190
Approaching Planktonic Food Webs: Competition, Coexistence, and Chaos
stituents of the total ingested food than among different kinds of food particles. In a phosphorus-limited system, zooplankton growth might therefore
be controlled by the total amount of ingested P in relation to ingested C.
If we assume that the grazers are able to capture algae. bacteria. and
detritus with comparable efficiencies, the concentrations of food P and C
available to the grazers can be written as P = P a + P b and C = C a + C b + C;.
with P a and P b [(~g P) rl] being the concentrations of algal and bacterial P,
and Ca' C". and Cd [(mg C) rl] the concentrations of algal, bacterial, and
detrital C. With this notation we can apply the same zooplankton growth
model as in the previous chapter (Eqs. (5.5) and (5.6». While the phosphorus cycle is semiconservative in the sense that recycled P is generally available to autotrophs. the energy flow in food webs (which closely follows the
organic carbon cycle) is necessarily dissipative. with respiratory energy
losses from every biotic compartment. In contrast to P release by grazers,
as described in Section 4.5. organic C release must also account for respiratory losses. If we denote the specific C release of the grazers by Pc (day·\
the release rate can be described by the balance between ingestion (I).
growth (g), and respiration (r):
Pc = I-(g+ r).
(6.23)
Equation (6.23) describes the total release rate of both particulate and
dissolved forms of organic carbon, which must be further differentiated
into a fraction fp Pc entering the pool of particulate detritus and a fraction
(1 - fp )Pc entering the dissolved organic pool. According to Olsen et al.
(1986a), the particulate fraction amounted to 80% of total organic C release
(that is, fp = 0.8). for Daphnia feeding on Scenedesmus under varying
degrees of P limitation.
Carbon Cycling in a Eutrophication Gradient. Mass-balance equations for
algae and bacteria in the presence of a nonselective grazer can be described
in the same formalism as in Section 2.5. If we use indices a and b denoting
process rates and state variables of algae and bacteria, respectively, the
balances between gains and losses from each compartment of carbon biomass [C. and C b ; (mg C) rl] and particulate phosphorus [Po and P ~ (~g P) rl]
can be written as
C; = (P; - {D + FZ))C;
1; = v;C; -{D+ FZ)F;
(6.24)
(6.25)
for i = a, b. As before. D and FZ are losses due to dilution and grazing, while
the terms p; and V; C; denote growth and P uptake in compartment i.
Phosphorus uptake is assumed to be controlled by internal and external P
concentrations as in Eqs. (3.4). (3.5), with the parameters given in Table 3.3.
Algal growth rate (Pa; day·l) is determined by internal P stores according to
the Droop model [Eq. (3.2)], and also with parameters as in Table 3.3.
Approaching Planktonic Food Webs: Competition, Coexistence, and Chaos
stituents of the total ingested food than among different kinds of food particles. In a phosphorus-limited system, zooplankton growth might therefore
be controlled by the total amount of ingested P in relation to ingested C.
If we assume that the grazers are able to capture algae. bacteria. and
detritus with comparable efficiencies, the concentrations of food P and C
available to the grazers can be written as P = P a + P b and C = C a + C b + C;.
with P a and P b [(~g P) rl] being the concentrations of algal and bacterial P,
and Ca' C". and Cd [(mg C) rl] the concentrations of algal, bacterial, and
detrital C. With this notation we can apply the same zooplankton growth
model as in the previous chapter (Eqs. (5.5) and (5.6». While the phosphorus cycle is semiconservative in the sense that recycled P is generally available to autotrophs. the energy flow in food webs (which closely follows the
organic carbon cycle) is necessarily dissipative. with respiratory energy
losses from every biotic compartment. In contrast to P release by grazers,
as described in Section 4.5. organic C release must also account for respiratory losses. If we denote the specific C release of the grazers by Pc (day·\
the release rate can be described by the balance between ingestion (I).
growth (g), and respiration (r):
Pc = I-(g+ r).
(6.23)
Equation (6.23) describes the total release rate of both particulate and
dissolved forms of organic carbon, which must be further differentiated
into a fraction fp Pc entering the pool of particulate detritus and a fraction
(1 - fp )Pc entering the dissolved organic pool. According to Olsen et al.
(1986a), the particulate fraction amounted to 80% of total organic C release
(that is, fp = 0.8). for Daphnia feeding on Scenedesmus under varying
degrees of P limitation.
Carbon Cycling in a Eutrophication Gradient. Mass-balance equations for
algae and bacteria in the presence of a nonselective grazer can be described
in the same formalism as in Section 2.5. If we use indices a and b denoting
process rates and state variables of algae and bacteria, respectively, the
balances between gains and losses from each compartment of carbon biomass [C. and C b ; (mg C) rl] and particulate phosphorus [Po and P ~ (~g P) rl]
can be written as
C; = (P; - {D + FZ))C;
1; = v;C; -{D+ FZ)F;
(6.24)
(6.25)
for i = a, b. As before. D and FZ are losses due to dilution and grazing, while
the terms p; and V; C; denote growth and P uptake in compartment i.
Phosphorus uptake is assumed to be controlled by internal and external P
concentrations as in Eqs. (3.4). (3.5), with the parameters given in Table 3.3.
Algal growth rate (Pa; day·l) is determined by internal P stores according to
the Droop model [Eq. (3.2)], and also with parameters as in Table 3.3.