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I was wondering when you'd show up; you rarely disappoint by failing to do so either. You and your associates' frustrations are certaintly palpable at a great deal of naivete and scientific ignorance displayed by many of those who argue against evolution. You certainly are erudite and comprehensive with the material that you present and cite so as to edify the misinformed or woefully ignorant. I epathize with your discomfiture nevetheless, and value a great deal of your material so that I can with credibility point out how wrongheaded certain arguments are. Truly the quality of debate and discourse has de-evolved to an abysmal low point. That being said, there are serious problems with fundamental tenets contained in your response; specifically that of an increase of population size (although your objection is duly noted in that the simulation is totally unrealistic). The overwhelming problem that I have with your rebutal is that it totally fails to address the issue of population genetic equilibrium, and secondly ignores the issue of biological burden by unviable decendents.

First off, allow me to preface my response with a quote from a paper titled The Evolution of Aging - How New Theories Will Change the Future of Medicine^{1 by Theodore C. Goldsmith:}

The importance of this question is determined by your preconception of the answer.¹

This work cites a brief biography of Goldsmith: "During his more than 30 years at NASAÃ‚Â’s Goddard Space Flight Center, Theodore Goldsmith held many different positions mainly specializing in the design, development, and management of digital data systems for NASA scientific spacecraft such as the International Ultraviolet Explorer, International Sun-Earth Explorer, Space Shuttle, and the Hubble Space Telescope. He has been a computer programmer, digital systems engineer, microcircuit designer, and project manager and is a recipient of NASAÃ‚Â’s Exceptional Service Medal. Prior to joining NASA, Goldsmith worked for the National Institutes of Health.

In 1995 he became interested in the digital aspects of genetics and has written numerous articles about genetics, evolution theory, and aging theory.

Goldsmith has a degree in electrical engineering from the Massachusetts Institute of Technology and is the CEO of a small Internet company. He lives with his wife in Annapolis, Maryland.

At the very beginning (Summary section) of his book he writes that "This question [i.e,. aging] has baffled scientists for nearly 150 years and remains a mystery. Scientists disagree over even the general nature of aging. Is aging the result of fundamental limitations that apply to all living things, or are organisms designed by nature to age because a limited life span conveys some advantage? All of the scientific theories either fail to fully explain observed animal characteristics or conflict with generally accepted evolution theory.

There can be no doubt in anybody's mind that Goldsmith is a real scientist, and is emminently qualified as an expert concerning ToE, i.e., he knows what he's talking about. It will come to no suprise whatsoever to anybody that the cited work is an excellent read and that sections 2 & 5 (titled "Evolution Theory" and "Digital Genetics and Evolution Theory" respectively) will be a joy to behold. This is because there is a most emminent and profound connection to digital communication theory and biology (especially evolutionary biology), and a space communications expert is emmininently qualified to speak about not just the former but the all encompasing latter. It can be assured that there's not much of anything at all that the latter does not encompass.

Genetic equilibrium is defined as the state at which the fraction of the population having harmful mutations is constant. This state should eventually be reached if conditions are more or less unchanging. When a population is at equilibrium, then the chance that a decendent will have a new, harmful mutation not possessed by the parent is smaller than the chance that the decendents will die without producing offspring. Its immaterial how particularly lethal a mutation may be, since less harmful mutations become increasingly prevelent in the gene pool as a whole. It's not necessarily that the organisms possessing a harmful mutation is unable to reproduce, but the rate of harmful mutation still influences the chances of not reproducing (as previously stated). In other words, the chance that an organism can survive and reproduce is less than the chance that an organism has no new harmful mutations, when the population is at equilibrium.

For argument's sake, I'd like to set aside for a moment the issue of asexual reproduction that is central to the simulation that originated this thread and consider what was published in Proc. Natl. Acad. Sci. USA Vol. 94, pp. 8380-8386, August 1997, stating that the great majority of mutations are partially dominant and that this has a larger effect on zygote survival than the recessive part. This roughly doubles the number of mutations and means that whatever probabilities may superficially be inferred, they should actually be squared. That is, if a survival rate of (1/e)² is calculated, it should really be (1/e)⁴. As such, the difficulty would be much more extreme than may at first glace be evident.

