Application of Trigonometric Approximation to Describe Head Shapes of Alate Aphids

A trigonometric approximation was used to describe the head shape of common vegetable-feeding aphids, Aphis gossypii Glover, Aulacorthum solani (Kaltenbach), Brevicoryne brassicae (Linné), Macrosiphum euphorbiae (Thomas), and Myzus per-sicae (Sulzer). After acquiring and standardizing digital images of the alate aphids, a frontal curve was represented as a set of points in a given domain, -π/2 ≤ x ≤ π/2. Then, the points were approximated by the function, Coefficients of the function were calculated by multiple regression analysis, and the averages of coefficients were used to reconstruct the generalized shape of each species.