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

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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

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Maternal optimum

Paternal optimum

Growth-enhancing locusUnimprintedgene

Cis-actingmaternal modifiers

Cis-actingpaternal modifiers

Conflict over resources

Paternal expression

Mat

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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

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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