text: Müllers 1879 account was one of the earliest uses of a mathematical model in evolutionary ecology, and the first exact model of frequency-dependent selection. Mallet calls Müllers mathematical assumption behind the model "beguilingly simple". Müller presumed that the predators had to attack n unprofitable prey in a summer to experience and learn their warning coloration. Calling a and a the total numbers of two unprofitable prey species, Müller then argued that, if the species are completely unalike they each lose n individuals. However, if they resemble each other,
  then species 1 loses
   individuals,
  and species 2 loses
   individuals.
  Species 1 therefore gains
  and species 2 similarly gains
   in absolute numbers of individuals not killed.
  The proportional gain compared to the total population of species 1 is
  and similarly for species 2
  , giving the per head fitness gain of the mimicry when the predators have been fully educated.
  Hence, Müller concluded, the proportion g1:g2 was
  , which equals , and the rarer species gains far more than the commoner one.
  The model is an approximation, and assumes the species are equally unprofitable. If one is more distasteful than the other, then the relative gains differ further, the less distasteful species benefiting more (as a square of the relative distastefulness) from the protection afforded by mimicry. This can be thought of as parasitic or quasi-Batesian, the mimic benefiting at the expense of the model. Later models are more complex and take factors such as rarity into account. The assumption of a fixed number n to be attacked is questionable. Müller also effectively assumed a step function, when a gradual change (a functional response) is more plausible.