one of the new genes in a new species.  The goal of evolution in this example is for the "copy gene" to mutation, one nucleotide at a time, into the "evolution gene."

 

Let us assume the "copy gene" and "evolution gene" are each 20,000 nucleotide pairs long.

 

Let us further assume the "copy gene" starts out being 95% identical to the "evolution gene."  The 95% represents the 19,000 nucleotide pairs of the "copy gene" which are identical to the same nucleotides, in the same positions, in the "evolution gene."

 

This means that evolution must fix the other 5% of the nucleotide pairs to create a new, fully functional gene complex.

 

In other words, evolution only has to fix 1,000 nucleotides (i.e. 5%) on the copy gene to equal the evolution gene.  Sounds easy, doesn't it.  Let's see if it is easy.

 

It is the job of evolution to "fix" the 1,000 "wrong" nucleotide pairs.  Evolution does this by mutating one nucleotide pair at a time.  Actually we don't worry about "pairs" of nucleotides; we only care about one side of the "pair" because the other side automatically follows the main side (e.g. if an 'A' is on one side a 'T' is automatically on the other side).  Thus, we are only concerned about the main side of the DNA in the gene complex.

 

The computer simulation starts out with a "copy gene" with 20,000 nucleotides on one side of the DNA.  Of course this gene complex only exists in a computer.

 

The simulation randomly mutates one of the "nucleotides" (i.e. nucleotide positions) at a time.

 

Given the speed of computers, even home computers, a computer can simulate tens of thousands of random, sequential mutations fairly quickly.

 

After each random mutation, we can assess how many "right" nucleotides there are in the "copy gene."

 

For example, using just one randomly chosen computer simulation of 75,000 sequential point mutations (we are only dealing with one DNA strand and applying 75,000 consecutive point mutations to this one "copy gene").

 

These are the results of the first ten mutations:

 

Column 1 is the mutation number (i.e. 1 equals the first mutation)

Column 2 is the number of "right" nucleotides after the latest mutation

Column 3 is the percentage of "right" nucleotides after the latest mutation

Column 4 is the type of mutation

 

Results of a Single Computer Simulation, Where 10 Randomly Selected Mutations Were Sequentially Applied to the Copy Gene:

 

 1                19001                  95.005%    "good" mutation

 2                19000                  95%           "bad" mutation

 3                18999                  94.995%    "bad" mutation

 4                18998                  94.99%      "bad" mutation

 5                18997                  94.985%    "bad" mutation

 6                18996                  94.98%      "bad" mutation

 7                18995                  94.975%    "bad" mutation

 8                18994                  94.97%      "bad" mutation

 9                18993                  94.965%    "bad" mutation

10               18992                  94.96%      "bad" mutation

 

Here are some other selected mutation points of this simulation so the reader can see the overall trend.  The first column is the mutation number (i.e. 1000 means the 1,000th consecutive point mutation as applied to this "copy gene").  The second column is the number of "right" nucleotides.  The third column is the percentage of "right" nucleotides.

 

Results of a Single Computer Simulation, Where 100,000 Randomly Selected Mutations Were Sequentially Applied to the Copy Gene:

 

Column #1: Simulation # (only the first 10,000 are shown)

Column #2: # of "right" nucleotides after the number of simulations)

 

1000          18082                  90.41%

2000          17229                  86.145%

3000          16438                  82.19%

4000          15701                  78.505%

5000          14998                  74.99%

6000          14347                  71.735%

7000          13741                  68.705%

8000          13181                  65.905%

9000          12666                  63.33%

10000        12154                  60.77%

 

Note the overall downward trend.  This is because most of the nucleotides start out as "right" nucleotides, thus most of the early mutations turn a "right" nucleotide into a "wrong" nucleotide.

 

Continuing on after 10,000 simulations, somewhere between the 15,000th mutation and the 16,000th mutation, the percent of "right" nucleotides dropped below 50%.

 

15000                  10043        50.215

16000                  9736          48.68

 

Somewhere between the 37,000th and 38,000th mutation the percentage of "right" nucleotides dropped below 30%.

