.Data
One or more time series of population sizes.
'Projection' objects inherit from a standard array, and can be treated as
such. Therefore, if vector
is specified, the 'Projection' object will
behave as:
if a single vector
is given, a numeric vector of population sizes
of length time+1
if multiple vector
s are given, a numeric matrix of population
projections where each column represents a single population projection and
is of length time+1
if vector="n"
, a numeric matrix of population projections where each column
represents a single stage-biased projection and is of length time+1
.
if vector="diri"
, a numeric matrix of population projections where each
column represents projection of a single vector draw and each column is of
length time+1
.
vec
Age- or stage-based population vectors. vec
will be:
If a single vector
is specified, a numeric matrix of demographic
vectors from projection of vector
through A
. Each column
represents the densities of one life (st)age in the projection.
If multiple vector
s are specified, a three-dimensional array of
demographic vectors from projection of the set of initial vectors through
A
. The first dimension represents time (and is therefore equal to
time+1
). The second dimension represents the densities of
each stage (and is therefore equal to the dimension of A
).
The third dimension represents each individual projection (and is
therefore equal to the number of initial vectors given).
If vector="n"
, a three-dimensional array of demographic vectors from
projection of the set of stage-biased vectors through A
. The first
dimension represents time (and is therefore equal to time+1
). The
second dimension represents the densities of each stage (and
is therefore equal to the dimension of A
). The third
dimension represents each individual stage-biased projection (and is
therefore also equal to the dimension of A
).
Ifvector="diri"
, a three-dimensional array of demographic vectors from
projection of the dirichlet vector draws projected through A
. The first
dimension represents time (and is therefore equal to time+1
). The second
dimension represents the densities of each stage (and
is therefore equal to the dimension of A
). The third
dimension represents projection of each population draw (and is therefore equal
to draws
).
Some examples for understanding the structure of 3D arrays returned when
return.vec=TRUE
: when projecting a 3 by 3 matrix for >10 time intervals,
element [11,3,2] represents the density of stage 3 at time 10
for either vector 2 (multiple vectors), stage-bias 2 (vector="n"
) or draw 2
(vector="diri"
); note that because element 1 represents t=0, then t=10
is found at element 11. The vector [,3,2] represents the time series of densities
of stage 3 in the projection of vector 2 / stage-bias 2 / draw 2. The matrix [,,2]
represents the time series of all stages in the projection of vector 2 / stage-bias
2 / draw 2.
Note that the projections inherit the labelling from A
and vector
, if
it exists. Both stage and vector names are taken from the COLUMN names of A
and vector
respectively. These may be useful for selecting from the
projection
object, and are used when labelling plots of Projection
objects containing multiple population projections.
Set return.vec = FALSE
when calling project
to prevent population
vectors from being saved: in this case, vec
is equal to
numeric(0)
. This may be necessary when projecting large numbers of
vectors, as is the case when vector = "diri"
.
bounds
The bounds on population dynamics (only for deterministic
projections). These represent the maximum and minimum population sizes
achieveable at each time interval of the projection. bounds
is a
matrix with 2 columns (lower and upper bounds, in that order), and the
number of rows is equal to time + 1
.
mat
The matrix/matrices used in the population projection. In their
raw form mat
is always a three-dimensional array, where the third
dimension is used to index the different matrices. However, by using the
mat()
accessor function below, it is possible to choose different ways
of representing the matrices (matrix, list, array).
Aseq
The sequence of matrices used in the projection. For deterministic
projections (where there is only 1 matrix) this will always be rep(1, time)
.
For stochastic projections (with more than 1 matrix), if Aseq
is given
to project
as a numeric or character vector then this slot will take
that value. If a matrix describing a random markov process is passed, the
Aseq
slot will be a single random chain.
projtype
The type of projection. Either "deterministic" (single matrix;
time-invariant), or "stochastic" (multiple matrices; time-varying).
vectype
The type of vector passed to project
. May be "single"
(one vector; one population projection), "multiple" (more than one vector;
several population projections), "bias" (stage-biased vectors;
vector = "n"
), or "diri" (vectors drawn from the dirichlet
distribution; vector = "diri"
).