Why are neutral [sterile] female flowers present in inflorescences when they are reproductively incompatible?
Sterile flowers enrich pollination quality by promoting pollen export and import, while limiting the mating costs of geitonogamy associated with large fertile displays.



You are actually looking for this paper: Link: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3523656/

Sterile flowers increase pollinator attraction and promote female success in the Mediterranean herb Leopoldia comosa


  Key Results
  
  The presence of sterile flowers almost tripled pollinator attraction,
  supplementing the positive effect of the number of fertile flowers on
  the number of bees approaching inflorescences. Although attracted bees
  visited more flowers on larger inflorescences, the number visited did
  not additionally depend on the presence of sterile flowers. The
  presence of sterile flowers improved all aspects of plant performance,
  the magnitude of plant benefit being context dependent. During weather
  favourable to pollinators, the presence of sterile flowers increased
  pollen deposition on stigmas of young flowers, but this difference was
  not evident in older flowers, probably because of autonomous
  self-pollination in poorly visited flowers. Total pollen receipt per
  stigma decreased with increasing fertile display size. In the
  population with more pollinators, the presence of sterile flowers
  increased fruit number but not seed set or mass, whereas in the other
  population sterile flowers enhanced seeds per fruit, but not fruit
  production. These contrasts are consistent with dissimilar
  cross-pollination and autonomous self-pollination, coupled with the
  strong predispersal inbreeding depression exhibited by L. comosa
  populations.