Research

Which factors determine the rate of the adaptive process? How does the adaptive architecture of quantitative traits look like? We derive approximations for basic properties like fixation probabilities and -times of beneficial alleles; and we analyse the distribution of allelic effects of adaptations under various model assumptions.

• Hermisson J. and Pennings P.S. (2005)
  Soft sweeps: Molecular population genetics of adaptation from standing genetic variation.
  Genetics 169: 235-2352.
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  This article analyses the fixation probability for alleles that segregate in a population in mutation-selection-drift balance and become beneficial after an environmental change and compares it to the fixation probability for single new mutations. Various demographic scenarios (bottlenecks) are considered. There is also a new analytical approximation for the fixation time of beneficial alleles.

In a series of papers, we use the so-called moving optimum model to investigate the process of adaptation under gradual environmental change:

• Kopp M. and Hermisson J. (2007)
  Adaptation of a quantitative trait to a moving optimum.
  Genetics 176: 715-719.
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  This article provides an initial analysis of the phenotypic effect sizes of adaptations that contribute to adaptation of a simple two-locus trait under stabilizing selection with a moving optimum. We identify key factors that determine whether adaptations with small or large effect are favored.

• Kopp M. and Hermisson J. (2009a)
  The genetics of phenotypic adaptation I: Fixation of beneficial mutations in the moving optimum model.
  Genetics: 182: 233-249.
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  This article extends the analysis of the previous paper by, first, providing an highly accurate approximation for the fixation time of a single beneficial allele under moving optimum selection and, second, by investigating the order of fixations in simulations of a full multilocus model. We find that the fastest time to fixation is for alleles with intermediate effect, for which fixation depends equally strong on genetic and environmental factors.

• Kopp M. and Hermisson J. (2009b)
  The genetics of phenotypic adaptation II: The distribution of adaptive substitutions in the moving optimum model.
  Genetics 183: 1453-1476.
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  Here, we use the moving optimum model to calculate the distribution of phenotypic effect sizes of fixations over a longer bout of adaptation. We show that the mean size of fixed mutations depens on a composite parameter that integrates over both ecological and genetic factors.

How many adaptive events have happened in the recent past of a population? And which are the adaptive genes? Taking advantage of data generated by new sequencing technologies, we design tests and methods to detect positive selection from genome-wide polymorphism data. The goal of this project is to describe the footprint of selection in biologically realistic - complex - scenarios (time-, space-, and frequency-dependent selection, recurrent mutation, standing genetic variation, adaptation at multiple loci, etc.).

We call it a soft selective sweep if a beneficial allele does not trace back to a common ancestor at the time when positive selection first started. This can either happen if adaptation occurs from standing genetic variation or if the beneficial allele is introduced repeatedly into the population by recurrent mutation or migration. The phenomenon is discussed in a series of three articles:

• Hermisson J. and Pennings P.S. (2005)
  Soft sweeps: Molecular population genetics of adaptation from standing genetic variation.
  Genetics 169: 235-2352.
  (add/hide details) (pdf)

  The first article discusses the consequences on the footprint of positive selection on linked neutral variation if adaptation occurs from standing genetic variation.

• Pennings P.S. and Hermisson J. (2006a)
  Soft sweeps II - Molecular population genetics of adaptation from recurrent mutation or migration.
  Mol. Biol. Evol. 23: 1076-1084.
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  Here we use coalescent theory to derive the probability that multiple independent origins of a beneficial allele are involved in its fixation and show that this is a realistic biological scenario.

• Pennings P.S. and Hermisson J. (2006b)
  Soft sweeps III - The signature of positive selection from recurrent mutation.
  PLoS Genetics: e186.
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  The article describes how the footprint of positive selection (site-frequency spectrum at linked neutral sites and LD pattern) is changed if beneficial mutation is recurrent. We find that statistical tests based on LD are much better suited to detect positive selection under these conditions.

Is speciation without spatial separation of the incipient species a plausible evolutionary scenario? We design and analyze genetically explicit models for the evolution of assortative mating under frequency-dependent disruptive selection.

• Pennings P.S., Kopp M., Meszena G., Dieckmann U. and Hermisson J. (2008).
  An analytically tractable model for competitive speciation.
  American Naturalist 171: E44-E71.
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  In this paper, we study whether assortative mating can evolve with respect to a trait that under frequency-dependent disruptive selection that is determined by one genetic locus with two alleles. This simplification allows for an exhaustive analytical treatment. Depending on the ecological and genetic parameters, we describe five evolutionary regimes, including evolution of complete reproductive isolation from random mating in small steps. We show how the results can be explained by the interplay of natural and sexual selection.

