More Than One Limiting Nutrient - P and N Limitation
57
By the same kind of reasoning as in Section 3.4, we can assign the lower
and upper quartiles of the distribution in Fig. 3.10 as low and high
parameter values. Thus, we will assume that Q'N,IIQ'", = 12.2 (Ilg N) (Ilg Pt
and that Q'N,/Q''',2 = 5.9 (Ilg N) (Ilg pt. Since N is a much larger cell constituent than P, it is reasonable to assume that much of the variability in
"optimum" N:P ratios is due to variability in the subsistence quota for P. If
we assign the low and high minimum P:C ratios given in Table 3.1 to species 1 and 2 [that is, Q''',I = 2.5 (Ilg P) (mg C)'I and Q''',2 = 5.2 (Ilg P) (mg ct],
the corresponding subsistence ~uotas for N become Q~I = 30.5 (Jl8 N) (mg Cr
l
and Q'N,2 =30.7 (Ilg N) (mg Cr . If we assume identical storage capacities for
P in both species (Q"",IIQ'",I = Q"",2IQ''',2 = 7.5; typical parameter val~e in
Table 3.1), the maximum P:C ratios become Q"I'.I = 18.8 (Ilg P) (mg Cr and
Q"",2 = 39.0 (Ilg P) (mg ct. Plankton algae are generally found to have
lower storage capacities for N than for P (Turpin 1988), so that we would
expect that Q"".JQ''',I >Q"N.JQ'N,I· Ifwe assume Q"N,I'Q'N,I= Q"N,2'Q'N,2 = 4, as
indicated by Goldman and McCarthy (1978), the maximum N:C ratios
become Q"N,I = 121.9 (Ilg N) (mg C)'I and Q"N,2 = 122.8 (Ilg N) (mg C)'I. This
set of model parameters gives atomic C:N:P ratios at nutrient-saturated
growth equal to 137.4:14.4:1 for species 1, and 66.2:7.0:1 for species 2.
With this combination of subsistence quotas for Nand P in the two
species, the relative uptake affinities for Nand P must be located within the
triangular region in Fig. 3.9 in order to have coexistence between the two
species at certain N:P supply ratios. If we assume that species 1 has maximum uptake affinities for both Nand P equal to the typical parameter
value given in Table 3.1 [a~,l = a~,l= 6.51 (mg ct day"I], then choosing a~.2
=10.5 I (mg cr
l day"1 and a~,2 = 8.5 I (mg C)'I day"1 yields a parameter
combination close to the center of the feasible region for coexistence in
Fig. 3.9. The resulting set of model parameters are summarized in Table 3.4.
Table 3.4. Nand P uptake and utilization parameters in the species pair considered in Fig. 6.13,
as well as the corresponding Monod half-saturation parameters [given by Eq. (3.11) )
Parameter
Species 1
Species 2
Unit
Q'"
Subsistence P quota
2.5
5.2
().Ig P) (mg Cr'
Q"p
Maximal P quota
18,8
39,0
().Ig P) (mg cr'
a'
"
Maximal P uptake affinity
6.5
10,5
I (mg Cr' dat'
K'
"
Monod parameter
0.46
0.59
().Ig P) r'
Q'N
Subsistence N quota
30,S
30,7
().Ig N) (mg Cr'
Q"N
Maximal N quota
121.9
122,8
().Ig N) (mg cr'
a' N
Maximal N uptake affinity
6.5
8.5
I (mg Cr' dat'
K'
"
Monod parameter
5.63
4.33
().Ig N) r'
57
By the same kind of reasoning as in Section 3.4, we can assign the lower
and upper quartiles of the distribution in Fig. 3.10 as low and high
parameter values. Thus, we will assume that Q'N,IIQ'", = 12.2 (Ilg N) (Ilg Pt
and that Q'N,/Q''',2 = 5.9 (Ilg N) (Ilg pt. Since N is a much larger cell constituent than P, it is reasonable to assume that much of the variability in
"optimum" N:P ratios is due to variability in the subsistence quota for P. If
we assign the low and high minimum P:C ratios given in Table 3.1 to species 1 and 2 [that is, Q''',I = 2.5 (Ilg P) (mg C)'I and Q''',2 = 5.2 (Ilg P) (mg ct],
the corresponding subsistence ~uotas for N become Q~I = 30.5 (Jl8 N) (mg Cr
l
and Q'N,2 =30.7 (Ilg N) (mg Cr . If we assume identical storage capacities for
P in both species (Q"",IIQ'",I = Q"",2IQ''',2 = 7.5; typical parameter val~e in
Table 3.1), the maximum P:C ratios become Q"I'.I = 18.8 (Ilg P) (mg Cr and
Q"",2 = 39.0 (Ilg P) (mg ct. Plankton algae are generally found to have
lower storage capacities for N than for P (Turpin 1988), so that we would
expect that Q"".JQ''',I >Q"N.JQ'N,I· Ifwe assume Q"N,I'Q'N,I= Q"N,2'Q'N,2 = 4, as
indicated by Goldman and McCarthy (1978), the maximum N:C ratios
become Q"N,I = 121.9 (Ilg N) (mg C)'I and Q"N,2 = 122.8 (Ilg N) (mg C)'I. This
set of model parameters gives atomic C:N:P ratios at nutrient-saturated
growth equal to 137.4:14.4:1 for species 1, and 66.2:7.0:1 for species 2.
With this combination of subsistence quotas for Nand P in the two
species, the relative uptake affinities for Nand P must be located within the
triangular region in Fig. 3.9 in order to have coexistence between the two
species at certain N:P supply ratios. If we assume that species 1 has maximum uptake affinities for both Nand P equal to the typical parameter
value given in Table 3.1 [a~,l = a~,l= 6.51 (mg ct day"I], then choosing a~.2
=10.5 I (mg cr
l day"1 and a~,2 = 8.5 I (mg C)'I day"1 yields a parameter
combination close to the center of the feasible region for coexistence in
Fig. 3.9. The resulting set of model parameters are summarized in Table 3.4.
Table 3.4. Nand P uptake and utilization parameters in the species pair considered in Fig. 6.13,
as well as the corresponding Monod half-saturation parameters [given by Eq. (3.11) )
Parameter
Species 1
Species 2
Unit
Q'"
Subsistence P quota
2.5
5.2
().Ig P) (mg Cr'
Q"p
Maximal P quota
18,8
39,0
().Ig P) (mg cr'
a'
"
Maximal P uptake affinity
6.5
10,5
I (mg Cr' dat'
K'
"
Monod parameter
0.46
0.59
().Ig P) r'
Q'N
Subsistence N quota
30,S
30,7
().Ig N) (mg Cr'
Q"N
Maximal N quota
121.9
122,8
().Ig N) (mg cr'
a' N
Maximal N uptake affinity
6.5
8.5
I (mg Cr' dat'
K'
"
Monod parameter
5.63
4.33
().Ig N) r'