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We study the connection between the observed star formation rate-stellar mass(SFR-$M_*$) relation and the evolution of the stellar mass function (SMF) bymeans of a Subhalo Abundance Matching technique coupled to merger treesextracted from a N-body simulation. Our approach, which considers both galaxymergers and stellar stripping, is to force the model to match the observed SMFat redshift $z>2$, and let it evolve down to the present time according to theobserved (SFR-$M_*$) relation. In this study, we use two different sets of SMFsand two SFR-$M_*$ relations: a simple power law and a relation with amass-dependent slope. Our analysis shows that the evolution of the SMF is moreconsistent with a SFR-$M_*$ relation with a mass-dependent slope, in agreementwith predictions from other models of galaxy evolution and recent observations.In order to fully and realistically describe the evolution of the SMF, bothmergers and stellar stripping must be considered, and we find that both havealmost equal effects on the evolution of SMF at the massive end. Taking intoaccount the systematic uncertainties in the observed data, the high-mass end ofthe SMF obtained by considering stellar stripping results in good agreementwith recent observational data from the Sloan Digital Sky Survey (SDSS). At$\log M_* < 11.2$, our prediction at z=0.1 is close to \citet{li-white09} data,but the high-mass end ($\log M_* > 11.2$) is in better agreement with\citet{dsouza15} data which account for more massive galaxies.

Constraints on the Evolution of the Galaxy Stellar Mass Function I: Role of Star Formation, Mergers and Stellar Stripping