1. exp. mm. Biol. Ecol., 1976, Vol. 22, pp. 69-77; @ worth-Holland Publis~ng Company USE OF PRINCIPAL COMPONENTS ANALYSIS TO DESCRIBE THE SNAIL SHELL RESOURCE FOR HERMIT CRABS ARMAND M. KURIS’ Department of Zoology, University of Michigan, Am Arbor, Michigan, U.S.A. and MICHAEL S. BRODY’ Bodega Marine Laboratory, U~iver~j~y of California, Bodega Bay, California, U.S.A. Abstract: Principal components analysis of morphometric data from snail shells occupied by hermit crabs enables the important dimensions of the shell to be described and quantified. A high correlation of the first principal component with crab size shows this component to be a better estimator of overall shell size than any of the original morphometric variates. Principal component II separated the shells utilized by adjacent populations of Coenobita and Calcintts according to shape. INTRODUCTION A hermit crab must occupy a snail shell or perish, Vance (1972a) has demonstrated experimentally that an increased avaiiability of snail shells increased the density of a natural population of hermit crabs, confirming some previous suppositions (Haas, 1950; Provenzano, 1960; Reese, 1969; Hazlett, 1970a). Size and shape (snail taxa as modified bywear, encrustation and predator damage) are the two important parameters of snail shells as a resource for hermit crabs. Both are amenable to mea- surement. Shell size is an important determinant of the potential growth (Drapkin, 1963; Markham, 1968; Kuris & Brody, unpubl.) and susceptibility to predation (Vance, 1972b) of the hermit crab occupant. Vance (1972a) used stepwise multiple regression to select the most highly correlated pair of variables among five shell- size and crab-size measurements. This procedure becomes increasingly unsatis- factory as species diversity of occupied shells increases and when many shells are in poor condition. Another potential di~culty in the choice of a single variable is that it is unlikely that the hermit crab is ‘estiiating’ shell size in such a simplistic way; rather, the hermit crab presumably employs a Gestalt of the overall size-related suitability of the shell in question. A statistic describing overall size is needed. When a principal components analysis (PCA) is made on a matrix of morphometric data drawn from a sample of related organisms, the first component (PC I) always seems to estimate size (see Blackith & Reyment, 1971 for a technical discussion; Present addresses: ‘Department of Biological Sciences, University of California, Santa Barbara, California, U.S.A., and * Department of Zoology, University of Texas, Austin, Texas, U.S.A. 69