Barite and Acantharians
There is still some uncertainty, but some recent research is detailed below:

In research reported in the article Barite in the ocean – occurrence, geochemistry and
palaeoceanographic applications (Griffith and Paytan, 2012), recent observations and research found that


  Using the non-carbonate Sr content in
  suspended particles to track the presence of
  acantharia, van Beek et al. (2007) suggest that
  acantharian dissolution does contribute signifi-
  cantly to barite formation in the upper 500 m of
  the water column


However, a lack of a definitive correlation between the barite concentrations and acantharian distributions suggest that


  these organisms are
  not required for the formation of barite in the
  water column (Bertram &amp; Cowen, 1997)


and that further observations


  provided direct evidence to support
  the water column micro-environment mechanism
  of marine barite formation and to verify that
  barite can form in the absence of acantharia.


The concentration of strontium in barite is a record of the Sr isotopic composition of the formation fluids, which according to the article has its source from sea water, sediments (both marine and terrigenous) and hydrothermal fluids. 

It is this last point, particularly about the Sr concentrations in sea-water, which according to the article Sedimentation of acantharian cysts in the Iceland Basin: Strontium as a ballast for deep
ocean particle flux, and implications for acantharian reproductive strategies (Martin et al. 2010) state can fluctuate by several percent  


  By precipitating celestite, Acantharia can reduce surface
  seawater strontium (Sr) concentrations by up to 5%


Experimentally the authors found that


  Sr fluxes we report are
  too high to be attributed to nonacantharian sources.