416 John Woods
zooplankton in the WB model are defined by sets of 15 and 22 parameters respectively. So the phytoplankton are defined by a single location in 15-dimensional
parameter space.
We can see the value of this description by considering the effect of competition.
In 18.9.2 I described a numerical experiment of Al Battran et al (1998) in which
there was competition between 16 varieties of the WB phytop1ankton, the difference lying in values of just one parameter. The 10cations of these varieties in
parameter space are fixed, apart from a spread in that one dimension. As time
marches on, the less well fitted varieties become extinct, so the spread in parameter
space becomes narrower. In the numerical experiment of Nogueira et al (2001),
described in 18.9.4, the three competing types of diatoms had different sizes. All15
parameters had different values, determined allometrically. So they do not share a
common position in any dimension of parameter space. But they (and similar types
of different sizes) are constrained to lie on the allometric locus. In the mutation
experiment (18.9.3), the simulation was initialised with a popuIation of identic al
phytoplankton, which then diffused one-dimensionally through parameter space.
Natural selection limited the spread, as in Al Battran et al. (1998). This dispersion
of varieties through parameter space is small compared with the distance between
the locations of different species. The scope of intra-population distribution in
parameter space will be much less than the spacing between species. (See also the
discussion of evolution in 18.3.2.)
18.16.2 Parametrizing biodiversity
Suppose that marine biologists have performed all the experiments needed to
establish the biological primitive equations for, say, the thousand most common
species of plankton in the North Atlantic. How can we use that information to
design function groups for our LE models? The first step is to sort the species into
groups that have the same equations. The species in each group have different values of the parameters in the shared equations. We want to reduce them to a single
set of parameters for the functional group (FG) to be used in the model. The value
of each FG parameter is an average of the values for all the species in the set for
which we have experimental values. Its location in parameter space williie within
the cluster formed by the species in the same functional group. But where exactly?
One answer is to assume that the functional group occupies a fixed location in
parameter space. That is Fasham's (1990) "robust" parametrization. A more
sophisticated approach takes account of the relative abundance of the species contributing to the functional group. This can be done by making each parameter an
average of the species values weighted by its biomass (bi)' Thus Pj (the FG value
of the lh parameter) will be computed from the species values Pj,i where i denotes
the species.
Pj = ~;[biPj,i]l~;[bi]
We saw earlier (18.9) that the demographic consequences of competition
between species in the same functional group is determined by two factors: (1) the
zooplankton in the WB model are defined by sets of 15 and 22 parameters respectively. So the phytoplankton are defined by a single location in 15-dimensional
parameter space.
We can see the value of this description by considering the effect of competition.
In 18.9.2 I described a numerical experiment of Al Battran et al (1998) in which
there was competition between 16 varieties of the WB phytop1ankton, the difference lying in values of just one parameter. The 10cations of these varieties in
parameter space are fixed, apart from a spread in that one dimension. As time
marches on, the less well fitted varieties become extinct, so the spread in parameter
space becomes narrower. In the numerical experiment of Nogueira et al (2001),
described in 18.9.4, the three competing types of diatoms had different sizes. All15
parameters had different values, determined allometrically. So they do not share a
common position in any dimension of parameter space. But they (and similar types
of different sizes) are constrained to lie on the allometric locus. In the mutation
experiment (18.9.3), the simulation was initialised with a popuIation of identic al
phytoplankton, which then diffused one-dimensionally through parameter space.
Natural selection limited the spread, as in Al Battran et al. (1998). This dispersion
of varieties through parameter space is small compared with the distance between
the locations of different species. The scope of intra-population distribution in
parameter space will be much less than the spacing between species. (See also the
discussion of evolution in 18.3.2.)
18.16.2 Parametrizing biodiversity
Suppose that marine biologists have performed all the experiments needed to
establish the biological primitive equations for, say, the thousand most common
species of plankton in the North Atlantic. How can we use that information to
design function groups for our LE models? The first step is to sort the species into
groups that have the same equations. The species in each group have different values of the parameters in the shared equations. We want to reduce them to a single
set of parameters for the functional group (FG) to be used in the model. The value
of each FG parameter is an average of the values for all the species in the set for
which we have experimental values. Its location in parameter space williie within
the cluster formed by the species in the same functional group. But where exactly?
One answer is to assume that the functional group occupies a fixed location in
parameter space. That is Fasham's (1990) "robust" parametrization. A more
sophisticated approach takes account of the relative abundance of the species contributing to the functional group. This can be done by making each parameter an
average of the species values weighted by its biomass (bi)' Thus Pj (the FG value
of the lh parameter) will be computed from the species values Pj,i where i denotes
the species.
Pj = ~;[biPj,i]l~;[bi]
We saw earlier (18.9) that the demographic consequences of competition
between species in the same functional group is determined by two factors: (1) the