FUNCTIONAL COMPLEXES AND ADDITIVITY IN PERFORMANCE: A TEST CASE WITH "FLYING" FROGS.

The origin and maintenance of morphological integration and of novel character complexes are common themes in recent literature (e.g., Cheverud, 1982; Wake and Larson, 1987; Zelditch and Carmichael, 1989; Wake and Roth, 1989), but the quantitative effects of such character complexes on performance have received much less attention (but see Shaffer and Lauder, 1985; Wainwright and Lauder, 1986; Andrews et al., 1987). The possible synergistic consequences for whole organism performance of coupling behavioral innovations with certain morphological features has been explored (e.g., Kingsolver, 1988; Emerson and Koehl, 1990), but the possibility that the individual elements of some morphological complexes may interact synergistically among themselves to affect performance has not. Nonadditive interactions among individual traits could contribute to the depth of the valleys between adaptive peaks of morphological variation and the steepness of the fitness surface that translates phenotypic variation into fitness variation (Lande, 1986 and references therein). Any such interactions would thus have important consequences for the rate of evolutionary origin and integration of complex design (e.g., Kingsolver and Koehl, 1985; Burger, 1986; Dawkins, 1986; Kingsolver, 1988). We present a quantitative study of the additivity of the performance capability in a suite of morphological characters associated with "flying" in frogs. "Flying" frogs have evolved independently in both New and Old World families of treefrogs (Duellman, 1970; Liem, 1970). These frogs are not capable of powered flight but glide through the forest canopy. Old World "flying" species (family Rhacophoridae) are readily identified by a unique suite of derived morphological features: enlarged hands and feet, full webbing between all fingers and toes, lateral skin flaps on the arms and legs, and reduced weight per snout-vent length (Liem, 1970; Emerson, unpubl.). These modifications of flying frogs reduce their "wing" loading (W, weight per projected area) relative to nonflyers and affect several aspects of their aerodynamic performance. Wind tunnel experiments (Emerson and Koehl, 1990) indicate that the flyer features listed above 1) increase the horizontal distance traveled (proportional to [L1/D] ,Ilx where L is lift and D is drag) during a fall from a given height by a frog in the "flying posture" (described in Emerson and Koehl, 1990), 2) reduce the minimum speed (U,,m) required for a falling frog to begin to glide, 3) increase the drag (Dgo), and hence the time aloft of a parachuting frog, and 4) improve maneuverability by reducing the tuming radius (inversely proportional to [CL/W,max where CL is the lift coefficient) achieved by a given banking angle. (The derivation of these performance variables, [L/D]mL,a Umm,, Dgo, and [CL/I Vmax, is explained in Emerson and Koehl, 1990.) The present study examines whether individual elements of the flying character complex interact in an additive fashion in their effects on these four aspects of performaince (e.g., if structure A increases performance by three units and if structure B increases it by five units, does the presence of A and B together increase performance by exactly eight units?).