396 John Woods
theoretical ecology these are predicted by models comprising equations for the rate
of change of the population as a whole. In Eulerian simulations the equations
describe contributions to demographic change in each ceH of the Eulerian grid
(each layer in a one-dimensional simulation). But individual-based models do not
have equations for populations: the demographic time series are emergent properties ofthe simulation.
18.8.3 Computing demography
We noted in 18.5 that the primary task ofindividual-based modelling is to compute the demographic time series of each population. That is done in two stages. As
the model is being integrated, a chronological record is created of every demographic event in every sub-population, with the name of its particle and the time.
These events include reproduction (with the number of offspring), the number of
plankters in the particle's sub-population that are eaten, or lost to starvation, disease or other cause of death), and the number of plankters emigrating to another
particle's sub-population (a technical procedure used in particle management,
18.10.4). This chronological register is called the Parish Register, by analogy with
the record used in human demography (the water column replacing the parish). A
computer program called Lifespan (Lythgoe, 1990) is used to analyse the Parish
Register. It generates the demographic time series for each population.
18.8.4 Emergent demography
As is often the case in primitive equation simulations of complex systems, the
emergent properties can be counter-intuitive. That is because our intuition is
coloured by simple models in which we can easily discem cause and effect.
Changes in the demographic time series of Virtual Plankton Ecosystems often
exhibit features tbat seem unreasonable at first glance. Consider, for example the
time series in Fig. 18.4. The only change in the environment is a slow rise in the
concentration of dissolved nitrogen in the mixed layer on 1 st March each year.
Annual primary production is nutrient limited, so it increases with time. But, we
see that there is a steady decline in the phytoplankton biomass on 1 st March; while
there is no significant change in the zooplankton biomass at that time of year.
This counter-intuitive result is explained by a change in the foraging behaviour
of zooplankton triggered by the rise in phytoplankton production. This response is
an emergent property of the VPE. The model equations include a simple control
rule for foraging behaviour that was not designed with any particular scenario in
mind. The information available in the demographic time series stimulated conjectures about possible causes for this unexpected response ofthe demographic attractor to a change in nitrogen stock. But the demographic data were not sufficient to
test those conjectures. The actual cause was found by studying the audit trails of
individual particles. In this case we found that there was a complex sequence of
events involving changes in the pattern of diel migration of zooplankton, summer
fertilization of the phytoplankton and the success of carnivorous predation, which
together led to the observed multi-year trends in the winter populations. Detailed
theoretical ecology these are predicted by models comprising equations for the rate
of change of the population as a whole. In Eulerian simulations the equations
describe contributions to demographic change in each ceH of the Eulerian grid
(each layer in a one-dimensional simulation). But individual-based models do not
have equations for populations: the demographic time series are emergent properties ofthe simulation.
18.8.3 Computing demography
We noted in 18.5 that the primary task ofindividual-based modelling is to compute the demographic time series of each population. That is done in two stages. As
the model is being integrated, a chronological record is created of every demographic event in every sub-population, with the name of its particle and the time.
These events include reproduction (with the number of offspring), the number of
plankters in the particle's sub-population that are eaten, or lost to starvation, disease or other cause of death), and the number of plankters emigrating to another
particle's sub-population (a technical procedure used in particle management,
18.10.4). This chronological register is called the Parish Register, by analogy with
the record used in human demography (the water column replacing the parish). A
computer program called Lifespan (Lythgoe, 1990) is used to analyse the Parish
Register. It generates the demographic time series for each population.
18.8.4 Emergent demography
As is often the case in primitive equation simulations of complex systems, the
emergent properties can be counter-intuitive. That is because our intuition is
coloured by simple models in which we can easily discem cause and effect.
Changes in the demographic time series of Virtual Plankton Ecosystems often
exhibit features tbat seem unreasonable at first glance. Consider, for example the
time series in Fig. 18.4. The only change in the environment is a slow rise in the
concentration of dissolved nitrogen in the mixed layer on 1 st March each year.
Annual primary production is nutrient limited, so it increases with time. But, we
see that there is a steady decline in the phytoplankton biomass on 1 st March; while
there is no significant change in the zooplankton biomass at that time of year.
This counter-intuitive result is explained by a change in the foraging behaviour
of zooplankton triggered by the rise in phytoplankton production. This response is
an emergent property of the VPE. The model equations include a simple control
rule for foraging behaviour that was not designed with any particular scenario in
mind. The information available in the demographic time series stimulated conjectures about possible causes for this unexpected response ofthe demographic attractor to a change in nitrogen stock. But the demographic data were not sufficient to
test those conjectures. The actual cause was found by studying the audit trails of
individual particles. In this case we found that there was a complex sequence of
events involving changes in the pattern of diel migration of zooplankton, summer
fertilization of the phytoplankton and the success of carnivorous predation, which
together led to the observed multi-year trends in the winter populations. Detailed