Fitness landscapes and Fitness landscapes and coevolution: from physics to coevolution: from physics to

biologybiologyFrances TaschukFrances Taschuk

March 24, 2008March 24, 2008

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Fitness landscapesFitness landscapes

• Peaks represent local fitness maxima

• Here: fitness relates to feeding efficiency of crossbills on different conifers

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Kauffman and JohnsenKauffman and Johnsen

• Rugged multipeaked fitness landscapes• NK model: N=number of traits

K=interacting traits within species

C=interacting traits in other species

• In trying to maximize their own fitness, coevolutionary species change one another’s fitness landscapes

Tuning Tuning

• Parameters can be adjusted so that coevolving species reach steady state (“analogue of Nash equilibrium”)

• More rugged landscapes (high K/C ratio) take less time to reach equilibrium because more local maxima

CoevolutionCoevolutionPresence of more interconnected species in model makes it take longer to reach equilibrium

AvalanchesAvalanches

• When optimized for maximum sustained fitness, model ecosystem is subject to changes that propagate throughout

When K is close to optimal value of 10, log-log plot shows straight line, suggesting a power law relationship

Adaptive surfaces in biologyAdaptive surfaces in biology

• Idea of adaptive landscape has been around in biology since 1932

• Originally used to describe genetic fine-tuning, but has also been used to visualize larger-scale phenotypic evolution

• Little information is available about people trying to fit real data to landscapes

• '...why, if species have descended from other species by insensibly fine gradations, do we not everywhere see innumerable transitional forms?' (Darwin)

• Looks at molecular function to address question of evolutionary intermediates

Poelwijk et al in Poelwijk et al in Nature Nature (2007)(2007)

1. Modeling adaptation of bacterial β-lactamase to the antibiotic cefotaxime

– Know resistance phenotype, so can reconstruct intermediates (5 mutations needed)

– 5! different possible trajectories– Fitness result of a given mutation depends on order

– “balance of structural and functional benefits

•b, c, d unlikely to happen

•Found18 paths of type a

2. Evolution of isopropylmalate dehydrogenase– Studied mutational intermediates affecting binding

of cofactors (NADP less optimal than NAD)– In vitro measurements revealed single-peaked

landscape; mutations not order-dependent– In vivo measurements found a valley on fitness

landscape, making some routes from NADP to NAD inaccessible

NADP NAD

3. Evolution of regulatory interactions- In hormone/receptor model, function could

continue while receptors diverged because there was a ligand that could activate both

- In the case of lac, new interaction offset deteriorations - robust network allows evolvability

Decaestecker et al in Decaestecker et al in NatureNature (2007) (2007)

• Observation of “Red Queen” dynamics between Daphnia and Pasteuria ramosa (parasite)

• Reasons to expect coevolution:– Genetic variation in Daphnia resistance– Genotype-specific interactions– Daphnia population genetics change during

parasite epidemics

• Collected dormant Daphnia eggs and parasite samples from different depths— “snapshot in the arms race”

• Exposed Daphnia to parasites from previous, contemporary, and subsequent growing seasons

MethodsMethods

Contemporary parasites are more infectious

ReferencesReferences

Kauffman and Johnsen. 1991. Coevolution to the edge of chaos: coupled fitness landscapes, poised states, and coevolutionary avalanches. Journal of Theoretical Biology, 149.

Poelwijk et al. 2007. Empirical fitness landscapes reveal accessible evolutionary paths. Nature, vol. 445.

Decaestecker et al. 2007. Host-parasite “Red Queen” dynamics archived in pond sediment. Nature, vol 450.

Also:Benkman. 2003. Divergent selection drives the adaptive radiation of crossbills.

Evolution.A simple model of the evolution of simple models of evolutionhttp://daphnia.cgb.indiana.edu/images/Daphnia_DGC.png