Fig. 2.
Selection based on hummingbird visitation rates to plants of Ipomopsis in experimental arrays studied by Campbell et al. (1997). (A) The surface shows the best quadratic approximation to the selection surface as defined in Fig. 1, where Y = relative visit rate (absolute visit rate divided by mean visit rate), X1 = optical density (a measure of colour) standardized to a mean of zero and variance of 1, and X2 = corolla width standardized to a mean of zero and variance of 1. For this data set, γ12 = –0·267 (P < 0·0151). Filled circles show the data, with red indicating I. aggregata, pink indicating hybrid and white indicating I. tenuituba. The dashed lines connect the predicted visitation for plants that have the four possible combinations of mean trait values for the two species. The solid line shows the direction of the first projection obtained using Version 1·3 (2003) of the projection pursuit regression program of Schluter and Nychka available at http://www.zoology.ubc.ca/~schluter/software.html. (B) The cubic spline estimate of visitation as a function of the first projection. The solid line shows the predicted value, and the dotted lines show ± 1 s.e. Both coefficients in the projection are significantly different from zero based on 1000 bootstrap values. After pilot runs, the smoothing parameter λ was set to 4 to minimize generalized cross-validation function (GCV) at 0·234.