About 90 percent of DNA is empirically non-functional (or at least no function for those regions has been ascertained), and in general mutations to those regions have no effect. Of the remaining functional 10 percent (having a demonstrated influence on the properties of an organism), and has been qualitatively shown to be used to direct the synthesis of proteins that guide the metabolism of the organism. To that functional portion of DNA, mutations can be either neutral, beneficial, or harmful. Probably less than half of the mutations to functional DNA are neutral. 999/1000 of mutations to the majority of functional DNA is harmful or fatal (the remainder may be beneficial). Those assumptions are actually not realistic, in that they do not take into account the interactions between various mutations. Nor do they distinguish major mutations, which change the shape of proteins, from minor mutations, which do not. Furthermore, they do not consider that beneficial mutations observed are generally only of a restricted kind not useful for explaining evolution. However, the assumptions are stipulated for consideration because they are indeed so widely used.

Harmful mutations result in organisms less likely to survive, and so these mutations tend to be eliminated from a population. Beneficial mutations also tend to be eliminated, but purely by chance, and less often; they tend to be preserved (hence the term "beneficial mutation"). As these mutations accumulate, a species can gradually adapt to its environment. Neutral mutations on the other hand, curiously, are generally eliminated, but sometimes can spread to the whole population. When this occurs, a mutation is said to be fixed within the population. The rate of evolution, then, is the rate at which mutations - beneficial or neutral - mutations are fixed within gene pools of organisms.

If decendents of organsisms have on the average one harmful mutation each, then a population will degenerates. This is known as "error catastrophe" and inherently puts a bound on how many non-neutral mutations can occur per generation. It cannot be much more than about one per generation, and in fact, it must be significantly less, since most non-neutral mutations are harmful.

Rates of evolution are computed using the likelihood that various mutations will be passed on to offspring. If for each individual having a mutation, two of its offspring also have it, then the mutation will rapidly spread through the population. If less than one offspring has it, the mutation will tend to be eliminated. This is frequently termed the difference (ratio) between the number of offspring to individuals with or without the mutation. A "selective advantage" of .01 means that the chance of a mutation being passed on to an offspring is about 1.01 times higher than the chance of DNA lacking the mutation being passed on to offspring. A value of .01 is considered to be high. After k generations, the frequency of this mutation in the population should increase by a ratio of 1.01^k. Different mutations in the same individual have a multiplier effect. So if an individual has two mutations with selective advantages of s and t, respectively, then this individual will have about (1+s)*(1+t) offspring per parent. Thus their combined effect is a selective advantage of (1+s)*(1+t) - 1. For small s and t, that is, much less than one, this expression is about equal to s + t, so we can often think of selective advantages as additive.

It should be noted that as a population evolves, the average fitness of the population will increase, i.e., each individual will not have such an advantage over others as it might have had in the beginning. As competition increases, the effect of beneficial mutations will be less pronounced. We can assume that the number of offspring possessing selective advantage within the herd will be reduced by the same factor, so that the average individual will have about one offspring per parent and the general tendency being a trend towards a selective advantage of zero (all individuals subsequently will be penalized to the same extent). However, the frequency of mutations with time will not be affected. This, also, will have the additional affect of keeping the size of the population roughly constant.

For a population of sexually reproducing organisms, where n mutations are propagating throughout the gene pool, each individual having an average of m mutations, the mutations will be distributed more or less randomly (due to the effect of crossing over, or recombination, of sexual reproduction). The number of mutations per individual will thus be distributed as a binomial, or, normal, distribution, due to the randomizing effect of crossing over. The standard deviation (σ) of the number of mutations per individual won't exceed (√ m)/2, i.e., only about 31% of the population will have a number of mutations differing from m by more than (√m)/2. Moreover, only about 4.6% of the population will have a number of mutations differing from m by more than √m. The normal distribution with mean zero and σ=1 ∝ e ^{- x * x / 2}, where e ~ 2.718.

Suppose there are 1000 beneficial mutations with a selective advantage of 1 spreading through a population, and suppose each mutation has a frequency of 1/2, that is the mean number of mutations per individual will be 500. Since √500 ~ 23, σ can be computed to ~11.5. This would imply 31% of the population has >511.5 or < than 488.5 mutations, or about 16% having >511.5 mutations, and 2.3% of the population >523 mutations. Based on the assumption that the average individual will have on the average one decendent surviving (and thus a selective advantage of zero), the individuals with 511.5 mutations can be calculated having 211.5 times that many decendents (or, over 2,000 progeny per individual). The individuals having 523 mutations will have over 8 million decendents each! Nor are these extreme cases, in that merely a bit over 2% of the population will have >523 mutations. Nevertheless, the largest contribution to the speed of evolution will be obtained from that miniscule number of individuals with >667 mutations!

