This material has been published in CAB Reviews, issue 7, No. 016, 2012, doi: 10.1079/PAVSNNR20127020, the only accredited archive of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by CABl. The electronic version of this article is the definitive one. It is located here: http://www.cabi.org/cabreviews Potential of GLMM in modelling invasive spread: Supplement D Analysing time series data of phenotypic measurements – trade-off in sexual reproduction and vegetative growth of perennial ryegrass (Lolium perenne)? J. Thiele1* and B. Markussen2 Address: 1 Institute of Landscape Ecology, University of Muenster, Robert-Koch-Str. 28, 48149 Muenster, Germany. 2 Department of Basic Sciences and Environment, University of Copenhagen, Thorvaldsensvej 40, 1871 Frederiksberg C, Denmark. *Correspondence: J. Thiele. Email: jan.thiele@uni-muenster.de Introduction In this example, we analyse repeated phenotypic measurements of perennial ryegrass (Lolium perenne) from a greenhouse experiment. We hypothesize that there is a trade- off between sexual reproduction (flower stems) and vegetative propagation (tillers) within polycormons of this species. This is not directly a study of biological invasions, however, we want to find out, if less flowering plants (cultivars, in this case) would be more competitive and could invade seminatural grasslands. Similar repeated measures designs are quite often used in invasion biology. We acknowledge that we adopted some ideas from an example presented by Fox (2002) for this analysis. Sexual reproduction or, more precisely, the degree of flowering of the plants, was modified by cold treatments (vernalisation). Cold temperature (< 6° C) are a prerequisite for flowering of perennial ryegrass. The shorter the cold period, the lower the number of flowering stems that emerge afterwards. In this way, plants (polycormons) of perennial ryegrass with varying numbers of flowering stems were produced. The plants were grown from seeds that were collected from six populations and, when they had produced several tillers, they were split into four ‘clones’ of three tillers in order to replicate each individual genotype in four cold treatments. Two clones from different populations were planted together in a pot in order to create a competitive situation among plants. The same genotype combinations were repeated in the four cold treatments. The experiment comprised 640 pots, because there were 8 combinations of populations of the competing clones, and the population combinations were repeated 20 times (with different genotype combinations) in each of 4 cold treatments. As the pots contained two clones which were investigated at three time points, the whole dataset has got a sample size of 3840, but the effective sample size is 3777 because of some missing data. At each of the three time points, the diameter of clones (i.e. polycormon diameter) was measured and the number of flowering stems was counted. The latter will be used as a predictor variable, because it was manipulated, and the clone diameter will be used as the response (dependent variable). The diameter of the other plant in the pot will be used as a covariate that represents the amount of competition. More details on the experimental setup can be found in Thiele et al. (2009).