near neutrality

Gillespie JH 1994 Substitution processes in molecular evolution. III. Deleterious alleles. Genetics 138:943-952.

  • there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious
  • only the optimum and HDD models appear to be reasonable candidates for silent evolution
  • none of the models are viewed as good candidates for protein evolution
  • none are both biologically reasonable and exhibit the variability in substitutions commonly observed in protein sequence data
  • the optimum model
  • the fitness of a diploid individual is determined by using a quadratic deviation fitness function centered at zero on the sum of the values of the two alleles
  • as with the house-of-cards model, the value of an allele is chosen from a normal distribution and is independent of that of the parent allele
  • each new mutation is assigned a value from a standardized normal distribution
  • φ(y) = 1 − σy2
  • the optimum model will be parametrized by α = 2Nσ
  • the rate under the optimum model is, like the gamma shift model, asymptotically equal to 1 / √(α)
  • if the most common allele under the optimum model has a value near zero (as it will for large α), then Equation 1 shows that the selection coefficient of mutant alleles will be approximately − σy2
  • the square of a normal random variable is gamma-distributed with parameter β = ½
  • there is a certain irony in this observation
  • I have on two occasions argued that the gamma shift model is entirely ad hoc, with no conceivable biological justification
  • now it appears that the gamma shift model could be viewed as an approximation to n optimum model
  • other aspects of the substitution processes are not at all like the optimum model
  • the optimum model shares the property that the time until the next mutation to enter the population depends on the fitness of the currently fixed allele
  • this is the origin of the clustering
  • there are no biologically realistic models in which most of the substitutions of mutations of very small effect are deleterious
  • it is difficult to imagine a model that allows the evolution to less fit states without the return evolution to more fit states
  • this conclusion seems inescapable despite the huge investment our field has in the notion that most of the sites fixed in evolution are deleterious
  • the rate of substitution under the optimum model is much less dependent on α
  • the optimum model is a much more acceptable model of molecular evolution than is the house-of-cards model
  • it captures the spirit of deleterious model in that the rate of substitution is decreasing unction of the strength of selection
  • fitnesses are bounded under the optimum model
  • the compression of fitnesses near one allows or continuing evolution