• Kopp M. and Hermisson J. (2008).
  Competitive speciation and costs of choosiness.
  Journal of Evolutionary Biology 21: 1005-1023.
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  In a follow-up to the previous paper, we investigate how the likelihood of speciation is affected by costs of female choosiness. We study different types of costs and conclude that speciation is still possible as long as costs are moderate or weak.

Speciation in allopatric (spatially separated) populations can easily occur by the accumulation of genetic "Dobzhansky-Muller" incompatibilities. Under which conditions is this still possible in populations that are not fully separated, but still exchange migrants? We are interested in the emergence and maintenance of genetic incompatibilities in structured populations.

Even genetically diverged populations or incipient species may still be linked by residual gene flow. We are particularly interested under which conditions adaptations can still cross an emerging species boundary. We also want to describe the genetic footprint of such trans-specific adaptation.

The identification of mechanisms that are responsible for the maintenance of genetic variation in natural population is a classical problem in population genetics. In epistatic systems, we need to distinguish expressed variation that is visible on the phenotypic level (i.e., the heritable part of the phenotypic variation) and hidden variation that is only expressed after an environmental or genetic distortion. We study these quantities in multilocus models of quantitative genetics.

• Hermisson J., Hansen T.F. and Wagner G.P. (2003).
  Epistasis in polygenic traits and the evolution of genetic architecture under stabilizing selection.
  American Naturalist 161:708-734.
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  This article studies the so-called multilinear model of epistasis. Analytical results show that epistasis generally reduces the level of genetic variation that is phenotypically expressed in mutation-selection balance.

• Alvarez-Castro J.-M., Kopp M. and Hermisson J. (2009).
  Effects of epistasis and the evolution of genetic architecture: exact results for a 2-locus model.
  Theoretical Population Biology 75: 109-122.
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  For a two-locus model with epistasis, we extend the results of the previous paper to include genetic drift. We present analytical results based on the "House of Gauss" and the "Stochastic House of Gauss" approximations. Individual-based computer simulations show that these new predictions perform considerably better than previous ones (based on the Gaussian or House of Cards approximation) for most parameter combinations.

• Hermisson J. and Wagner G.P. (2004).
  The Population Genetic Theory of Hidden Variation and Genetic Robustness.
  Genetics 16 8:2271-2284.
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  Featured in Nature Reviews Genetics Vol. 6 Feb 2005 (pdf)

  We show that epistatic systems generically harbor considerable amounts of hidden genetic variation that can lead to large increases in the phenotypically expressed genetic variation after either a genetic or environmental disturbance of the population. Mutational robustness or canalization (see below) is not needed to explain the release of genetic variation under these circumstances.

How does selection shape the genetic architecture of phenotypic traits and thus the boundary conditions for its own action? Are certain features of the genetic architecture like mutational robustness evolvable traits? And is evolvability itself an evolvable trait? These questions of second-order evolution have been heatedly debated in recent years.

• Hermisson J. and Wagner G.P. (2005).
  Evolution of phenotypic robustness.
  Book chapter appeared in: Robust Design: A Repertoire from Biology, Ecology, and Engineering, E. Jen (ed.), Oxford University Press, Oxford, pp 47-70.
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  A review to clarify the concepts of canalization and genetic robustness.

• de Visser J.A.G.M., Hermisson J., Wagner G.P. et. al. (2003).
  Perspective: evolution and detection of genetic robustness.
  Evolution 57:1959-1972.
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  This is a consensus paper that summarizes concepts, results, and research issues that have been identified at a workshop on phenotypic robustness at the Santa Fe Institute (organized by JH and GPW).

A series of papers investigates how the genetic architecture evolves under various selection regimes.

• Hermisson J., Hansen T.F. and Wagner, G.P. (2003).
  Epistasis in polygenic traits and the evolution of genetic architecture under stabilizing selection.
  American Naturalist 161:708-734.
  (add/hide details) (pdf)

• Alvarez-Castro J.-M., Kopp M. and Hermisson J. (2009).
  Effects of epistasis and the evolution of genetic architecture: exact results for a 2-locus model.
  Theoretical Population Biology 75: 109-122.
  (add/hide details) (pdf)

  The two above articles discuss the evolution of genetic architecture under stabilizing selection. It is shown that canalization (robustness) of a trait is not a target of selection and usually not maximized at an evolutionary equilibrium. Mutational robustness (i.e. small mutational effects) primarily evolves for loci with high mutation rates. We also stress the importance of evolutionary inertia and stochastic fluctuations for the evolution of genetic architecture.

