January 2018: Fisher’s Famous Theorem Has Been “Flipped”

 

The 2014 edition of Genetic Entropy stated that a publication was in preparation that would disprove the historically pivotal “Fundamental Theorem of Natural Selection”, developed by Ronald Fisher. This key new paper has finally been published.

 

Ronald Fisher was one the great scientists of the last century, and his theorem, published in 1930, and was the foundational work that gave rise to neo-Darwinian theory and the field of population genetics. This new paper shows that Fisher’s mathematical formulation and his conclusion were wrong. Furthermore, the new paper corrects Fisher’s work — thus reversing Fisher’s thesis and establishing a new theorem. Fisher had claimed that his theorem was a mathematical proof of evolution — making the continuous increase in fitness a universal and mathematically certain natural law. The corrected theorem shows that just the opposite is true — fitness must very consistently degenerate — making macroevolution impossible. The new paper by Basener and Sanford, is in the Journal of Mathematical Biology (available here).

 

Fisher described his theorem as “fundamental”, because he believed he had discovered a mathematical proof for Darwinian evolution. He described his theorem as equivalent to a universal natural law — on the same level as the second law of thermodynamics. Fisher’s self-proclaimed new law of nature was that populations will always increase in fitness — without limit, as long as there is any genetic variation in the population. Therefore evolution is like gravity — a simple mathematical certainly. Over the years, a vast number of students of biology have been taught this mantra — that Fisher’s Theorem proves that evolution is a mathematical certainty.

 

The authors of the new paper describe the fundamental problems with Fisher’s theorem. They then use Fisher’s first principles, and reformulate and correct the theorem. They have named the corrected theorem The Fundamental Theorem of Natural Selection with Mutations. The correction of the theorem is not a trivial change — it literally flips the theorem on its head. The resulting conclusions are clearly in direct opposition to what Fisher had originally intended to prove.

 

In the early 1900s, Darwinian theory was in trouble scientifically. Darwin’s writings were primarily conceptual in nature, containing a great deal of philosophy and a great deal of speculation. Beyond simple observations of nature, Darwin’s books generally lacked genuine science (experimentation, data analysis, the formulation of testable hypotheses). Darwin had no understanding of genetics, and so he had no conception of how traits might be passed from one generation to the next. He only had a very vague notion of what natural selection might actually be acting upon. He simply pictured life as being inherently plastic and malleable, so evolution was inherently fluid and continuous (think Claymation). When Mendel’s genetic discoveries were eventually brought out of the closet, it could be seen that inheritance was largely based upon discrete and stable packets of information. That indicated that life and inheritance were not like Claymation, and that biological change over time was not based upon unlimited plasticity or fluidity. Mendel’s discrete units of information (later called genes), were clearly specific and finite, and so they only enabled specific and limited changes. At that time it was being said: “Mendelism has killed Darwinism”.

 

Fisher was the first to reconcile the apparent conflict between the ideas of Darwin and the experimental observations of Mendel. Fisher accomplished this by showing mathematically how natural selection could improve fitness by selecting for desirable genetic units (beneficial alleles), and simultaneously selecting against undesirable genetic units (deleterious alleles). He showed that given zero mutations, the more there are good/bad alleles in the population, the more natural selection can improve the fitness of the population. This is the essence of Fisher’s Theorem. This was foundational for neo-Darwinian theory — which now reigns supreme in modern academia.

 

Remarkably, Fisher’s theorem by itself illustrates a self-limiting process — once all the bad alleles are eliminated, and once all the individuals carry only good alleles, then there is nothing left to select, and so selective progress must stop. The end result is that the population improves slightly and then becomes locked in stasis (no further change). It is astounding that Fisher’s Theorem does not explicitly address this profound problem! Newly arising mutations are not even part of Fisher’s mathematical formulation. Instead, Fisher simply added an informal corollary (which was never proven), which involved extrapolation from his simple proof. He assumed that a continuous flow of new mutations would continuously replenish the population’s genetic variability, thereby allowing continuous and unlimited fitness increase.

 

The authors of the new paper realized that one of Fisher’s pivotal assumptions was clearly false, and in fact was falsified many decades ago. In his informal corollary, Fisher essentially assumed that new mutations arose with a nearly normal distribution – with an equal proportion of good and bad mutations (so mutations would have a net fitness effect of zero) . We now know that the vast majority of mutations in the functional genome are harmful, and that beneficial mutations are vanishingly rare. The simple fact that Fisher’s premise was wrong, falsifies Fisher’s corollary. Without Fisher’s corollary – Fisher’s Theorem proves only that selection improves a population’s fitness until selection exhausts the initial genetic variation, at which point selective progress ceases. Apart from his corollary, Fisher’s Theorem only shows that within an initial population with variant genetic alleles, there is limited selective progress followed by terminal stasis.