For individuals with an average of 500 mutations each, σ=11.5, individual with 667 mutations each, σ=14.5 from the mean. The number of such individuals with respect to the number of individuals with 500 mutations ~ e ^{- 14.5 * 14.5 / 2}, (e^-105). This computes to ~2.5 * 10^-46 and each such individual has 2¹⁶⁷, or about 10⁵⁰ times as many offspring in compensation. In any reasonable sized population, it is doubtful that even one such prolific individual would be found. On the other hand, if each of these mutations had a selective advantage of .01, the greatest contribution to evolution would come then from individuals with 502 or 503 mutations each.

Instead, let's give each mutation a selective advantage of 1/1000. Thus, even an individual with all 1000 beneficial mutations will have a selective advantage of (1 + 1/1000)¹⁰⁰⁰ - 1, which is 2.718 - 1, not unreasonable. Then each mutation will increase its frequency by a factor of 2.718 in 1000 generations, and will increase its frequency by a factor of about a million in 14,000 generations. Thus if the population is about a million, we get 1000 beneficial mutations fixing in 14,000 generations, or, about one per 14 generations. Now, if we just had one beneficial mutation spreading through the population with a selective advantage of 2.718 - 1, then it would spread through the population in 14 generations, giving the same rate of evolution. So the end result is that we do not get any gain by having mutations spreading through the population in parallel, and we cannot obtain rates of evolution faster than would be obtained by single mutations with selective advantages of about 1 (assuming that no individual has a selective advantage of more than about 1.) This means that large populations cannot lead to significantly increased rates of evolution, unless some individuals have tremendously high selective advantages. The only advantage of a large population is that if there are say 100 mutations with selective advantages of .01, they can spread through the population in parallel, leading to a rate of evolution similar to that of one mutation with a selective advantage of about 1.

Not all the beneficial mutations are preserved, however. The number that are preserved (fix) is twice the selective advantage. If a mutation has a selective advantage of .01, then the chance that it will fix (reach a frequency near 1) is .02. Thus, even most of the beneficial mutations are lost, but the number that are saved is higher for mutations having a greater selective advantage.

Lets assume that the selective advantage of an individual relative to the average individual is not larger than about 1, i.e., no individual has more than about twice as many offpsring as the typical individual. Suppose also, that 100 mutations fix per generation and have a selective advantage of .01. These mutations increase their frequency in the popululation by 1.01 each generation. The number of mutations in a typical individual at equilibrium that have not yet fixed will be 100 ∑₁^{n.99ⁿ, where n=100. This is equivalent to 100*100 or 10,000. Here σ=50, and so the selective advantage of a typical individual with 50 extra beneficial mutations is only .5 over an average individual. A typical individual with a selective advantage of .5 would have only 1.5 times as many children per parent as an average individual. But we obtain a rate of evolution of 100 mutations per generation. The population size to permit this must have 5000 beneficial mutations per generation (since only 1/50 of them fix). Furthermore, with 1000 harmful mutations/beneficial mutation, we can calculate 5 million harmful mutations per generation. The population size would probably have to be substantially larger than 5 million to prevent error catastrophe.}

Suppose instead, that there was a 1000 mutation fix per generation, having a selective advantage of .002 (a selective advantage of 0.01 is untenable, or, as previously explained the selective advantages of typical individuals would become astronomical). The number of mutations in a typical individual at equilibrium that have not yet fixed will be 1000∑₁ⁿ1/(1+s)ⁿ, where s = .002 and n=500. This is 1000*500 or 500,000. In this case σ=350, and so the selective advantage of a typical individual with 350 extra beneficial mutations is only 350*.002 or .7 over an average individual. In this case a rate of evolution of 1000 mutations per generation is observed (even so the fitness advantage of each mutation is much less). The population size to permit this must have 250,000 beneficial mutations per generation (since only 2*s or 1/250 of the beneficial mutations fix). With 1000 harmful mutations to a beneficial one, this is 250,000,000 harmful mutations per generation. The population size would probably have to be substantially larger than 250 million to prevent error catastrophe.

