Why Sex? And Why Only in Pairs?

Motty Perry Hebrew University and University of Essex

Philip RenyThe University of Chicago

Arthur RobsonSimon Fraser University

May 2007

Outline of the Talk

• A brief introduction to the evolutionary approach to the question of “Why Sex?”

• The “Biparental Sex Puzzle”; Why sex is always biparental.

• The obstacles to triparental sex are minor.

• The two leading theories for the maintenance of sex

* The Deleterious Mutations theory – does not provide a resolution to the puzzle.

* The Red Queen theory – provides a resolution.

* Wiesmann (1886):

“…the creation of hereditary individual characters to form the material upon which natural selection may work."

* Maynard Smith (1978);

The Twofold Cost of Males

Why Sex?

♀ ♂ ♀ ♂

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♀ ♂ ♀* ♂

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♀ ♂ ♀* ♀*

↓ ↓ ↓

♀ ♂ ♀* ♀* ♀* ♀*

↓ ↓ ↓ ↓ ↓

♀ ♂ ♀ ♂

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The Twofold Cost of Males

The central puzzle of sex:

What is the purpose of such a costly enterprise?

* Salmon mate once and die;

* There are species with 500 mating compatibility class;

* Male Seahorses bear their young;

* Females Praying Mantises eat the male during sex starting with his head.

* The female Indian Lizard, collect and store sperm for up to six months, and then "choose" one of them to fertilize her egg.

Each offspring produced by any known sexual species is produced from the genetic material of precisely two individuals.

That is, sex is always biparental.

“The biparental-sex puzzle."

2. The mating coordination costs.

3. The cost of unproductive males.

1. The requisite genetic machinery that must be developed.

Obstacles to Triparental Sex

The New England Journal of Medicine, May 16, 2002

Genetic Material: 1/2,1/4,1/4

HLA region

3 pronuclei in the center of this - 69 chromosomes - embryo

2. The mating coordination costs.

1. The requisite genetic machinery that must be developed.

Obstacles to Triparental Sex

Adapting the genetic machinery for biparental sex to triparental sex seems a minor obstacle (if at all) relative to the development of that machinery in the first place.

Nature Reviews-Genetics, vol.3, 262-273.

2. The mating coordination costs.

3. The cost of unproductive males.

1. The requisite genetic machinery that must be developed.

Obstacles to Triparental Sex

There is no additional coordination cost to triparental sex over biparental sex in the many species already coordinating three or more individuals for mating.

(1/2;1/4;1/4) triparental sex displays twofold cost of males. Thus, it achieved at no additional cost of males relative to biparental sex.

Adapting the genetic machinery for biparental sex to triparental sex seems a minor obstacle (if at all) relative to the development of that machinery in the first place.

1) The Deleterious Mutation theory

2) Red Queen theory

genetic mixing reduces mutational load

genetic mixing reduces the impact of parasitic attack by increasing genotypic variability

The Deleterious Mutations Model (Kondrashov (1988))

A leading explanation for the maintenance of sex

in large populations is Kondrashov’s (1982, 1988)

Deleterious Mutation hypothesis in which sex is

advantageous because it halts the otherwise steady

accumulation of harmful mutations

The Deleterious Mutations Model (cont.))

Mutations at all loci are equally harmful. Offspring's survival probability is determined by its total number of mutations.

• Individuals are haploid. They live one generation and their genome has infinitely many loci.

a…b…a….c…g…d…a…b…g……..…• As individuals develop into adults, they independently receive mutations according to a Poisson distribution with mutation rate μ, these are added to the mutations they were borne with.

a…b…a….c…g…d…a…b…g……..…

s i 1 iK

.•An offspring with i<K mutations survives with probability

fitness

K

2 1

• The equilibrium fitness (i.e., the equilibrium fraction of surviving offspring) in an asexual population, is

• asexual population; the life-cycle is

mutations-reproduction-selection-mutations.

e

fitness

K

•Restrict attention to the threshold model where

1

• The frequency with which an offspring from parents having n and m mutations has i mutations is

• sexual population; the life-cycle is

mutations-recombination-selection-mutations.

• Thus, the fraction of offspring having i mutations after recombination is,

• Let qi denote the frequency of individuals in a given generation with i mutations after selection. After mutations arrive according to the Poisson process, the fraction of individuals with i mutations is

q i e

j 0

i

q j i j

i j!.

n mi

12

n m i 12

i.

qi

n m i

qn qm

n mi

12

n m.

a…b…a….c…g…d…a…b…g……..…father’s ploidd…a…a….b…c…d…g…d…a……..…mother’s ploid

•The fraction of individuals with i<K mutations after selection is,

•The equilibrium distribution of mutations is characterized by the additional condition that

•Kondrashov demonstrates that the equilibrium fitness of a sexual population exceeds twice that of an asexual population so long as the mutation rate is sufficiently high.

• The magnitude of the genomic mutation rate is now the focus of an ongoing debate.

