This study applies flexible statistical methods to morphometric measurements obtained via light and scanning electron microscopy (SEM) to discriminate closely related species of Gyrodactylus parasitic on salmonids. For the first analysis, morphometric measurements taken from the opisthaptoral hooks and bars of 5 species of gyrodactylid were derived from images obtained by SEM and used to assess the prediction performance of 4 statistical methods (nearest neighbours; feed-forward neural network; projection pursuit regression and linear discriminant analysis). The performance of 2 methods, nearest neighbours and a feed-forward neural network provided perfect discrimination of G. salaris from 4 other species of Gyrodactylus when using measurements taken from only a single structure, the marginal hook. Data derived from images using light microscopy taken from the full complement of opisthaptoral hooks and bars were also tested and nearest neighbours and linear discriminant analysis gave perfect discrimination of G. salaris from G. derjavini Mikailov, 1975 and G. truttae Gläser, 1974. The nearest neighbours method had the least misclassifications and was therefore assessed further for the analysis of individual hooks. Five morphometric parameters from the marginal hook subset (total length, shaft length, sickle length, sickle proximal width and sickle distal width) gave near perfect discrimination of G. salaris. For perfect discrimination therefore, larger numbers of parameters are required at the light level than at the SEM level.

Let Z1, …, Zn be i.i.d. random vectors (‘points') defined in having common density f(x) that is assumed to be continuous almost everywhere. For a fixed but otherwise arbitrary norm |.| on , consider the fraction Vn of those points Z1, …, Zn that are the lth nearest neighbour (with respect to |.|) to their own kth nearest neighbour, and write Sn for the fraction of points that are the nearest neighbour of exactly k other points. We derive the stochastic limits of Vn and Sn, as n tends to∞, and show how the results may be applied to the multivariate non-parametric two-sample problem.