CASE STUDY: Steady State Phosphorus Model of Lake Wingra (Wisconsin) in Summer

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Source:

“Looking for Surprise in Managing Stressed Ecosystems”, Orie L. Loucks, Bioscience Vol. 35 No. 7. Narrative and case study design by Robert R. Gotwals, Jr.

Goal:

To evaluate the flow of phosphorus in a freshwater lake..

Background Reading:

This is a highly simplified model that evaluates the flow of phosphorus through the various components in a freshwater lake, including fish, phytoplankton, sediment, etc. The purpose of the model is fundamentally to develop an understanding of the complex interactions of all of the components, and to experiment with the effects of changing the various parameters of the model.

NOTE: this model uses a combination of direct measurements and estimates based on intuition and other sources. As such, this model is speculative in nature.

Building the Model:

This model concerns itself with the measurement of phosphorus (in milligrams per square meters) of six components:

Phosphorus enters the water as dissolved inorganic phosphorus. For this model, start with a water input rate of 1.7 mg/m2/day. From the water, phosphorus is absorbed by the phytoplankton in the water at a rate of uptake of 25 day-1, according to this algorithm:

Uptake of phosphorus by phytoplankton = dissolved inorganic phosphorus in water / rate of uptake

From the phytoplankton, phosphorus can take two paths:

  1. Phytoplankton die, becoming detritus. Death of phytoplankton (actually the amount of release of phosphorus due to their deaths) depends upon the death rate of phytoplankton, set initially at 10:

    Death of phytoplankton = Phytoplankton/ phytoplankton death rate

  2. Phytoplankton are also food for zooplankton, and the phosphorus in the phytoplankton gets transferred to zooplankton at a rate of 15 , according to:

    Zooplankton eat phytoplankton = Phytoplankton / rate of predation of zooplankton on phytoplankton

Zooplankton can transfer their phosphorus in three ways:

  1. Zooplankton are eaten by fish at a predation rate of 0.4 day-1 :

    Fish eat zooplankton = Zooplankton / rate of predation of fish on zooplankton

  2. Zooplankton also deposit phosphorus back into the water in the form of dissolved inorganic phosphorus in the form of excrement, according to:

    Zooplankton excrement = Zooplankton / rate of excrement (set at 18 /day)

  3. Zooplankton also die, becoming detritus:

    Zooplankton deaths = Zooplankton / rate of zooplankton death ( 0.2 /day)

Fish also contribute phosphorus back to the water through excrement. In this model, they do not contribute phosphorus back to the system through detritus, only through excrement:

Fish excrement = Fish / rate of fish excrement (2 /day)

Phosphorus in the detritus can change six ways:

  1. Dead zooplankton
  2. Dead phytoplankton
  3. Zooplankton, being detritus feeders, decrease the amount of phosphorus in the detritus by feeding on it:

    Detritus feeding = Detritus / Rate of detritus feeding (0.2 /day)

  4. Detritus also settles, becoming part of the sediment:

    Settling = Detritus / rate of settling (2.0 /day)

  5. Some of the phosphorus is taken up from the sediment:

    Uptake = Sediment / Rate of uptake (2.0 /day)

  6. Finally, some of the phosphorus returns to the water through dissolution of phosphorus from the detritus:

    Dissolution of detritus = Detritus / Rate of dissolution ( 4.5 /day)

Sediment also returns phosphorus to the water (in addition to the changes in the sediment in its interaction with the detritus):

Dissolution of sediment = Sediment / rate of dissolution of sediment (2.0 /day)

Initial Conditions:

Run this model for 365 days. Initial conditions are as follows:


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