Adaptationism and the Adaptive Landscape
Genomic imprinting, mathematical models, and notions of optimality
in evolution
Overview
• Adaptationism
• Zoom and Grain in the adaptive landscape
• Mathematical models of genomic imprinting
Adaptationism• Primary role for natural selection in evolution
– versus drift, historical and developmental constraints, etc.
• Modern debate framed by the Sociobiology wars (Wilson, Dawkins, Lewontin, Gould, etc.)
• Continuation with Evolutionary Psychology, but • Partial reconciliation in most fields
– Tests of selection, contemporary systematics
Types of adaptationism
• Empirical– Central causal role for selection
• Explanatory– Selection answers the big questions
• Methodological– Selection is a good organizing concept
– Godfrey-Smith (2001)
The Adaptive Landscape
• Natural selection is conceived of as a hill-climbing algorithm
Caveats
• Units (genotype vs. phenotype, population vs. individual fitness)
• High dimensionality• Topology of the landscape• Dependence on other
organisms• Hill-climbing metaphor
implies a deterministic process
Zoom level 1
• High level analyses invoke rugged landscapes, which emphasize the role of historical contingency
Zoom level 2
• Intermediate levels of analysis focus on local regions with a small number of peaks, emphasizing optimization
Zoom level 3
• Low-level analyses reveal the discontinuities in the fitness landscape, emphasizing drift, recombination, etc.
Zoom level 3
• Low-level analyses reveal the discontinuities in the fitness landscape, emphasizing drift, recombination, etc.
Sickle-cell anemia
• HbA / HbA– Susceptible
• HbA / HbS– Resistant
• HbS / HbS– Sickle-cell
Resistantparents
Susceptible Resistant Sickle-cell
Population-genetic timescale
• Mendelian segregation recreates sub-optimal phenotypes every generation
HbA / HbS
HbA / HbAHbS / HbS
~100 generations
Mutation timescale
• The mutation giving rise to the HbS allele represents a partial adaptation to malaria
HbA + HbS
HbA
~104 generations
Chromosomal rearrangement timescale
• A (hypothetical) rearrangement could give rise to a single chromosome containing both the HbA and HbS alleles. This new allele should sweep to fixation.
HbA + HbS
HbA
HbAS
~108 generations
Immune-system evolution timescale
• In principle, we could ask why our immune system is susceptible to malaria at all.
HbA + HbS
HbA
Ig-HbASIgMIgAIgGIgE
~1010+ generations
Genomic Imprinting
• Non-equivalence of maternal and paternal genomes
• Normal development in mammals requires both
Genomic Imprinting
• Epigenetic differences result in differences in expression
• DNA methylation– reversible
chemical modification of the DNA
Oogenesis Spermatogenesis
gene 1 gene 2 gene 1 gene 2
gene 1 gene 2
gene 1 gene 2
Reciprocal heterozygotes are non-equivalent
≠
Conflict over resources
Growth factor expression level
Incl
usiv
e fi
tnes
s
Fitness increases as more resources are acquired for self
Fitness decreases as cost to siblings becomes too great
Maternal optimum
Paternal optimum
Asymmetries in relatedness
Paternal expression
Mat
ern
al e
xpre
ssio
n
Maternal optimum
Paternal optimum
Growth-enhancing locusUnimprintedgene
Cis-actingmaternal modifiers
Cis-actingpaternal modifiers
Conflict over resources
Paternal expression
Mat
ern
al e
xpre
ssio
n
Paternal optimum
Maternal optimum
Growth-suppressing locusUnimprintedgene
Cis-actingmaternal modifiers
Cis-actingpaternal modifiers
Conflict over resources
Game-theoretic / stability analysis models of imprinting
• X - expression level
• Wm - matrilineal fitness
• Wp - patrilineal fitness
• U - individual fitness• V - fitness of other offspring• G - resource demand• C - cost of gene expression• 2p - fraction of mother’s
offspring with the same father
€
X = xm + xp
€
∂Wm
∂X=
∂U
∂G+
1
2
∂V
∂G
⎡
⎣ ⎢ ⎤
⎦ ⎥∂G
∂X−
∂C
∂X
€
∂Wp
∂X=
∂U
∂G+ p
∂V
∂G
⎡
⎣ ⎢ ⎤
⎦ ⎥∂G
∂X−
∂C
∂X
€
∂Wp
∂X−
∂Wm
∂X= p −
1
2
⎛
⎝ ⎜
⎞
⎠ ⎟∂V
∂G
∂G
∂X
€
∂Wp
∂X>
∂W
∂X>
∂Wm
∂X
€
∂V
∂G< 0,
∂G
∂X> 0 →
€
unimodality → ˆ X p > ˆ X m
Growth enhancer:
Population-genetic models• Two sibs, paternal imprinting
• A - unimprinted allele• a - imprintable allele
• a = A when maternally inherited
• a -> (a) when paternally inherited
• AA = aA• a(a) = A(a)
• Fitness of unimprinted sibs: 1– e.g., AA, AA
• Fitness if both imprinted: 1+u– e.g., a(a), A(a)
• If only one is imprinted:– e.g., AA & A(a)
– Imprinted fitness: 1-s for A(a) – Unimprinted fitness: 1+t for AA
Population-genetic models
• Parameters: allele frequencies, fitnesses, frequency of multiple paternity
– Spencer, Feldman, and Clark 1998 Genetics
Population-genetic models• Two sibs, paternal imprinting
• A - unimprinted allele• a - imprintable allele
• a = A when maternally inherited
• a -> (a) when paternally inherited
• AA = aA• a(a) = A(a)
• Fitness of unimprinted sibs: 1– e.g., AA, AA
• Fitness if both imprinted: 1+u– e.g., a(a), A(a)
• If only one is imprinted:– e.g., AA & A(a)
– Imprinted fitness: 1-s for A(a) – Unimprinted fitness: 1+t for AA
• Monandrous females:– a invades A if u > s– a stable if u > t/2
• Polyandrous females:– a invades A if s < 0– a stable if u > t/2
Predictions and contradictions• Game-theoretic
• Imprinting requires multiple paternity (p < 1/2)
• Allele favoring lower expression will be completely silenced– maternal silencing of
growth enhancers– paternal silencing of growth
suppressors
• Population-genetic
• Particular combinations of s, t, and u can produce stable polymorphisms
• Multiple paternity is not required
• Maternal silencing for growth enhancers is more likely, but paternal silencing can occur
Paternal expression
Mat
ern
al e
xpre
ssio
n
Maternal optimum
Paternal optimum
Growth-enhancing locusUnimprintedgene
Cis-actingmaternal modifiers
Cis-actingpaternal modifiers
Paternally silenced growth enhancer
Reduced paternal expression would be favored from these points
Key assumption• Game-theoretic models assume that the unimprinted
expression level is at its optimum before the introduction of an imprinted allele
• Is this assumption a good one?
• Gene expression array analyses of population-level variation reveal a high level of variation
• This implies a good opportunity for selection to find the optimum
Separation of timescales in the evolution of imprinting
Unimprinted alleles are restricted to a subspace in the fitness landscape
Imprinting opens up a new dimension in strategy space
If mutations that quantitatively change gene expression are much more common than those that give rise to imprinting, imprinting will always arise in the context of an optimized expression level
Take-home message• Choice of a particular modeling framework implies
certain assumptions that can affect your interpretation of your results
• When smart people doing reasonable things disagree, there is probably something interesting going on