124
Nutrients. Algae and Herbivores - the Paradox of Enrichment Revisited
be considered a representative random sample oflakes in general; as the data
were collected to investigate the relationship between tlushing and retention,
it is very likely that lakes with very low and very high dilution rates are overrepresented.
By evaluating the relative parameter sensitivities of the persistence
boundary [Eqs. (A8.7)-(A8.1O)] for the parameter values in Table 5.1, we
find that D~ is very robust to changes in the algal growth and loss parameters: a 1 % increase in the maximal algal growth rate (Ji) or the algal
sinking loss rate (00) results in only a 0.05% decrease or a 0.001% increase
in D~ . On the other hand, the persistence boundary is very sensitive to
changes in grazer growth and loss parameters: a 1% increase in the maximal grazer growth rate (g~ or the grazer mortality rate (b) results in either
a 1.7% increase or a 0.7% decrease in the critical dilution rate D~. The result
suggests that a grazer population should be most vulnerable to predation
when the water renewal time is close to the persistence boundary; in that case,
only a modest increase in the mortality rate (b) caused by predatory losses
might be sufficient to make the grazer extinction point stable.
The persistence boundary is also very sensitive to changes in the stoichiometric properties of the organisms: a 1 % increase in the algal subsistence quota (Q~ or the grazer P content (8) results in either a 1.7%
increase or a 1.7% decrease in the critical dilution rate D~. This result may
suggest that the rotifers should be the zooplankton group most likely to
succeed in lakes with high dilution rates, as many rotifers have high maximal growth rates (cf. Fig. 4.22) and low phosphorus requirements compared to other groups (Hessen and Lyche 1991) •
For dilution rates below the persistence boundary, grazer extinction can
also result if the P loading is sufficiently low. If the input concentration is
below a critical level PILI defined by (A6.23), there will not be any stationary
points with non-zero zooplankton biomass. Substituting the model parameters in Table 5.1 into Eq. (A6.23) gives P'£ = 0.68 (Jig P) r
l for D = D:.
With the lowest total P value observed in the NIV A survey shown in Fig. 2.3
being 1.4 (Jig P) r., we can expect the critical input concentration P'£ to be
exceeded in all of the 355 Norwegian lakes investigated in that survey, even
if we assume zero P retention and no load decay.
If the input concentration is above the critical level (P£ > P'£), and the
dilution rate is above the persistence boundary (D > D~ ), an additional
internal stationary point comes into existence. This stationary point is
characterized by grazer growth rate being limited only by algal P content, and
not by algal biomass in terms of carbon. In Appendix A6 it is shown that at
this stationary point, algal growth rate is independent of the P loading
conditions, while both phyto- and zooplankton biomasses are directly
proportional to the input concentration P LI and thus, also proportional to
each other. In Appendix A7 it is shown that if this stationary point exists,
then it will always be locally unstable.
Nutrients. Algae and Herbivores - the Paradox of Enrichment Revisited
be considered a representative random sample oflakes in general; as the data
were collected to investigate the relationship between tlushing and retention,
it is very likely that lakes with very low and very high dilution rates are overrepresented.
By evaluating the relative parameter sensitivities of the persistence
boundary [Eqs. (A8.7)-(A8.1O)] for the parameter values in Table 5.1, we
find that D~ is very robust to changes in the algal growth and loss parameters: a 1 % increase in the maximal algal growth rate (Ji) or the algal
sinking loss rate (00) results in only a 0.05% decrease or a 0.001% increase
in D~ . On the other hand, the persistence boundary is very sensitive to
changes in grazer growth and loss parameters: a 1% increase in the maximal grazer growth rate (g~ or the grazer mortality rate (b) results in either
a 1.7% increase or a 0.7% decrease in the critical dilution rate D~. The result
suggests that a grazer population should be most vulnerable to predation
when the water renewal time is close to the persistence boundary; in that case,
only a modest increase in the mortality rate (b) caused by predatory losses
might be sufficient to make the grazer extinction point stable.
The persistence boundary is also very sensitive to changes in the stoichiometric properties of the organisms: a 1 % increase in the algal subsistence quota (Q~ or the grazer P content (8) results in either a 1.7%
increase or a 1.7% decrease in the critical dilution rate D~. This result may
suggest that the rotifers should be the zooplankton group most likely to
succeed in lakes with high dilution rates, as many rotifers have high maximal growth rates (cf. Fig. 4.22) and low phosphorus requirements compared to other groups (Hessen and Lyche 1991) •
For dilution rates below the persistence boundary, grazer extinction can
also result if the P loading is sufficiently low. If the input concentration is
below a critical level PILI defined by (A6.23), there will not be any stationary
points with non-zero zooplankton biomass. Substituting the model parameters in Table 5.1 into Eq. (A6.23) gives P'£ = 0.68 (Jig P) r
l for D = D:.
With the lowest total P value observed in the NIV A survey shown in Fig. 2.3
being 1.4 (Jig P) r., we can expect the critical input concentration P'£ to be
exceeded in all of the 355 Norwegian lakes investigated in that survey, even
if we assume zero P retention and no load decay.
If the input concentration is above the critical level (P£ > P'£), and the
dilution rate is above the persistence boundary (D > D~ ), an additional
internal stationary point comes into existence. This stationary point is
characterized by grazer growth rate being limited only by algal P content, and
not by algal biomass in terms of carbon. In Appendix A6 it is shown that at
this stationary point, algal growth rate is independent of the P loading
conditions, while both phyto- and zooplankton biomasses are directly
proportional to the input concentration P LI and thus, also proportional to
each other. In Appendix A7 it is shown that if this stationary point exists,
then it will always be locally unstable.