Resource-Limited Growth Sterner (1997) investigated the effect of food quality on

Chapter 5, Problem 12

(choose chapter or problem)

Resource-Limited Growth Sterner (1997) investigated the effect of food quality on zooplankton dynamics. In his model, zooplankton may be limited by either carbon (C) or phosphorus (P). He argued that when food quantity is low, demand for carbon increases relative to demand for phosphorus in order to to satisfy basic metabolic requirements and that there should be a curve separating C- and P-limited growth when food quantity CF (measured in amount of carbon per liter) is graphed as a function of the C:P ratio of the food, f = CF :PF .He derived the following equation for the curve separating the two regions: CF = m aC g CZ aP g PZ f Here, m denotes the respiration rate, g the ingestion rate, and aC (aP ) the assimilation rate of carbon (phosphorus). CZ and PZ are, respectively, the carbon and the phosphorus content of the zooplankton. (a) Show that the graph of y = CF ( f ) approaches the horizontal line y = m aC g as f . (b) The graph of CF ( f ) has a vertical asymptote. Let f = CF :PF (the C:P ratio of the food). Show that the vertical asymptote is at CF PF = CZ PZ aP aC (c) Sketch a graph of CF ( f ) as a function of f . (d) The graph of CF ( f ) separates C-limited (below the curve) from P-limited (above the curve) growth. Explain why this graph indicates that when food quantity is low, the demand for carbon relative to phosphorus increases. 1