Conditions for the initial increase of new alleles with frequency dependent selection

The paper presents the derivation of conditions for the initial increase of a new allele in a fairly general model of a one locus genetic system. Incorporated within the model are frequency dependent selection coefficients which allow the study of viability differences, fertility differences, segregation distortion and certain forms of non-random mating. Since in many models it is necessary to go beyond linear terms, quadratic, cubic and quartic terms are also derived explicitly and details given of their extension to higher degrees.