I. To determine if allogeneic hematopoietic stem cell patients treated with a probiotic compared to those not assigned to receive a probiotic have differences in: a) composition and proportion of the major gut bacterial phylotypes in stool (to be analyzed for changes pre- and post-initiation of probiotics and for association with development of aGVHD); b) measures of inflammation as assessed by cytokine or receptor production (interleukin [IL]-6, IL-8, tumor necrosis factor [TNF]-alpha, TNF-receptor 1, interferon-gamma, IL-2R, IL-10); c) qualitative measures of immune reconstitution as determined by sequential measurements of conventional T cells, regulatory T regulatory, B cells and natural killer (NK) cells; d) antibody class/subclass production; e) biomarkers associated with GVHD-elafin, regenerating islet-derived 3 alpha (Reg3a), suppressor of tumorigenicity-2 (ST2), hepatocyte growth factor (HGF); and/or urinary tryptophan metabolites; f) markers of gut barrier function including blood levels of endotoxin and microbial deoxyribonucleic acid (DNA).