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haldane_1937 [2019/09/15 03:08]
floyd
haldane_1937 [2019/09/16 03:35] (current)
floyd
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-Haldane, J. B. (1937). The effect of variation of fitness. //The American Naturalist//, 71(735), 337-349.+====Haldane 1937==== 
 + 
 +Haldane, J. B. S. (1937). The effect of variation of fitness. //The American Naturalist//, 71(735), 337-349.
  
 Links Links
   * https://www.journals.uchicago.edu/doi/abs/10.1086/280722   * https://www.journals.uchicago.edu/doi/abs/10.1086/280722
 +  * {{private:haldane1937.pdf}} (internal lab link)
  
 Abstract: In a species in equilibrium variation is mainly due to two causes. Some deleterious genes are being weeded out by selection at the same rate as they are produced by mutation. Others are preserved because the heterozygous form is fitter than either homozygote. In the former case the loss of fitness in the species is roughly equal to the sum of all mutation rates and is probably of the order of 5 per cent. It is suggested that this loss of fitness is the price paid by a species for its capacity for further evolution. Abstract: In a species in equilibrium variation is mainly due to two causes. Some deleterious genes are being weeded out by selection at the same rate as they are produced by mutation. Others are preserved because the heterozygous form is fitter than either homozygote. In the former case the loss of fitness in the species is roughly equal to the sum of all mutation rates and is probably of the order of 5 per cent. It is suggested that this loss of fitness is the price paid by a species for its capacity for further evolution.
-Nf + N\mu+ 
 +Takeaway: Haldane considers the effects of deleterious mutations. Estimates are given for mutation-selection equilibrium allele frequencies and average reduction of fitness in the population. Fitness reduction is only a function of, and proportional to, mutation rates. The average individual in a population has a fitness that is a small fraction of the maximum theoretically possible if the genome were free of deleterious mutations.  
 + 
 + 
 ===Notes=== ===Notes===
 ==Symbols== ==Symbols==
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   * $f$ is the relative average fitness of individuals carrying the mutant allele.    * $f$ is the relative average fitness of individuals carrying the mutant allele. 
   * $y$ is half the number of heterozygotes, which are $2y$.    * $y$ is half the number of heterozygotes, which are $2y$. 
-  * Here, $p$ is the mutant allele frequency. +  * $p$ is the mutant allele frequency.  
 +  * $F$ is the total fitness of an individual over all loci subject to purifying selection in the genome
   * Here, $s$ is the reduction in fitness of the mutation. $s = 1-f$.    * Here, $s$ is the reduction in fitness of the mutation. $s = 1-f$. 
  
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-Mutated copies are removed by selection each generation ($1-f$ survive). +Mutated copies are removed by selection each generation ($f$ survive). 
  
 $$N x (1-f) $$ $$N x (1-f) $$
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 $$x  (1-f) = x - fx \approx \frac{\mu}{1 - f} - \frac{\mu f}{1 - f} = \mu \left(\frac{1-f}{1-f}\right) = \mu\mbox{.}$$ $$x  (1-f) = x - fx \approx \frac{\mu}{1 - f} - \frac{\mu f}{1 - f} = \mu \left(\frac{1-f}{1-f}\right) = \mu\mbox{.}$$
  
 +Again, this is independent of the fitness effect and only a function of the mutation rate. 
 +
 +==Multiple Loci==
 +
 +Pages 345--346 describe the predictions over all loci in the genome. Assuming mutations are independent both in occurrence and in fitness effects the average individual in the population has an expected fitness of 
 +
 +$$F = \prod_i (1-m_i)$$
 +
 +where $m$ is the mutation rate $\mu$ at the $i$<sup>th</sup> locus for recessive mutations and $m=2\mu$ for dominant effects. 
 +
 +If the per nucleotide per generation mutation rate is $10^{-8}$, a tenth of our 3.3 billion base pair genome is under purifying selection, and the majority of mutations are recessive in fitness effects then
 +
 +$$F \approx (1-10^{-8})^{3.3 \times 10^8}\approx 0.037\mbox{.}$$
 +
 +Therefore, our fitness is predicted to be a small fraction, approximately 3--4%, of its theoretical maximum without mutations (both new mutations that have occurred in our own genomes and mutations that we have inherited from our ancestors). 
  
 +==Other things==
 +Haldane discusses the effects of inbreeding and sex-linkage on these prediction and goes through quite a bit of additional logical details in the introduction as well as some examples from insects later in the paper. 
  
  
haldane_1937.1568516892.txt.gz · Last modified: 2019/09/15 03:08 by floyd