Transcript General

Limits on the
Rate of Evolution
Sally Otto
Department of Zoology
University of British Columbia
Rates of morphological evolution
vary enormously...
Some species have changed rapidly in appearance
over tens to hundreds of thousands of years.
Cichlids in African rift lakes
Columbines
Sticklebacks in BC
freshwater lakes
Hawaiian
Drosophila
Others have remained similar in appearance
over tens to hundreds of million years.
Crocodiles
Monotremes
Sequoias
Lungfish
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??
?? The largest unsolved puzzle in evolution ??
RATE OF ENVIRONMENTAL CHANGE
Fast rates of
morphological evolution
occur in novel environments...
e.g. Honeycreepers
on the Hawaiian islands
and E. coli in a novel glucose environment
(Lenski and Travisano 1994)
but the rate slows in a static environments.
APPEARANCE OF MUTATIONS
Evolution can only go where mutations lead it.
The rate of beneficial mutation
can limit the rate of evolution,
especially in novel environments
and in small populations.
(de Visser et al 1999)
EFFICIENCY OF SELECTION
Natural selection does not cause
instantaneous adaptation.
The spread of
beneficial alleles
takes time...
...and new beneficial alleles are often lost by drift.
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...
1
but this is only an average.
0
Aa
2
3
In 1927, Haldane proved the classic result that the
probability of fixation (P) of a new beneficial mutation
is approximately 2s in a population of LARGE and
CONSTANT size, ignoring other loci.
Where does 2s come from?
Branching Process



Poisson distribution of offspring per parent
One offspring per parent on average
1+s offspring per parent carrying a rare beneficial
mutation
e (1s) (1  s) j
1P  
(1  P) j
j!
j
 e (1s)P
When s is small, P is approximately 2s.
Natural populations do not, however, remain constant
in size, but experience



expansions
contractions
fluctuations
In populations changing in size (Nt),
what is the probability
of fixation of a new allele?
Exponential growth
If a population is growing or shrinking, the average
number of offspring per parent is not one but


1+r for wildtype parents
(1+r)(1+s) for parents carrying a
beneficial allele

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
Population growth is generally limited, however, and
decreases as population size approaches carrying
capacity (K).
2 (s  r)
Pt 
r Nt
1
s K
 2 (s+r) when Nt << K
 2s when Nt approaches K
Population Size
Growing
Shrinking
(r=0.01, K=10000)
Pt
2s
10
(r=0.01, K=1000)
1
s=0.001
s=0.01
8
0.8
6
0.6
4
0.4
2
s=0.01
|
10
|
1000
s=0.001
0.2
|
10000
|
10000
|
1100
Time (Measured by Population Size)
|
1000
Beneficial mutations are:


more likely to fix in growing populations
less likely to fix in shrinking populations
Deleterious mutations are:


less likely to fix in growing populations
more likely to fix in shrinking populations
Population dynamics are as important as selection
in determining the fate of new mutations.
Evolutionary forces will reinforce,
rather than counteract,
externally caused changes
in population size.
ARCHITECTURAL CONSTRAINTS
Genomic architecture:



Pleiotropy
Gene number
Linkage relationships

I - Pleiotropy
“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)
One
Gene
One
Gene
X
One
Trait
Several
Traits
Teosinte-Maize divergence
Doebley et al (1995) examined the effects of two QTLs on:
•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
o
•Number of branches in the 1 lateral inflorescence
Teosinte
Maize
 The two QTLs significantly affected 9/9 & 8/9 traits!
Scenario
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).
How does pleiotropy affect the rate of evolution?
1. Fewer alleles are favourable overall (sT = sd + sp
must be positive).
2. Among these, the overall selective advantage is
lessened.
These quantities can be calculated
for any given distribution of pleiotropic effects.
Probability
Half-normal
Uniform
Exponential
- 0.05
- 0.04
- 0.03
- 0.02
- 0.01
Pleiotropic selection (sp )
0
Probability
60
- sd
40
Uniform
sT > 0
sT < 0
- 0.05
- 0.04
- 0.03
20
- 0.02
- 0.01
0
Pleiotropic selection (sp )
1. Fraction favourable
sd
2 | sp |
2. Overall selective advantage
s T|s
T
0
sd

2
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.
Polyploidy among animals
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
?
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 specialize
for 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.

III - Genetic Associations
“For, unless advantageous mutations occur
so seldom that each has had time to become
predominant before the next appears, they
can only come to be simultaneously in the
same gamete by means of recombination.”
- R. A. Fisher (1930)
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
Without recombination
AB AB AB
AB AB AB
AB AB AB
AB AB
AB AB
AB
AB
AB AB AB
aB AB AB
AB AB AB
AB AB
AB AB
AB
AB
Mutation
to a
Ab AB AB
aB aB aB
AB ABAB
AB AB
AB aB
AB
AB
Mutation
to b
Time
aB aB aB
aBaBaB aB
aB aBaBaB
aB
aB
aB
aB
ab ab ab
ab ab ab
ab ab ab
ab ab
ab ab
ab
ab
With recombination
On-going selection at one locus (B) reduces the fixation
probability of a new beneficial allele at a linked locus (A).
- N. Barton (1995)
sa = 0.01
sb = 0.01
Fixation Probability of a
2s
1.6 s
1.2 s
1
r=0.01
r=0.001
0.8
r=0.0001
0.6
r=0.00001
0.8 s
Freq(b)
0.4 s
0.4
0.2
Time
Evolution of recombination
A modifier gene that increases recombination
becomes 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)
rMM = 0.01 sa = 0.01
rMm = 0.02 sb = 0.1
Change in Modifier
rmm = 0.03 R = 0.001
1
0.0003
Freq(b)
0.0002
0.5
0.0001
0
0
Time
Selection acting on a modifier of recombination is :
2 s r / r
2 s3 r / N

for a tightly linked chromosome
for a one Morgan chromosome
: rate of beneficial mutations throughout population
per 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.