Covers of Point-Hyperplane Graphs

We construct a cover of the non-incident point-hyperplane graph of projective dimension 3 for fields of characteristic 2. If the cardinality of the field is larger than 2, we obtain an elementary construction of the non-split extension of SL_4 (F) by F^6.Comment: 10 pages, 3 figure

Why we should not dismiss a relationship between attractiveness and performance: a comment on Smoliga & Zavorsky (2015)

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.No abstrac

Bigger is fitter? Quantitative genetic decomposition of selection reveals an adaptive evolutionary decline of body mass in a wild rodent population

This is the final version of the article. Available from the publisher via the DOI in this record.In natural populations, quantitative trait dynamics often do not appear to follow evolutionary predictions. Despite abundant examples of natural selection acting on heritable traits, conclusive evidence for contemporary adaptive evolution remains rare for wild vertebrate populations, and phenotypic stasis seems to be the norm. This so-called "stasis paradox" highlights our inability to predict evolutionary change, which is especially concerning within the context of rapid anthropogenic environmental change. While the causes underlying the stasis paradox are hotly debated, comprehensive attempts aiming at a resolution are lacking. Here, we apply a quantitative genetic framework to individual-based long-term data for a wild rodent population and show that despite a positive association between body mass and fitness, there has been a genetic change towards lower body mass. The latter represents an adaptive response to viability selection favouring juveniles growing up to become relatively small adults, i.e., with a low potential adult mass, which presumably complete their development earlier. This selection is particularly strong towards the end of the snow-free season, and it has intensified in recent years, coinciding which a change in snowfall patterns. Importantly, neither the negative evolutionary change, nor the selective pressures that drive it, are apparent on the phenotypic level, where they are masked by phenotypic plasticity and a non causal (i.e., non genetic) positive association between body mass and fitness, respectively. Estimating selection at the genetic level enabled us to uncover adaptive evolution in action and to identify the corresponding phenotypic selective pressure. We thereby demonstrate that natural populations can show a rapid and adaptive evolutionary response to a novel selective pressure, and that explicitly (quantitative) genetic models are able to provide us with an understanding of the causes and consequences of selection that is superior to purely phenotypic estimates of selection and evolutionary change.The study was funded by a Swiss National Science Foundation (http://www.snf.ch) project grant (31003A_141110) awarded to EP

Consistent cooperation in a cichlid fish is caused by maternal and developmental effects rather than heritable genetic variation.

This is the author accepted manuscript. The final version is available from Royal Society via the DOI in this record.Studies on the evolution of cooperative behaviour are typically confined to understanding its adaptive value. It is equally essential, however, to understand its potential to evolve, requiring knowledge about the phenotypic consistency and genetic basis of cooperative behaviour. While previous observational studies reported considerably high heritabilities of helping behaviour in cooperatively breeding vertebrates, experimental studies disentangling the relevant genetic and non-genetic components of cooperative behaviour are lacking. In a half-sibling breeding experiment, we investigated the repeatability and heritability of three major helping behaviours performed by subordinates of the cooperatively breeding fishNeolamprologus pulcherTo experimentally manipulate the amount of help needed in a territory, we raised the fish in two environments differing in egg predation risk. All three helping behaviours were significantly repeatable, but had very low heritabilities. The high within-individual consistencies were predominantly due to maternal and permanent environment effects. The perceived egg predation risk had no effect on helping, but social interactions significantly influenced helping propensities. Our results reveal that developmentally plastic adjustments of provided help to social context shape cooperative phenotypes, whereas heritable genetic variation plays a minor role.Funding was provided by the ‘ProDoc’ program of the Swiss National Science Foundation (SNF, projects PDFMP3_137196 and 31003A_156881 to B.T.), and the ‘120% support grant’ to C.K. of the University of Bern