Drift, mutation, selection, and the evolutionary dispersion of mean - - PowerPoint PPT Presentation

Drift, mutation, selection, and the evolutionary dispersion of mean phenotypes

The Population-genetic Environment

mutation random genetic drift recombination

• The mutation rate per nucleotide

site scales negatively with the effective population size.

• For a given magnitude of random

genetic drift, unicellular eukaryotes have lower mutation rates than bacteria because there are more functionally significant genomic sites.

1000x Range of Variation in the Mutation Rate

Adult Dry Weight (฀g)

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 1010 1011

Effective Population Size (Ne)

104 105 106 107 108 109 Bacteria Unicellular eukaryotes Invertebrates Vertebrates Land plants

Negative Scaling of Effective Population Size with Organism Size

All deleterious mutations with effects <10-4 are free to fix; mutations with advantages <10-4 are invisible to selection. All mutations with absolute effects >10-8 are prone to selection.

individual phenotype

population mean population distribution genotype-specific distributions

Dispersion of Mean Phenotypes Over Time:

Col 1 vs Col 3 Col 5 vs Col 6 Col 8 vs Col 9 Col 11 vs Col 12 Col 14 vs Col 15 Col 17 vs Col 18 Col 20 vs Col 21

drift

fitness function population mean phenotype

selection mutation bias drift

Fitness function scaled by the power of drift, e2NeW. Phenotype distribution transformed by selection. Increased Ne. Null expectation defined by mutation bias and multiplicity

• f equivalent states.

NEUTRAL EQUILIBRIUM DISTRIBUTION OF MEAN PHENOTYPES

The Drift-Barrier Hypothesis

random genetic drift, mutation bias selection

The Limits to Natural Selection The Biophysical Limit

Many Cell Biological Traits Function in an Effectively Digital Manner:

• Simple genetic basis.
• Multiple degrees of freedom (alternative equivalent states).
• May experience approximately constant intracellular environments for

millions of years.

• Transcription-factor and microRNA binding sites.
• Post-translational modifications – phosphosites on proteins.
• Numbers of single and double carbon bonds in the tails of lipid molecules.
• Numbers of subunits in multimeric proteins: monomers, dimers, trimers, etc.

+ - - -

• + - -
• - + -
• - - +

+ + - - + - + - + - - +

• + + -
• + - +
• - + +

+ + + +

• + + +

+ - + + + + - + + - - -

• - - -

4μ01 · φ01 μ10 · φ10 2μ01 · φ23 3μ10 · φ32 3μ01 · φ12 2μ10 · φ21 μ01 · φ34 4μ10 · φ43

state = 0 1 2 3 4

Evolution of a Digital Phenotype

• The equilibrium probability of each state is proportional to the product of the total set of

transition rates towards the state pointing from both directions.

• Transition rates equal the products of mutation rates (mμ) and fixation probabilities (ϕ).
• At steady state, the flux rate must be equal in both directions.
• States with high multiplicities are attractors.

Effective Population Size

104 105 106 107 108 109

Mean Allelic Type (- / + = 0 / 1)

0.0 0.2 0.4 0.6 0.8 1.0

฀฀ = 0.0, ฀ = 103 ฀฀ = 0.0, ฀ = 104 ฀ = 0.5, ฀ = all ฀ = 1.0, ฀ = 103 ฀ = 1.0, ฀ = 104

Gaussian selection on a single site, with optimum ϴ and width ω 0 1 + - Mutation bias (β = 0.1): Suboptimal, but neutral alleles Optimal allele is least frequent. Wide range of conditions in which populations shift between alternative states.

Effective Population Size

106 107 108 109

Mean Phenotype

0.0 0.5 1.0 1.5 2.0

฀฀ = 1.0 ฀ = 1.5 ฀ = 2.0

106 107 108 109

Mean Haplotype Frequency

0.0 0.2 0.4 0.6 0.8 1.0

Optimum phenotype:

The Drift / Mutation Barrier with Two Sites: Average driven from optimum by mutation bias.

• Succession of predominant

haplotypes with increasing Ne.

• Equivalent but divergent - + and + -

haplotypes profit from multiplicity.

• Broad domain of haplotype drift.

+ +

• -

+ +

• -
• +

+ -

Effective Population Size

105 106 107 108 109

Mean Allelic Type

1 2 3 4 5

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

105 106 107 108 109

Mean Allelic Type

1 2 3 4 5

2 5 10 20 30 50

Optimum phenotype, ฀ = Number of sites =

Increasing the number of sites can increase the gradient of the drift barrier, and even reverse its direction: Five sites, increasing optimum. Increasing numbers of sites,

• ptimum = 2.0.

Mean Phenotype Probability

Selection Mutation

• Steady-state distribution = neutral distribution x e2NeW.

With sufficiently strong mutation bias away from the direction of selection, the probability distribution of mean phenotypes can be bimodal, mimicking the expectations for an adaptive landscape with two peaks.

The Origin of the Rules of Life

The Drift-barrier and the Scaling of Organismal Features

• The reduction in effective population size that accompanies

increased organism size leads to –

• The passive expansion of genome size and gene number.
• An increased mutation rate.
• Reduced maximum growth-rate.

5 10 15 20 25 10-5 10-4 10-3

N = 105, s = 0.01, k = 0.02, ∆U = 0.1U

100 200 300 400 500 10-7 10-6 10-5

N = 107, s = 0.01, k = 0.02, ∆U = 0.1U

Mean Genome-wide Deleterious Mutation Rate Generations (106)

Quasi-equilibrium Mutation Rates Resulting From Deleterious-mutation Load

Effective selection for antimutators Biased production of mutators DRIFT BARRIER

• Equilibrium mutation rate is inversely

proportional to the effective population size.

