386 lohn Woods
2) Biological Lagrangian Integration retains the intrinsic dynamical stability ofthe
plankton ecosystem, because the biological equations are integrated along the
trajectories of individual organisms. Stability is a pre-requisite for successful
prediction, and therefore for effective use of plankton ecosystem models in
practical applications.
3) One of the emergent properties of simulations derived from Biological
Lagrangian Integration is intra-population variability. This arises from turbulent
dispersion of particle trajectories. It is absent from simulations based on Eulerian integration. Lomnicki (1988) was among the first to draw attention to the
statistical bias that arises from neglecting intra-population variability. Barkmann & Woods (1996) give an example in which the bias approaches a factor of
two.
18.5.2 The WB food chain model
Twenty years ago, I needed a simple model to use while developing a practical
method of individual-based simulation in plankton ecology. On the advice of colleagues in Kiel (Bemd Zeitzschell and Juergen Lenz), I based it on the classical
food chain in which copepods graze on diatoms (Cushing 1995). This WB model
Woods & Barkmann (1994) (Fig. 18.2) contains four explicit (i.e. particle-based)
populations: phytoplankton, herbivorous zooplankton, dead plankton (detritus) and
faecal pellets. The model also contains two implicit populations: camivorous zooplankton, and bacteria attached to the detritus and faecal pellets. The WB model has
a modular structure; each module describes one basic process. It is designed to
accept biological primitive equations, when they are available. In practice, the
WB model incorporated pseudo-BPEs similar to those used in Eulerian modelling
(Evans & Fasham 1993). It is sufficiently realistic to justify analysis of simulations
based on it, such as the Azores VPE (18.7.2). Trials showed that substituting true
BPEs (i.e. those based on reproducible laboratory experiments) can lead to significantly different results. That was the case in (unpublished) models by Wolfgang
Barkmann and Lucas Partridge who used BPEs for photosynthesis derived from
laboratory experiment by Geider et al. (1997). However, the precise form of the
equations does not matter for my lecture, which is concemed with the technology
of primitive equation modelling, and not with the scientific nuances of particular
models.
18.6 The Lagrangian Ensemble method
The Lagrangian-Ensemble (LE) method (Woods & Barkmann 1994) provides a
well-engineered implementation of individual-based, biological-Lagrangian modelling for applications in plankton ecology. It is designed to use biological primitive equations when they are available. Where they are not available, it uses
"consensus" equations from the marine biology literature, as in the WB model.
Integrating the WB model by the LE method generates the demographic history of
2) Biological Lagrangian Integration retains the intrinsic dynamical stability ofthe
plankton ecosystem, because the biological equations are integrated along the
trajectories of individual organisms. Stability is a pre-requisite for successful
prediction, and therefore for effective use of plankton ecosystem models in
practical applications.
3) One of the emergent properties of simulations derived from Biological
Lagrangian Integration is intra-population variability. This arises from turbulent
dispersion of particle trajectories. It is absent from simulations based on Eulerian integration. Lomnicki (1988) was among the first to draw attention to the
statistical bias that arises from neglecting intra-population variability. Barkmann & Woods (1996) give an example in which the bias approaches a factor of
two.
18.5.2 The WB food chain model
Twenty years ago, I needed a simple model to use while developing a practical
method of individual-based simulation in plankton ecology. On the advice of colleagues in Kiel (Bemd Zeitzschell and Juergen Lenz), I based it on the classical
food chain in which copepods graze on diatoms (Cushing 1995). This WB model
Woods & Barkmann (1994) (Fig. 18.2) contains four explicit (i.e. particle-based)
populations: phytoplankton, herbivorous zooplankton, dead plankton (detritus) and
faecal pellets. The model also contains two implicit populations: camivorous zooplankton, and bacteria attached to the detritus and faecal pellets. The WB model has
a modular structure; each module describes one basic process. It is designed to
accept biological primitive equations, when they are available. In practice, the
WB model incorporated pseudo-BPEs similar to those used in Eulerian modelling
(Evans & Fasham 1993). It is sufficiently realistic to justify analysis of simulations
based on it, such as the Azores VPE (18.7.2). Trials showed that substituting true
BPEs (i.e. those based on reproducible laboratory experiments) can lead to significantly different results. That was the case in (unpublished) models by Wolfgang
Barkmann and Lucas Partridge who used BPEs for photosynthesis derived from
laboratory experiment by Geider et al. (1997). However, the precise form of the
equations does not matter for my lecture, which is concemed with the technology
of primitive equation modelling, and not with the scientific nuances of particular
models.
18.6 The Lagrangian Ensemble method
The Lagrangian-Ensemble (LE) method (Woods & Barkmann 1994) provides a
well-engineered implementation of individual-based, biological-Lagrangian modelling for applications in plankton ecology. It is designed to use biological primitive equations when they are available. Where they are not available, it uses
"consensus" equations from the marine biology literature, as in the WB model.
Integrating the WB model by the LE method generates the demographic history of