The Collaborative International Dictionary of English v.0.48:

Predominance \Pre*dom"i*nance\, n. [Cf. F. pr['e]dominance.]
   1. The quality or state of being predominant; superiority;
      ascendency; prevalence; predomination.
      [1913 Webster]

            The predominance of conscience over interest.
                                                  --South.
      [1913 Webster]

   2. (Astrol.) The superior influence of a planet. --Shak.
      [1913 Webster]

WordNet (r) 3.0 (2006):

predominance
    n 1: the state of being predominant over others [syn:
         predominance, predomination, prepotency]
    2: the quality of being more noticeable than anything else; "the
       predomination of blues gave the painting a quiet tone" [syn:
       predomination, predominance]

Moby Thesaurus II by Grady Ward, 1.0:

87 Moby Thesaurus words for "predominance":
   accomplishment, advantage, ascendance, ascendancy, authority,
   balance of power, charisma, charm, clout, consequence, control,
   credit, deanship, dominance, dominancy, domination, dominion,
   effect, eminence, eminent domain, enchantment, esteem, excellence,
   favor, force, good feeling, greatness, hegemony, hold, importance,
   incidental power, incomparability, influence, influentiality,
   inimitability, insinuation, lead, leadership, leverage, magnetism,
   majority, mastery, moment, one-upmanship, overlordship,
   personality, persuasion, potency, power, precedence, predominancy,
   predomination, preeminence, preponderance, prepotence, prepotency,
   prerogative, pressure, prestige, primacy, principality, priority,
   privilege, purchase, reign, repute, right-of-way, rule, say,
   seniority, skill, sovereignty, suasion, subtle influence, success,
   suggestion, superiority, supremacy, suzerainship, suzerainty, sway,
   transcendence, transcendency, upper hand, virtuosity, weight,
   whip hand