• Carter A.J.R., Hermisson J., and Hansen T.F. (2005).
  The role of epistatic gene interactions in the response to selection and the evolution of evolvability.
  Theoretical Population Biology 68, 179-196.
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• Hansen T.F., Alvarez-Castro J.-M., Carter A.J.R., Hermisson J. and Wagner G.P. (2006).
  Evolution of genetic architecture under directional selection
  Evolution 60: 1523-1536.
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  The two previous articles treat the impact of directional selection on the genetic architecture. It is shown that the outcome crucially depends on the directionality of epistasis.

• Kopp M. and Hermisson J. (2006).
  The evolution of genetic architecture under frequency-dependent disruptive selection.
  Evolution 60: 1537-1550.
  (add/hide details) (pdf, online appendices)

  Here, we show that selection pressures on the genetic architecture can be much stronger under disruptive selection (at so-called evolutionary branching points) than under stabilizing selection. A genetic architecture of a trait results where most genetic variation is maintained at only few major loci.

• Hermisson J., Wagner H. and Baake M. (2001).
  Four-state quantum chain as a model for sequence evolution.
  Journal of Statistical Physics 102: 315-343.
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  We introduce a mapping of a four-letter sequence space model to a quantum chain model in physics and discuss error threshold phenomena in relation to physical phase transitions. Results on the equilibria and the evolutionary dynamics are presented.

• Hermisson J., Redner 0., Wagner H. and Baake E. (2002).
  Mutation-selection balance: ancestry, load, and maximum principle.
  Theoretical Population Biology 62: 9-46.
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  This article introduces concepts and tools based on ancestry to derive and analyze equilibrium properties of sequence space models with epistasis. In particular, we discuss how error threshold phenomena depend on the epistasis of the fitness landscape.

Is speciation without spatial separation of the incipient species a plausible evolutionary scenario? We design and analyze genetically explicit models for the evolution of assortative mating under frequency-dependent disruptive selection.

• Pennings P.S., Kopp M., Meszena G., Dieckmann U. and Hermisson J. (2008).
  An analytically tractable model for competitive speciation.
  American Naturalist 171: E44-E71.
  (add/hide details) (pdf)

  In this paper, we study whether assortative mating can evolve with respect to a trait that is under frequency-dependent disruptive selection and is determined by one genetic locus with two alleles. This simplification allows for an exhaustive analytical treatment. Depending on the ecological and genetic parameters, we describe five evolutionary regimes, including evolution of complete reproductive isolation from random mating in small steps. The results can be explained by the interplay of natural and sexual selection.

• Kopp M. and Hermisson J. (2008).
  Competitive speciation and costs of choosiness.
  Journal of Evolutionary Biology 21: 1005-1023.
  (add/hide details) (pdf)

  In a follow-up to the previous paper, we investigate how the likelihood of speciation is affected by costs of female choosiness. We study different types of costs and conclude that speciation is still possible as long as costs are moderate or weak.

A key-phenomenon from the adaptive dynamics literature is 'evolutionary branching'. This term describes the adaptive split of a single (clonal) lineage into two separate lineages through a series of mutations of small effect. It occurs when disruptive selection is generated by negatively frequency-dependent interactions. The recognition of the ubiquity of evolutionary branching in mathematical models has been very stimulating in sympatric speciation research. However, recently it became clear that sympatric speciation is but one possible response to negative frequency-dependent selection.

• Rueffler C., Van Dooren T.J.M., Leimar O. and Abrams P.A. (2006).
  Disruptive selection and then what?
  Trends in Ecology and Evolution 21: 238-245.
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  In this review article we present an overview of potential evolutionary consequences to disruptive selection. It forms the basis of one or our research focuses: Which path should we expect evolution to take when alternative evolutionary responses exist to a given selection pressure?

• Kopp M. and Hermisson J. (2006).
  The evolution of genetic architecture under frequency-dependent disruptive selection.
  Evolution 60: 1537-1550.
  (add/hide details) (pdf, online appendices)

  In this paper, we use modifier theory to study the evolution of phenotypic effect sizes of loci contributing to a trait under frequency-dependent disruptive selection. We find that the phenotype distribution of the population evolves to match the available ecological niches. Typically, this is achieved by the evolution of a higly asymmetric genetic architecture where most of the genetic variation is concentrated on a small number of major loci.

In the presence of several resources, when should we expect consumers to be generalists that are relatively efficient foragers on all resources and when should we expect consumers that are specialized on one resource on the expense of being inefficient on other resources? When consumers have a noticeable effect on the density of their prey, frequency dependence arises naturally making adaptive dynamics an attractive modelling framework.

