deletions | additions       diff --git a/Results.tex b/Results.tex  index 9e2f885..8a5df2a 100644  --- a/Results.tex  +++ b/Results.tex 
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xylose (Figure~\ref{fig:shift}), and, each responder group exhibits a range of substrate  specificites (Figure~\ref{fig:shift}).  A density profile for each responder is generated for the experimental and  control treatment at each of the sampling time points using relative abundances  from sequence libraries . The difference in center of mass for each set of  density profiles (control and experimental) is measured (supp. MM) and each KDE  curve represents the collection of density shifts calculated for all responders  in the $^{13}$C-cellulose or $^{13}$C-xylose treatment . We observe xylose  utilizers having a smaller density shift (0.008 $\pm$ 0.008 g mL$^{-1}$) than  cellulose utilizers (0.015 $\pm$ 0.009 g mL$^{-1}$), with few exceptions.   \subsection{Xylose responders at day 1 have more estimated rRNA operon copy numbers per genome  than xylose responders at days 3 and 7, and, Xylose responders have more rRNA operon copy numbers  than cellulose responders.}