in spring when illumination becomes sufficient above the shallowest significant
mixing barrier for net increase (growth − grazing) to exceed stock losses due to
mixing. Thus, a somewhat more realistic model would simulate control of primary
production by seasonally varying sunlight and include the decrease of light with
depth, at least to the bottom of a mixing layer. Since phytoplankton (P) growth varies
non-linearly with irradiance (the P vs. E relation), and irradiance decreases
exponentially downward, the integration of production in the mixing layer should be
by summing production stepwise down the water column, rather than by integrating
the available light and then applying a P vs. E relation to the mean E. Mixing
variation must be included in at least simplified fashion, say by varying the mixed-
layer depth through simulated seasons. Phytoplankton can be considered to be evenly
distributed through the mixed layer, absent below, with losses to depth when the layer
shallows, dilution when it deepens. Nutrient limitation and grazing are independent
factors that terminate spring blooms, so they must be included as alternative controls
of the phytoplankton stock. Zooplankton can be taken to sustain their stock within the
mixed layer by swimming, which may or may not be realistic for protozoan grazers.
(^) Evans and Parslow (1985) developed a model quite similar to that of Franks et al.,
with the added features just listed. It is modified somewhat here. They represented
control of phytoplankton growth rate by multiplying the nutrient-limitation effect by
the light-limitation effect. It is likely preferable, as represented in the equations below,
and as applied by Denman and Peña (1999), to choose at each time step the lesser of
the rates set by light or by nutrients; that is, to strictly apply Liebig’s “law of the
minimum”.
(^) The model has the following equation set:
(^) Change of mixing depth,
(^) Change of nutrient,
(^) G = phytoplankton growth rate, d−1 = min{V
max (–exp(–αEz/Vmax)), Vmax^ N/(Ks + N)}
(^) Change of phytoplankton,
(^) Change of herbivores,
(^) The Δ[M
z, N, P, or H]/Δt values, as implemented in the model, are whole-day (24 h)