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

Drift, mutation, selection, and the evolutionary dispersion of mean phenotypes recombination random mutation genetic drift The Population-genetic Environment

1000x Range of Variation in the Mutation Rate • 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.

Negative Scaling of Effective Population Size with Organism Size 10 9 Bacteria Unicellular eukaryotes All mutations with absolute Invertebrates effects >10 -8 are prone to 10 8 Vertebrates Effective Population Size (N e ) Land plants selection. 10 7 10 6 10 5 All deleterious mutations with effects <10 -4 are free to fix; mutations with 10 4 advantages <10 -4 are 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 invisible to selection. Adult Dry Weight ( ฀ g)

Dispersion of Mean Phenotypes Over Time: population mean population distribution genotype-specific distributions individual phenotype fitness function selection mutation bias Col 1 vs Col 3 Col 5 vs Col 6 drift Col 8 vs Col 9 drift Col 11 vs Col 12 Col 14 vs Col 15 Col 17 vs Col 18 Col 20 vs Col 21 population mean phenotype

Increased N e . Phenotype distribution transformed by selection. Fitness function scaled by the power of drift, e 2NeW . NEUTRAL EQUILIBRIUM Null expectation defined by DISTRIBUTION OF mutation bias and multiplicity MEAN PHENOTYPES of equivalent states.

The Drift-Barrier Hypothesis The Biophysical Limit random genetic drift, mutation bias The Limits to Natural Selection selection

Many Cell Biological Traits Function in an Effectively Digital Manner: • 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. • Simple genetic basis. • Multiple degrees of freedom (alternative equivalent states). • May experience approximately constant intracellular environments for millions of years.

Evolution of a Digital Phenotype + + - - + - + - + - - - - + + + 4 μ 01 · φ 01 3 μ 01 · φ 12 2 μ 01 · φ 23 μ 01 · φ 34 - + - - + - - + + - + + - - - - + + + + - - + - - + + - + + - + μ 10 · φ 10 2 μ 10 · φ 21 3 μ 10 · φ 32 4 μ 10 · φ 43 - + - + + - - - - - - + - - + + state = 0 1 2 3 4 • Transition rates equal the products of mutation rates (m μ ) and fixation probabilities ( ϕ ). • At steady state, the flux rate must be equal in both directions. • 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. • States with high multiplicities are attractors.

Gaussian selection on a single site, with optimum ϴ and width ω Mutation bias ( β = 0.1): + - Wide range of conditions in which populations shift 0 1 between alternative states. 1.0 = 0.0, ฀ = 103 ฀฀ Mean Allelic Type (- / + = 0 / 1) = 0.0, ฀ = 104 ฀฀ ฀ = 0.5, ฀ = all 0.8 ฀ = 1.0, ฀ = 103 ฀ = 1.0, ฀ = 104 0.6 0.4 Optimal allele is least frequent. 0.2 Suboptimal, but neutral alleles 0.0 10 4 10 5 10 6 10 7 10 8 10 9 Effective Population Size

The Drift / Mutation Barrier with Two Sites: + + 2.0 Optimum phenotype: ฀฀ = 1.0 1.5 Mean Phenotype ฀ = 1.5 ฀ = 2.0 Average driven from optimum 1.0 by mutation bias. 0.5 - - 0.0 10 6 10 7 10 8 10 9 • Broad domain of haplotype drift. 1.0 + + Mean Haplotype Frequency - - - + 0.8 + - • Succession of predominant 0.6 haplotypes with increasing N e . 0.4 • Equivalent but divergent - + and + - 0.2 haplotypes profit from multiplicity. 0.0 10 6 10 7 10 8 10 9 Effective Population Size

Increasing the number of sites can increase the gradient of the drift barrier, and even reverse its direction: 5 Optimum phenotype, ฀ = 1.0 4 1.5 Mean Allelic Type 2.0 Five sites, increasing optimum. 2.5 3.0 3 3.5 4.0 4.5 5.0 2 1 0 10 5 10 6 10 7 10 8 10 9 5 Number of sites = 2 4 5 Mean Allelic Type 10 20 30 3 50 Increasing numbers of sites, 2 optimum = 2.0. 1 0 10 5 10 6 10 7 10 8 10 9 Effective Population Size

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. • Steady-state distribution = neutral distribution x e 2NeW . Selection Probability Mutation Mean Phenotype

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.

