Resource versus ratio-dependent consumer-resource models: A Bayesian perspective

There is an ongoing debate in the literature regarding the appropriate mathematical description of consumer resource interactions, particularly with respect to the issue of resource vs. ratio-dependent functional response models. Early formulations of consumer-re source exploitation of the Lotka-Volterra type described predator consumption rates as linear functions of prey density (see Berryman 1992). This characterization has since been questioned by many researchers (e.g., Holling 1959, DeAngelis et al. 1975). Numerous consumer-resource functional response models have been proposed, each implying different system behaviors and stabilities. In a series of recent articles R. Arditi and colleagues have advocated a modification of these functional responses so that consumer exploitation of a resource is related to the ratio of the resource to the consumer (Arditi and Ginzburg 1989, Arditi et al. 1991, Arditi and Saiah 1992). This view has been challenged by Oksanen et al. (1992) who favor are source-dependent functional response. Diehl et al. (1993) have offered the perspective that simplified descriptions of consumer-resource dynamics are counter productive because they preclude a true mechanistic understanding of the complex interactions that occur. We argue that resource vs. ratio dependence should not be approached as a dichotomy, but rather as a continuum, and propose a Bayesian perspective as a useful context in which to view the issue. From this vantage ratio dependence can be a matter of degree, which varies among systems, and serves as a useful surrogate to characterize underlying mechanisms. Previous research has shown that resource vs. ratio dependence is difficult to ascertain from field data (Carpenter et al. 1994). This difficulty may, in part, result from spatial and temporal aggregation of the data such that resource/ratio dependence is in fact manifest at an intermediate level. We demonstrate the Bayesian approach with a simple ex ample, using time-series data from a mesocosm nutrient-enrichment experiment.