WHAT IS FREQUENCY‐DEPENDENT SELECTION?

The term "frequency-dependent selection" has been used variously to mean slightly different things, although in the discovery of the phenomenon and the development of the concept, the term has had an unambiguous, exact meaning. The purpose of this note is to state precisely the meaning of the term "frequency-dependent selection," and by way of clarification to discuss an instance of its misuse and confusion with other phenomena (Wallace, 1975). The essential feature of frequency-dependent selection is that fitnesses are not fixed, but variable, and the values they take on vary as functions of the frequencies of the diploid genotypes they characterize. This feature by itself describes frequency-dependence in a broad sense, but it is the addition of a second feature which gives the phenomenon the theoretical impact that has been the source of much interest. This second feature, refining the definition to a particular type of frequency-dependent selection, requires that the fitness values vary so as to favor rare types, and become approximately equal as an intermediate frequency is approached. This feature insures the maintenance of a balanced polymorphism without the consequence of segregational load at equilibrium. A demonstration of a fitness value that gets increasingly larger as the associated genotype becomes more frequent would show frequencydependence in the broad sense, but would not be particularly interesting. In the development of the concept of frequency-dependent selection, interest was clearly focused on rare type advantage because of the theoretical importance of that type of frequency-dependence. This was true to the extent that many authors have used the term "frequency-dependent selection" to refer to the specific type of frequency-dependence in which rare types are favored; that is, frequency-dependence as a form of balancing selection (Anderson and Watanabe, 1974; Ehrman, 1968; Huang, Singh, and Kojima, 1971; Kojima and Huang, 1972; Kojima and Tobari, 1969; Kojima and Yarbrough, 1967; Nassar et al., 1973; Tobari and Kojima, 1967). I will follow this precedent and use "frequency-dependence" to refer to rare type advantage, and "frequency-dependence in the broad sense" to include all types of variable fitness. Several authors have pointed out the necessity of exact computational methods in determining the operation of frequency-dependent selection: spurious indications of frequency-dependence can arise in systems having constant fitness values as a result of inappropriately applied mathematics (Prout, 1965, 1969). Ayala and Campbell (1974) give a particularly clear example of this. If, in a system with constant fitness values where the heterozygote has the highest fitness (i.e. a system which will lead to a stable polymorphism), the relative frequency of genotypes in successive generations are compared, the frequency changes appear to be due to frequency-dependent selection. The appropriate ratio should be the absolute frequencies (i.e, not corrected to 100%) in the progeny generation compared to the relative frequency of genotypes in the previous, or parental, generation. This distinction is made explicit in Table 1 of this paper. Fitness is the ratio of line c to line a. Calculations of fitness based on the ratio of line d to line a may give spurious indications of frequency-dependence in the broad sense. Another example of this kind is given by Spiess and Langer (1964), and a detailed work on the pitfalls and requirements of such calculations is provided by Prout (1965, 1971). A common description of frequency-dependence is that fitnesses vary, favoring rare types, as functions of gene frequency. Such a statement must be approached with caution. An adult population can be characterized by genotype and gene frequencies. The gametic output of that population can be characterized by gene frequencies but not by genotype frequencies. The reconstitution of genotype frequencies in the next generation requires a specification of a mating system. If mating is at random, zygotic genotypes will be in the proportions p', 2pq, and if. If mating is not random, zygotic genotype frequencies will be in some other proportions determined by the mating system. Inasmuch as sexual selection has been demonstrated to be potentially of utmost importance among the various components of selection (Bundgaard and Christiansen, 1972), the as-