Nutrient Phytoplankton Zooplankton Modeling

Nutrient – Phytoplankton – Zooplankton Modeling

Models incorporating nutrients, phytoplankton and zooplankton are widely applied in marine and freshwater systems in both applied and research situations. Consider our interest in partitioning dissolved and particulate phosphorus in trophic state modeling and in simulating solids concentrations in toxic substances modeling.

Equations of state are developed for each of the three variables: nutrients (n), phytoplankton or algae (a) and zooplankton (z).

Phytoplankton mass balance: building from a simple exponential model,

respiration,

and zooplankton grazing,

combining the equations yields,

where:

Let’s take a closer look at each component,

Growth

The growth (kg) term is a ‘maximum specific’ value and varies as a function of nutrients (n), temperature (T) and light (I),

with the nutrient function described by the Michaelis-Menten or Monod models,

the temperature function utilizing either a linear or theta model,

or a function describing an optimum temperature,

and the light function using either a saturating (Michaelis-Menten / Monod) approach,

or an inhibition (Steele) relationship,

Note that application of the light function requires additional computations.

where ke is the light extinction coefficient which includes components for absorption by water, dissolved color, inanimate suspended particles and phytoplankton,

Non-Predatory Losses

The non-predatory losses, respiration and excretion, are grouped into a single, first-order term (kra in the equation above). Fundamentally, these processes represent losses of organic carbon through the release carbon dioxide and extracellular byproducts. In the phytoplankton mass balance, the processes represent the overall loss of biomass (chlorophyll). Phytoplankton respiration and excretion will form part of the nutrient mass balance developed later. The respiration rate coefficient is typically made to vary with temperature using a theta function. Due to the impact of this term on the mass balance, some modelers choose to express respiration as a percentage of the growth rate. Otherwise, the effects of light, temperature and nutrients on growth often lead to a net negative growth rate coefficient which imposes a more dramatic response in behavior than is evidenced in nature.

Predatory Losses

Predatory loss refers to the grazing of phytoplankton by zooplankton. The grazing loss term includes a zooplankton grazing rate, a temperature effect, and the abundance of phytoplankton and zooplankton,

Note that the product of the zooplankton grazing rate and the zooplankton concentration is simply a first order loss term (d-1). That loss is then influenced by temperature and, through a Michaelis-Menten function, the abundance of algae.

Zooplankton mass balance: basically gains through grazing and losses to respiration,

with the introduction of two new terms, aca (gC∙mgChl-1), the carbon to chlorophyll ratio of the phytoplankton, used to convert phytoplankton consumption to zooplankton biomass, and e (dimensionless), a grazing efficiency factor ranging from 0®1 which accommodates losses due to ‘sloppy feeding’, i.e. production of detritus. This term is important not only to the zooplankton mass balance, but also is found in that for nutrients as a means of nutrient recycle. The respiration term, which could be modified to account for temperature effects, will also be part of the nutrient mass balance.

Nutrient mass balance: losses to phytoplankton growth and gains from recycle due to phytoplankton respiration and zooplankton respiration and egestion,

here, introducing two more terms, apa (mgP∙mgChl-1), the phosphorus to chlorophyll ratio of the phytoplankton, used to convert phytoplankton respiration to phosphorus, and apc (mgC∙gC-1), the phosphorus to carbon ratio of the zooplankton, used to convert zooplankton respiration to phosphorus.

These three equations thus represent a simple nutrient-food chain model which can be used to gain understanding of predator-prey dynamics.