Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model

Much of the current theory of adaptation is based on Gillespie's mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyse a simple fitness landscape model with tunable ruggedness based on the Rough Mount Fuji (RMF) model originally introduced by Aita et al. [Biopolymers 54:64-79 (2000)] in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulae for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly-fit first step backgound in a recent evolution experiment with a microvirid bacteriophage [Miller et al., Genetics 187:185-202 (2011)].Comment: 43 pages, 12 figures; revised version with new results on the number of fitness maxim

Greedy adaptive walks on a correlated fitness landscape

We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length $L$. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached. The landscape is of the rough mount Fuji type, which means that the fitness value assigned to a sequence is the sum of a random and a deterministic component. The random components are independent and identically distributed random variables, and the deterministic component varies linearly with the distance to a reference sequence. The deterministic fitness gradient $c$ is a parameter that interpolates between the limits of an uncorrelated random landscape ($c = 0$) and an effectively additive landscape ($c \to \infty$). When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence. Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for $L \to \infty$, different from its values for $c=0$ and $c = \infty$, if $c$ is scaled with $L$ in an appropriate combination.Comment: minor change

Exact Results for Amplitude Spectra of Fitness Landscapes

Starting from fitness correlation functions, we calculate exact expressions for the amplitude spectra of fitness landscapes as defined by P.F. Stadler [J. Math. Chem. 20, 1 (1996)] for common landscape models, including Kauffman's NK-model, rough Mount Fuji landscapes and general linear superpositions of such landscapes. We further show that correlations decaying exponentially with the Hamming distance yield exponentially decaying spectra similar to those reported recently for a model of molecular signal transduction. Finally, we compare our results for the model systems to the spectra of various experimentally measured fitness landscapes. We claim that our analytical results should be helpful when trying to interpret empirical data and guide the search for improved fitness landscape models.Comment: 13 pages, 5 figures; revised and final versio

Multidimensional epistasis and the transitory advantage of sex

Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional fitness landscapes in the presence of sign epistasis. Here we present a comparative numerical study of sexual and asexual evolutionary dynamics of haploids on tunably rugged model landscapes under strong selection, paying special attention to the temporal development of the evolutionary advantage of recombination and the link between population diversity and the rate of adaptation. We show that the adaptive advantage of recombination on static rugged landscapes is strictly transitory. At early times, an advantage of recombination arises through the possibility to combine individually occurring beneficial mutations, but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks. These findings are explained by means of well established results for a setup with only two loci. In accordance with the Red Queen hypothesis the transitory advantage can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.Comment: 34 pages, 9 figures and 8 supplementary figures; revised and final versio

The large-scale footprint in small-scale Rayleigh-B\'enard turbulence

Turbulent convection systems are known to give rise to prominent large scale circulation. At the same time, the `background' (or `small-scale') turbulence is also highly relevant and e.g. carries the majority of the heat transport in the bulk of the flow. Here, we investigate how the small-scale turbulence is interlinked with the large-scale flow organization of Rayleigh-B\'enard convection. Our results are based on a numerical simulation at Rayleigh number $Ra = 10^8$ in a large aspect ratio ($\Gamma=32$) cell to ensure a distinct scale separation. We extract local magnitudes and wavenumbers of small scale turbulence and find significant correlation of large scale variations in these quantities with the large-scale signal. Most notably, we find stronger temperature fluctuations and increased small scale transport (on the order of $10\%$ of the global Nusselt number $Nu$) in plume impacting regions and opposite trends in the plume emitting counterparts. This concerns wall distances up to $2\delta_\theta$ (thermal boundary layer thickness). Local wavenumbers are generally found to be higher on the plume emitting side compared to the impacting one. A second independent approach by means of conditional averages confirmed these findings and yields additional insight into the large-scale variation of small-scale properties. Our results have implications for modelling small-scale turbulence.Comment: 19 pages, 9 figures, accepted at the Journal of Fluid Mechanic

Geräuschbeurteilung von Lenkhelfpumpen anhand der Druckpulsation

Bei hydraulischen Systemen werden durch die zeitlich ungleichmäßige Förderung von hydrostatischen Verdrängerpurnpen im Druckmedium Wechseldrücke erzeugt. Die daraus resultierenden Wechselkräfte machen sich sowohl im Hydrauliksystem selbst, als auch in den angrenzenden Elementen, als störende Geräusche bemerkbar. Der Bericht beschreibt eine Möglichkeit der Pulsationsbewertung, so daß laute Pumpen bereits direkt nach der Montage erkannt werden und zur Nacharbeit weitergeleitet werden können

Translation and psychometric properties of the German version of the University of the West of England Interprofessional Questionnaire (UWE-IP)

© 2017 Taylor & Francis. The implementation of a bachelor degree in Interprofessional Health Care at the University of Heidelberg, Germany, has fostered the need to evaluate the impact of this innovative programme. The University of the West of England Interprofessional Questionnaire (UWE-IP) was developed for longitudinal evaluation of an interprofessional curriculum. The UWE-IP consists of 35 items in four scales: “Communication and Teamwork Scale,” “Interprofessional Learning Scale,” “Interprofessional Interaction Scale,” and “Interprofessional Relationships Scale.” The UWE-IP was translated to German according to international guidelines. Psychometrics were assessed: reliability of the four scales was tested with Cronbach‘s alpha and confirmatory factor analysis was performed to examine the underlying factor structure. The sample consisted of 326 datasets. Reliability for the scales was between 0.75 and 0.90. The underlying factor structure showed a good fit. We conclude that the German UWE-IP shows good psychometrics and recommend its use for evaluation of interprofessional learning activities. These results add to the body of knowledge on evaluation instruments in interprofessional education