58
Algae and Nutrients: Uptake and Utilization of Limiting •••
Algal Competition in a Gradient ofN:P Supply Ratios. The eight differential
equations given by Eqs. (3.18), (3.19), (3.24), together with process rates
and parameters given by equations (3.20) - (3.23) and Table 3.4, constitute
a chemostat-type model of two species competing for Nand P. At a fixed
dilution rate (D), a gradient of N:P supply ratios can be simulated by
running the model under varying input concentrations of inorganic Nand
P (N L and P L ). Since we must have RL > S·R,I for R = N, P, in order to have a
non-zero biomass of species i at a given dilution rate, input concentrations
were chosen such that RL > Max(S·v S·R,2). Using the numerical methods
described in Appendix A9, the model was run to equilibrium for different
combinations of dilution rates and input concentrations. Model runs were
initiated by simulating the inoculation of nutrient-sufficient cells from both
species (that is, QR.I = Q"R.I for i = 1,2 and R = N, P) into a sterile system
with Sp = P L and SN = NL (trials with other choices of initial conditions did
not affect the equilibrium solution). Fig. 3.11 shows the simulation results
expressed as equilibrium biomass fractions of species 1 for different combinations ofN:P supply ratios and dilution rates.
N : P supply ratio (at: at)
10
15
20
25
1.0 -.--+------+-----=:::1=;.000~~--_+____,
0.8
0.6
0.4
0.2
0.04------£--~~~~~----~--------~r----------;
4
6
8
10
12
N : P supply ratio ([J.lg N] [J.lg P] -1 )
Fig. 3.11. Coexistence in a gradient of N:P supply ratios at different dilution rates. Solid curves
Equilibrium fraction species 1 of total biomass at a given dilution rate (curve label)