These data support the analyses and figures presented in Comte et al. 2024 (Global Change Biology; DOI:10.1111/gcb.17271).Ecological and evolutionary theories have proposed that species traits should be important in mediating species responses to contemporary climate change; yet empirical evidence has so far provided mixed evidence for the role of behavioral, life history or ecological characteristics in facilitating or hindering species range shifts.Table A1 provides a brief synthesis of the relevant empirical studies linking species traits to contemporary range shifts (used in Figure 3).Table A2a provides outputs of simulations used to discuss the extent to which range shifts-trait associations at the leading edge are mediated by climate exposure, thereby blurring the perceived predictive power of traits (used in Figure 4).Table A2b provides outputs of simulations used to discuss the extent to which range shifts-trait associations at the trailing edge are mediated by climate exposure, thereby blurring the perceived predictive power of traits (used in Figure 4).Table A3a provides morphological traits for birds used to assess functional biases in species redistribution research (used in Figure 5).Table A3b provides morphological traits for fishes used to assess functional biases in species redistribution research (used in figure 5).