sex

Testing A Hypothesis for the Evolution of Sex: 

Testing A Hypothesis for the Evolution of Sex Volkan Sevim Dept. of Physics, FSU

Testing A Hypothesis for the Evolution of Sex: 

Testing A Hypothesis for the Evolution of Sex E. Tuzel, V. Sevim and A. Erzan, 'Evolutionary Route to Diploidy and Sex', Proc. Natl. Acad. Sci. USA, Vol. 98, 13774 (2001) E. Tuzel, V. Sevim and A. Erzan, 'Strategies for The Evolution of Sex', Phys. Rev. E 64, 061908 (2001) B. Orcal, E. Tuzel, V. Sevim, N. Jan and A. Erzan, 'Testing a Hypothesis for the Evolution of Sex', Int. J. Mod. Phys. C 11, 973 (2000)

Testing a Hypothesis for the Evolution of Sex: 

Testing a Hypothesis for the Evolution of Sex OUTLINE Overview Definition of problem Model Results

I-Overview: 

Problems about the evolution of sexual reproduction Origin of sex Maintenance of sex What is the advantage of sex? What are the costs? I-Overview

I-Overview - Some problems: 

Cellular-Mechanical Costs Meiosis (Takes 10h-100h while mitosis takes 15min-4h in eukaryotic cells) Syngamy Karyogamy I-Overview - Some problems Some Costs of Sex (W. M.Lewis Jr., 1987)

I-Overview - Some problems: 

I-Overview - Some problems Recombination Breaks up high-fitness allele combinations Some Costs of Sex (W. M.Lewis Jr., 1987)

I-Overview - Some problems: 

I-Overview - Some problems Fertilization Increases the risk of disease transmission Increases the vulnerability due to reduction of motility Waste of gametes, waste of effort transmitting the gametes Some Costs of Sex (W. M.Lewis Jr., 1987)

I-Overview - Some problems: 

I-Overview - Some problems Twofold cost of sex for anisogamous species (J.M. Smith) 1/1 1/2 1/4

I-Overview Some theories about benefits of sex (J.M. Smith, 1999): 

I-Overview Some theories about benefits of sex (J.M. Smith, 1999) Sexual populations evolve faster Sex produces more genetically diverse offspring Sex makes repair of damaged DNA easier Sex helps production of offspring with fewer harmful mutations

II-Definition of Problem: 

II-Definition of Problem Hypothesis: 'Sex evolved from individuals in the tail of the fitness distribution curve. It is a strategy devised to escape extinction due to too many deleterious mutations.' Jan, Stauffer, Moseley (2000) Theory in Biosciences 119, 166-168

III-Model: 

III-Model Computer simulations and mean-field equations used for testing Results show such a mechanism could be successful

III-ModelA model to keep track of mutations: 

III-Model A model to keep track of mutations Individual Bit string Genome a haploid a diploid

III-Model: 

III-Model Bit strings consist of 15 bits (8 bits used in presentation for simplicity) Assumption: All mutations are deleterious and recessive. m represents number of expressed mutations Fitness is a decreasing function of m Deleterious mutation Wild-type gene Wild type (Highest possible fitness) m=1 m=1 Not expressed Not expressed Not expressed EXPRESSED

III- Model:Before the introduction of sex and diploidy: 

III- Model: Before the introduction of sex and diploidy 3 Stages in a MC Step Mutation with a constant probability Selection due to excessive number of mutations Reproduction - Making up the deficit by replication to keep population constant Each MC Step corresponds to an equal interval in time scale Monte-Carlo Simulation : A simulation which consists of a recurring set of random events.

III-ModelStage 1- Exposition to random mutations with a constant probability: 

III-Model Stage 1- Exposition to random mutations with a constant probability Generate a random number, R (0  R  1) If Randlt;G then flip a randomly chosen bit (Backward mutations are allowed) Else go next individual 1000 individuals (Carrying capacity) Scan all individuals G: Mutation rate per genome per MC Step,110-3 )

III-ModelStage 2:Selection due to excessive number of mutations: 

III-Model Stage 2:Selection due to excessive number of mutations mandlt;m=4 survives m=m=4 survives with probability P(m =4)=0.5 mandgt;m=4 dies m= m: Threshold

III-ModelStage 3-Last stage in a MC step: Making up the deficit to keep population constant: 

III-Model Stage 3-Last stage in a MC step: Making up the deficit to keep population constant Dead Alive Pick an individual randomly and replicate it Reach 1000 individuals at the end of MC step

III-Model30000 MC steps later: A steady state is reached: 

III-Model 30000 MC steps later: A steady state is reached Why mutation build-up (Muller’s Ratchet) do not cause all individuals to accumulate at m=4 ? Backward mutations cause a weak flow towards m=0 andlt;mAandgt; 2.4 Wild-Type ~2%

III-ModelTime Evolution Equations for Haploid Population: 

III-Model Time Evolution Equations for Haploid Population Where T is the transformation matrix and L is the size of a haploid genome.