 

37000                  6073          30.365

38000                  5953          29.765

 

As predicted, eventually the percentage of "good" mutations stabilized around 25%.

 

 

Multiple Simulations

 

A single simulation may tell us the trend of degeneration, but it doesn't really prove anything.  But the power of the computer again comes to our aid.  My home computer can do 50,000 simulations, similar to the one above, in less than four hours.

 

However, each simulation only runs to the point that the percentage of "good" mutations drops below 85% (which is 10% less than the starting percentage).  At this point it is considered "impossible" that future mutations will ever raise the "good" mutations above the initial level of 19,000 "good" mutations.  The reader will understand why in a moment.

 

On average, the number of "right" nucleotides dropped below 85% on the 2,313th mutation (i.e. simulation).

 

Note that 10% of the total number of nucleotides is 2,000 and 15% of the nucleotides is 3,000.  Thus, within an average of only 2,313 mutations, the total number of "right" nucleotides had dropped by 2,000 to a total of 3,000 wrong nucleotides.  This should give the reader an idea of how quickly the number of "right" nucleotides drops when starting out with 95% "right" nucleotides.

 

To insure I was getting consistent data, I actually ran the 500,000 simulations in 10 sets of 50,000 simulations.  It is actually best to do it this way to make sure your patterns are consistent.  These ten groups of 50,000 simulations tell us a lot about mutating a "copy gene" into an "evolution gene."

 

Let us consider the results of the computer simulations.

 

First, let us consider only the first mutation of these 500,000 simulations:

 

1st mutation was a "bad" mutation:                    475,123     95.02%

1st mutation was a "neutral" mutation:       16,470     3.29%

1st mutation was a "good" mutation:           8,407     1.68%

 

These are very consistent with our predicted results above:

1st mutation predicted to be a "bad" mutation:          95%

1st mutation predicted to be a "neutral" mutation:     3.33%

1st mutation predicted to be a "good" mutation:        1.67%

 

Now let us look at the "maximum" percentage of "good" mutations achieved for each simulation.  To gather this information, for each simulation, and after each and every mutation, the "maximum" percentage of "good" mutations was kept track of.  The "highest" "maximum" percentage, for each simulation, was recorded.

 

Out of the 500,000 simulations, the maximum percentage of "good" mutations that was ever achieved was 95.015%.  This was 19,003 "right" nucleotides.  In other words, among the 500,000 simulations, none of these simulations ever achieved 19,004 "right" nucleotides!!

 

And the 19,003 level of "right" nucleotides was achieved in only 4 of the 500,000 simulations.

 

Here is the complete table of the maximum achieved percentage of "right" nucleotides among the 500,000 different simulations:

 

Above 95.015% (above 19,003)             0                 0%

# Achieved 95.015% (19,003)                4                 0.0008%

# Achieved 95.01% (19,002)                             167             0.03%

# Achieved 95.005% (19,001)                8,648                   1.7%

# Achieved 95% (19,000)                        24,496       4.9%

# Achieved 94.995% (18,999)                 466,685     93.3%

 

In the above discussion, we predicted that only 2 simulations, out of 500,000, would have the first 3 consecutive mutations all be "good" mutations.  There were actually 4 simulations which achieved 19,003 "right" nucleotides.  This is not surprising because there are multiple ways to reach 19,003 "right" nucleotides other than just the first 3 mutations being correct.

 

Nevertheless, achieving 19,003 "right nucleotides" would be an "outlier," meaning it would be a very rare event, and the number of outliers is always hard to predict.

 

In order for the "copy gene" to randomly mutate into an "evolution gene," it would be necessary to achieve 20,000 "right" nucleotides.  Yet, not even 19,004 "right" nucleotides (starting with 19,000 "right" nucleotides!!) were achieved in 500,000 attempts (i.e. 500,000 simulations).

 

Another interesting result of the 500,000 simulations was how quickly the total number of "right" nucleotides dropped below 19,000, never to rise to the 19,000 level again.

 

This is critical to understand: by the time the 11th mutation was calculated, in all 500,000 simulations, the total number of "right" nucleotides was below 19,000, and never achieved 19,000 "good" mutations again.

