3 Simulate spatial distributions
With mobsim random and aggregated species distributions
can be simulated. This can be done in two ways. Either, simulated
coordinates of individuals can be added to an observed or simulated
species abundance distributions, or species abundances and distributions
can be simulated simultaneously with just one function call.
3.1 Random distributions
In spatial statistics for point patterns a random distribution of
points in a given area is called Poisson process. Accordingly, the
function to add random coordinates to an existing species abundance
distribution is called sim_poisson_coords. Here is an
example of its application.
abund1 <- c(20,10,10,5,5)
comm1 <- sim_poisson_coords(abund_vec = abund1, xrange = c(0,1), yrange = c(0,1))The community object includes x and y coordinates, as well as the
species identity for every individual in the community.
mobsim offers functions for exploring and plotting the
community objects.
## [1] "community"## No. of individuals: 50
## No. of species: 5
## x-extent: 0 1
## y-extent: 0 1
##
## x y species
## Min. :0.0028 Min. :0.016 species_1:20
## 1st Qu.:0.2423 1st Qu.:0.150 species_2:10
## Median :0.5300 Median :0.469 species_3:10
## Mean :0.5144 Mean :0.483 species_4: 5
## 3rd Qu.:0.8217 3rd Qu.:0.797 species_5: 5
## Max. :0.9911 Max. :0.991
As mentioned above, abundances and (random) spatial distributions can
be also simulated at the same time using
sim_poisson_community, which essentially calls
sim_sad and sim_poisson_coords
consecutively.
comm2 <- sim_poisson_community(s_pool = 20, n_sim = 200,
sad_type = "lnorm",
sad_coef = list(cv_abund = 1))
plot(comm2)
3.2 Aggregated positions
Aggregated, or clustered species distributions are simulated based on
the Thomas process, also known as Poisson cluster process, in
mobsim (Morlon et al. 2008, Wiegand & Moloney 2014).
For each species, the Thomas process first distributes a given number of
mother points in the landscape. Then, offspring points are distributed
around the mother points according to a bivariate Gaussian distance
kernel, where the average displacement between mother and offspring
points is called sigma. The offspring points constitute the
final distribution of the species.
By variations in the size of clusters (sigma), the
number of clusters (mother_points), and the mean number of
individuals per cluster (cluster_points) the Thomas process
can generate a large range of different species distributions with
intraspecific aggregation.
It is important to note the each species distribution is simulated
independently from the other species. That means the Thomas process in
mobsim cannot be used to simulate spatial dependence
between different species, i.e. interspecific aggregation or
segregation.
Here is one example for a community with intraspecific aggregation:
First, we change the size of the clusters using the argument
sigma.
comm3a <- sim_thomas_coords(abund_vec = abund1, sigma = 0.05)
oldpar <- par(mfrow = c(1,2))
plot(comm3)
plot(comm3a)
Second, we change the number of clusters per species using the
argument mother_points.
comm3b <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02, mother_points = 1)
oldpar <- par(mfrow = c(1,2))
plot(comm3)
plot(comm3b)
Third, we change the average number of points (i.e. individuals) per
cluster using the argument cluster_points.
comm3c <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02, cluster_points = 5)
oldpar <- par(mfrow = c(1,2))
plot(comm3)
plot(comm3c)
Each of these parameters can be either set to the same equal value for all species as in the examples before, or individually for all species by providing a vector with a length equal to the number of species. For example, each species can has its specific number of clusters.
comm4 <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02,
mother_points = c(5,4,3,2,1))
plot(comm4)
Please note that there can be clusters with zero individuals, so the simulated number of clusters does not necessarily match the parameter settings.
In analogy to random distributions, there is a function to simulate abundances and aggregated distributions at the same time.
comm5 <- sim_thomas_community(s_pool = 100, n_sim = 500, sad_type = "lnorm",
sad_coef = list(cv_abund = 1), sigma = 0.05)
plot(comm5)