1Current phylogenetic comparative methods modeling quantitative trait evolution 2 generally assume that, during speciation, phenotypes are inherited identically 3 between the two daughter species. This, however, neglects the fact that species 4 consist of a set of individuals, each bearing its own trait value. Indeed, because 5 descendent populations after speciation are samples of a parent population, we can 6 expect their mean phenotypes to randomly differ from one another potentially 7 generating a "jump" of mean phenotypes due to asymmetrical trait inheritance at 8 cladogenesis. Here, we aim to clarify the effect of asymmetrical trait inheritance at 9 speciation on macroevolutionary analyses, focusing on model testing and parameter 10 estimation using some of the most common models of quantitative trait evolution. We 11 developed an individual-based simulation framework in which the evolution of species 12 phenotypes is determined by trait changes at the individual level accumulating across 13 generations and cladogenesis occurs then by separation of subsets of the individuals 14 into new lineages. Through simulations, we assess the magnitude of phenotypic jumps 15 at cladogenesis under different modes of trait inheritance at speciation. We show that 16 even small jumps can strongly alter both the results of model selection and parameter 17 estimations, potentially affecting the biological interpretation of the estimated mode 18 of evolution of a trait. Our results call for caution interpreting analyses of trait 19 evolution, while highlighting the importance of testing a wide range of alternative 20 models. In the light of our findings, we propose that future methodological advances 21 in comparative methods should more explicitly model the intra-specific variability 22 around species mean phenotypes and how it is inherited at speciation. 23 Understanding the mechanisms underlying the evolution of phenotypic traits is 25 fundamental when addressing questions about functional diversity, ecological 26 interactions, and the overall build-up of biodiversity (Futuyma and Agrawal, 2009; 27 Katzourakis et al., 2009; Campbell and Kessler, 2013). Inferences about the processes 28 governing phenotypic changes are facilitated by the use of macroevolutionary models, 29 which deal with the evolution of phenotypic traits among related species (Stanley, 30 1979; Lande, 1980; Felsenstein, 1985 Felsenstein, , 2004. These macroevolutionary models are 31 able to infer the evolution of a phenotype under a variety of scenarios including 32 neutral or adaptive evolution (Lande, 1976; Beaulieu et al., 2012), as well as early 33 and rapid phenotypic differentiation (Harmon et al., 2010; O'Meara, 2012). These 34 models have been used to address a variety of evolutionary processes, helping us 35 understand, for instance, body size evolution in mammals (Venditti et al., 2011; 36 Slater, 2013), adaptation in Anolis lizards (Losos, 2011), evolutionary processes in 37 extinct and extant vertebrates (Wagner, 2017; Si...