Limits on the Rate of Evolution

Sally Otto

Department of ZoologyUniversity of British Columbia

Rates of morphological evolution

vary enormously...

Some species have changed rapidly in appearanceover tens to hundreds of thousands of years.

Cichlids in African rift lakes

Columbines

Sticklebacks in BCfreshwater lakes

HawaiianDrosophila

Others have remained similar in appearanceover tens to hundreds of million years.

Crocodiles

Sequoias Lungfish

Monotremes

The largest unsolved puzzle in evolution

What factors set the pace of evolutionary change?

?? ??

Rate of Environmental Change Appearance of Mutations Efficiency of Selection Architectural Constraints

…but what are their relative roles??

Fast rates ofmorphological evolution

occur in novel environments...

e.g. Honeycreepers on the Hawaiian islands

RATE OF ENVIRONMENTAL CHANGE

and E. coli in a novel glucose environment

(Lenski and Travisano 1994)

but the rate slows in a static environments.

Evolution can only go where mutations lead it.

The rate of beneficial mutationcan limit the rate of evolution,

especially in novel environmentsand in small populations.

(de Visser et al 1999)

APPEARANCE OF MUTATIONS

EFFICIENCY OF SELECTION

Natural selection does not causeinstantaneous adaptation.

The spread ofbeneficial alleles

takes time...

...and new beneficial alleles are often lost by drift.

Aa

1

2

0

3

but this is only an average.

In a population of constant size, each parent produces one offspring, on average.

Individuals carrying a new beneficial allele may have more offspring, say 1+s, on average...

In 1927, Haldane proved the classic result that theprobability of fixation (P) of a new beneficial mutationis approximately 2s in a population of LARGE andCONSTANT size, ignoring other loci.

Where does 2s come from?

Poisson distribution of offspring per parent One offspring per parent on average 1+s offspring per parent carrying a rare beneficial

mutation

Branching Process

When s is small, P is approximately 2s.

1 P e (1s) (1 s) j

j!(1 P) j

j

e (1s)P

expansions contractions fluctuations

Natural populations do not, however, remain constantin size, but experience

In populations changing in size (Nt),what is the probability

of fixation of a new allele?

Exponential growth

1+r for wildtype parents (1+r)(1+s) for parents carrying a

beneficial allele

If a population is growing or shrinking, the averagenumber of offspring per parent is not one but

P 2 (s + r)

(Otto and Whitlock 1997)

Fixation probability with exponential growth:

r=-0.005 r=0 r=0.01 r=0.1

s=0.01 0.012 0.020 0.039 0.197

s=-0.01 0.002 4*10-4 10-5 2*10-20

Diploid population of initial size 100.

Logistic Growth

2 (s+r) when Nt << K

2s when Nt approaches K

Population growth is generally limited, however, and decreases as population size approaches carryingcapacity (K).

Pt 2 (s r)

1 r

s

N tK

Population Size

Growing Shrinking

2

4

6

8

10

1000|

10000|

10|

s=0.001

s=0.01

Pt

2s

0.2

0.4

0.8

1

s=0.001

s=0.01

1100|

1000|

10000|

Time (Measured by Population Size)

(r=0.01, K=1000) (r=0.01, K=10000)

0.6

more likely to fix in growing populations less likely to fix in shrinking populations

Beneficial mutations are:

Population dynamics are as important as selection in determining the fate of new mutations.

less likely to fix in growing populations more likely to fix in shrinking populations

Deleterious mutations are:

Evolutionary forces will reinforce,

rather than counteract,externally caused changes

in population size.

ARCHITECTURAL CONSTRAINTS

Pleiotropy Gene number Linkage relationships

Genomic architecture:

“As a result of complex biochemical, developmental, and regulatory pathways, a single gene will almost always influence multiple traits, a phenomenon known as pleiotropy.”

- Lynch and Walsh (1998)

I - Pleiotropy

One Gene

One TraitX

One Gene

SeveralTraits

Teosinte Maize

•Length of internodes in the ear •Number of fruitcases in a row on the ear •Tendency of ear to shatter •% of fruitcases with single vs. two kernels •% lateral branches with male tassels •Degree to which fruitcases are stacked•Number of internodes in the lateral branches •Average length of these internodes •Number of branches in the 1o lateral inflorescence

Doebley et al (1995) examined the effects of two QTLs on:

The two QTLs significantly affected 9/9 & 8/9 traits!

Teosinte-Maize divergence

Consider a trait subject to direct artificial or natural selection.

An allele that causes a direct beneficial effect (sd) on this trait may fail to become established due to deleterious pleiotropic effects (sp).

Scenario

1. Fewer alleles are favourable overall (sT = sd + sp must be positive).

2. Among these, the overall selective advantage is lessened.

How does pleiotropy affect the rate of evolution?

