Package overview

population

Class population:

habitat

a Raster with values that can be used in other computations.

accessible

vector of indices of cells in habitat that migrants will attempt to go to

habitable

vector of indices of cells in habitat that may have positive population

genotypes

character vector of the genotypes

N

matrix indexed by (habitable cells) x (genotypes) giving the number of each genotype in each habitable cell

Set-up:

This can be initiated with make_population() by specifying the following:

habitat

The path to the file where the raster is stored.

inaccessible.value

The values in the raster that should be marked as inaccessible.

uninhabitable.value

The values in the raster that should be marked as not habitable.

genotypes

A character vector of genotypes.

Example:

pop <- make_population(
                 habitat = system.file("extdata/test_raster.gri",package="landsim"),
                 inaccessible.value = "NA",
                 uninhabitable.value = 0.0,
                 genotypes = c( "aa", "aA", "AA" )
             )

migration

One structure we use several times is the setup for smoothing (with migrate); for this we need to know:

Class migration:

kern

function that gives weights for neighboring cells as a function of Euclidean distance

sigma

scaling factor on distance before being passed to kern

radius

maximum range of the smoother

normalize

normalization factor applied to the smoother

Example:

migr <- migration(
                 kern = "gaussian",
                 sigma = 100,
                 radius = 1000,
                 normalize = 1.0
             )

migration.matrix

A migration.matrix object extends a migration object, in that it has a precomputed migration matrix, and hence is tied to a particular population setup (although this is not included). This has additional entries

Class migration.matrix:

M

The pre-computed migration matrix.

Example:

This is added with the function setup_migration().

migr <- setup_migration( migr, population=pop )

vital_rate

Vital rates may be numbers or vectors but may also be functions, to allow them to depend on the current state of the system. We would like to have the parameters in these visible, changeable, and carried around with them. To this end, we define vital objects by specifying a function and auxialliary parameters that will be kept along with the function.

Simple example:

This class allows assigning and accessing things directly from the environment of the function, without having them clutter up the global environment.

f <- vital( function (N,...) { N+x }, x=3 )
f(10)

## [1] 13

f$x

## [1] 3

f$x <- 12
f(10)

## [1] 22

Example:

germ.vital <- vital(
             function (N, ...) {
                out <- r0 / ( 1 + migrate(rowSums(N),competition)/carrying.capacity )
                return( cbind( aa=out, aA=s*out, AA=s^2*out ) )
             },
             r0 = 0.01,  # one in ten seeds will germinate at low densities
             s = 1.5,    # multiplicative selective benefit of the A allele
             carrying.capacity = 10,
             competition = migration(
                                     kern="gaussian",
                                     sigma=100,
                                     radius=300,
                                     normalize=1
                                 )
         )

Note that this also has a migration object as part of its definition. This needs to be set up also:

germ.vital <- setup_vital(germ.vital,pop)

demography

Several of the base demographic parameters we might want to specify (as a fixed number or a layer), or compute (as a function of the current population state). Such parameters can be either something numeric or else a function that is applied to N to get the result.

To do a single generation we need to know:

Class demography:

prob.seed

parameter object for probability of seeding per individual per year

fecundity

parameter object for mean number of seeds per seeding individual per year

prob.germination

parameter object for probability of germination

prob.survival

parameter object for probability of survival of already existing individuals

pollen.migration

migration object for pollen dispersal (normalized to total pollen production)

seed.migration

migration object for seed dispersal (normalized to 1)

genotypes

vector of names of the genotypes represented by the layers

mating

genotype x genotype x genotype tensor, with entry [i,j,k] the probability that genotypes i and j combine to make offspring genotype k

Example:

demog <- demography(
        prob.seed = 0.2,
        fecundity = 100,
        prob.germination = germ.vital,
        prob.survival = 0.9, 
        seed.migration = migr,
        pollen.migration = migration(
                         kern="gaussian",
                         sigma=300,
                         radius=900,
                         normalize=10
                     ),
        genotypes = c("aa", "aA", "AA")
     )

This can be set up for use with a population with setup_demography, which sets up all the associated migration and vital objects.

demog <- setup_demography(demog,pop)