Summary and Conclusions
59
Figure 3.11 shows that species 2 (which was designed to be the superior
competitor for N) dominates at low N:P supply ratios and is gradually displaced by species 1 (the superior competitor for P) with increasing supply
ofN relative to P. As pointed out by Turpin (1988), the range ofN:P supply
ratios supporting coexistence is not independent of the dilution rate; on the
contrary, it is shifted toward the lower end of the N:P gradient by increasing growth rate. This downward displacement of the N:P interval of coexistence is probably caused by the assumption of less storage capacity for N
than P, which makes the equilibrium cellular N : P ratio at equal Nand P
limitation (Q·N.JQ·P) decrease with increasing growth rate for both species.
The two parameter sets given in Table 3.4 are carefully designed to
satisfy the conditions for coexistence given by Eqs. (ALl), (A1.2), (A1.8). If,
on the other hand, the two competing species were such that their relative
uptake affinities were not within the triangular region in Fig. 3.9, but still
gave the same relative isocline positions as in Fig. 3.8, we would have found
no region of coexistence. Instead, we would have found a sharp transition
fr0';fl s~ecies 2 ~? sp~~ies 1 at a N:P supply r.atio equal t? S·N.I IS·p•2• If we
mamtam that PI = P 2' we would have S N.I/S P.2 = K N.IIK P.2' and therefore
that this critical N:P supply ratio is independent of the dilution rate.
3.8 Summary and Conclusions
In the course of this chapter we have developed a simple model of P-limited
growth in phytoplankton populations. The model is able to represent a
suite of observed phenomena related to algal growth and nutrient uptake
including: flexible nutrient utilization in response to nutrient supply rate,
fast bidirectional nutrient exchange processes between cells and water,
enhanced nutrient uptake capacity with increasing nutrient limitation, and
threshold effects in the growth response to external nutrient concentration.
The present model is a member of the same family of nonequilibrium
extensions to the Monod model, but is able to account for a larger number
of phenomena with the same number of parameters as in models of Droop
(1983), Burmaster (1979), and Morel (1987). It is shown that this model
framework can also be applied to other food web components that utilize
dissolved inorganic nutrients (like bacteria), and that it can be extended to
represent situations where more than one nutrient may be limiting (like N
and P).
The model contains five key parameters that are considered fundamental
to the processes of phytoplankton growth and nutrient utilization under
phosphorus limitation: maximum growth rate (p", minimum and maximum cell quota (Q' and Q'1, maximum nutrient uptake affinity (a', and
threshold nutrient concentration for positive net uptake (S1. As very few
phytoplankton species have been characterized by the full set of parame-
59
Figure 3.11 shows that species 2 (which was designed to be the superior
competitor for N) dominates at low N:P supply ratios and is gradually displaced by species 1 (the superior competitor for P) with increasing supply
ofN relative to P. As pointed out by Turpin (1988), the range ofN:P supply
ratios supporting coexistence is not independent of the dilution rate; on the
contrary, it is shifted toward the lower end of the N:P gradient by increasing growth rate. This downward displacement of the N:P interval of coexistence is probably caused by the assumption of less storage capacity for N
than P, which makes the equilibrium cellular N : P ratio at equal Nand P
limitation (Q·N.JQ·P) decrease with increasing growth rate for both species.
The two parameter sets given in Table 3.4 are carefully designed to
satisfy the conditions for coexistence given by Eqs. (ALl), (A1.2), (A1.8). If,
on the other hand, the two competing species were such that their relative
uptake affinities were not within the triangular region in Fig. 3.9, but still
gave the same relative isocline positions as in Fig. 3.8, we would have found
no region of coexistence. Instead, we would have found a sharp transition
fr0';fl s~ecies 2 ~? sp~~ies 1 at a N:P supply r.atio equal t? S·N.I IS·p•2• If we
mamtam that PI = P 2' we would have S N.I/S P.2 = K N.IIK P.2' and therefore
that this critical N:P supply ratio is independent of the dilution rate.
3.8 Summary and Conclusions
In the course of this chapter we have developed a simple model of P-limited
growth in phytoplankton populations. The model is able to represent a
suite of observed phenomena related to algal growth and nutrient uptake
including: flexible nutrient utilization in response to nutrient supply rate,
fast bidirectional nutrient exchange processes between cells and water,
enhanced nutrient uptake capacity with increasing nutrient limitation, and
threshold effects in the growth response to external nutrient concentration.
The present model is a member of the same family of nonequilibrium
extensions to the Monod model, but is able to account for a larger number
of phenomena with the same number of parameters as in models of Droop
(1983), Burmaster (1979), and Morel (1987). It is shown that this model
framework can also be applied to other food web components that utilize
dissolved inorganic nutrients (like bacteria), and that it can be extended to
represent situations where more than one nutrient may be limiting (like N
and P).
The model contains five key parameters that are considered fundamental
to the processes of phytoplankton growth and nutrient utilization under
phosphorus limitation: maximum growth rate (p", minimum and maximum cell quota (Q' and Q'1, maximum nutrient uptake affinity (a', and
threshold nutrient concentration for positive net uptake (S1. As very few
phytoplankton species have been characterized by the full set of parame-