In the open oceans, the organisms that float about in the open water, either permanently or during their larval development, consist of microalgae (the phytoplankton) and zooplankton. In many areas of the world, there is essentially a paradox in that there are very large numbers and standing amounts of biomass of zooplankton, but very little in the way of phytoplankton for them to eat. This comes about because production of the plants is being consumed by the animals in such a way that their standing stock is at very small levels in the water. Calculations using the amounts of nutrients in the water and the estimated rate of uptake and productivity of the algae make it easy to demonstrate that algal biomass can be very small, sometimes as small as 0.5% of the amounts expected. The rest is being consumed by grazing as fast as it is produced.
This has important consequences where there are marked seasonal differences in intensity or period of light. During spring, light intensity and period of daylight increase in the higher latitudes of the Northern Hemisphere. Phytoplankton then increase in abundance and biomass. In most areas, it takes some weeks for the populations of zooplankton to respond, because their reproduction is slower. Therefore, there is an algal bloom, followed by a decline. The decline is due to two processes, the first of which is grazing by increasing numbers of zooplankton. The second process is availability of nutrients. As phytoplankton increase in abundance, they take nutrients out of the water. When grazed and digested by zooplankton, some of the nutrients are released back into the water, but in smaller amounts. Thus, production of phytoplankton is slowed because there are smaller amounts of nutrients.
The whole situation can be made much more complex where there are higher-level consumers, such as fish, that eat the zooplankton. It is then possible for the amount of grazing to be reduced and for the algae to become much more numerous and abundant in the waters. In these circumstances, the control of algal productivity is very much a combination of bottom-up (nutrients control productivity) and top-down (grazers are controlled by predators and therefore do not control the algae, but are themselves top-down controlled). Whichever outcome is going to happen in some area is therefore dependent on the availability of light, the seasonality of availability of light and of nutrients, the magnitudes of abundances of populations of zooplankton, the availability and intensity of activities of predators, etc.
that can be sustained by available resources. rv is the rate of increase, V is the amount of vegetation present, and rmv is the intrinsic rate of increase, that is, how much the biomass would increase in the absence of any limit or constraint due to shortage of resources. As V gets closer to K (the biomass increases toward its carrying capacity), there is a decrease in rm the rate of growth. At the carrying capacity (K), there is no further increase.
Meanwhile, herbivores are eating plants at rate cl (how much is eaten by a single herbivore when food is freely available, i.e., V is large), which is reduced when the amount of food is smaller. This consumption by herbivores is at a rate
where c1 and V are as above and d1 is a constant describing how consumption changes from i to 0 due to decreased amounts of food.
At any moment, the biomass of plants is therefore changing at a rate rv = rmv(1 - V/K) -ci(l -edlV)/V 
The population of herbivores is, however, also changing at a rate m = -ai + c2(l -e-dV/V
where a is the rate of decrease per capita when there is no food; c2 is a constant describing how the decrease is less when food is available.
All other factors being held constant, the grazer-plant interaction will reach an equilibrium (i.e., at populations V ' and H' ) when
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