Quasi-equilibrium Mutation Rates Resulting From Deleterious-mutation Load 10 -3 Effective selection for antimutators Mean Genome-wide Deleterious Mutation Rate drift around 10 -4 DRIFT BARRIER the drift barrier Biased production of mutators Population size = 10 5 N = 10 5 , s = 0.01, k = 0.02, ∆ U = 0.1 U 10 -5 0 5 10 15 20 25 10 -5 • Equilibrium mutation rate is inversely proportional to the effective population size. 10 -6 Population size = 10 7 N = 10 7 , s = 0.01, k = 0.02, ∆ U = 0.1 U 10 -7 0 100 200 300 400 500 Generations (10 6 ) mutation-rate classes

1000x Range of Variation in the Mutation Rate • 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.

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

Ecological and Physiological Scaling Laws Metabolic Rate per unit Weight in Mammals Fenchel (1974, Oecologia) Savage et al. (2007, PNAS)

Maximum Growth-rate Scaling Law: the cost of eukaryogenesis and multicellularity. ~1000x decline in maximum growth potential over 20 order-of-magnitude size increase Bacteria Yeasts Cyanobacteria 10 2 10 2 Amoebozoa Green algae Maximum Exponential Growth Rate (days -1 ) Maximum Exponential Growth Rate (days-1) Ciliates Diatoms Rotifers Dinoflagellates Crustaceans Cryptophytes 10 1 10 1 Nematodes Haptophytes Cnidarians Herbaceous angiosperms Molluscs Annelids 10 0 10 0 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Mass at Maturity ( ฀ g) Mass at Maturity ( ฀ g) • • Scaling is positive only in bacteria. Shallower scaling in autotrophs.

Growth-rate Scaling Under the Drift Barrier 10 4 , 10 5 , or 10 6 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? monomer trimer pentamer heptamer dimer tetramer hexamer octamer

Known Oligomerization Structures for the Enzymes of Central Metabolism Eubacteria Archaea Uni.Euks. Land plants Metazoans Glycolysis: Hexokinase Glucose 6-phosphate isomerase Phosphofructokinase Fructose bisphosphate aldolase Triosephosphate isomerase Glyceraldehyde phosphate dehydrogenase Phosphoglycerate kinase Phosphoglucomutase Enolase Pyruvate kinase Citric-acid cycle: Citrate synthase Citrate synthase Isocitrate dehydrogenase Isocitrate dehydrogenase Fumarase Fumarase Malate dehydrogenase Malate dehydrogenase Monomer Dimer Monomer Dimer Trimer Trimer Tetramer Hexamer Tetramer Hexamer Octamer Octamer

Enzymes with Identical Multimeric States Need Not Have the Same Structural Basis Dihydrodipicolinate synthase (involved in lysine synthesis) (Griffin et al. 2008). • Dayhoff et al. (2010) estimate that about two-thirds of protein families containing homomers exhibit phylogenetic variation in the binding interfaces.

Distribution of Homomeric Types: approximate constancy across the Tree of Life 0.8 Eubacteria Archaea (n = 4269) (n = 455) 0.6 • Roughly two thirds of proteins are multimeric, 0.4 independent of phylogenetic lineage. 0.2 0.0 0.8 Invertebrates Unicellular Eukaryotes Frequency • In all cases, the distributions are approximately (n = 141) (n = 630) 0.6 negative exponential in form. 0.4 0.2 • There is no gradient in the level of complexity 0.0 0.8 with organismal complexity, which is Land Plants Vertebrates dramatically different than what we see (n = 206) (n = 3271) 0.6 gene structure and genomic architecture. 0.4 0.2 0.0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Number of Subunits