R M Cullen MD MSc MFM BA DipStats DipProfEthics

May 2015

standard evolutionary theory offers only a plausible explanation for complex adaptations

This is an old, but still standard model of how the bat wing might have evolved The issue is that there a large number of intermediate steps, most of which did not confer a reproductive advantage (i.e natural selection did not operate to increase their incidence in the population)

A central problem in evolutionary theory concerns the development of complex adaptive features such as eyes and wings. These are the 'modifications' central to Darwin's conception of evolution as descent with modification from a common ancestor.

Darwin had a plausible explanation for the development of eyes. He postulated that in every individual there was an undirected source of inherited variation, and was certain that modifications as complex as eyes were the cumulative result of numerous small modifications each of which conferred a reproductive advantage to its possessor. That is, an animal with half a wing would have more offspring that lived to themselves have offspring than an animal with no part of a wing.

Richard Dawkins in the blind watchmaker uses an analogy to explain the concept of cumulative selection. This starts (generation 0) with a random string of 28 letters/spaces and a goal of "methinks it is like a weasel". Each generation is a number of 'mutations' of the preceding generation. For example there might be 20 'offspring' in generation one, , each with one letter different from the parent. The daughter closest to the 'target' is bred from (i.e twenty daughter strings from her string are generation two) and the granddaughter closest to the target is bred from to form the members of generation three. This algorithm generates "methinks it is like a weasel" in around 2n generations (on average) where 'n' is the length of the string.

This example illustrates how some animal might develop an eye. However it is not a biologically realistic example as the number of offspring a string has is either zero or "all of them", there can never be a generation of strings all reading "methinks it is like a weasel", and mutations are much, much too common.

However, it is not too difficult to convert this to a more biologically realistic model. First, assume a constant population size, say 100 million. Imagine, in this example that eyes come in thirds - an animal can have one third of an eye, two-thirds of an eye, or a whole eye, and that if a parent has one-third of an eye offspring have one-third of an eye unles the offspring gets another "one third of an eye" mutation in which case it will have two-thirds of an eye. Imagine also that one offspring in a million has a "one-third of an eye mutation". In the original unmutated population every adult has, on average, one offspring that itself lives to have offspring (constant population size). Let us invent a parameter "selection advantage", so that an individual with one-third of an eye has twice as many offspring that live to have offspring compared to an unmutated individual. An individual with two thirds of an eye has four times as many, and an individual with a whole eye has eight times as many.

Then, the table shows the number of individuals with no eye, one-third of an eye, two-thirds of an eye and a whole eye in the beginning (generation 0) and after one and two generations.

gen	no eye	1/3 eye	2/3 eye	whole eye
0	100,000,000	0	0	0
1	99,999,900	100	0	0
2	99,999,700	300	0	0

All 100,000,000 individuals in this population have eyes after a mere 75 generations in this model!

gen	no eye	1/3 eye	2/3 eye	whole eye
0	100,000,000	0	0	0
1	99,999,900	100	0	0
2	99,999,700	300	0	0
10	99,897,798	102,202	0	0
20	48,810,676	51,185,458	3883	0
21	32,282,775	67,706,918	10,324	0
22	19,245,943	80,729,383	24,687	0
28	364,000	97,717,798	1,918,201	1
35	828	28,464,421	71,524,985	9,765
40	1	1,223,045	98,344,559	432,395
50	0	221	18,170,722	81,829,057
60	0	0	21,680	99,978,320

It takes from generation 61-75 to extinguish the 2/3 eyed individuals from the population.

This model demonstrates the power of cumulative selection in the presence of a relative reproductive advantage at every step of the process. In this case, the relative reproductive advantage (2) at each step is what drives both the emergence of the modification and its spread through the population.

The model is simplistic. It takes no account of the fact that both parents contribute inherited material to offspring and the mutation rate is far too high.

