NOTE The fuzzy structure of populations James A. Schaefer and Chris C. Wilson Abstract: The human perception of biological organization has profound implications for the study, management, and conservation of living things. Traditional methods of classification, which imply all-or-nothing group membership, are inconsistent with the modern synthesis, which stresses variability and unique individuals. We propose that fuzzy classi- fication, which allows fractional membership in multiple clusters, can more realistically denote many forms of biologi- cal organization, such as populations. We used fuzzy clustering to depict the ambiguous structure of a migratory caribou (Rangifer tarandus) herd, based on affinities in space use, and walleye (Stizostedion vitreum) stocks, based on genetic dissimilarities among multilocus genotypes. In both cases, fuzzy memberships conveyed the degree of uncer- tainty of belonging while resolving cluster memberships for unambiguous and problematic individuals. Vagueness im- plies that borderline group identity cannot be remedied with more resolving power. Fuzzy classification is more in tune with the empirical and philosophical foundations of our discipline and can reconcile our need to classify with an inher- ently vague biological world. Résumé : La perception humaine de l’organisation biologique a d’importantes répercussions sur l’étude, la gestion et la conservation des êtres vivants. Les méthodes de classification traditionnelles, qui exigent le placement dans un groupe sur une base de tout ou rien, sont incompatibles avec la synthèse moderne qui valorise la variabilité et les individus marginaux. Nous croyons que la classification floue, qui permet l’appartenance fractionnelle à plusieurs regroupements, peut décrire de façon plus réaliste bon nombre de formes d’organisation biologique, telles que les populations. Nous utilisons un regroupement flou pour décrire la structure ambiguë d’un troupeau de caribous (Rangifer tarandus) migra- teurs d’après leurs affinités dans l’utilisation de l’espace, ainsi que de stocks de dorés (Stizostedion vitreum) d’après la dissimilarité de leurs génotypes à de nombreux locus. Dans les deux cas, l’appartenance floue met en lumière le degré d’incertitude relié à l’appartenance, tout en réussissant à classer aussi bien les individus qui ne présentent pas d’ambiguïté et ceux qui posent des problèmes. Le caractère vague de la méthode a pour conséquence que les limites de l’identité de chacun des regroupements ne peuvent être définies plus précisément. La classification floue correspond mieux aux fondements empiriques et philosophiques de la biologie et permet de concilier notre besoin de classifier et le monde biologique qui est fondamentalement vague. [Traduit par la Rédaction] 2241 Schaefer and Wilson Introduction Classification is a cornerstone for understanding in biol- ogy. Studies in demography, biogeography, phylogeny, and taxonomy are often intent on, or dependent on, the identifi- cation of discrete organism groups. By placing similarly re- lated objects into fewer clusters, classification can simplify the task of information processing. Not surprisingly, it is one of the most common statistical procedures of biologists (James and McCulloch 1990). In our view, conventional biological classification has re- mained detached from the philosophical underpinnings of the discipline. Traditional cluster analysis, with its focus on assigning absolute group memberships to objects, is rooted in the Aristotelian notion of “class”, the view that variation is an imperfect manifestation of an archetype (Mayr 1988). In contrast, biopopulations are “individuals” (Ghiselin 1966). They are collections of lower-level entities, characterised by internal cohesion and spatiotemporal localisation, and hence defy the classical definition of class (Ghiselin 1969; Hull 1976; Mayr 1988; Baum 1998). This implies a particular methodology for biology: classification might be construed as an attempt to uncover blurred discontinuities among groups rather than a search for rigid boundaries (Brown and Lomolino 1998; Van Regenmortel 1998). We propose that fuzzy-set theory (Zadeh 1965) represents a formal mathematical approach closely allied with this phi- losophy of biology. Despite the label, fuzzy-set theory is an exact approach to handle items displaying continuous varia- tion and place them into classes without distinct boundaries. It generalizes traditional classification, where an object is either a member of a set or it is not, to permit graded membership. Fuzzy membership coefficients vary from 0 to 1, conveying the degree of belonging to a group. Remarkably, although Can. J. Zool. 80: 2235–2241 (2002) DOI: 10.1139/Z02-184 © 2002 NRC Canada 2235 Received 27 February 2002. Accepted 16 October 2002. Published on the NRC Research Press Web site at http://cjz.nrc.ca on 24 January 2003. J.A. Schaefer. 1 Biology Department, Trent University, 1600 West Bank Drive, Peterborough, ON K9J 7B8, Canada. C.C. Wilson. Ontario Ministry of Natural Resources, Aquatic Ecosystems Science Section, 1600 West Bank Drive, Peterborough, ON K9J 8N8, Canada. 1 Corresponding author (e-mail: jschaefer@trentu.ca).