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We present an upgraded version of the \MOCCA code for the study of dynamicalevolution of globular clusters (GCs) and its first application to the study ofevolution of multiple stellar populations. We explore initial conditionsspanning different structural parameters for the first (FG) and secondgeneration of stars (SG) and we analyze their effect on the binary dynamics andsurvival. Here, we focus on the number ratio of FG and SG binaries, its spatialvariation, and the way their abundances are affected by various cluster initialproperties. We find that present-day SG stars are more abundant in clustersthat were initially tidally filling. Conversely, FG stars stay more abundant inclusters that were initially tidally underfilling. We find that the ratiobetween binary fractions is not affected by the way we calculate thesefractions (e.g. only main-sequence binaries (MS) or observational binaries,i.e. MS stars $> 0.4 M_{\odot}$ mass ratios $> 0.5$). This implies that the MSstars themselves are a very good proxy for probing entire populations of FG andSG. We also discuss how it relates to the observations of Milky Way GCs. Weshow that \MOCCA models are able to reproduce the observed range of SGfractions for Milky Way GCs for which we know these fractions. We show how theSG fractions depend on the initial conditions and provide some constraints forthe initial conditions to have more numerous FG or SG stars at the Hubble time.

MOCCA: Dynamics and evolution of binary stars of multiple stellar populations in tidally filling and underfilling globular star clusters