Summary1. Information-theory procedures are powerful tools for multimodel inference and are now standard methods in ecology. When performing model averaging on a given set of models, the importance of a predictor variable is commonly estimated by summing the weights of models where the variable appears, the so-called sum of weights (SW). However, SWs have received little methodological attention and are frequently misinterpreted. 2. We assessed the reliability of SW by performing model selection and averaging on simulated data sets including variables strongly and weakly correlated to the response variable and a variable unrelated to the response. Our aim was to investigate how useful SWs are to inform about the relative importance of predictor variables. 3. SW can take a wide range of possible values, even for predictor variables unrelated to the response. As a consequence, SW with intermediate values cannot be confidently interpreted as denoting importance for the considered predictor variable. Increasing sample size using an alternative information criterion for model selection or using only a subset of candidate models for model averaging did not qualitatively change our results: a variable of a given effect size can take a wide range of SW values. 4.Contrary to what is assumed in many ecological studies, it seems hazardous to define a threshold for SW above which a variable is considered as having a statistical effect on the response and SW is not a measure of effect size. Although we did not consider every possible condition of analysis, it is likely that in most situations, SW is a poor estimate of variable's importance.

1. Freshwater amphipods Gammarus fossarum and Gammarus pulex are widespread in Europe, with some evidence of cryptic diversity in the former. We used DNA barcoding to assess genetic diversity within and among amphipod populations and examined mate discrimination and pre-copulatory pair formation between genetically divergent individuals. 2. Eight distinct G. fossarum and four distinct G. pulex molecular operational taxonomic units (MOTUs) were detected. Among the 33 amphipod populations sampled, 11 contained a single MOTU, 11 had two and 11 were composed of three sympatric MOTUs. Genetic divergences between sympatric MOTUs (G. fossarum and G. pulex MOTUs combined) ranged up to 28% (Kimura two parameter estimates). 3. In amphipod populations containing sympatric MOTUs, pre-copulatory pair formation was random between MOTUs diverging by <4%. However, pre-copulatory pairs involving amphipod individuals from MOTUs diverging by >4% were rare, suggesting mate discrimination between sympatric, highly divergent MOTUs. 4. Although the likelihood decreased with genetic distance between partners, pre-copulatory pair formation in the laboratory can occur between MOTUs diverging by c. 16% and led to successful mating: most female amphipod carried viable, fertilised eggs 48 h post-mating. 5. Data showed high cryptic diversity in the G. fossarum/G. pulex groups, even at a small spatial scale. Mate discrimination between genetically divergent amphipods in natural populations suggests that some of the MOTUs found in G. fossarum and G. pulex may be separated into (sub)species. However, amphipods from different MOTUs can still form pre-copulatory pairs and females produce viable eggs. Overall, data suggest that cryptic diversity is common in the G. fossarum/G. pulex groups and that pre-zygotic isolation through mate discrimination, rather than post-zygotic incompatibility, is likely to drive cryptic speciation.