  Nuclear star clusters (NSCs) are dense star clusters located at the centre of
galaxies spanning a wide range of masses and morphologies. Analysing NSC
occupation statistics in different environments provides an invaluable window
into investigating early conditions of high-density star formation and mass
assembly in clusters and group galaxies. We use HST/ACS deep imaging to obtain
a catalogue of dwarf galaxies in two galaxy clusters in the Shapley
Supercluster: the central cluster Abell 3558 and the northern Abell 1736a. The
Shapley region is an ideal laboratory to study nucleation as it stands as the
highest mass concentration in the nearby Universe. We investigate the NSC
occurrence in quiescent dwarf galaxies as faint as $M_{I} = -10$ mag and
compare it with all other environments where nucleation data is available. We
use galaxy cluster/group halo mass as a proxy for the environment and employ a
Bayesian logistic regression framework to model the nucleation fraction
($f_{n}$) as a function of galaxy luminosity and environment. We find a notably
high $f_n$ in Abell 3558: at $M_{I} \approx -13.1$ mag, half the galaxies in
the cluster host NSCs. This is higher than in the Virgo and Fornax clusters but
comparable to the Coma Cluster. On the other hand, the $f_n$ in Abell 1736a is
relatively lower, comparable to groups in the Local Volume. We find that the
probability of nucleation varies with galaxy luminosity remarkably similarly in
galaxy clusters. These results reinforce previous findings of the important
role of the environment in NSC formation/growth.