The simple population genetics model in which beneficial mutations are not too rare and, when combined, are still beneficial, does not correspond to reality in all cases, as a number of considerations can show. And of course, this is undoubtedly no surprise to population geneticists. It is indeed plausible that beneficial mutations can cause other, previously beneficial mutations to become harmful. Thus the benefits to be obtained by independent mutations may be correlated in some way, positively or negatively.

THE conventional model of adaptation in asexual populations posits that rare high fitness clones become sequentially fixed via relatively rapid selective sweeps alternated by periods during which the population waits for the next beneficial mutation to arise. This model of Ã‚Â“periodic selectionÃ‚Â” (Atwood et al. 1951a) enjoys a certain amount of empirical support and underlies much of the current theory of adaptation based on the convenient assumption of Ã‚Â“strong-selection, weak-mutationÃ‚Â” (Orr 2005). Early experiments with microbes that led to the original description of periodic selection showed erratic Ã‚Â“sawtoothÃ‚Â” dynamics in the frequency of neutral mutations and were interpreted as resulting from the sequential occurrence of beneficial mutations sweeping through the population to fixation (Novick and Szilard 1950; Atwood et al. 1951a,b). Later work confirmed these earlier findings (Paquin and Adams 1983) and emphasized that a consequence of the sequential selective sweeps is the continual purging of all genetic and phenotypic variation, leading to the preservation of the wild type (Koch 1974; Levin 1981).
However, under some conditions (e.g., large populations, high mutation rates, novel environmental conditions) beneficial mutations may be sufficiently common that they co-occur in the population. In the absence of recombination, this may lead to competition between separate clones that each carry different beneficial mutations, a phenomenon called Ã‚Â“clonal interferenceÃ‚Â” (Gerrish and Lenski 1998). Theoretical work has shown that clonal interference leads to increased fitness effects and longer fixation times of those beneficial mutations that ultimately win the competition (Gerrish and Lenski 1998; Gerrish 2001; Rozen et al. 2002; Wilke 2004). Empirical evidence of clonal interference has begun to accumulate over recent years (Lenski et al. 1991; de Visser et al. 1999; Miralles et al. 1999; Yedid and Bell 2001; Rozen et al. 2002; Shaver et al. 2002; Colegrave 2002), showing its potential significance for adaptation of asexual populations. However, most of the available evidence of clonal interference is inferential and indirect support is scarce.²

Dr. Jerry Bergman has written that "[t]he primary basis of macroevolution is presumably the occurrence of mutations, which are accidental changes in the DNA. This includes both DNA that codes for protein and that which has other roles in the cell. This changed DNA can result in an observable change in the phenotype (the physical appearance) of the organism. These mutations ultimately provide the differences that are selected for (or against) by natural selection (Mayr, 2001; Wise, 2002, p. 163). The critical importance of mutations in providing the raw material for evolution is widely acknowledged by Darwinists, and is almost universally mentioned in biology textbooks (Mayr, 2001). In the words of one of the founders of the modern neoDarwinian theory, and one of the most eminent evolutionists, Harvard professor Ernst Mayr: Ã‚Â“Ultimately, all variation is, of course, due to mutationÃ‚Â” (Mayr, 1967, p. 50). The primary architect of neoDarwinism was Theodosius Dobzhansky who wrote that Ã‚Â“the process of mutation is the only source of the raw materials of genetic variability, and hence of evolutionÃ‚Â” (Dobzhansky, 1957, p. 385, emphasis mine). Dobzhansky concluded that Ã‚Â“evolution is possible only because heredity is counteracted by another process opposite in effectÃ‚Â—namely, mutationÃ‚Â” (1951, p. 25, emphasis mine). The conclusion that mutations are the key to evolution is the basis of modern neoDarwinism (Mayr, 2001).

Other sources of variation, such as sexual reproduction, genetic crossing over, and transposition, primarily produce only rearrangements of existing information and do not create new genetic information. These other mechanisms of change yield phenotypic variations that will produce, at best, only a limited amount of microevolution. Therefore, the source of all genetic variety required for macroevolution ultimately is mutations.

