1. The population genetics of sex and recombination
Why have sex?
The population genetics of sex and recombination
Sally Otto
Department of Zoology
University of British Columbia

2. INTRODUCTION Asexuals: The unit of reproduction is the individual
Sexuals: The unit of reproduction is the couple
Unless the sexual couple produces twice as many offspring
as the asexual individual, there will be a cost of sex.
The "sexual female propagates her genome,
or any given element of her genome,
only half as efficiently as the asexual female"
— Bell 1982

3. Risk of not finding a mate Risk of disease transmission during mating
Other costs of sex:
Cost of finding a mate
Risk of not finding a mate
Risk of disease transmission during mating
Loss of heterozygosity
Destruction of favorable gene combinations
Despite these costs of sex, the vast majority
of eukaryotic organisms are sexual
The paradox of sex

4. What might offset the cost of sex?
Paternal contribution to the production and rearing of offspring
What might pay the cost of sex?
Most explanations of sex stem from the idea that sex can generate greater variability through chromosomal segregation and recombination.

5. But sex does not always diversify an offspring population:
Genetic Variance
in Fitness
Without sex AB ab Ab aB AB ab Ab aB
0.0060
WAB = 1
WAb = 0.9
WaB = 0.9
Wab = 0.81 ab AB
0.0045
Ab or aB
With sex

6. An increase in genetic variation (Vg) generally improves
the response of a population to selection.
Identify the conditions under which sex and recombination increase genetic variation
Determine the extent to which this force favors the evolution of sex and recombination

7. Genotypes that are more common than expected based
on Hardy-Weinberg or linkage equilibrium are
typically more common because they have been favored by selection.
By destroying these genetic associations, sex and recombination
typically reduce the average fitness of offspring.
RECOMBINATION LOAD

8. Genetic variation in fitness is increased by sex and recombination
Determining when sex and recombination are favored is essentially a search for the conditions where:
Genetic variation in fitness is increased by sex and recombination
Recombination load is weak or reversed
Recombination
load
D Vg

9. Three-locus Model M A B RMM rMM RMm rMm Rmm rmm Wij
Genotype at a modifier
locus determines the
probability of recombination:
RMm
rMm
Rmm
rmm
i,j = 1 for AB
= 2 for Ab
= 3 for aB
= 4 for ab
Genotype at selected loci determines fitness:
Wij

10. ASIDE: Are sex and recombination interchangeable???
In general, NO, because sex involves both segregation and recombination.
Segregation at one locus can exert selection for/against sex
(Kirkpatrick and Jenkins 1989; Chasnov 2000; Agrawal 2001*)
In haploid models, however, the probability of sex and the probability of recombination enter into models as their product.
(True also for special diploid models where HW is maintained by selection.)
Models that examine the fate of alleles that modify recombination rates inform us about the fate of alleles that modify the probability of engaging in sex.

11. Directional selection
Spread of a beneficial mutation
Mutation-selection balance
Fluctuating selection (with a long period) ]
1.75
Beneficial
Positive epistasis
Multiplicative
1.5
Negative epistasis
1.25
Haploid Fitness 1
0.75
Positive epistasis
Multiplicative
0.5
Deleterious
Negative epistasis
0.25 1 2
Number of mutations
(1+s)2+e
Haploid Fitness: 1
1+s

12. e < 0 e = 0 e > 0 Initial Population D = 0 D < 0 D = 0
0.4
D = 0
0.3
0.2
0.1 AB Ab aB ab
e < 0
e = 0
e > 0
D < 0
D = 0
D > 0 AB Ab aB ab
0.1
0.2
0.3
0.4 AB Ab aB ab
0.1
0.2
0.3
0.4
0.4
0.3
0.2
0.1 AB Ab aB ab

13. Directional selection30
Rec load = 
D Vg =  20
Decreased recombination 10
0.1
0.2
0.3
0.4
0.5
Rec
Increased recombination
-10
Rec load = 
D Vg = 
-20
Decreased recombination
-30
(Barton 1995; Otto and Feldman 1997)

14. Implications Sex/recombination may evolve when: Epistasis is negative
0.1
0.2
0.3
0.4
0.5
-30
-20
-10 10 20 30
Decreased recombination
Increased recombination
Rec
Implications
Sex/recombination may evolve when:
Epistasis is negative
Epistasis is weak or linkage tight
Variance in epistasis is low
Broader conditions favor the evolution of a bit of sex/rec than frequent sex/rec.

15. Less restrictive explanations???
Temporal variation in selection (e.g. host-parasite mediated):
Disequilibrium may reflect past not current selection
Sex/recombination can gain an immediate
fitness benefit by breaking down disequilibrium
But fluctuations have to be very rapid (2~5 generations)
(Barton 1995; Peters and Lively 1999)
Rec load = 

16. Spatial variation in selection:
Disequilibrium may reflect distant not local selection
Sex/recombination can gain an immediate
fitness benefit by breaking down disequilibrium
High rates of sex/recombination may evolve when
Rec load =  /
Cov(sA,sB) > 0
&
e << 0 sA
Cov(sA,sB) < 0
&
e > 0 sB sB sA
deme deme 2
deme deme 2
(Pylkov et al 1998; Lenormand and Otto 2000)

17. Disequilibrium generated by genetic drift:
Disequilibrium may be generated by the chance background on which mutations appear or random drift in finite populations.
Drift by itself does not bias D
When D > 0 (Vg ), selection acts more rapidly and D dissipates.
When D < 0 (Vg ), selection acts less rapidly and D remains.
Drift with selection generates, on average, negative disequilibrium that reduce the response to selection
Selection for increased sex/rec, especially when there is strong selection, a small population size, and low initial sex/rec.
(Otto and Barton 1997, 2001; Barton and Otto 2002)

18. Comparing the force of drift and epistasis:
Proportional change in sex/rec over 50 generations with very strong selective sweeps (1+s = 2) / 4
Initial favorable allele frequency = 0.01 3
r = 0.1 mm
% change in sex/rec
r = 0.15 Mm
r = 0.2 2 MM e
= -1.21 e
= -1 1 e
= -0.2 e
= 0 ∞ 50
100
500
1000
10000
100000
Population size (2N) e -1
= 1
(Otto and Barton 2001)

19. / 3
Implications 2 1 ∞ 50
100
500
1000
10000
100000 -1
Population size (2N)
Small populations: Effect of epistasis < effect of drift
Large populations: Effect of epistasis > effect of drift
Effect due to drift alone can be larger than the best case scenario with epistasis alone

20. Conclusions
Conditions favoring the evolution of sex and recombination are surprisingly persnickety
DATA
...epistasis, variance in epistasis, strength of selection,
form of species interactions, form of spatial variation,
frequency of beneficial sweeps...