In the real world of terran biology there are hundreds of steps to reach a complex adaptive modification such as an eye or a wing. Moreover most of those steps either confer no reproductive advantage or they may even be associated with a reproductive disadvantage. Consider the "three step eye" example above. Imagine that there is now a step between the one-third eye and two-third eye, a fourth equally improbable mutation is required and it confers no reproductive advantage compared to having one-third of an eye. Now evolution gets stuck for a relatively long period. If the whole population has one-third of an eye, then 100 offspring each generation will have the "neutral" step, but it may well take, on average, about 140 generations before the first "two-thirds eye" animal appears, as each of these neutral offspring has only a one in a million chance of being the sire of a two-third-eye child.

The real, and unacknowledged (in public), problem for standard evolutionary theory occurs when a sequence of intermediary steps that do not confer a relative reproductive advantage is required for a complex adaptive feature.

Imagine that there are five intermediate steps between 'one-third-eye' and 'two-third-eye' and that there is, once again, one chance in a million that an individual at one step will have a child with the mutation of the next step. How many generations will it take, on average, before the first individual with 'two-third-eye' appears?

The table below shows the first two generations of this model. One hundred new occurences of the first intermediate mutation occur each generation, and those individuals with the first intermediate mutation reproduce at the same rate as organisms with 1/3 of an eye. As there is only one chance in a million that an individual with the first intermediate mutation will have a child that lives to reproduce and has the second intermediate mutation, no individuals with both the first and second intermediate mutations exist at the end of generation two.

gen	1/3 eye	Int 1	Int 2	Int 3	Int 4	Int 5	2/3 eye
0	100,000,000	0	0	0	0	0	0
1	99,999,900	100	0	0	0	0	0
2	99,999,800	200	0	0	0	0	0

The phrase 'one chance in a million' reveals that the underlying process is probabilistic. However, there is no loss of rigor in using the concept of expected value to convert this to a deterministic model. In the tables above I have assumed that in a population of 100,000,000 if 'success' occurs at a rate of one in a million, then the expected number of successes in the one hundred million trials is 100. Of course, in a real experiment the actual number might be 99, or 102, or even 87. However over a reasonable number of trials the long term average will trend towards 100.

In the table below I have used the same idea, so when there have been one million individuals with the intermediate stage one mutation I have allowed the first individual with both the intermediate stage one and two mutations to occur. At the other end, when there have been one million individuals with all five intermediate stage mutations, then the first individual with 2/3 of an eye appears. The model assumes that the next intermediate stage mutation can only occur in individuals with the immediate prior stage intermediate mutation.

With these conditions, then we see the following

gen	1/3 eye	Int 1	Int 2	Int 3	Int 4	Int 5	2/3 eye
0	100,000,000	0	0	0	0	0	0
1	99,999,900	100	0	0	0	0	0
2	99,999,800	200	0	0	0	0	0
141	99,985,899	14,100	1	0	0	0	0
3,917	99,607,532	391,700	767	1	0	0	0
22,118	97,787,990	2,187,540	24,289	180	1	0	0
65,904	93,408,815	6,373,989	212,424	4,694	77	1	0
140,578	85,942,287	13,069,548	941,859	44,680	1,581	44	1

This is a dramatically different picture! In this model, complex adaptive features require a large initial population, millions of generations, and a 'build' process where at every necessary step that does not confer a reproductive advantage there is no possible bypass which does confer a reproductive advantage. Complex adaptive features also require parallel evolution in other body parts. An eye is useless without a connection to a part of the brain that processes the signals received.

Humans are supposed to have shared a common ancestor with chimpanzees some 300,000 generations ago. There are an enormous number of differences at the genetic level between humans and chimpanzees. In terms of those complex adaptations which are said to distinguish humans from chimpanzees have there been enough generations for these to have evolved by cumulative selection?

A similar question might be posed with respect to the eye. Can evolutionary biologists construct an eye from nothing in a series of steps where the chains of consecutive steps that don't confer a reproductive advantage are not too long?

Propagandists for evolution, such as Professor Dawkins, do not merely gloss over the problems. They deliberately mislead. Standard evolutionary theory provides a plausible explanation for the evolution of the eye but the 'methinks it is like a weasel' analogy is rhetoric not proof. Darwin, and those who have followed him, provide a plausible explanation, but it is nothing more than that. This might be even more obvious if we consider the evolution of hemoglobin.