Primitive Equation Modelling ofPlankton Ecosystems
381
matically how people change their minds. Casti (1997) states that the subject is still
in a "pre-Galileo" era.
That may be true of complex systems that depend on the behaviour ofhigher animals. However, most species on Earth are micro-organisms. The behaviour of a
simple micro-organism is not mediated by a brain that can change its mind. It follows rules of behaviour that are hard-coded into its genes. Their behaviour may
adapt to circumstances, but they do so in a predictable way, which is also encoded
in their genes. All these rules can be established by reproducible laboratory experiments. So ecosystems that involve only micro-organisms may be classified as
Complex Non-adaptive Systems. They offer the promise of predictability, even
though they involve biology. The plankton ecosystem falls into that category.
18.3.2 Evolution
Here I make a short digression to deal with concern that biology is not conservative like physics, which obeys laws frozen since the Big Bang. Evolution is the
quintessence of biology, so biologic al primitive equations change with time. That
being the case, how can we describe the plankton ecosystem as being non-adaptive? The answer is that the statistical rules governing evolutionary changes in the
biological primitive equations are known, and can be incorporated into our models.
In fact it is natural to do so with individual-based models, in which integration of
the biological equations follows individual organisms and their offspring through
lineages.
The genetically-controlled rules governing the physiology and behaviour of a
micro-organism remain unchanged during its life. In the case of non-sexual reproduction, the rules are normally passed on unchanged to the individual's offspring.
Occasiona1ly the genes may suffer mutation, leading to changes in the rules. Accumulation of mutations can lead to competitive advantage within a limited range of
environmental conditions (see 18.9); that is how bio-zonation evolves (Longhurst
1998). How does mutation affect our plan to use primitive equations to model an
evolving plankton ecosystem? Biological Lagrangian Integration has the essential
property of accurately simulating inheritance between the generations in a lineage.
We can include statistical rules governing occasional abrupt changes in the biological primitive equations of individuals (or rather in their parameter values; see
18.16). Sometimes these changes are fatal, often they are neutral, occasionally they
are beneficial. We can also modify the model to include sexual reproduction, which
creates new sets of parameters in the primitive equations drawn haphazardly from
those encoded in the genes ofthe parents.
Both mutation and sexual reproduction introduce a stochastic element into inheritance of primitive equations. The statistical rules governing these changes are well
known and can be found in standard textbooks, such as Roughgarden (1996). It is
technically straightforward to extend PE models to include them. It is possible to
design a modelling technique to accurately calculate the demographic consequences of competition between varieties with primitive equations modified by sex
or mutation. The requirement is that the simulation has a significant demographic
381
matically how people change their minds. Casti (1997) states that the subject is still
in a "pre-Galileo" era.
That may be true of complex systems that depend on the behaviour ofhigher animals. However, most species on Earth are micro-organisms. The behaviour of a
simple micro-organism is not mediated by a brain that can change its mind. It follows rules of behaviour that are hard-coded into its genes. Their behaviour may
adapt to circumstances, but they do so in a predictable way, which is also encoded
in their genes. All these rules can be established by reproducible laboratory experiments. So ecosystems that involve only micro-organisms may be classified as
Complex Non-adaptive Systems. They offer the promise of predictability, even
though they involve biology. The plankton ecosystem falls into that category.
18.3.2 Evolution
Here I make a short digression to deal with concern that biology is not conservative like physics, which obeys laws frozen since the Big Bang. Evolution is the
quintessence of biology, so biologic al primitive equations change with time. That
being the case, how can we describe the plankton ecosystem as being non-adaptive? The answer is that the statistical rules governing evolutionary changes in the
biological primitive equations are known, and can be incorporated into our models.
In fact it is natural to do so with individual-based models, in which integration of
the biological equations follows individual organisms and their offspring through
lineages.
The genetically-controlled rules governing the physiology and behaviour of a
micro-organism remain unchanged during its life. In the case of non-sexual reproduction, the rules are normally passed on unchanged to the individual's offspring.
Occasiona1ly the genes may suffer mutation, leading to changes in the rules. Accumulation of mutations can lead to competitive advantage within a limited range of
environmental conditions (see 18.9); that is how bio-zonation evolves (Longhurst
1998). How does mutation affect our plan to use primitive equations to model an
evolving plankton ecosystem? Biological Lagrangian Integration has the essential
property of accurately simulating inheritance between the generations in a lineage.
We can include statistical rules governing occasional abrupt changes in the biological primitive equations of individuals (or rather in their parameter values; see
18.16). Sometimes these changes are fatal, often they are neutral, occasionally they
are beneficial. We can also modify the model to include sexual reproduction, which
creates new sets of parameters in the primitive equations drawn haphazardly from
those encoded in the genes ofthe parents.
Both mutation and sexual reproduction introduce a stochastic element into inheritance of primitive equations. The statistical rules governing these changes are well
known and can be found in standard textbooks, such as Roughgarden (1996). It is
technically straightforward to extend PE models to include them. It is possible to
design a modelling technique to accurately calculate the demographic consequences of competition between varieties with primitive equations modified by sex
or mutation. The requirement is that the simulation has a significant demographic