I'm Benjamin Wölfl.

The standard model in molecular population genetics assumes that selection on a phenotypic trait leads to simple directional selection on its genetic basis. Under this traditional sweep model one expects hard or soft selective sweeps as a footprint of selection in DNA (deoxyribonucleic acid) polymorphism data.
In contrast, polygenic adaptation refers to a scenario where phenotypic adaptation results from a collective change in the allele frequencies at many underlying genes (Boyle et al., 2017). If selection on single loci is constrained by epistatic interaction with its genetic background, allele frequency trajectories differ strongly from the sweep model expectations. As a result, different footprints are expected when genomic material is sampled and sequenced. Empirical evidence indicates that polygenic adaptation occurs frequently in nature.
Most literature on polygenic adaptation assumes a deterministic model for allele frequency changes (Chevin and Hospital, 2008; Jain and Stephan, 2017). However, recent results (Hermisson and Pennings, 2017; Höllinger et al., 2019) show that genetic drift is crucial for the pattern. In Höllinger et al. (2019), an analytical approach based on Yule branching processes was introduced to address this problem. This stochastic model incorporates genetic drift. In this funding period, we will apply this approach to various selection scenarios on quantitative traits, including spatially and temporally heterogeneous selection (“moving optimum”, see Jones et al. 2014, Matuszewski et al. 2015) and truncation selection. Based on these results, we will develop statistical frameworks to detect footprints of polygenic adaptation from replicated evolution experiments.
Methodologically, the research program will encompass three elements: (1) analytical modeling, (2) computer simulations and (3) linking theory and empirics, i.e., replicated evolution experiments.

References:
[1] Wölfl B. (2019) Footprints of polygenic adapation of a quantitative trait under stabilizing selection. MSc thesis, University of Amsterdam and Vrije Universiteit Amsterdam, Netherlands.
[2] Wölfl, Benjamin; Hermisson, Joachim; Höllinger, Ilse (2019): Footprints of polygenic adaptation of a quantitative trait under stabilizing selection. figshare. Poster.
[3] Höllinger I. (2018) Mathematical Models of Speciation and Polygenic Adaptation. PhD thesis, University of Vienna, Austria
[4] Boyle EA, Li YI and Pritchard JK. An expanded view of complex traits: From polygenic to omnigenic. Cell. (2017) doi: 10.1016/j.cell.2017.05.038
[5] Höllinger I, Pennings PS, Hermisson J (2019) Polygenic adaptation: From sweeps to subtle frequency shifts. PLOS Genetics 15(3): e1008035. https://doi.org/10.1371/journal.pgen.1008035
[6] Hermisson J and Pennings PS. Soft sweeps and beyond: understanding the patterns and probabilities of selection footprints under rapid adaptation. Methods Ecol. Evol. 8(6), 700–716. (2017) doi: 10.1111/2041-210X.12808
[7] Matuszewski S, Hermisson J and Kopp M. Catch me if you can: Adaptation from standing genetic variation to a moving phenotypic optimum. Genetics 200(4), 1255–1274. (2015) doi: 10.1534/genetics.115.178574
[8] Jones AG, Bürger R and Arnold SJ. Epistasis and natural selection shape the mutational architecture of complex traits. Nat. Commun. 5, 3709. (2014) doi: 10.1038/ncomms4709
[9] Barghi N, Tobler R, Nolte V, Jakšić AM, Mallard F, Otte KA, Dolezal M, Taus T, Kofler R, Schlötterer C (2019) Genetic redundancy fuels polygenic adaptation in Drosophila. PLOS Biology 17(2): e3000128. https://doi.org/10.1371/journal.pbio.3000128
[10] Chevin LM and Hospital F. Selective sweep at a quantitative trait locus in the presence of background genetic variation. Genetics 180(3), 1645–1660. (2008) doi: 10.1534/genetics.108.093351
[11] Jain K and Stephan W. Rapid adaptation of a polygenic trait after a sudden environmental shift. Genetics 206(1), 389–406. (2017) doi: 10.1534/genetics.116.196972
[12] Harold P. de Vladar and Nick Barton. Stability and Response of Polygenic Traits to Stabilizing Selection and Mutation. Genetics, 197(2):749–767, 2014. ISSN 0016-6731. doi: 10.1534/genetics. 113.159111. URL http://www.genetics.org/content/197/2/749.
[13] K. Jain and W. Stephan. Response of polygenic traits under stabilizing selection and mutation when loci have unequal effects. G3: Genes, Genomes, Genetics, 6(5):1065–1074, 2015.
[14] B.C. Haller and P.W. Messer. SLiM 3: Forward genetic simulations beyond the Wright-Fisher model. Molecular Biology and Evolution, 36(3):632—-637, 2019.