 

In other words, after the 11th mutation, every one of the 500,000 simulations was below 19,000 "right" nucleotides, and never achieved 19,000 "right" nucleotides after the 11th mutation.

 

Only once in 500,000 simulations was the 10th mutation at 19,000 "right" nucleotides.  Here is the progress of that one simulation.

 

Simulation number 29,058 in the seventh set (of ten sets) of 50,000 simulations:

 

1st mutation (good)      95.005%    19,001 "right" nucleotides

2nd mutation (bad)       95%           19,000 "right" nucleotides

3rd mutation (good)     95.005%    19,001 "right" nucleotides

4th mutation (bad)        95%           19,000 "right" nucleotides

5th mutation (bad)        94.995%    18,999 "right" nucleotides

6th mutation (bad)        94.99%      18,998 "right" nucleotides

7th mutation (bad)        94.985       18,997 "right" nucleotides

8th mutation (good)      94.99                   18,998 "right" nucleotides

9th mutation (good)      94.995       18,999 "right" nucleotides

10th mutation (good)    95%           19,000 "right" nucleotides

 

Even though this simulation "kept its head above water" longer than any other simulation, it only achieved 19,001 "right" nucleotides.

 

This shows just how quickly the overwhelming problems created by the vast number of "right" nucleotides (which always mutate into a "wrong" nucleotide) prevented a significant net accumulation of "right" nucleotides.

 

While there is some flexibility in the exact sequence of an "evolution gene," these numbers make it very, very clear that even taking into account a reasonable amount of flexibility, converting a "copy gene" into an "evolution gene" is impossible, even starting at 95% identical nucleotides.

 

 

Starting At Even Higher Percentages

 

If we had started at 97% "right" nucleotides, instead of 95% "right" nucleotides, an even higher percentage of the first mutations would be "bad" mutations.  This is because there is a higher percentage of "right" nucleotides to mutate into "wrong" nucleotides.

 

There is actually a paradox involved.  Study this next sentence very, very carefully because it will become important in future discussions:

 

The higher the percentage of "right" initial nucleotides, the lower the probability that the first few mutations will result in a net gain in the number of "right" nucleotides.

 

Let us consider some comparison statistics.

 

 

Simulations Where "Plus Two" or Above Was Achieved

 

"Plus two" means the simulation achieved 2 nucleotides higher than were it started.  For example, if it started at 19,000, "plus two" means a simulation achieved 19,002 "right" nucleotides or above.

 

At 95% (initial percentage of "right" nucleotides), 19,000 nucleotides started as "right" nucleotides.  Among 500,000 simulations, 167 simulations achieved "plus two" nucleotides or above (i.e. 19,002).  Also, 4 simulations achieved "plus three" nucleotides (i.e. 19,003).

 

At 97%, 19,400 nucleotides started as "right" nucleotides.  Among 500,000 simulations, only 51 simulations achieved "plus two" (as opposed to 167) nucleotides (i.e. 19,402).  Also, only 1 simulation achieved "plus three" (as opposed to 4) nucleotides (i.e. 19,403).

 

At 99%, 19,800 nucleotides started as "right" nucleotides.  Among 500,000 simulations, only 4 simulations achieved "plus two" nucleotides (i.e. 19,802).  Also, none of the simulations achieved "plus three" nucleotides (i.e. 19,803).

 

Clearly, as the initial percentage of nucleotides start out as "right" nucleotides, it is harder to achieve a "plus two" and "plus three" condition.

 

 

How Quickly Simulations Dropped Below Initial

 

The next question to answer is how many mutations did it take for the simulation to drop below the initial "right" nucleotide level, never to rise above it again.

 

At 95%, by the 11th mutation, every simulation was below the initial number of "right" nucleotides, never to achieve the initial number of "right" nucleotides again.

 

At 97%, by the 9th mutation, every simulation was below the initial number of "right" nucleotides, never to achieve the initial number of "right" nucleotides again.

 

At 99%, by the 6th mutation, every simulation was below the initial number, never to achieve the initial level of "right" nucleotides.

 

We conclude from this set of data that the higher percentage of initial "right" nucleotides, the faster the DNA will deteriorate.

