Mathematics and
BioSciences Group

University of Vienna

Faculty of Mathematics
Oskar-Morgenstern-Platz 1
A-1090 Vienna, Austria

Max F. Perutz Laboratories
Dr. Bohrgasse 9
A-1030 Vienna, Austria


    Joachim Hermisson
    Sylvain Mousset
    Jitka Polechová
    Meike Wittmann



    Software (msms)



Press & Public




Claus Rueffler - Senior Postdoc

Home    Publications    CV    Teaching     

Faculty of Mathematics
Oskar-Morgenstern-Platz 1, Room 9.138
A-1090 Vienna
T: +43 (0) 1 4277 - 50776

With October 2013 I have moved to Uppsala University, Sweden. My new homepage can be found here.

General Interests

I am a theoretical biologist interested in ecology and evolution. More specifically, I am interested in the evolution and maintenance of phenotypic diversity and the responsible processes at the level of genes, genotype-phenotype maps, species and communities. So far, I have worked mostly on models that were designed to answer rather general questions and that were not geared towards specific systems. My main tools are mathematical models based on the "Adaptive dynamics" approach.

Current projects

Mechanisms of Phenotype Determination

A current focus is the project "Multidimensional adaptive dynamics and the evolution of phenotype determination" (link), which is financed by the WWTF. A description of the project in the online newspaper of the University of Vienna can be found here (in german). Andreas Baumann, Helene Weigang and Hannes Svardal were part of the project.

The project originates from the observation that many heterogeneous environments favor different phenotypes in different places or at different times. Phenotypic diversity can either result from genetic diversity or from a single genotype capable of producing different phenotypes. A single genotype might produce different phenotypes, for example in response to an environmental cue (phenotypic plasticity) or through a randomisation mechanism (bet-hedging). A large part of the existing theoretical literature attempts to give conditions under which one of these specific mechanisms is favored over a phenotypically monomorphic population. Recently, it has become clear that in many circumstances different evolutionary responses are favored simultaneously (Rueffler et al. 2006, TREE 21). The aim of this project is twofold. First, we want to determine how selection pressures arising from various ecological interactions determine which of the possible phenotype determining mechanisms might evolve first and possibly pre-empt any selection driving one of the alternative responses. Second, the outcome of the evolutionary process does not only depend on the selection pressure exerted by the environment but also on the available phenotypic variation on which selection can act upon. Hence, we want to explore how constraints on the level of the genetic architecture and the developmental process affect the evolutionary dynamics of phenotype determining mechanisms.

The Evolution of Division of Labor

Consider an organism which contains some kind of repeated module such as cells or iterated body segments. Assume furthermore that these modules were ancestrally identical and involved in more than one biological task. When do you expect that division of labor evolves such that different modules become specialized for alternative tasks and when do you expect that the modules stay undifferentiated and all keep executing the same set of tasks? This question has been addressed repeatedly in the context of specific systems such as germ-soma differentiation or caste formation in eusocial insects. However, there should also be general, non-system specific conditions that have to be fulfilled for functional differentiation between modules to be favored by natural selection.


One way to look at this problem is by means of fitness landscapes. Assume that the phenotype of each module can be described by a one-dimensional quantitative trait. As long as both modules are characterized by the same trait value functional differentiation between modules has not taken place (black curve). Functional differentiation is favored by natural selection if a combination of trait values that is a maximum in the constrained trait space (black dots) is a saddle point in the extended trait space (Figure a). Functional differentiation is not favored if such a point is a fitness maximum in the extended trait space (Figure b). Together with Günter Wagner and Joachim Hermisson I identified general system independent conditions leading to such saddle points and therefore to the evolution of function differentiation (Rueffler et al. 2012, PNAS). As part of her Diploma thesis Helene Weigang looked at this problem in a frequency-dependent context (Rueffler and Weigang, in prep.).

Past projects

The evolutionary ecology of resource specialization


In the presence of different resources, when should we expect a generalist phenotype and when specialized phenotypes? To answer this question I studied a model of one evolving consumer feeding on two resources. Based on this model, three different factors determine the evolutionary dynamics of resource specialization. The first factor is the quality of the trade-off that prevents consumers from being specialized for different resources simultaneously. In accordance with many previous models it appeared that strong trade-offs favor specialists whereas weak trade-offs favor generalists. Second, the final stop of evolution also depends on the foraging trait that is considered to evolve. It appears that some traits are under frequency-dependent selection while others are not (Rueffler et al. 2006, Am. Nat. 167). In the first case, different specialized consumers can coexist, and these types can emerge at an evolutionary branching point, a scenario not possible in the second case. The third decisive factor is whether consumers a capable of actively choosing which prey type to attack. In this case, both the parameter space allowing for coexistence and the likelihood for such a polymorphism to emerge through a series of mutations of small effect is greatly increased (Rueffler et al. 2007, Am. Nat. 169). In the future, it will be interesting to incorporate diet choice behavior into a wider range of models for the evolution of resource specialization.

Adaptive dynamics theory


Darwinian evolution is the process by which organisms adapt to their ever-changing environment. In order to understand the principles that govern evolutionary change, mathematical models play a vital role. A relatively new and increasingly popular framework for the study of long-term phenotypic evolution is 'adaptive dynamics'. Mathematically, AD is related to dynamical systems theory and evolutionary game theory. Biologically, AD is especially suited to describe long-term evolution under frequency-dependent selection. A defining feature of adaptive dynamics is that the fitness of a specific phenotype is derived from an explicit ecological scenario accounting for various interactions between the evolving population under study and its (possibly coevolving) biotic and abiotic environment. As part of my PhD thesis, I embedded Levins' classical graphical fitness set approach for the study of evolutionary change of two correlated traits into the adaptive dynamics framework. Levins' theory was designed to study evolution on fixed fitness landscapes, whereas most realistic ecological scenarios result in fitness landscapes that change as the population evolves. It appeared that the frequency-independent theory can be extended in a rather straightforward way to incorporate scenarios where selection is frequency-dependent, turning Levins_ idea into useful tool in adaptive dynamics modeling (Rueffler et al. 2004, TPB 65).

The evolution of plant breeding systems


My interest in the evolution of plant breeding systems stems from my master's thesis, for which I conducted empirical research on the maintenance of gynodioecy in the Rock pink Dianthus sylvestris. In this species (and many others), plants with pistillate (female) flowers and with perfect (hermaphroditic) flowers coexist in many populations. This breeding system is believed to represent a transitional state in the evolution from hermaphroditic species to dioecious species. In principle, individuals with only pistillate flowers have a disadvantage compared to individuals with perfect flowers, because they pass on their genes only via seeds and not via both pollen and seeds. Hence, an explanation is needed for the maintenance of female individuals. In the population of D. sylvestris that I investigated it appeared that pistillate flowers suffer less from seed predation by various insect species than perfect flowers, resulting in a higher per flower seed set in pistillate flowers than in perfect flowers (Collin et al. 2002, Oecologia 131).