- 0.04 - 0.03 - 0.02 - 0.01- 0.05

Pleiotropic selection (s )p

0

Probability

Uniform

Half-normal

Exponential

These quantities can be calculatedfor any given distribution of pleiotropic effects.

- 0.04 - 0.03 - 0.02 - 0.01- 0.05

20

40

60

Pleiotropic selection (s )p

0

Probability

Uniform

s > 0 T

- s d

s < 0 T

|s |2

s

p

d

2

ss d

0s|TT

1. Fraction favourable 2. Overall selective advantage

In general, when pleiotropy is extensive and strong…

Only a fraction of alleles that are beneficial to the trait will be favourable overall.

Among these, pleiotropy on average halves the selective advantage.

Implications

• Pleiotropy will slow evolutionary change, especially when selection acts weakly on novel functions ( GxE).

• The exact traits that have been favoured by natural selection will be difficult to identify, because even costly phenotypic changes may have arisen pleiotropically.

II - Gene Number

When genetic change is constrained by pleiotropy,the rate of evolution may be increased

by gene or genome duplication.

Reproduction Insects Fish Amphibia Reptiles Mammals

Parthenogens 80 10 4 14 (1) 0

Sexuals (3) 20 (2) 24 (2) 1 1

? 0 17 0 0 0

Polyploidy among animals

Key polyploid events early in the evolution of vertebrates, ray-finned fish, salmonids, catostomids...

Gene conservation

Among ancient polyploids, a surprisingly high fraction of gene duplicates are preserved:

• ~ 8-13% retained in duplicate in yeast (Wolfe & Shields 1997)• ~ 50% retained in duplicate in vertebrates (Nadeau & Sankoff 1997) • ~ 50% retained in duplicate in Xenopus (Hughes & Hughes 1993)• ~ 50% retained in duplicate in salmonids & catastomids (Bailey et al 1978)• ~ 72% retained in duplicate in maize (Ahn & Tanksley 1993)

“Gene duplication...allows each daughter gene to specializefor one of the functions of the ancestral gene.” (Hughes 1994)

Rate of adaptation

Implications

• Polyploidy events have occurred repeatedly among animals and plants.

• Polyploids are not evolutionary dead-ends and may have higher rates of evolution.

• Polyploidization may have played a key role in evolution, freeing genes from the constraints of pleiotropy and allowing the evolution of more complex patterns of gene expression.

“For, unless advantageous mutations occurso seldom that each has had time to becomepredominant before the next appears, theycan only come to be simultaneously in thesame gamete by means of recombination.”

- R. A. Fisher (1930)

III - Genetic Associations

CONCLUSIONS

Evolutionary change is limited by a variety of factors (environmental change, mutation, selection, genomic architecture).

We are gaining a better appreciation for the effects of these various factors,but determining their relative roles remains one of the most important open questions in evolutionary biology.

Fisher-Muller Hypothesis

aBAB

ABAB

ABAB

AB

AB

AB

AB AB

ABAB

AB

AB

aBAB

ABAB

AB

ABAB

AB AB

ABAB

aB

aB

aBAb

abab

abab

ab

abab

ab ab

abab

ab

ab

abab

Mutation to b

ABAB

ABAB

ABAB

AB

AB

AB

AB AB

ABAB

AB

AB

Mutation to a

aBaBaB

aBaBaB

aBaB aB

aBaB aBaBaB

aB

With recombination

Without recombination

Time

2 s

1.6 s

1.2 s

0.8 s

0.4 sFreq(b)

Fixation Probability of a

Time

r=0.00001

r=0.0001

r=0.001

r=0.011

0.8

0.6

0.4

0.2

sa = 0.01sb = 0.01

On-going selection at one locus (B) reduces the fixationprobability of a new beneficial allele at a linked locus (A).

- N. Barton (1995)

Evolution of recombination

A modifier gene that increases recombinationbecomes associated with beneficial alleles

that are more likely to fix.

As these successful alleles spread,the modifier is dragged along

by genetic hitchhiking.

By increasing the fixation probability of beneficial mutations,modifiers that increase recombination rise in frequency.

- Otto & Barton (1997)

Time

0.0001

0.0002

0.0003

Change in Modifier

0

1

0.5

0

Freq(b)

sa = 0.01

sb = 0.1

R = 0.001

rMM = 0.01

rMm = 0.02

rmm = 0.03

Selection acting on a modifier of recombination is :

2 s r / r for a tightly linked chromosome2 s3 r / N for a one Morgan chromosome

: rate of beneficial mutations throughout populationper chromosome per generation

s: average selection coefficient of beneficial mutation

r: average rate of recombination between genes

r: effect of modifier on r

N: population size

The Fisher-Muller mechanism can select

for increased recombination and sex

within a population, but the effect is weak

unless linkage is tight or

beneficial mutations are common.