[continued from previous message]   
      
   >> be interested in your comments on mathematical vs simulation vs   
   >> observe and infer approaches the study of population genetics.   
   > Population genetics is limited by the mathematical and simulation   
   > analysis that they have been able to do.  A lot was accomplished before   
   > we had computers to play with, but even with computers population   
   > genetics is still limited due to what is not understood about the   
   > biology.  It is still subject to GIGO (garbage in garbage out).   
   >   
   > The basic underlying biology of qualitative genetics (Mendelian   
   > inheritance) was worked out within a century of Mendel's mathematical   
   > approach.  Chromosomes were discovered to behave in Mendelian fashion in   
   > meiosis (the production of sperm and egg) and we figured out what genes   
   > were and that they had regulatory sequences.  It made Mendelian genetics   
   > pretty much totally understood.   
   >   
   > As I mentioned we still do not understand why the infinite allele model   
   > works so well in quantitative population genetics.  It is a model that   
   > was needed to facilitate computation so that we could actually produce   
   > some answers, but everyone understands that there are a finite number of   
   > genes far fewer than anything close to infinite.  The human genome might   
   > only have 15,000 coding genes, but as I also mentioned it looks like we   
   > may not fully understand the biology, and the actual biology may make   
   > the genome appear to generate a near infinite number of apparent   
   > alleles.  We haven't worked out all of the biology.  We need to get a   
   > better understanding of how dominance and gene interactions really   
   > affect the population genetics.  Quantitative genetics currently do not   
   > have adequate means for the analysis of dominance and epistasis (gene   
   > interactions).  Nearly all the papers looking for the effects of   
   > dominance and epistasis in populations under selection conclude that the   
   > effects are minimal, but that is likely not true.   
   >   
   >>   
   >> I've mentioned here previously a partially completed computer program   
   >> to simulate a population of ~10,000 "genomes", subject to sexual   
   >> reproduction, with chromosomes, recombination and crossover,   
   >> controlled randomisation, and mutations using various selection   
   >> coefficient profiles, etc. I've been curious to attempt to explore   
   >> fixation, viable selection coefficient distributions, genetic load and   
   >> so on.   
   >   
   > Probably all such programs that track alleles and assign selection   
   > coefficients to alleles do not model how the genome actually evolves.   
   >   
   > In reality selection coefficients and genetic load assignments have to   
   > change as the allele frequencies in the populations change, but we   
   > currently do not have a good way to do that, nor can we predict which   
   > ones need to change with time and allele frequency.   
   >   
   > The selection coefficient of a specific genotype can be dependent on the   
   > allele frequency at another locus, so background genetics matter as well   
   > as the environment.   
   >   
   > Humans average a genetic load of 1.5 to 2.  These are lethal   
   > equivalents, so if you were homozygous for your genetic load you would   
   > be dead.  Drosophila studies indicate that over 50% of the genetic load   
   > is due deleterious loci that are only 10% lethal or less when   
   > homozygous.  10% lethal is just the percentage reduction from the   
   > expected frequency of homozygotes in the population.  So in test crosses   
   > where you expect 50% homozygotes you only find 45% homozygotes.  The   
   > sporadic lethality of such homozygotes is likely due to environmental   
   > influence, interaction with other sublethals, or deleterious   
   > interactions with normally non lethal variants segregating in the   
   > population.   
   >   
   > How we calculate the lethal load and identify lethal loci is not that   
   > accurate, mainly due to gene interactions messing with identification   
   > and quantifying the lethal load.  There are multiple examples of a fully   
   > lethal recessive trait associated with one loci that when crossed into   
   > another genetic background is not lethal or incompletely lethal (only a   
   > fraction of the homozygotes die).  Natural selection occurs in some   
   > lines kept to carry recessive lethals so eventually the homozygotes do   
   > not die.  Other loci in the genome were selected that counteracted the   
   > lethality.   
   >   
   > We also know that we have issues because of recombinant inbred lines.   
   > You can take two to 6 highly inbred mouse lines that have all been   
   > inbred long enough to be over 99% inbred (99% of the alleles are   
   > identical by descent and homozygous).  These lines can have been   
   > selected to be more reproductively successful than wild-type (more   
   > litters and more pups per litter).  It could be claimed that the lethal   
   > load in these lines was zero.  In the case of two inbred lines what they   
   > do is cross them together and then backcross to one of the lines several   
   > times so that they start mating full sibs that have different parts of   
   > the donor genome and subsequent inbreeding produces lines where 12.5% of   
   > the donor genome is fixed (homozygous) dispersed around the genome. Each   
   > recombinant inbred line has a different 12.5% of the donor genome so you   
   > can use around 20 recombinant inbred lines to genetically map variants   
   > from the donor genome.  The problem is that many of these recombinant   
   > inbred lines start to fail to reproduce enough progeny to maintain the   
   > recombinant inbred lines.  It turns out that parts of the donor genome   
   > has a lethal load when combined with the genetic background of the other   
   > highly inbred line.  They lose the lines if they continue to inbreed   
   > them, so they start maintaining the lines as inbred as they can make   
   > them, but they remain heterozygous for parts of the donor genome.   
   >   
   > This just means that all the simplistic models of assigning genetic load   
   > and selection coefficients to genotypes are inadequate to model what   
   > actually happens.   
   >   
   >>   
   >> Inconclusive so far, but the exercise has been an impetus to try and   
   >> understand some of the principles involved. I plan to get back to it,   
   >> but further study of pop gen first would help verify my assumptions   
   >> and modelling.   
   >>   
   >> My initial approach was to start with a supposed selection coefficient   
   >> distribution. The data I could find suggested some lethal (-1), some   
   >> deleterious (-1 < x < near-neutral), many neutral or near-neutral   
   >> (zero or just under), and a small number beneficial (just above zero).   
   >> Using this, determine if the population grows or goes extinct through   
   >> genetic load. However, I found it difficult to find definitive data,   
   >> and so instead flipped the approach to reverse-engineer a "break-even"   
   >> selection coefficient distribution.   
   >>   
   >> One question that presents itself is how to model overall relative   
   >> fitness of an individual carrying multiple mutations. The simple   
   >> solution is to just add them together. Of course, in nature complex   
   >> and dynamic non-linear effects apply, which are beyond a simple   
   >> simulation.   
   >> However, it seems to me that a well-constructed simulation could give   
   >> a reasonably indicative picture.   
   > Doing something like this right takes a lot of advanced modeling and   
   > dealing with biology that we haven't yet completely worked out.  We know   
   > that things like gene interaction and dominance need to be in the   
   > models, but we don't know how much, nor can we predict when these things   
   > are factors.   
   >   
      
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