Appendix A: from S. R. Hall et al., “Inedible Producers in Food Webs: Controls on Stoichiometric Food Quality and Composition of Grazers”

In this appendix, we provide analytical results to support the description of the food web model (eqq. [1]) presented in the text. This model considers interactions between edible and inedible producers (AE and AI, respectively) and two grazers (G1 and G2). Simultaneously, it tracks the nutrient : carbon ratio of the edible producer (Q), nutrient sequestered in edible producers (i.e., the product of Q and AE, denoted as QAE), and available nutrient resources (R) over gradients of nutrient (S) and light (L) supply. For compactness, we write the Monod function for light as and for edible and inedible producers, B p L/(b L) B p L/(b L) E E I I respectively. These functions BE and BI increase with light supply, from 0 to an asymptote of 1. They can be thought of as the degree to which producers are limited by light (Hall 2004). Some of these results, particularly those concerning the food chain and grazer coexistence, have been presented in detail elsewhere for a similar model (Hall 2004). Thus, they are presented summarily here. Two tables accompany this appendix. Table A1 summarizes the variables, parameters, and synthetic quantities, while table A2 describes qualitative response of the food web components to increases in nutrient and light supply in the original model (eqq. [1]).