 

Since we now know that the vast majority of mutations are deleterious, therefore we can no longer assume that the mutations and natural selection will lead to increasing fitness. For example, if all mutations were deleterious, it should be obvious that fitness would always decline, and the rate of decline would be proportional to the severity and rate of the deleterious mutations.

 

To correct Fisher’s Theorem, the authors of the new paper needed to reformulate Fisher’s mathematical model. The problems with Fisher’s theorem were that: 1) it was initially formulated in a way that did not allow for any type of dynamical analysis; 2) it did not account for new mutations; and 3) it consequently did not consider the net fitness effect of new mutations. The newly formulated version of Fisher’s theorem has now been mathematically proven. It is shown to yield identical results as the original formulation, when using the original formulation’s assumptions (no mutations). The new theorem incorporates two competing factors: a) the affect of natural selection, which consistently drives fitness upward; and 2) the affect of new mutations, which consistently drive fitness downward. It is shown that the actual efficiency of natural selection and the actual rate and distribution of new mutations determined whether a population’s fitness will increase of decrease over time. Further analysis indicates that realistic rates and distributions of mutations make sustained fitness gain extremely problematic, while fitness decline become more probable. The authors observe that the more realistic the parameters, the more likely becomes fitness decline. The new paper seems to have turned Fisher’s Theorem upside down, and with it, the entire neo-Darwinian paradigm.

 

Supplemental Information — Fisher’s informal corollary (really just a thought experiment), was convoluted. The essence of Fisher’s corollary was that the effect of both good and bad mutations should be more or less equal — so their net effect should be more-or less neutral. However, the actual evidence available to Fisher at that time already indicated that mutations were overwhelmingly deleterious. Fisher acknowledged that most observed mutations were clearly deleterious — but he imagined that this special class of highly deleterious mutations would easily be selected away, and so could be ignored.  He reasoned that this might leave behind a different class of invisible mutations that all had a very low-impact on fitness — which would have a nearly equal chance of being either good or bad. This line of reasoning was entirely speculative and is contrary to what we now know.  Ironically, such “nearly-neutral” mutations are now known to also be nearly-invisible to natural selection — precluding their role in any possible fitness increase. Moreover, mutations are overwhelmingly deleterious — even the low impact mutations. This means that the net effect of such “nearly-neutral” mutations, which are all invisible to selection, must be negative, and must contribute significantly to genetic decline. Furthermore, it is now known that the mutations that contribute most to genetic decline are the deleterious mutations that are intermediate in effect — not easily selected away, yet impactful enough to cause serious decline.

 

January 2018: More Real World Evidence of Genetic Degeneration

 

The newest edition of Genetic Entropy (2014), has shown that genetic degeneration is not just a theoretical concern, but is observed in numerous real-life situations. Genetic Entropy has reviewed research that shows: a) the ubiquitous genetic degeneration of the somatic cells of all human beings; and b) the genetic germline degeneration of the whole human population. Likewise Genetic Entropy has reviewed research that shows rapid genetic degeneration in the H1N1 influenza virus. Genetic Entropy also documents “evolution in reverse” in the famous LLEE bacterial experiment (article available here).

 

• A new paper (Lynch, 2016) written by a leading population geneticist, shows that human genetic degeneration is a very serious problem. He affirms that the human germline mutation rate is roughly 100 new mutations per person per generation, while the somatic mutation rate is roughly 3 new mutations per cell division. Lynch estimates human fitness is declining 1-5% per generation, and he adds; “most mutations have minor effects, very few have lethal consequences, and even fewer are beneficial.”
   

• Our new book “Contested Bones” (available at ContestedBones.org) cites evidence showing that the early human population referred to as Neanderthal (Homo neanderthalensis) was highly inbred, and had a very high genetic load (40% less fit than modern humans) (Harris and Nielsen, 2016; Roebroeks and Soressi, 2016). See pages pages 315-316. This severe genetic degeneration probably contributed to the disappearance of that population (PrÜfer et al., 2014; Sankararaman et al., 2014).
   

• Similarly, the new book Contested Bones (pages 86-89), cites evidence that the early human population referred to as “Hobbit” (Homo floresiensis), was also inbred and apparently suffered from a special type of genetic degeneration called “reductive evolution” (insular dwarfing) (Berger et al., 2008; Morwood et al., 2004). This results in reduced body size, reduced brain volume, and various pathologies (Henneberg et al., 2014).
   

• Contested Bones (pages 179-210) also cites evidence that the early human population referred to as Naledi (Homo naledi), was likewise inbred and suffered from “reductive evolution”, again resulting in reduced body size, reduced brain volume, and various pathologies.
   

• Contested Bones (pages 53-75) also cites evidence that many other early human populations, broadly referred to as Erectus (Homo erectus), were inbred and suffered from “reductive evolution” (Anton, 2003). However, it seems the genetic degeneration of Erectus was less advanced—generally resulting in more moderate reductions in body size, brain size, and pathologies. Indeed, many paleoanthropologists would fold both Hobbit and Naledi into the more diverse Erectus category.
   