 

 

How Many Simulations Never Achieved the Initial Condition

 

In each simulation there was a "first mutation."  In most cases this first mutation was a "bad" mutation.  The question becomes, in what percentage of the simulations was the first mutation a "bad" mutation, and the simulation was never able to achieve the initial condition of "right" nucleotides.  For example, at 95%, what percent of the time was the first mutation a "bad" mutation and subsequent mutations never achieved the initial 19,000 "right" nucleotide level?

 

At 95%, 93.3% of the simulations never achieved the initial number of "right" nucleotides.

 

At 97%, 96.0% of the simulations never achieved the initial number of "right" nucleotides.

 

At 99%, 98.7% of the simulations never achieved the initial number of "right" nucleotides.

 

 

How Quickly Did Simulations Reach an Unrecoverable Condition

 

When the deterioration of the DNA dropped 10% below the initial level of "right" nucleotides, it was considered impossible for the simulation to ever recover enough to reach the initial level.  The simulation was terminated at this point.

 

At 95%, by the 2,313th mutation, the percentage of "right" mutations had, on average, dropped by 10% (i.e. from 95% to below 85% or from 19,000 "right" nucleotides to below 17,000 "right" nucleotides).

 

Note that a drop of 10% amounted to the total number of "right" nucleotides deteriorating by 2,000.  Thus, within 2,313 mutations, the number of "right" nucleotides had dropped by 2,000!!

 

At 97%, by 2,244 mutations, the number of "right" nucleotides had deteriorated by 2,000.

 

At 99%, by 2,179 mutations, the number of "right" nucleotides had deteriorated by 2,000.

 

We can clearly see that the higher the initial number of "right" nucleotides, the faster the DNA will deteriorate by 10%.

 

All of this results in a paradox for evolution:

 

Kehr's Paradox: The higher the percentage of initial correct nucleotides, the more quickly the DNA will deteriorate because of random mutations.

 

While this paradox may seem obvious after our discussion, it actually is far more significant to the evolution debate than appears on the surface.

 

 

Looking At This Another Way

 

The above numbers reveal very, very critical concepts.  The overall concept is that the higher the initial percentage of "right nucleotides," the faster the DNA will deteriorate.  Eventually, the DNA will deteriorate to 25%, no matter what percentage of "right" nucleotides it starts with.

 

But what if we don't know the actual percentage of "right" nucleotides?  How can we get an idea of the initial percentage of "right" nucleotides?

 

Ponder that last question before reading on because the answer should be obvious from Kehr's Paradox.

 

The answer is by studying the ratio (i.e. percentage) of "good" mutations to "bad" mutations.

 

What the above data tells us is that if, for a particular species, the percentage of "good" mutations is very, very rare; then we can logically conclude that this DNA has a very, very high percentage of "right" nucleotides.

 

In other words, if we know the percentage of initial "right" nucleotides, we can take a good guess at calculating the probability that early mutations will be "good" or "bad."

 

However, if we don't know the initial percentage of "right" nucleotides, we can look at the percentage of "good" mutations versus "bad" mutations and take a good guess at how many "right" nucleotides there are at any given time.  In the next chapter, this concept will be discussed in more detail.

 

 

Conclusion

 

The theory of evolution depends heavily on new genetic material.  Without new genetic material there are no new species and there is no evolution.  Period.  Random, pointless, directionless mutations are at the heart and soul of neo-Darwinism.

 

With the discovery of DNA the debate between the theory of evolution and creation science should have made a major turn.  Suddenly, fossil morphology should have taken a "back seat" to the analysis of DNA in terms of studying mutations to determine the probability of evolution.

 

However, that didn't happen.  The reason is that a study of DNA mutations is a massive, massive embarrassment to the theory of evolution for several reasons.

 

When science sees something that is not favorable to the theory of evolution, the discovery gets buried.

 

Thus, instead of DNA and probability analysis, which is embarrassing to the theory of evolution, nineteenth century morphology is still the main tool of evolutionists.

 

The next chapter will further explain why science has avoided any mathematical discussion of how new genetic material is created.