Imagine Gregor Mendel's original experiment: He crossed pea plants and translated the observations into the genetic inheritance patterns which we know today as Mendel's laws. These rules form the basis of genetics and explain how genetic variation can indeed be conserved over time. Due to basic biology education this seems obvious, however back in the days a controversial idea called blending theory was still around. Mendel was lucky to have chosen two traits the contributing loci of which are residing different chromosomes and therefore inferred the law of independent assortment. If however the two loci were on the same chromosome the probability of their common inheritance is somewhat more difficult to derive - however, it grows with genetic distance and stays below a half. It is such rules that govern the biological processes which we want to understand better.
Traditionally genetics and especially the theoretical part of it was pre-occupied with simple traits that have a binary phenotype - as in Mendel's case. In contrast we are studying how complex trait that have a continuos phenotype - think about body height or cancer risk. One can see that this adds complexity because now we need to have an idea of how many different loci add up in order to give rise to a complex trait. Secondly, one has to think about the way in which many different loci are being inherited.
In order to find properties of how such complex traits evolve we utilize mathematical and computational tools. Practically, those established properties could be used in order to better predict hidden phenotypes like disease risks and to pinpoint genetic reasons. For such tasks a statistical test would be used and this works like that: From our improved undertanding of how complex traits are evolving we can decide wether a data set at hand which was derived from a natural population, e.g., of humans, is likely to have been undergoing this process.

Further reading: Polygenic adapation (Wikipedia)

We study the architecture of adaptation of a quantitative trait to a new optimum after a sudden shift in the environment. Using analytical theory and individual-based computer simulations we characterize the conditions under which adaptation occurs either due to sweeps at few loci or due to subtle frequency shifts at many loci. In particular, we analyze the impact of mutation rates, starting allele frequencies, number of loci, linkage, and strength of selection on the adaptive scenario. In a final step, we compare theoretical predictions with data from replicated evolution experiments of Drosophila subject to thermal stress. We find that the adaptive architecture is robust with respect to linkage and ploidy. Furthermore, we describe a route to link our theory to empirical data.

Quantified protein abundances and half-lifes are important because they provide an explanation of how much energy a cell has to invest in maintaining its protein pool. Particularly crucial to our understanding of bacterial metabolism is whether protein half-lifes are altered by differing cellular conditions. In the past, it has been difficult to investigate this, because in general the equipment was inadequate to precisely and accurately assess protein half-lifes. Now we have measured protein abundances and degradation rate constants at two different specific growth rates in a chemostat for Lactococcus lactis subsp. cremoris. We have accordingly determined the most suitable out of three models to retrieve the degradation rate constants from mass spectrometry experiments with metabolic labeling. In the light of this data, we can show that protein half-life is not correlated with relative abundance, mass or length. We failed to consistently show any dependence of the degradation rate constant distribution on the specific growth rate, to provide a protein turnover rationale for the metabolic shift from mixed-acid to homo-lactic fermentation or to estimate the costs of protein turnover accurately. The reported findings provide a better understanding of the protein economy of the model organism, assisting in strain optimization for the dairy industry and the advancement of genome-scale metabolic models.