Frozen Evolution. Or, that’s not the way it is, Mr. Darwin. A Farewell to Selfish Gene.

In general, the same rules apply to the spreading of memes as to the spreading of infectious diseases and the relevant processes can also be described by the same formal models (Anderson 1993).The most important parameter that determines the efficiency with which a meme will spread is its basic reproduction constant R₀, a dimensionless constant equal to the average number of individuals “infected” by the relevant meme by one bearer of the particular meme in the “naive” population, i.e. a population whose members had not previously encountered the meme.If this constant is larger than 1, the given gene can spread in the population and be retained in it for a long time, even if it is harmful to its bearers, i.e. if it reduces their fitness.The actual reproduction constant, R, in a population in which a certain fraction of individuals, q, was “infected” by the meme in the past, is understandably lower and decreases linearly with increasing fraction of infected individuals.If R decreases to a value of 1, the fraction of infected individuals remains constant in the population and the particular meme is retained endemically in the population.Each meme is differently “infectious” and each has a different threshold intensity, N_T, i.e. number of susceptible individuals, at which it can begin to spread in the population.A simple equation exists between the threshold density and R₀

               N_T  = N/R₀                                                                                   (1)

where N is the size of the population.If “meme infection” has occurred in the population, the value of R₀ can be calculated from the fraction of individuals that remained unaffected by the meme (s), as it holds that

    R₀ =[1/(1-s)] ln(1/s)                                                                                       (2)

On the basis of R₀we can then easily calculate the size of the fraction of persons in the population that it would be required to make immune to the particular meme through an effective campaign so that this meme would not be able to spread by horizontal transmission.

              p   > (1-1/R₀ )                                                                                 (3)

If, for example, a certain meme affects an average of 70% of individuals during its natural horizontal spreading in the population, then it would be necessary to “immunize” 41% of the so-far unaffected population in advance to prevent a future meme epidemic.Because the fraction of immunized persons gradually decreases in a natural way after the end of the epidemic, either through the deaths of immune individuals or forgetting, some meme epidemics can have a regular cyclic character, where the periodicity of the cycle will depend on the size of the population.