A comparison of methods to partition selection acting via components of fitness: Do larger male bullfrogs have greater hatching success?

We contrast three methods for measuring selection at sequential fitness components (here called the additive, changing variance, and independent methods). The independent method (Koenig and Albano, 1987; Conner, 1988) describes the relationship between a phenotypic character and one fitness component independent of other components. This method is appropriate when the question is whether or not a character has fitness consequences independent of selection at other stages. The additive (Arnold and Wade, 1984a) and changing variance (Kalisz, 1986; Koenig and Albano, 1987) methods measure selection via one component of fitness, taking into consideration constraints imposed by selection via earlier components in the sequence. These methods therefore more accurately track selection over a sequence of fitness components. Of these latter two methods, the changing variance method yields erratic results in simulation studies and is not recommended in its unmodified form. The additive method (equivalent to the changing variance method weighted as described in Wade and Kalisz [ 19891) explicitly partitions selection into additive components and is useful for measuring selection taking into account the constraints imposed by selection acting via prior fitness components. The methods often yield very different estimates of the relative degree to which the mean of a character is changed by selection acting via a particular component of fitness (the “strength” of selection). However, neither the additive nor independent method is inherently superior to the other; rather, these measures are complementary. Powerful techniques have recently been developed for quantifying selection (Lande and Arnold, 1983; Manly, 1985; Schluter, 1988; Crespi and Bookstein, 1989). A method of partitioning directional selection, derived by Arnold and Wade