Functions to fetch information about the size bins used in the model
described by params.
Value
w() returns a vector with the sizes at the start of each size bin
of the consumer spectrum.
w_full() returns a vector with the sizes at the start of each size
bin of the resource spectrum, which typically starts at smaller sizes than
the consumer spectrum.
dw() returns a vector with the widths of the size bins of the
consumer spectrum.
dw_full() returns a vector with the widths of the size bins of the
resource spectrum.
Details
To represent the continuous size spectrum in the computer, the size
variable is discretized into a vector w of discrete weights,
providing a grid of sizes spanning the range from the smallest egg size
to the largest maximum size. These grid values divide the full size
range into a finite number of size bins. The size bins should be chosen
small enough to avoid the discretisation errors from becoming too big.
You can fetch this vector with w() and the vector of bin widths with
dw().
The weight grid is set up to be logarithmically spaced, so that
w[j]=w[1]*10^(j*dx) for some fixed dx. This means that the bin widths
increase with size: dw[j] = w[j] * (10^dx - 1).
This grid is set up automatically when creating a MizerParams object.
Because the resource spectrum spans a larger range of sizes, these sizes
are discretized into a different vector of weights w_full. This usually
starts at a much smaller size than w, but also runs up to the same
largest size, so that the last entries of w_full have to coincide with the
entries of w. The logarithmic spacing for w_full is the same as that for
w, so that again w_full[j]=w_full[1]*10^(j*dx). The function w_full()
gives the vector of sizes and dw_full() gives the vector of bin widths.
You will need these vectors when converting number densities to numbers.
For example the size spectrum of a species is stored as a vector of
values that represent the density of fish in each size bin rather than
the number of fish. The number of fish in the size bin between w[j] and
w[j+1]=w[j]+dw[j] is obtained as N[j]*dw[j].
The vector w can be used for example to convert the number of individuals
in a size bin into the biomass in the size bin. The biomass in the
jth bin is biomass[j] = N[j] * dw[j] * w[j].
Of course all these calculations with discrete sizes and size bins are
only giving approximations to the continuous values, and these approximations
get better the smaller the size bins are, i.e., the more size bins are
used. However using more size bins also slows down the calculations, so
there is a trade-off. This is why the functions setting up MizerParams
objects allow you to choose the number of size bins no_w.
Examples
str(w(NS_params))
#> num [1:100] 0.001 0.00119 0.00142 0.0017 0.00203 ...
str(dw(NS_params))
#> num [1:100] 0.000193 0.000231 0.000275 0.000329 0.000392 ...
str(w_full(NS_params))
#> num [1:226] 2.12e-13 2.53e-13 3.02e-13 3.61e-13 4.30e-13 ...
str(dw_full(NS_params))
#> num [1:226] 4.10e-14 4.90e-14 5.84e-14 6.97e-14 8.32e-14 ...
# Calculating the biomass of Cod in each bin in the North Sea model
biomass <- initialN(NS_params)["Cod", ] * dw(NS_params) * w(NS_params)
# Summing to get total biomass
sum(biomass)
#> [1] 601591842546