Phylogenetic divergence of cell biological features

  1. Michael Lynch  Is a corresponding author
  1. Arizona State University, Arizona
4 figures, 1 table and 1 additional file


An idealized overview of the model for the evolution of the distribution of mean phenotypes, given here for a trait under stabilizing selection.

The upper panel denotes a hypothetical phenotype distribution at a single point in time. The population consists of multiple genotypes, each having an expected genotypic value (red) but a range of phenotypes (black distributions) resulting from variance in residual deviations (environmental effects and nonadditive genetic factors). The phenotype distribution for the entire population (red) is the sum of these genotype-specific curves, and has a mean denoted by the blue line. The exact location of this overall distribution can wander over time, owing to the joint forces of selection, mutation, and random genetic drift. The lower panel gives the overall distribution of population means over a long evolutionary time span, with 11 locations at specific points of time being denoted by the short vertical lines. Persistent mutational bias towards smaller phenotypes prevents the overall distribution of means from coinciding with the fitness-function optimum, and random genetic drift causes a dispersion of means around the overall average value.
Stationary distributions of mean phenotypes, with optimum phenotype θs=0 and κ=104.

Results are given for three different values of θm for the condition in which σN2/κ=108 (colored curves), and four different values of σS2 for the case in which the mutational mean coincides with the optimum (black curves). The parametric values used in these plots assume a scale on which the phenotypic standard deviation is 1.0, so a mean phenotype of ±0.001 is equivalent to a shift of 0.1% phenotypic standard deviations from the optimum.
Stationary distributions of mean phenotypes with a hyperbolic fitness function, Equation (14) with α=1 and β=0.03 and denoted by the dashed line.

Black distributions denote results for various effective population sizes (Ne=103 to 106), with phenotypic variance σz2=1, mutational variance σN2=1, and the mean phenotype under neutrality (distribution given by the dotted line) θm=10. Blue and red distributions denote the effects of altering θm and σN2.
An example of a bimodal stationary distribution of mean phenotypes, with mutation pressure to the left and selection pressure to the right, with the forms of these two functions being such that their product is a minimum at the valley in the landscape.

Most of the time, a population will reside in one domain or the other, wandering over a range of phenotype space to the left or the right of the valley, but occasionally a transition will be made across the valley impelled by a stochastic series of drift and mutational events. Populations crossing the valley to the right are pulled by selection pressure, whereas those crossing to the left are pulled by the multiplicity of mutational opportunities.


Table 1
Formulae for mean population fitness, W¯(z¯), and the rate of change of the mean phenotype resulting from selection, Ms(z¯), obtained from Equations (4) and (6), respectively.




ω2ω2 + σz2exp(( z¯θs )22(ω2 + σz2))

σA2(z¯θs)ω2 + σz2


1α exp{β[ z¯(βσz2/2) ]}

σA2αβexp{β[ z¯(βσz2/2) ]}α


11 + exp[ (β/γ)(z¯z) ]

σA2(β/γ)1 + exp[ (β/γ)(z¯z) ]

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  1. Michael Lynch
Phylogenetic divergence of cell biological features
eLife 7:e34820.