Imagine being an individual like Summer Stiers, a 31-year-old woman from Oregon coping with dysfunction in multiple organ systems and no diagnosis after years of visits to doctors and medical tests. As described in a recent article in the New York Times Magazine (February 22, 2009), Ms. Stiers had gone to the National Institutes of Health to be assessed in the Undiagnosed Diseases Program, hoping that “all these tests were something I could do and make a difference, so someone else wouldn’t have to go through this, having things go wrong and not knowing what is coming next.” Anyone who has suffered from symptoms that were difficult to associate with a particular, recognized clinical condition will be more likely to appreciate how important classification can be.Even if the label for a disease does not immediately dictate a useful intervention, it can often offer increased insight into what can be expected, which is likely to be a benefit for at least some patients and in at least some circumstances.

Last fall, Jeffrey Parsons and Yair Wand, writing in Nature (455:1040-1041, 2008; doi:10.1038/4551040a; http://www.nature.com/nature/journal/v455/n7216/full/4551040a.html) addressed the role of classification in science through an examination of a few relatively high-profile issues that were or are regarded as sources of controversy. One of their claims was that a research community could employ multiple definitions for entities or phenomena that were preferentially employed in different circumstances. I have similarly argued that there are probably multiple useful definitions for many of the key concepts in biology and medicine and that the preferred classification scheme in a given domain can depend on the experimental or observational question motivating the investigation, which I have referred to as the Principle of Purpose-Dependent Ontology (Greenspan, 2004). Specific examples of concepts associated with multiple definitions that I have discussed elsewhere include: epitope map, epitope, gene, gene (or gene product) function, and life (Greenspan and Monafo, 1987; Greenspan, 1992; Greenspan and Cooper 1995; Greenspan, 1998; Greenspan and DiCera, 1999; Greenspan, 2001; Greenspan 2002; Greenspan, 2004; Greenspan, 2007).

Parsons and Wand also emphasize that an exercise in classification can embody two (or more) goals that inherently conflict. For example, they argue that groupings should ideally facilitate prediction of the attributes of the entities contained therein (of obvious importance in medicine) and should also exhibit stability in the face of newly encountered entities requiring assignment. Unfortunately, they suggest, efforts devoted to increasing such predictive power may undermine efforts devoted to increasing stability (see below). This challenging aspect of classificatory reality highlights the need to relinquish the unreasonable expectation that there will be a single globally superior scheme for grouping the entities and processes relevant to every discipline and sub-discipline.

Considering this reasonable preference for groupings with predictive value, it should come as no surprise that a key thesis in their article is the distinction between what they term “categories” and what they term “classes.” Parsons and Wand use “category” to refer to a grouping containing entities that may share no features in common, so that membership in the category implies no necessary attributes. Thus, categories represent groupings with low or no predictive value. In contrast, membership in what they call a “class” guarantees possession of a finite list of attributes such that association of an entity with a relevant class permits certain predictions regarding one or more properties of that member of the grouping.

Of course, as the authors acknowledge, in biology the relationship of class membership to the attributes of the entities in the class is fundamentally unstable. In fact, such instability is a critical and necessary property of entities that evolve. Thus, I am not confident that the goal of biologists should be to assign molecules, cells, organisms, or biological entities at higher levels of organization to what Parsons and Wand regard as classes.

An illustrative example of the problematic nature of such rigid groupings in biology is provided by a recent finding in connection to dung beetles, as described in a research news item at the-scientist.com (Dolgin, 2009). Trond Larsen, a biologist at Princeton, studied beetles of the subfamily Scarabaeinae in the Peruvian rainforest. He and his co-authors found (Biology Letters, 2009) one beetle species, Deltochilum valgum Burmeister (out of 132 species studied), that was morphologically highly similar to the other species in the subfamily but that had distinguished itself with respect to behavioral traits. This one species had abandoned the hallowed traditions of coprophagy and taken up predation on millipedes as its exclusive means of obtaining food. Thus, according to the speculation of Larsen et al., intense competition for a limited resource had led this one species of beetle to lose a defining behavioral feature of the entire subfamily of which it is a part.

