Kyle F. Edwards, Christopher A. Klausmeier, and Elena Litchman. 2011. Evidence for a three-way trade-off between nitrogen and phosphorus competitive abilities and cell size in phytoplankton. Ecology 92:2085–2095.

Appendix C. Competitive ability in the Monod model.

Whereas the Droop model relates growth rate to internal nutrient concentration, the Monod model assumes that internal concentration is constant, and relates growth directly to external nutrient concentration:

where μ_max is growth rate at infinite resource concentration, K_μ is the half-saturation constant for growth, R is external nutrient concentration, and m is specific mortality rate. The break-even nutrient concentration for a species is R* = , which approaches R* → as m → 0. Therefore, as m → 0, for species with equal mortality, the superior competitor will be the species with the greater ratio , which we refer to as the Monod affinity. The Droop model and the Monod model are interconvertable at equilibrium (Morel 1987). Therefore, parameters measured for the Droop and Monod models should, in principle, make the same predictions for relative competitive abilities. Bruggeman (in press) has compiled Monod affinities under phosphorus limitation for freshwater phytoplankton; in the Results we compare these affinities to C^P.

LITERATURE CITED

Morel, F. M. M. 1987. Kinetics of nutrient uptake and growth in phytoplankton. Journal of Phycology 23:137–150