Modularity, like the responsiveness that gives rise to it during development and evolution, is a universal property of living things and a fundamental determinant of how they evolve. Modularity refers to the properties of discreteness and dissociability among parts and integration within parts. There are many other words for the same thing, such as atomization (Wagner, 1995), individualization (Larson and Losos, 1996), autonomy (Nijhout, 1991b), dislocation (Schwanwitsch, 1924), decomposability (Wimsatt, 1981), discontinuity (Alberch, 1982), gene nets (Bonner, 1988), subunit organization (West-Eberhard, 1992a, 1996), compartments or compartmentation (Garcia-Bellido et al., 1979; Zuckerkandl, 1994; Maynard-Smith and Szathmary, 1995; Kirschner and Gerhart, 1998), and compartmentalization (Gerhart and Kirschner, 1997). One purpose of this chapter is to give consistent operational meaning to the concept of modularity in organisms. Seger and Stubblefield (1996, p. 118) note that organisms show “natural planes of cleavage” among organ systems, biochemical pathways, life stages, and behaviors that allow independent selection of different ones. They ask, “What determines where these planes of cleavage are located” and suggest that a “theory of organic articulations” may give insight into the laws of correlation, without specifying what the laws of articulation may be. Wagner (1995, p. 282) recognizes the importance of modularity and proposes a “building block” concept of homology where structural units often correspond to units of function, but concludes (after Rosenberg, 1985) that “there exists no way to distinguish an adequate from an inadequate atomization of the organisms.” Here I propose that modularity has a specific developmental basis (see also West-Eberhard, 1989, 1992a, 1996; see also Larson and Losos, 1996). Modular traits are subunits of the phenotype that are determined by the switches or decision points that organize development, whether of morphology, physiology, or behavior. Development can be seen as a branching series of decision points, including those caused by physical borders such as membranes or contact zones of growing or diffusing parts (e.g., see Meinhardt, 1982; see also chapter 5, on development). Each decision point demarcates the expression or use of a trait—a modular set—and subordinate branches demarcate lower level modular subunits, producing modular sets within modular sets.
A homotopy-theoretic universal property of Leinster's operad for weak ω-categories