III-ModelTime Evolution of Haploid m Distribution: 

III-Model Time Evolution of Haploid m Distribution Solutions (distribution) are independent of G (mutation rate) Simulations give a different distribution for the weak driving limit G0. System becomes unstable (chaotic) for G1. MF equations cannot describe this regime.

III-ModelPHASE 2: SEX: 

III-Model PHASE 2: SEX The New Stage in the Monte-Carlo Step Mutation with a constant probability Selection due to excessive number of mutations Sex - Conversion to diploidy via syngamy (fusion) Making up the deficit by replication

III- ModelPhase 2: Sex: 

III- Model Phase 2: Sex Phase 1: Haploid Steady State Phase 2: Turning the sex on with different mechanisms Sex at the threshold (Suggested by the hypothesis-Model A) Sex with a constant probability (Null Hypothesis-Model B) Threshold Matings occur only at the tail (m=4)

III-ModelPhase 2: Sex at the threshold of extinction (Model A): 

III-Model Phase 2: Sex at the threshold of extinction (Model A) Tail of distribution (m=4) ~1% of total population m=4 individuals Odd guy waits next MC step Fusion New diploids (possibly mandlt;4) 21 Reproduction Individuals below the threshold (m=4) are not allowed to have sex

III-ModelPhase 2: Sex at the threshold of extinction (Model A): 

III-Model Phase 2: Sex at the threshold of extinction (Model A) A diploid with m=1 If new formed diploid has mandlt;4 it can escape from extinction Diploids are not allowed to clone (Deficit is made up by cloning haploids) Diploids can engage in sex again when they have 4 homozygous mutations. But each diploid can produce only one gamete. m=4 diploids Produce one gamete and die New diploid (possibly mandlt;4) Fusion of random gametes 21 Reproduction (Worst case scenario)

IV-ResultsPhase 2: Sex at the threshold of extinction (Model A): 

IV-Results Phase 2: Sex at the threshold of extinction (Model A) A macroscopic sexual population established (~45%)

IV-Results Phase 2: Sex at the threshold of extinction (Model A): 

IV-Results Phase 2: Sex at the threshold of extinction (Model A) The percentage of sexual population vs. G Threshold mechanism for conversion to sex is successful

III-ModelPhase 2: The Null Hypothesis-Sex with a Const. Probability (Model B): 

III-Model Phase 2: The Null Hypothesis-Sex with a Const. Probability (Model B) Matings can occur anywhere All individuals Mark individuals to mate with a constant probability, s (conversion rate), regardless of their m value Odd guy waits next MC step Mate marked individuals Coexisting Pop.

III-ModelPhase 2: The Null Hypothesis-Sex with a Const. Probability (Model B): 

III-Model Phase 2: The Null Hypothesis-Sex with a Const. Probability (Model B) Diploids are not allowed to clone (Deficit is made up by cloning haploids) Diploids can engage in sex if they are selected. But each diploid can produce only one gamete. Produce one gamete and die Fusion of random gametes 21 Reproduction (Worst case scenario)

IV- Results Phase 2: The null hypothesis-Sex with a const. probability (Model B): 

Steady state distribution of coexisting asexual and sexual populations for G= 210-3, s=10-4 andlt;mAandgt;2.4, andlt;mSandgt;1.3 A macroscopic sexual population established (~30%) IV- Results Phase 2: The null hypothesis-Sex with a const. probability (Model B)

IV- Results Phase 2: The null hypothesis-Sex with a const. probability (Model B): 

IV- Results Phase 2: The null hypothesis-Sex with a const. probability (Model B) The percentage of sexual population vs. s/G A threshold mechanism seems not necessary

Slide31: 

IV- Results Comparison of Gained Fitness

IV- Results Effects of Diploidy and Sex: 

IV- Results Effects of Diploidy and Sex * Model A with obligatory mating: In this case all sexuals forced to mate in every MC step. This increased # of matings per MC step. Mutations accumulate slower Selects-out mutations thru death

Conclusion: 

Conclusion A threshold mechanism for establishing a steady state population of sexuals within a finite population is sufficient but not necessary. Net gain in fitness with the threshold mechanism (suggested by the hypothesis) is higher compared to net gain in the constant probability mechanism Mean-field equations may not describe such a system for all range of parameters. Diploidy has a capability of masking the deleterious mutations and slowing down their cumulative effects Sex reduces the deleterious mutation load via syngamy.