Differential Loss Rates and Invadability of Equilibria
185
10
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-
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I
8
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(I)
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Species 1
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superior
Z
bQ
competitor
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-- 4
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~
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-
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pecles .... .....--.p,..
superior
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competitor
Z
0
0.0
0.1
0.2
0.3
0.4
0.5
P supply rate ([)lg P] liter- 1 d- 1 )
Fig. 6.14. Regions of competitive dominance of species 1 and 2 (separated by the solid line) in a
two-dimensional gradient of N and P loading rates (dilution rate D = 0.01 day·I). Dashed lines
represent the N:P ratio of the copepod grazer, and, for comparison, the N:P ratio of the daphnid
grazer used in Fig. 6.12
possible in the absence of grazers (cf. Fig. 3.10). To test this hypothesis, we
can modify the model by assuming a grazer with a different N:P ratio, while
leaving all other parameters unchanged. In the investigation of Andersen and
Hessen (1991), copepods and daphnids represented the extremes with respect
to N:P ratios, with copepods having more N and less P per unit dry weight.
The results of running the model with a grazer elemental composition
considered typical for copepods [ON = 215 (J.1g N) (mg ct and Op = 12 (J.1g N)
(mg C).I; O,/Op = 17.9 (J.1g N) (J.1g ptJ are shown in Fig. 6.14.
Changing the N:P ratio of the grazer preserves the qualitative result that
the boundary between the regions of competitive dominance is sharp, with
a negligible intermittent region of coexistence. While the critical N:P
loading ratio lies close to the copepod N:P ratio at low loading rates, it
deviates markedly from this line with increasing nutrient loading (Fig.
6.14). The change in grazer Nand P requirements thus improves the competitive ability of species 2, but the advantage is seen to decrease with
increasing nutrient loading. Qualitatively, the results in Fig. 6.14 are still in