... The Dawkins macroevolutionary model actually helps to show why mutations that are expressed virtually always result in loss of information or corruption of the gene. Most all expressed mutations yield proteins that have reduced function, such as illustrated by sickle cell anemia. Some mutations, like adrenoleukodystrophy, cause a complete loss of function (Lewis, 2003, p. 26). This result fits with BattenÃ‚Â’s report that most mutations are harmful and most of the remainder seem to have neither positive nor negative effect. Mutations that are actually beneficial are extraordinarily rare and involve insignificant changes. Mutations seem to be much more degenerative than constructive... (Batten, 2002, p. 163)."³ Jerry Bergman has seven degrees, including in biology, psychology, and evaluation and research, from Wayne State University, in Detroit, Bowling Green State University in Ohio, and Medical College of Ohio in Toledo. He has taught at Bowling Green State University, the University of Toledo, Medical College of Ohio and at other colleges and universities. He currently teaches biology, microbiology, biochemistry, and human anatomy at the college level and is a research associate involved in research in the area of cancer genetics. He has published widely in both popular and scientific journals. But without any doubt Dr. Bergman is not a real scientist in the real sense of the word scientist.

One of the most significant issues pertainant to most harmful single-gene mutations will be in that they at least come to the birth. In any species, viable individuals that are not able to reproduce will still require pregnancy and nurture, will consume food and occupy territory, and possibly compete for mates. In addition to not being able to reproduce, these individuals will make it more difficult for the remaining population to survive. Their genetic defects will be of many different kinds and will appear at many different stages of life. If a species has a considerable fraction of such individuals, it would appear that the species survival would be rather complicated mathematically (due to the added burden). It is reasonable to assume that such individuals would be an impediment not only to their own survival, but to other individuals reproduction. So we can assume (say) that for every ten such individuals, one other individual becomes unable to reproduce. This implies that if 10/11 of the population is defective in this way, then the population will die out no matter how many offspring each parent has.

Suppose there is one new harmful mutation per gamete, on the average. Then it follows that the chance of a gamete being free from a new, harmful mutation is ^1/2.718 (~37%). This means that at equilibrium, only ^1/2.718^{of the zygotes can become reproducing adults. Of the remaining 63% of individuals, >1/2 will probably give birth and this entails that there will likely be more defective births than defect-free births. Even so, this seems like an unbearable rate of mutation, especially for higher organisms such as mammals which must care for their young and have a limited number of pregnancies (not overlooking that there are other causes of mortality in addition to single-gene genetic defects).}

If there are three non-neutral mutations per zygote for humans, the majority are probably harmful, leading to only 1/(2.718)^1.5 of the zygotes able to reproduce. Although this is only merely 22%, it implies that only about a fourth of all babies would be able to survive to reproduce, since single-gene mutations are likely to come to birth.

Given that 10 percent of DNA is considered to be functional, a mutation to the functional DNA will change amino acid coding more than 2/3 of the time, and if it does, the mutation will be harmful about 9/10 of the time or more (according to estimates by biologists). The fact that silent sites vary between organisms about 5 times as much as replacement sites implies by simple population genetics that at least 4/5 of the substitutions at replacement sites must be harmful. Furthermore, some proteins (fibrinogen peptide) vary about twice as much as silent sites, implying that about half of the substitutions at silent sites are harmful, by evolutionary assumptions. This in turn implies that 9/10 of the substitutions at replacement sites are harmful. So we see that there is not much room for altering this 9/10 figure. Thus we can assume that 2/3 of the point mutations to functional DNA are harmful. The non-functional DNA changes at the same rate as that at which mutations occur.

Standard reference materials, such as Encyclopedia Britannica state that observed mutation rates in humans appear to be between .5 and 4 per 100,000 gametes (sperm or eggs). However, there is a lot of variation from gene to gene (males seemingly mutate faster than females). Nevertheless, the average for all organisms is about 1/100,000 gametes, while for humans the average is about 4/100,000 gametes. For humans this would intimate ~8 mutations per zygote on the average, at 100,000 genes in the human. It is important to keep in mind that females produce about one egg per month for about 30 years, about 360 in all. During their most fertile periods, they can often become pregnant a few months after a previous pregnancy ends. This implies that the percentage of zygotes that can, if fertilized, survive until birth is at least 10 percent and probably much higher, including the effects of all kinds of genetic defects, even those that affect many genes. . At equilibrium, only about ^1/(2.718)^8/3 or about 7% of the zygotes could develop into reproducing individuals. This would imply that probably about a tenth of the babies at most could grow up and reproduce, at equilibrium. One way to reconciled these figures with reality is the conclusion that the human race is only a few hundred generations old at most, initially defect-free, or that the harmful mutations are clustered in a few individuals who are very unlikely to have surviving offspring.

