Context. Galaxy evolution and the effect of environment are most often studied using scaling relations or some regression analyses around some given property. These approaches however do not take into account the complexity of the physics of the galaxies and their diversification. Aims. We here investigate the effect of cluster environment on the evolution of galaxies through multivariate unsupervised classification and phylogenetic analyses applied to two relatively large samples from the WINGS survey, one of cluster members and one of field galaxies (2624 and 1476 objects respectively). Methods. These samples are the largest ones ever analysed with a phylogenetic approach in astrophysics. To be able to use the Maximum Parsimony (cladistics) method, we first performed a pre-clustering in 300 clusters with a hierarchical clustering technique, before applying it to these pre-clusters. All these computations used seven parameters: B-V, log(Re), nV , µe , Hβ , D4000 , log(M *). Results. We have obtained a tree for the combined samples and do not find different evolutionary paths for cluster and field galaxies. However, the cluster galaxies seem to have accelerated evolution in the sense they are statistically more diversified from a primitive common ancestor. The separate analyses show a hint for a slightly more regular evolution of the variables for the cluster galaxies, which may indicate they are more homogeneous as compared to field galaxies in the sense that the groups of the latter appear to have more specific properties. On the tree for the cluster galaxies, there is a separate branch which gathers rejunevated or stripped-off groups of galaxies. This branch is clearly visible on the colour-magnitude diagram, going back from the red sequence towards the blue one. On this diagram, the distribution and the evolutionary paths of galaxies are strikingly different for the two samples. Globally, we do not find any dominant variable able to explain either the groups or the tree structures. Rather, co-evolution appears everywhere, and could depend itself on environment or mass. Conclusions. This study is another demonstration that unsupervised machine learning is able to go beyond the simple scaling relations by taking into account several properties together. The phylogenetic approach is invaluable to trace the evolutionary scenarii and project them onto any biavariate diagram without any a priori modelling. Our WINGS galaxies are all at low redshift, and we now need to go to higher redshfits to find more primitve galaxies and complete the map of the evolutionary paths of present day galaxies.