• An important but overlooked paper, written by leading population geneticists (Keightley et al., 2005), reported that the two hypothetical populations that gave rise to modern man and modern chimpanzee both must have experienced continuous genetic degeneration during the last 6 million years. The problems associated with this claim should be obvious. Their title is: Evidence for Widespread Degradation of Gene Control Regions in Hominid Genomes, and they state that there has been the “accumulation of a large number of deleterious mutations in sequences containing gene control elements and hence a widespread degradation of the genome during the evolution of humans and chimpanzees.” (emphasis added). 
   

• A new paper (Gaur, 2017), shows that if a substantial fraction of the human genome is functional (is not junk DNA), then the evolution of man would not be possible (due to genetic degeneration). Gaur states that human evolution would be very problematic even if the genome was 10% functional, but would be completely impossible if 25% or more was functional. Yet the ENCODE project shows that at least 60% of the genome is functional.
   

• A new paper (Rogers and Slatkin, 2017), shows that mammoth populations were highly inbred and carried an elevated genetic load (likely contributing to their extinction due to “mutational meltdown”).  
   

• A paper (Kumar and Subramanian, 2002) shows that mutation rates are similar for all mammals, when based on mutation rate per year (not per generation). This means that mammals (both mice and men) should degenerate similarly in the same amount of time. This suggests that the major mutation mechanisms are not tightly correlated to cell divisions.
   

• A new paper (Ramu et al., 2017), shows that the tropical crop, cassava, has been accumulating many deleterious mutations, resulting a seriously increasing genetic load, and a distinct decline in fitness.
   

• Another paper (Mattila et al. 2012), shows high genetic load in an old isolated butterfly population. “This population exemplifies the increasingly common situation in fragmented landscapes, in which small and completely isolated populations are vulnerable to extinction due to high genetic load.”
   

•  Another paper (Holmes, E. C. 2003), shows that all RNA viruses must be young—less than 50,000 years. This is consistent with our H1N1 influenza study that show that RNA virus strains degenerate very rapidly.

 

References:

 

Anton S.C., Natural History of Homo erectus, Yearbook of Physical Anthropology 46:126-169, 2003.

Berger L.R. et al., Small-bodied humans from Palau, Micronesia, PLOS ONE 3(3):e1780, 2008. 

Gaur, D. 2017. An Upper Limit on the Functional Fraction of the Human Genome. Genome Biol. Evol. 9(7):1880–1885. doi:10.1093/gbe/evx121 Advance Access publication July 11, 2017

Harris K. and Nielsen R., The genetic cost of Neanderthal Introgression, Genetics 203: 881-891, 2016.

Henneberg M. et al., Evolved developmental homeostasis disturbed in LB1 from Flores, Indonesia denotes Down syndrome and not diagnostic traits of the invalid species Homo oresiensis, Proc Natl Acad Sci, USA 111(33):11967-11972, 2014.

Holmes, E. C. 2003 Molecular Clocks and the Puzzle of RNA Virus Origins. Journal of Virology Apr. 2003, p. 3893–3897

Keightley PD, Lercher MJ, Eyre-Walker A. (2005). Evidence for widespread degradation of gene control regions in hominid genomes. PLoS Biol 3(2): e42.

Kumar S. and  Subramanian, S. 2002. Mutation Rates in Mammalian genomes. PNAS 99 (2), 803-808.

Lynch, M. 2016. Mutation and Human Exceptionalism: Our Future Genetic Load. Genetics, Vol. 202, 869–875  http://www.genetics.org/content/202/3/869

Morwood M.J. et al., Archaeology and age of a new hominin from Flores in eastern Indonesia, Nature 431:s3, 2004.

Mattila A., et al. 2012. High genetic load in an old isolated butterfly population. PNAS | Published online August 20, 2012. www.pnas.org/cgi/doi/10.1073/pnas.1205789109  

PrÜfer K. et al., A complete genome sequence of a Neanderthal from the Altai Mountains, Nature 505(7481):43-49, 2014.

Ramu, P., et al. 2017. Cassava haplotype map highlights fixation of deleterious mutations during clonal propagation. Nature Genetics 49 (6) 959-965.

Roebroeks W. and Soressi M., Neandertals Revised, Proc Natl Acad Sci, USA 113(23):6372-6379, 2016.

Rogers R. and Slatkin, M. 2017. Excess of genomic defects in a woolly mammoth on Wrangel island. PLOS Genetics | doi: 10.1371/journal.pgen.1006601 March 2, 2017

Rupe, C. and Sanford, J. 2017. Contested Bones. FMS Publications, Waterloo, NY

Sankararaman S. et al., e genomic landscape of Neanderthal ancestry in present-day humans, Nature 507(7492):354-357, 2014.