The pre-eminent evolution-apologetic web-site cites a rate of evolution for silent sites at 4.61 per billion years.⁴ It would be reasonable to assume that this rate is attributable to point mutations, since silent sites are essentially neutral (not changing the amino acid coded). However, sometimes silent sites are conserved for other reasons, implying that the rate of mutation could be higher. Mammals typically have genomes of at least 1.5 billion base pairs, and assuming 10% being functional, there would be 150 million base pairs of functional DNA. Now, assuming a mutation per base pair every 200 million years (4.61/ billion years), 150 million point mutations in the functional DNA are implied with at least 100 million harmful mutations every 200 million years; 2/3 of those mutations are harmful. Fibrinogen peptide mutates about once every 100 million years, meaning a harmful mutation every year on the average. Thus each gamete would have one harmful mutation per year of generation time. With a one year generation time, this would be an intolerable rate of mutation (as mentioned above only 37 percent of the zygotes could have offspring). It only gets worse for organisms that have longer generation times. If one assumes that the rate of mutation slowed down for these latter organisms, then it had to be even higher for the earlier ones.

According to Takahata and Sata, a rate of 10^-9 substitutions per base pair year for humans and apes is assumed.⁵ This amounts to 2 * 10^-8 substitutions per base pair per generation (assuming a 20 year generation time).⁶ Takahata and Satta state that "the human ancestral lineage became distinct from the NWM 57.5 million years (Myr) ago, the OWM 31 Myr ago, the gorilla 8.0 Myr ago, and the chimpanzee 4.5 Myr ago." If the true rate of substitution were 10x smaller, then these age estimates should be 10 times larger, with the divergence from NWM (new world monkeys) at 575 Myr ago. So there is not much room for change in the substitution rate, by evolutionary assumptions. However, the true rate would have to be about twice as large, on evolutionary assumptions, since silent sites also appear to be about half conserved, and this implies 4 * 10^-8 substitutions per base pair per generation, and an extremely high death rate. A mutation rate of 2 * 10^-8 per generation has been inferred.⁷ These figures have been supported by direct evidence and are regarding rate of change per generation (so copying errors could be even higher).

Standard reference materials, such as Encyclopedia Britannica will provide the following information:

15 - 20% of diagnosed pregnancies miscarry. Up to 60 percent are due to faulty chromosomes. This includes all miscarriages after the first two weeks of pregnancy. Before that, one can only speculate. It is thought that more than 60 percent of conceptions are spontaneously aborted, including spontaneous abortions during the first two weeks. 40 to 50 percent of spontaneous abortions have chromosomal abnormalities. 3 to 4% of newborns have birth defects. At least 50% have a genetic contribution. About 7% of all births show some mental or physical defect. Genetic defects (often minor) are present in 10% of adults.

The fertilized egg implants in the uterus on about the seventh day and subsequently causes hCG to be produced, which prevents menstruation. Cells in the fetus begin to differentiate after about the first week. After four weeks, only very primitive arms, eyes, legs, lungs, brain, and heart (mostly just stubs) appear. After about two months the fetus' organs begin to function, but not fully till after birth.

Since only a small percentage of genes are expressed in eggs and sperm and during the first two weeks of pregnancy, a correspondinly low percentage of single-gene genetic defects causing abortions should exist. Later, about 15 to 20% of pregnancies miscarry, and this can be caused by chromosomal abnormalities and other causes. Counting birth defects and adults with defects, some of which are minor and do not prevent reproduction, there should be about 5% of adults that cannot reproduce due to single-gene genetic defects. This means that at most 5 percent of zygotes will be aborted due to harmful single-gene mutations. So it is reasonable to estimate the total percentage of zygotes that cannot reproduce due to point mutations at about 10% (possibly much less). It would seem difficult to stretch the figures to make this more than about 30 percent in any event.

The womb being an exceedinly sheltered environment, a fetus will likely survive if it develops a heart and circulatory system, and as such one could expect most individuals with single gene defects to at least be born. Frog embryos have recently been produced lacking heads, and this is also claimed to be possible for humans.⁸

Based on genetic defects, the rate of harmful single-gene mutations in humans can be at most about 10%/gamete/generation (possibly 20 or 30%/gamete at the most). That conflicts sharply, however, with the rate of 3 or 4 mutations/generation that is often quoted. This conflicts even more with 4.61 mutations/billion Sagan-years already mentioned implying 15 mutations/gamete/generation that results in only an astronomically small portion surviving to reproduce). An exceedingly obscure and arcane solution to this would that the human race is actually young and the population has not yet reached genetic equilibrium. Facts notwithstanding, nobody is going to entertain that notion with any sort of seriousness.

