Previous models of particle feeding have focused on optimal solutions for particle acquisition or absorption. We propose two conceptual approaches to treat particle feeders as an integrated system of compartments, in hopes of understanding critical limiting factors that might be overlooked by focusing on only one part. The compartment model treats a particle feeder as a series of structures that process particles, with characteristic residence times within compartments and transfer points between them. These might change with overall particle food value and proportion of poor particles. As a non-exclusive alternative, the pathway model considers particle transfer as being analogous to enzyme control systems, with feedback loops that may involve interactions such as negative feedback between compartments that engage in no direct transfer. We examine these models in the light of some studies of particle handling by the deposit-feeding bivalves Yoldia limatula, Macoma secta, and M. nasuta, and the suspension-feeding oyster Crassostrea gigas. In Y. limatula, palp overloading results in feedback that shuts down the particle-collecting palp proboscis. In Macoma, nearly all particles are rejected, suggesting that rejection is necessary because digestion and gut residence time are limiting factors. We suggest that a whole-system approach is important in understanding particle processing by deposit feeders and suspension feeders. Additional key words: feeding, deposit feeding, suspension feeding, symmorphosis The purpose of this paper is to provide a conceptual framework for analyzing the processing of food particles by bivalve molluscs. We model the component organ systems as a series of compartments with transfer points between them, but with potential feedback loops among all potential compartments. Because the various compartments-ctenidium, palp, gut, and their components-have differing structures and functions, mechanisms are necessary for transfers of particles between them, e.g., the mucus string that transports particles between the ctenidium and palp in suspension feeders. Owing to disparate evolutionary origins and inherent structural difficulties, the supply of particles from one compartment to the next might cause overloading or rates of particle supply from one compartment that are below the capacity of another. In other words, the particle-processing system found in bivalve molluscs and other organisms might not function optimally with fixed transfer rates. Alternatively, the system might consist of a series of components whose individual processing rates are fixed and perfectly adapted to each other, much as has been suggested in arguments for other complex systems (Taylor & Weibel 1981; Weibel et al. 1991). We will first present a general compartment model for examining particle feeders such as bivalve molluscs. We describe compartments specifically for a selected group of bivalve species and show how problems ranging from phylogeny to the study of particle transfer between compartment structures can be studied. We will also use another conceptual model, derived from enzyme pathway analysis, to point out how interactions among the compartments can be considered. Finally, we will present some data on two species of deposit-feeding bivalves and some preliminary data on a suspension feeder to demonstrate how this approach allows a sharpening of our understanding of particle feeding and processing. This content downloaded from 207.46.13.52 on Mon, 24 Oct 2016 04:13:08 UTC All use subject to http://about.jstor.org/terms Models of particle processing Bivalve particle feeding Benthic particle feeders are typically divided into deposit feeders and suspension feeders. These represent a continuum rather than two discrete modes, although specific mechanisms of collection and processing may differ. Within the superfamily Tellinacea, for example, we encounter a range of morphologies, from those best suited for suspension feeding to those more efficient at deposit feeding (Yonge 1949; Pohlo 1966, 1967). Many particle-feeding species, including bivalves, switch from deposit to suspension feeding, depending upon substratum and hydrodynamic conditions (Taghon et al. 1980; Dauer 1983; Miller 1984; Olafsson 1986; Miller et al. 1992). The food source for both feeding types, however, is often quite similar, as it may consist of material resupplied by storm and other resuspension events (Miller et al. 1984; Frechette et al. 1989; Judge et al. 1993). In both bivalve feeding types, particles are collected actively, followed by one or more particle-processing stages, which usually involve particle rejection by the ctenidium and palp before particles enter the gut. Some food particles then pass directly through a tubular gut while others may be shunted to a diverticular structure where complete intracellular digestion occurs. Benthic particle feeders can be examined with regard to two principal problems. How do they deal with (1) variation of particle load (volume of particles supplied per unit time), and (2) varying proportions of particles of differing quality? Both deposit feeders and suspension feeders are confronted with widely varying particle loads and ranges of quality. Deposit feeders deal with high loads of particles that are mostly indigestible and that may require rejection before appropriate particles enter the gut (Lopez & Levinton 1987). They deal with this problem partly by non-random search and particle-collection strategies (Taghon et al. 1978; Levinton 1980; Whitlatch & Weinberg 1982), by variation of ingestion rate when local patches of high quality particles are encountered (Taghon 1981; Taghon & Jumars 1984), and by rejection of low quality particles (Hylleberg & Gallucci 1975; Taghon 1982). The bivalve Macoma nasuta typically rejects over 95% of the material that enters its incurrent siphon (Hylleberg & Gallucci 1975). By contrast, some sea cucumbers feed nearly indiscriminately, and digestive processing must be a major consideration in maximizing energy uptake (Powell 1977; Sloan & von Bodungen 1980). Suspension feeders also deal with a wide variety of particle loads and with particles of varying quality. At extreme loading, suspension feeders may adjust pumping rates, but bivalve molluscs also collect particles on the ctenidium and then reject those that are non-nutritive in the form of pseudofeces (Ki0rboe et al. 1980). There is growing evidence for qualitative selection (Newell & Jordan 1983; Ward & Targett 1989; MacDonald & Ward 1994) even of similar-sized organic particles (Shumway et al. 1985). Ingestion rates and other feeding processes appear to respond to changing content of non-nutritive particles (Bayne et al. 1989; Iglesias et al. 1992). Depending upon the degree of non-nutritive particle loading, cockles may respond by altering rates of particle uptake and the degree of rejection of particles as pseudofeces (Iglesias et al. 1992). In sum, particle feeders appear to respond in manifold and complex ways to the two cardinal problems outlined above. Previous conceptual approaches Three distinct but certainly not contradictory approaches have been applied to the modeling of particle processing, as well as other functional problems. The first approach involves models that place constraints upon feeding. Certain features of bivalve feeding have been argued to have characteristic hydrodynamic properties, and several authors have devised models that limit bivalves to certain physical mechanisms of particle processing, such as mechanical transport (Whitlatch & Weinberg 1982; J0rgensen 1989). More general models of particle feeding predict that certain particle sizes are collected with less efficiency than others, owing to hydrodynamic constraints (Rubenstein & Koehl 1977; Shimeta 1993). Processing rates also may be fixed, which could lead to characteristic transfer rates and loadings in a particle-processing chain. The second approach involves development of compensation models of feeding. Compensation is a change in behavior (e.g., rate of water transport through the siphon) following a change in feeding conditions (e.g., change in particle concentration in the water) that increases the rate of food uptake by the animal over the rate that would be found if no compensation occurred. For example, some studies report changes in rate of inflow that compensate for changes in phytoplankton concentration (Bayne et al. 1988). These models implicitly assume an array of optimal solutions corresponding to changing conditions and that bivalves can adjust at least in the direction of these optimal states. Finally, optimal models are more explicit renditions of compensation models. Such models take a series of boundary conditions and predict an optimal solution to foraging or digestion. For example, Penry & Jumars (1987) argued that during deposit feeding, particles 233 This content downloaded from 207.46.13.52 on Mon, 24 Oct 2016 04:13:08 UTC All use subject to http://about.jstor.org/terms Levinton, Ward, & Thompson Fig. 1. Conceptualization of a bivalve mollusc as a system of compartments with transfer between