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tokens: on redshift is smaller than the dependence on the dynamical state. There seems to be a slight although not very significant evolution of the sparsity with z . Higher-redshift ( z > 0.54) clusters have a slightly larger value of S 500/2500 by 18%, that is these profiles are less concentrated, which is not consistent with the low-redshift ( z 0.2) clusters at ∼1.8 σ . We found the same behaviour when excluding the outliers. There is a much stronger and significant variation of the sparsity with dynamical state: morphologically disturbed (high ⟨ w ⟩), non-CC (low C SB ), and disturbed (low M ) clusters have larger sparsity. For all parameters considered, the sparsity of the first and third bins is not consistent at more than 3 σ , and the difference between the sparsities of these bins is of the order of ∼50%. At the same time, the intrinsic scatter increases significantly, reaching ∼0.2 dex for the most disturbed or least concentrated objects. For example, the sparsity increases by 64% at a significance level of 3.4 σ between M −0.6 and M > 0.5, that is, between the one third most relaxed and the one third most disturbed as defined by this parameter. Only an upper limit on the intrinsic scatter can be estimated from the former ( 0.04 dex), while the intrinsic scatter for the latter reaches 0.25 ± 0.09 dex. There are strong outliers at high sparsity. Excluding the outliers yields the same qualitative results, although the variation between bins is weaker. This suggests a sparsity distribution skewed towards high values, with a skewness increasing with departure from dynamical relaxation. 7. Discussion 7.1. Dynamical state The first result of our study is that SZ-selected samples are dominated at all redshifts by disturbed and non-CC objects. Recent observational work on local clusters has converged to similar results (e.g. Lovisari et al. 2017 ; Rossetti et al. 2017 ; Andrade-Santos et al. 2017 ; Lopes et al. 2018 ). In particular, these works highlight the higher fraction of disturbed objects or the lower fraction of CC objects in SZ-selected samples as compared to X-ray-selected samples, a fact interpreted to be due to preferential detection of relaxed or more concentrated clusters in X-ray surveys. In contrast, there is little consensus in the literature concerning the evolution of the dynamical state, as determined from various morphological parameters. Studies of the evolution up to z ∼ 1 of the centroid shift and/or power ratios of X-ray-selected clusters indicate a larger fraction of disturbed clusters at high z ( Maughan et al. 2008 ; Jeltema et al. 2005 ; Weißmann et al. 2013 ). However, the latter study is also consistent with no evolution, and Nurgaliev et al. (2017) did not find any significant evolution in the redshift range 0.3 z 1 for the 400 d X-ray-selected clusters. These somewhat contradictory results may simply be due to selection effects: X-ray detectability is clearly not independent of cluster morphology. More peaked