Conventional wisdom holds that apes and humans diverged from their common ancestor about 5 Myr ago, and have about a 2% difference in DNA. The human genome has about 3 billion base pairs. Of this total about 300 million base pairs is functional DNA. Assuming that most of this 2% difference is non-functional, the implication is that of a rate of evolution of 2% in 10 Myr. That implies 6 million point mutations in 10 Myr in the functional DNA (2/3 of that would be harmful, or, 4 million in 10 million years). That works out to about two point mutations in the functional DNA/5 yrs (or 12 every generation). If one counts both parents, one derives 24 mutations/zygote. The probabilites then become ^1/2.718¹² (or less than 1/100,000) that a zygote will survive and be able to have offspring at equilibrium. That of course, in no way shape or form is ridiculous, and can be poo-pooh'd, and dismissed with an offhanded wave of the hand.

On the other hand, this so called "problem" can be made go away if the amount of functional DNA was actually at least by a factor of 12 less than what conventional wisdom suggests it should be. If that were true, there would only be about 25 million base pairs (<1% of total amount of DNA), and with only one harmful mutation per zygote could thus be inferred. This could be workable and estimates of total functional DNA would only be off by merely a little more than 90% (at least w're in the ballpark). Typical genes have 1000 base pairs, so this works out to 25,000 genes. But in all actuality even that rate of mutation is still too high, so there would probably have to be closer to 15,000 genes. Given that a typical cell has over 10,000 proteins, there are at least the number of genes present then as required for the functioning of a single cell. Whether there are enough genes available to specify a complete human being is really a trivial issue. Lets not quibble over estimates that humans have some 100,000 functional genes (the 85% error there gets us into the infield).

The converse to decreasing the amount of functional DNA by a factor of 12 would be a 12-fold increase in the time frame necessary for said genetic divergence to manifest itself (or ~60 Myrs) in that the mutation rate would decrease proportionately. But that still is too high a mutation rate, as mentioned earlier (just proportionately lower), and given a rate of about 5% of gametes having a harmful mutation, the time frame would have to be extended to about one Byrs. That shuldn't really be a problem considering all the billions of years of time just floating around everywhere. Nevertheless, if the mutation rate was indeed faster in the past, why did it ever slow down; to overlooking the aforementioned problems of it having been higher in the first place? One way to explain this would be the amount of functional DNA itself has decreased over time. This shouldn't really pose too many problems (increased genetic variation from lesser and lesser amounts of functional DNA).

We could assume the ape-human split occurred some 10 Myrs ago instead, and that the functional DNA is only about 100 million base pairs, and that the ape (chimpanzeee) human difference is only 1%. This would also reduce the mutation rate by a factor of 12, to one harmful mutation per generation. Under such circumstances only 1/e of the zygotes could survive due to mortality caused by single gene defects, and only a number of sources would be contradicted. We've already contradicted various sources about other things, why stop there?

a recent study has shown that mitochondrial DNA in humans mutates 20 times faster than previously thought, which would give rise to the current 3% difference in mitochondrial DNA among humans in about 6000 years (see: Parsons, Thomas J., et al.), and high observed substitution rates in the human mitochondrial DNA control region have also been reported.⁹ Chimpanzees and humans differ by 27 percent in their silent sites in mitochondrial DNA, nine times as much as humans differ from each other.¹⁰ At the current mutation rate of mitochondrial DNA, the ape-human split would be inferred having occurred 9*6000 years ago. However, that's about 90 times shorter than the conventionally held 5 million year figure, and leads to a corresponding rate of harmful mutations 90 times higher, with zygote survival rates of at most ^1/2.718^12*90 (or less than ^1/2.718¹⁰⁰⁰ with a 2% difference between humans and apes being assumed, and ^1/2.718^12*90*5) assuming a 10% difference.

Its conceivable that the rate of mutation is actually quite low, and that the divergence in DNA is entirely due to a few mutations that change many base pairs, e.g., inversions or copyings. The most likely reason attributable to the conventional 2% difference is probably due to point mutations or small insertions and deletions. Furthermore, inversions and recombination errors are improbable in non-functional DNA, as they require the repetition of a sequence (something unlikely in non-functional DNA that has been randomized by mutations). Since that would pose quite serious problems for evolutionary theory, that's not a very likely scenario.

