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

In studying genetic processes taking place at the level of populations, the nominal size of the population, i.e. the number of individuals in the population, is usually not as important as a parameter called the effective size of the population (Wright 1931).The effective size of a population is the size of an ideal panmictic population in which genetic processes, such as a change in the frequency of alleles through selection or drift, would occur at the same rate as in the real studied population.In a panmictic population with stable size in time, which contains the same number of males and females and in which generations do not overlap and no similar phenomena occur, the effective size of the population is equal to the nominal size, i.e. the actual number of individuals in the population.As soon as one of the conditions is not met, the effective size of the population is different, usually smaller.

            If, for example, the population does not contain the same number of males and females, the effective size of the population should be calculated according to the equation

N_e = 4N_m N_f /(N_m +N_f )                                                                                 (1)

where N_m is the number of males and N_f is the number of females in the population.It follows from the equation, amongst other things, that, when one of the sexes is represented in the population by a single representative, the effective size of the population will equal approximately 4, regardless of whether the other sex is represented by a hundred or a million representatives (Fig. V.8).

            Another deviation of the effective size of the population from thenominal size could be caused by random scatter in the number of progeny left by the individual parent pairs.If an individual transfers an average of k = 2 gamets to the subsequent generation (the population is stationary) and the organisms cross randomly within the population, then

                                                                                              (2)

where  is the scatter in the number of progeny left by the individual members of the population.If the distribution of progeny in the population corresponds to Poisson distribution, for which it holds that = k,  i.e. in our case = 2  then the effective and nominal  sizes of the population are roughly equal.If the scatter is greater than the average, which is almost a general rule in nature, then the effective size of the population is less than the actual size.If, on the other hand, all the individuals pass  the same number of gametes down to the subsequent generation, i.e. under conditions where  would be equal to 0, the effective size of the population would be approximately equal to twice the nominal size of the population (N_e = 2N – 1).

            If the size of the population changes from one generation to the next, then the effective size of the population must be calculated as the harmonic mean of the population size in the individual generations:

                                                                             (3)

where n is the number of generations and N_i is the size of the population in the i-th generation.If the population of a certain species of insects increases exponentially during 5 generations from 10 to 1,000,000 and decreases back to 20 in the next 5 generations, then the effective size of the population over the given period will equal approximately 54.It is apparent that the size of the population is determined more by the weight of the generation in which reduction of the population occurred than by generations with a large population.As the size of the population of the most numerous organisms, including parasitic organisms, mostly fluctuates substantially in time, the effective size of the population of these organisms can actually be rather low.Thus, genetic drift can have a substantial effect even in species that temporarily form very large populations in nature.

            Other factors that can substantially affect the size of the population include overlapping of the individual generations, permitting mutual crossing of the members of various generations, or the existence of a metapopulation as a set of constantly emerging and disappearing mutually reproductionally isolated populations.The latter demographic situation is again frequently encountered, for example, in microorganisms or parasitic organisms.