Population size = 105 Population size = 107

drift around the drift barrier

mutation-rate classes

• The mutation rate per nucleotide

site scales negatively with the effective population size.

• For a given magnitude of random

genetic drift, unicellular eukaryotes have lower mutation rates than bacteria because there are more functionally significant genomic sites.

1000x Range of Variation in the Mutation Rate

Inverse Scaling Between the Genome-wide Deleterious Mutation Rate and the Effective Population Size Across the Tree of Life

Ecological and Physiological Scaling Laws

Fenchel (1974, Oecologia) Metabolic Rate per unit Weight in Mammals Savage et al. (2007, PNAS)

~1000x decline in maximum growth potential over 20 order-of-magnitude size increase

Mass at Maturity (฀g)

10-910-810-710-610-510-410-310-210-11001011021031041051061071081091010

Maximum Exponential Growth Rate (days-1)

10-3 10-2 10-1 100 101 102 Bacteria Yeasts Amoebozoa Ciliates Rotifers Crustaceans Nematodes Cnidarians Molluscs Annelids

Maximum Growth-rate Scaling Law: the cost of eukaryogenesis and multicellularity.

• Scaling is positive only in bacteria.
• Shallower scaling in autotrophs.

Mass at Maturity (฀g)

10-810-710-610-510-410-310-210-1 100 101 102 103 104 105 106 107 108 1091010

Maximum Exponential Growth Rate (days-1)

10-3 10-2 10-1 100 101 102 Cyanobacteria Green algae Diatoms Dinoflagellates Cryptophytes Haptophytes Herbaceous angiosperms

Growth-rate Scaling Under the Drift Barrier

• 104, 105, or 106 biallelic (+/-)

growth-rate loci contributing independently to fitness.

• Free recombination (solid lines) or

complete linkage (dashed).

The Origin of Variation in Molecular Complexes:

Driven by adaptive processes unique to individual lineages? Or a consequence of biased mutation pressure and/or random drift?

dimer tetramer trimer hexamer heptamer

• ctamer

pentamer monomer

Eubacteria Archaea Uni.Euks. Land plants Metazoans Hexokinase Glucose 6-phosphate isomerase Phosphofructokinase Fructose bisphosphate aldolase Triosephosphate isomerase Glyceraldehyde phosphate dehydrogenase Phosphoglycerate kinase Phosphoglucomutase Enolase Pyruvate kinase Citrate synthase Isocitrate dehydrogenase Fumarase Malate dehydrogenase Citrate synthase Isocitrate dehydrogenase Fumarase Malate dehydrogenase

Monomer Dimer Trimer Tetramer Hexamer Octamer Monomer Dimer Trimer Tetramer Hexamer Octamer Glycolysis: Citric-acid cycle:

Known Oligomerization Structures for the Enzymes of Central Metabolism

(Griffin et al. 2008).

Dihydrodipicolinate synthase (involved in lysine synthesis) Enzymes with Identical Multimeric States Need Not Have the Same Structural Basis

• Dayhoff et al. (2010) estimate that about two-thirds of protein families containing

homomers exhibit phylogenetic variation in the binding interfaces.

Eubacteria (n = 4269)

0.0 0.2 0.4 0.6 0.8

Archaea (n = 455) Unicellular Eukaryotes (n = 630)

Frequency

0.0 0.2 0.4 0.6 0.8

Invertebrates (n = 141) Vertebrates (n = 3271)

2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8

Land Plants (n = 206)

2 4 6 8 10 12 14

Number of Subunits

Distribution of Homomeric Types: approximate constancy across the Tree of Life

• Roughly two thirds of proteins are multimeric,

independent of phylogenetic lineage.

• In all cases, the distributions are approximately

negative exponential in form.

• There is no gradient in the level of complexity

with organismal complexity, which is dramatically different than what we see gene structure and genomic architecture.

u 3v 2v v u u upward selection pressure downward selection pressure

Allelic Class

10 20 30

Frequency of Allelic Class

0.0 0.1 0.2 0.3 0.4 0.5

0.1 1.0 2.0 10.0 20.0

(u/v)e4Ns

• The probability distribution of alternative states is Poisson, with key parameter (u/v)e4Ns.

The Steady-state Evolutionary Distribution

• Substantial phenotypic variation among lineages,

even when selection and mutation are

• perating identically in all lineages
• Most common state is not the optimum.
• Under effective neutrality (Ns << 1), the form of

the distribution is independent of population size.

Center for Mechanisms of Evolution

Cell biology, biophysics, biochemistry, population genetics. Empirical, computational, theoretical. Inquiries welcome for positions: faculty, research scientists, postdocs, students.

Studio: $s:

15 Years of Mutation Accumulation:

• Genomic mutation: Matt Ackerman; Charles Baer; Dee Denver;

Sibel Kucukyildirim; Hongan Long; Sam Miller; Way Sung.

• Transcription error: Jean-Francois Gout; Weiyi Li.
• Somatic mutation: Stephan Baehr.

• Selective disadvantage of a mutator in an asexual population

= increase in genome-wide deleterious mutation rate

Excess number of mutations at equilibrium = ΔU / s X Effect / mutation = s Total effect on fitness = ΔU s, rate of removal by selection ΔU, increase in genome-wide rate

• f deleterious

mutation

The Magnitude of Selection Operating to Improve Replication Fidelity