Based on some selected genes, the difference in silent sites between humans and chimpanzees has been determined to be about 1.6%, and for gorillas 1.8%.¹¹ If silent sites are conserved about half of the time, an implied total difference of about 3% between humans and chimpanzees can be inferred. That the difference in the silent sites of the mitochondrial DNA between humans and apes is 27%, a significant fraction, is interesting indeed. Mitochondrial DNA is thought to mutate about 6 to 17 times faster than nuclear DNA, which is another correlation to the implied 2-3% difference in the silent nuclear DNA sites. Some sources suggest 3-5x as fast, although this would imply a 6% difference between silent nuclear DNA sites of humans and chipanzees.

Actually, there is good reason to believe that the difference between chimpanzees and human DNA is about 4 percent rather than 2 percent. About half of the DNA is in the form of repetitive sequences¹², which must have some function or else these sequences would long ago have been destroyed by random mutations. Since this part of the DNA probably would evolve much more slowly than the non-functional DNA, we would expect about an 8 percent difference in the non-functional DNA between humans and chimpanzees in order to make the total come out to 4%. One source even says that typical genes between humans and apes differ by 10%. An 8% difference would make the rates of survival per zygote about ^1/2.718⁴⁸ or worse. This is less than 10^-20

While recombination errors to repetitive DNA are common, recombinant only change the number of units of repetition. Repetitive DNA seems to resist point mutations, and it seems logical making the inferance that point mutations to repetetive DNA must harmful, for they seem to be eliminated from the population. Point mutations to repetitive DNA may affect the ability of cells to divide, or the ability of the DNA to wind around nucleosomes, or something similar. Mutations to such DNA probably would result in a non-viable zygote. The rate of harmful mutation to repetetive DNA would increase by a factor of 5 (i.e., going from 10% to 50% functional DNA) and by a factor of 3/2 (since there do not appear to be any silent sites in the repetitive DNA); variations from one repetition to the next are typically extremely rare. Based on the dating of ape-human divergence, this would imply a zygote survival rate of at most about ^1/2.718^{48 * 5 * (3/2)}. This assumes the aforementioned cited 8% difference in the DNA; for a 2% difference, the rate of zygote survival would be at most ^1/2.718⁹⁰. There are also grounds for thinking that mutations to this part of the DNA would be dominant, which would reduce the survival rates to ^1/2.718⁷²⁰ or, for a 2% difference, ^1/2.718¹⁸⁰.

The disasterous consequences of repetetive DNA mutation can be seen easily enough. The rate of mutation has been directly observed for hemophilia B gene, and is calculated to be about 3 * 10^-9 per base pair per gamete.¹³ Apart from any considerations of the date of ape-human divergence, this rate would, based on the repetitive DNA, lead to 4.5 harmful mutations per gamete, and a zygote survival rate of at most ^1/2.718^4.5 (~1%). If the mutations to repetitive DNA are dominant, which seems likely, it would be at most ^1/2.718⁹, or about 1/10,000. These rates would quickly cause the death of the human race; especially with consideration that a female has only about 400 eggs available for fertilization.

An inferrance can also be made with respect to this that the human race is young and not yet at equilibrium, and that these mutations to the repetitive DNA have a small selective disadvantage, which causes them to take longer to come to equilibrium. It is also possible that mutations to the repetitive DNA cause the death of cells in the germ line right away. If this is true, then such mutations also probably affect cells in the developing embryo as well. With about 50 cell divisions per generation, this would be about one mutation every 10 cell divisions, or about a 10% rate of cell death during the embryonic and fetal phase. 10% of the cells in an embryo or fetus in a non-functional state seems like an fairly unbearable burden. This could be further evidence that the human population is not at equilibrium, or else it can be assume that these mutations merely influence the ability of a zygote to thrive. Perhaps these mutations occur mainly in the male line, with as many as 400 cell divisions per generation. In such case the cell death rate would be reduced to about two percent at equilibrium (a much more viable value). Alternatively, the female line typically has about 25 cell divisions per generation. However, the problems mentioned previously as it pertains to single-gene mutations remain, since these are not likely to be expressed along the germ line.

Lets revisit some math so the issue of repetetive DNA can be seen in a better light:

[BREAK OUT THE BIG GUNS?] just wondering.