A subset of biologists and physicians, perhaps a relatively small subset, will be aware of the existence of units of classification that, strictly speaking, are neither mere categories nor the putatively more useful classes in the precise senses used by Parsons and Wand. I refer to fuzzy sets (Kosko, 1993) and what I think are most widely known as polythetic categories or family-resemblance groups (Needham, 1983). The latter entities have been claimed to solve the so-called species problem by the well-known evolutionary biologist, Massimo Pigliucci (2006). Whether or not they solve the problem entirely, polythetic classes, as well as fuzzy sets, offer a more useful way to think about biological variation than is permitted by the standard classes of Parsons and Wand.

Consider fuzzy sets. The membership function for a fuzzy set instead of being all-or-none permits degrees of membership. Thinking about a grouping as a geometrical object, the boundary of a fuzzy set is a somewhat hazy zone instead of the infinitesimally narrow line that demarcates the edges of a classical class. For example, instead of classifying people as rich or not-rich, it can be more useful for some purposes to grade richness in proportion to total resources denominated in some currency. Similarly, when dealing with biological entities or phenomena that are characterized by quantitative variation, there will be some questions for which classification will be more sensible if the relevant magnitudes are taken into account (even if in other instances an approach based on the relationship to a threshold value is useful). Thus, one might expect that certain physiological or pathophysiological phenotypes will correlate with the magnitudes of such quantities as blood pressure, mass, or metabolic rate. Simply noting if an individual’s value surpasses a particular cut-off value will not always be maximally informative.

Polythetic classes, also sometimes referred to as family-resemblance concepts (Wittgenstein, 1953), radial categories (Lakoff, 1987), or polytopic classes (Beckner, 1968), refer to groupings where only some of a series of attributes may be possessed by any member of class. In geometrical terms, such a grouping can be represented as a multi-dimensional enclosure with (in some cases, but not all) an “inner sanctum” containing one or more prototypical members possessing all of the class-defining attributes, and various numbers of “rooms” arrayed concentrically around the innermost space, with the number of membership-defining attributes possessed in each such compartment decreasing with distance from the central zone. So, while an element in the polythetic class could possess all of the attributes of interest (thereby justifying residence in the central compartment), no single element necessarily has to be prototypical, and no single attribute of interest has to be possessed by all members, although such can be the case. In Wittgenstein’s case, he illustrated the problem by considering definitions for “game.” He concluded that so single definition based on necessary and sufficient conditions adequately captures all reasonable uses of “game.”

Applying the notion of a polythetic class to the subfamily of beetles known as dung beetles, it is not essential for every species to exhibit coprophagy. A species that lacks this behavioral trait can still share numerous morphological (and, presumably, other) traits with the remaining species in the subfamily. As noted above, it is inherent in evolution that entities sharing all of a series of attributes (whether they are molecular, metabolic, physiological, morphological, or behavioral) can directly give rise to progeny that share fewer of these common traits.

Numerous categories of biological importance are more usefully regarded as polythetic in nature than as conventional classes of the Parsons-Wand variety. In fact, the inability of an assembly of elite (as assessed by one of the so-assembled) scientists to formulate a definitive definition of life (Koshland, 2002) can arguably be attributed to their mistaken assumption that living beings are a class, as opposed to a polythetic class. So, for example, from the perspective that “life” refers to a polythetic class of objects, a virus is alive in that it can replicate and evolve, exchange genetic material with living cells, and even “commandeer” some of the metabolic pathways of living cells. However, a virus is not “as alive” as a cell in that it does not have its own metabolism and cannot reproduce without parasitizing cells.

Physicians will no doubt also see the ease with which polythetic classes can be (are) applied in medicine, such as in the definition of clinical conditions. It is overwhelmingly clear that many diseases and syndromes vary in the presence or absence of one or more features in different patients and for a given disease or condition there may not be any single feature (symptom, sign, laboratory result, or radiological finding) that is absolutely determinative of the diagnosis. The genetic underpinnings of many clinical phenotypes are also heterogeneous in ways that both reflect the fundamental evolutionary processes that are at least partly responsible for them and that correspond to polythetic groupings of alleles at multiple loci.

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