Plankton Trajectories

Emergent plankton trajectories and audit trails

The Lagrangian Ensemble method describes the biomass of a plankton population in terms of a large number (up to millions) of particles. The trajectory of each particle is like that of a single plankter. It depends on two factors:

1. the motion of the water (currents, upwelling & turbulence), and
2. the motion of the plankter relative to the water (sinking & swimming).

An audit trail is a set of time series for one particle It documents:

1. the trajectory
2. the ambient environment along its trajectory,
3. the biological state of the plankton, and
4. the demographic properties of the sub-population.

Ambient environment

The ambient environment of a plankter comprises values of environmental fields at its location. The history of ambient environment depends on the plankter's trajectory and the evolution of the environmental fields.

Biological primitive equations

Biological primitive equations describe the behaviour, growth, reproduction and death of an individual plankter; also its risk of being eaten and its predation on other species, and on its own (i.e. cannibalism). Each of these equations is a function of the ambient environment. Individual-based modelling uses biological primitive equations (see "Biological primitive equations").

Phytoplankton

1. Trajectory of the diatom, turbocline depth, number of diatoms in the sub-population (note reproductions).
2. Nitrogen uptake from ambient nitrate and ammonium. Note replenishment of nitrogen pool after reproduction.
3. Ambient irradiance and photo-adaptation.
4. Ambient irradiance and energy pool. Note replenishment after each reproduction event.

Lineage

The biological state of an individual plankter develops according to the ambient environment along its trajectory. When it reproduces its properties are inherited by its offspring. For example the over-wintering body weight of a copepod infl uences the development of its offspring. And a mutation is inherited from generation to generation through its lineage. These are rules of the LEI-IBM metamodel. They make the virtual ecosystem more realistic.

Sub-population

Associated with each particle is information about a sub-population of plankters, which are biologically-identical because they follow the same trajectory, and therefore experience the same variation of ambient environment.

Intra-population variability

Each sub-population follows a unique trajectory and experiences a unique histroy of ambient environment. So its plankton always differ from those in other sub-populations, both in number and biological state. The statistics of demographic variation between sub-populations provides an estimate of the statistics of intra-population variability in natural populations. Neglecting intra-population variability leads to demographic errors in populationbased modelling. That error is avoided in virtual ecosystems, where intra-population variability is a well-founded emergent property.

Zooplankton

1. Diel migration, profile of food concentration, and satiation (Note the pause to feed in the phytoplankton maxima during the evening ascent.
2. Ingestion rate (diatoms per hour) and body weight (µgC)
3. Ambient irradiance, and decreasing number of zooplankton in the sub-population
4. Rising body weight in spring, maturity, gestation and hatching, and the new generation.