Research

The research theme at MaBS is the mathematical biology of evolution. Evolution is the unifying theory of the biological sciences, and our aim is to design advanced mathematical methods and models that account for the biological complexity involved in most evolutionary processes. Complexity arises on all levels of biological organization: molecular, organismal, and ecological. The key issues of evolutionary research, such as adaptation and speciation, are usually addressed in special sub-disciplines for each of these levels, i.e. molecular population genetics, quantitative genetics, and evolutionary ecology. We work on all three fields with the special goal to create an integrative approach, with a combination of models, concepts, and methods.

Topics

Population Genetics of Adaptation

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Tempo and mode of the adaptive process
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. (pdf)
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. (pdf)
- 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. (pdf)
- 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. (pdf)
Molecular signature of selection
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. (pdf)
- 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. (pdf)
- Pennings P.S. and Hermisson J. (2006b)
  Soft sweeps III - The signature of positive selection from recurrent mutation.
  PLoS Genetics: e186. (pdf)

Population Genetics of Speciation

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Sympatric speciation
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. (pdf)
- Kopp M. and Hermisson J. (2008).
  Competitive speciation and costs of choosiness.
  Journal of Evolutionary Biology 21: 1005-1023. (pdf)
Parapatric speciation

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.
Interspecific gene flow

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.

Evolutionary consequences of gene interactions (epistasis)

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Maintenance of expressed and hidden genetic variation
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. (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. (pdf)
- Hermisson J. and Wagner G.P. (2004).
  The Population Genetic Theory of Hidden Variation and Genetic Robustness.
  Genetics 16 8:2271-2284. (pdf)
  Featured in Nature Reviews Genetics Vol. 6 Feb 2005 (pdf)
Evolution of genetic architecture, canalization & mutational robustness, evolution of evolvability
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. (pdf)
- 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. (pdf)
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. (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. (pdf)
- 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. (pdf)
- 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. (pdf)
- Kopp M. and Hermisson J. (2006).
  The evolution of genetic architecture under frequency-dependent disruptive selection.
  Evolution 60: 1537-1550. (pdf)
Sequence space models and error thresholds
- 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. (pdf)
- Hermisson J., Redner 0., Wagner H. and Baake E. (2002).
  Mutation-selection balance: ancestry, load, and maximum principle.
  Theoretical Population Biology 62: 9-46. (pdf)

Frequency-dependent selection and interspecific interactions

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Sympatric speciation
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. (pdf)
- Kopp M. and Hermisson J. (2008).
  Competitive speciation and costs of choosiness.
  Journal of Evolutionary Biology 21: 1005-1023. (pdf)
Intraspecific phenotypic variation
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. (pdf)
- Kopp M. and Hermisson J. (2006).
  The evolution of genetic architecture under frequency-dependent disruptive selection.
  Evolution 60: 1537-1550. (pdf)
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. (pdf)
- 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. (pdf)
- 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. (pdf upon request)
Phenotypic plasticity
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. (pdf)
- Kopp M. and Tollrian R. (2003).
  Reciprocal phenotypic plasticity in a predator-prey system:
  inducible offences against inducible defences?
  Ecology Letters 6: 742-748. (pdf)
- Kopp M. and Gabriel W. (2006).
  The effect of an inducible defense in the Nicholson-Bailey model.
  Theoretical Population Biology 70: 43-55. (pdf)
Coevolution
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. (pdf)
- Kopp M. and Tollrian R. (2003).
  Reciprocal phenotypic plasticity in a predator-prey system:
  inducible offences against inducible defences?
  Ecology Letters 6: 742-748. (pdf)
Adaptive dynamics methodology
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. (pdf)

Methods

Our mathematical methods are quite diverse and follow the needs of the biological problem that is addressed. Often techniques from various mathematical fields are combined.

Stochastics

In molecular population genetics, evolution is modelled as a stochastic process. We use time-forward approaches based on branching processes (e.g. Hermisson et al. 2002) and diffusions (e.g. Hermisson and Pennings 2005) and time-backward approaches, which use the coalescent (e.g. Hermisson and Pennings 2006a ,b).

Differential equations

The deterministic models in quantitative genetics and evolutionary ecology are formalized as systems of differential and difference equations. We use various techniques from these fields to analyse the equilibrium structure (existence, stability, domains of attraction) of biological models (e.g. Hermisson et al. 2003).

Adaptive dynamics

Adaptive dynamics is an increasingly popular toolbox to model phenotypic evolution under realistic ecololgical scenarios (Metz et al. 1996; Dieckmann and Law 1996: J. Math. Biol. 34: 579-612; Geritz et al. 1998: Evol. Ecol. 12: 35-57). It combines elements from evolutionary game theory, the theories of dynamical systems and stochastic processes. For an exhaustive literature survey on adaptive dynamics see here.

Statistical methods

Statistical tests and methods link empirical data to patterns that are predicted from theoretical models. In the context of molecular data, we have used statistical analysis (Stoletzki et al. 2005). and have developed tests (Pennings and Hermisson 2006b).

Computer simulations

In complex biological situations, computer simulations are always needed to complement and validate the analytical analysis. Our simulation tools use various different techniques, including time forward ('Wright-Fisher') simulations using multinomial sampling (e.g. Kopp and Hermisson 2007), individual based simulations (e.g. Carter et al. 2005), and time-backward simulations using the coalescent (Pennings and Hermisson 2006b).