• Rueffler C., Metz J.A.J. and Van Dooren T.J.M. (2006).
  The evolution of resource specialization through frequency-dependent and frequency-independent mechanims.
  American Naturalist 167: 81-93.
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  In this article we show that whether interactions are frequency-dependent or not depends on the foraging traits considered evolvable. As a result, different traits involved in the foraging process have qualitatively different evolutionary dynamics.

• Rueffler C., Metz, J.A.J. and Van Dooren T.J.M. (2007).
  The interplay between behavior and morphology in the evolutionary dynamics of resource specialization.
  American Naturalist 169: E34-E52.
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  In the previous article it was assumed that consumers attack all prey upon encounter, irrespective of the consumers phenotype. In this article we relax this assumption by introducing a behavioural component: consumers decide upon encounter with a resource item whether or not to attack it in a way that maximizes their overall resource uptake. This added feature significantly facilitates the evolution of polymorphism in the consumer population.

• Abrams, P.A., Rueffler C. and Kim, G. (2008).
  Determinants of the strength of disruptive and/or divergent selection arising from resource competition.
  Evolution 62: 1571-1586.
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  In this article we re-investigate a classical model of intraspecific competition for resources and show that, in contradiction with the traditional view, the strength of disruptive selection at a branching point can be a unimodal function of the intensity of competition. This new finding emerges when one includes the possibility that the consumer population can drive heavily utilized resources to extinction.

In heterogeneous environments, an alternative to genetic polymorphisms is the evolution of phenotypic plasticity. For example, phenotypic plasticity plays a large role in predator-prey systems, both ecologically and evolutionarily. Plastic responses of prey to predators are known as inducible defenses. Similarly, plastic responses of predators to prey can be called inducible offenses.

• Kopp M. and Tollrian R. (2003).
  Trophic size polyphenism in Lembadion bullinum: costs and benefits of an inducible offense.
  Ecology 84: 641-651.
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  This empirical study shows that the protozoan predator Lembadion bullinum plastically adjusts its cell size to the size of the available prey.

• Kopp M. and Tollrian R. (2003).
  Reciprocal phenotypic plasticity in a predator-prey system:
  inducible offences against inducible defences?
  Ecology Letters 6: 742-748.
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  Here, we describe the one of the first examples of reciprocal phentypic plasticity. The ciliate Euplotes octocarinatus responds to the presence of its predator, Lembadion bullinum by developing an inducible defense. Lembadion reacts to this defense by increasing its mean cell size, that is, by an inducible offense. We speculate whether this reciprocal plasticity might be the result of (diffuse) coevolution.

• Kopp M. and Gabriel W. (2006).
  The effect of an inducible defense in the Nicholson-Bailey model.
  Theoretical Population Biology 70: 43-55.
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  In this paper we study how inducible prey defenses affect predator-prey population dynamics. Typically, inducible defenses increase stability and persistence, but there are exceptions to this rule.

Ecological interactions between species can lead to indirect frequency-dependent selection (for example, if predators adapt to exploiting the most common type of prey). Possible results are coevolutionary arms races or Red Queen dynamics.

• Kopp M. and Gavrilets S. (2006).
  Multilocus genetics and the coevolution of quantitative traits.
  Evolution 60: 1321-1336.
  (add/hide details) (pdf , online appendices 1, 2, 3)

  Predator-prey coevolution can lead to persistent coevolutionary cycles ('Red Queen dynamics'). Here, we investigate how these dynamics are influenced by the genetic architecture of the traits under reciprocal selection. We find that, with a large number of loci contributing, the dynacmis tend to be destabilized and the genetic variances of prey and predator are highly different.

• Kopp M. and Tollrian R. (2003).
  Reciprocal phenotypic plasticity in a predator-prey system:
  inducible offences against inducible defences?
  Ecology Letters 6: 742-748.
  (add/hide details) (pdf)

  Here, we describe the one of the first examples of reciprocal phentypic plasticity. The ciliate Euplotes octocarinatus responds to the presence of its predator, Lembadion bullinum by developing an inducible defense. Lembadion reacts to this defense by increasing its mean cell size, that is, by an inducible offense. We speculate whether this reciprocal plasticity might be the result of (diffuse) coevolution.

Adaptive dynamics is a relatively new toolbox to model the evolution of phenotypic traits under complex ecological scenarios (see section on methods).

• Rueffler C., Metz J.A.J. and Van Dooren T.J.M. (2004). Adaptive walks on changing landscapes: Levins' approach extended.
  Theoretical Population Biology 65: 165-178.
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  The article extends Levins' classical and influential geometrical approach to determine the optimal phenotype when two evolving traits are coupled by a trade-off. In our article we relax Levins' assumption that frequency dependence is absent.