* * *0 1... Kq q q

fittness

μ

asexual

sexual/2

''' *i i iq q q

'''''

'' ''0 1...

i

K

qq

q q

Triparental, (1/2)-(1/4)-(1/4) Sex

• Consider a match in which the mother has m mutations and the two fathers have n total mutations.

r m ,ni m

m nn

12

m 14

n 34

n n

,

• The offspring can have i mutations if for some m′≤m and some n′≤n, it receives m′ from the mother and n′ from the fathers, where m′+n′=i. The frequency with which an offspring has i mutations in this case is,

• The fraction of offspring having i mutations after recombination is,

q i

n m i

qm

j 0

n

q jqn j

r m ,ni .

• The fraction of individuals having i<K mutations after selection is qi′′′, which is related to qi′′ as before. The equilibrium distribution of mutations is again characterized by the additional condition that

''' *i i iq q q

K 5 K 20 K 60 K 80

1

2. 1

2. 3

2. 0

1. 0

1. 6

1. 4

0. 4

0. 7

0. 6

0. 3

0. 5

0. 5

2

1

1.5

3. 4

3. 5

3. 2

1. 9

2. 8

2. 7

0. 8

1. 4

1. 3

0. 7

1. 1

1. 0

2

1

2

4. 8

4. 8

4. 4

3. 0

4. 2

4. 1

1. 4

2. 3

2. 2

1. 1

1. 8

1. 7

2

1

3

7. 4

7. 1

6. 7

5. 6

7. 0

7. 1

2. 8

4. 3

4. 3

2. 2

3. 6

3. 6

2

1

4

9. 8

9. 3

8. 8

8. 6

10. 1

10. 2

4. 5

6. 6

6. 7

3. 6

5. 6

5. 7

2

1

6

14. 2

13. 2

12. 6

15. 3

16. 7

16. 8

8. 9

11. 8

12. 0

7. 3

10. 2

10. 4

2

1

8

17. 8

16. 5

15. 9

22. 7

23. 7

23. 7

14. 4

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18. 0

11. 9

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2

1

% Advantage of Triparental Sex over Biparental sexeach entry is also the percentage amount by which the growth rate of the triparental population exceeds that of the biparental population

• Consider an infinite population of hosts and a population of parasites.

• Determining the steady state distribution of genotypes in the sexual the steady state distribution of genotypes in the sexual host host population is crucial.population is crucial.

A Red Queen Model

• Occasionally, the two populations interact, when a randomly chosen individual i in the host population is infected with a parasite.

• This causes an epidemic in the host population killing a fraction δ of all individuals in the host population with the same genotype as individual i.

• The higher is δ and the more disperse is the genotype’s distribution that is created by sex, the more advantage sex is .

• Sex is helpful because it prevents any particular genotype from dominating the population, thereby reducing the potential reduction in the population from any single parasitic attack.

• If the host population is asexual the distribution of genotype is degenerate.

• The Hardy-Weinberg Theorem.

Population Genetic, A Detour

• Consider a sexual population and the simplest case of a single locus with two alleles a and b.

• In a single generation this population converges to the following steady state 16% 48% 36%.

• Assume that initially the population is composed of the following types 40% 60%.

• In a multi loci species, converges to the Robbins proportion takes longer

aa

bb

aa

ab

bb

• The Hardy-Weinberg Theorem.

Population Genetic, A Detour

• Consider a sexual population and the simplest case of a single locus with three alleles a, b and c.

• In a single generation this population converges to the following steady state

25% 4% 9% 20% 30% 12%

• Assume that initially the population is composed of the following types

45% 15% 25% 5% 5% 5%

• Note that population wide, 50% of the alleles are a, 20% are b and 30% are c.

aa

ab

bb

cc

ac

bc

aa

ab

bb

cc

ac

bc

• Beginning from Beginning from Robbins proportions, δ individuals of some randomly chosen genotype are killed by an epidemic. The population converges to its new Robbins proportions. The next epidemic occurs, once again killing δ individuals from a randomly chosen genotype, and so on indefinitely.

• Thus, a biparental population survives forever, and the effect on population fitness of each epidemic is determined by these successive Robbins proportions.

• The key theorem is that the above dynamics are unaffected by whether sexual reproduction is biparental or (1/4)-(1/4)-(1/2). This is because, for any given distribution of alleles, the distribution of genotypes in a (1/4)-(1/4)-(1/2) sexual population converges to the Robbins proportions just as it does in a biparental population.

•Hence, because our RQ dynamics depend only on the derived sequence of Robbins proportions, the population growth rate will be the same with either sexual system.

• Assume that the time between epidemics is not too shortAssume that the time between epidemics is not too short.

Conclusion:

Kondrashov’s deleterious mutation theory can explain why biparental sex dominates asexual reproduction, but cannot simultaneously explain why triparental sex is not observed.

The Red Queen theory, in contrast, can explain the simultaneous dominance of biparental sex over asexual reproduction and triparental sex, quadriparental sex, etc.

‘‘No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes, yet what else should he do if he wishes to understand why the sexes are, in fact, always two?’’

R.A. Fisher, 1930

Similarly, to understand why sex is always biparental, we are compelled to consider and develop a model of triparental sex.

Multinucleated embryos from in vitro fertilization

                                                                                                                                                    

Triploid zygote; 3 pronuclei in the center of this chromosomally abnormal – 69 chromosomes – embryo