Biodiversity in any sampling area depends on three components:
mobsim
provides functions to simulate communities and thereby control for all
these components. This vignette first shows how to simulate non-spatial
species abundance distributions (SADs) and second, how to simulate spatially-
explicit community data with mobsim
.
For this purpose mobsim
provides the function sim_sad
, which is a wrapper
around the function rsad
from the package sads.
In contrast to rsad
, sim_sad
allows simulating communities with user-defined
number of species and user-defined total number of individuals.
Here is an example for the simulation of an SAD using a log-normal model.
library(mobsim) abund1 <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", sad_coef = list("meanlog" = 5, "sdlog" = 0.5)) head(abund1) summary(abund1)
sim_sad
first simulates a relative species abundance distribution according
to the chosen SAD model and then samples the requested number of individuals
according to this relative abundance distribution. Because of the use of a relative abundance
distribution as intermediate step, in the log-normal model the mean abundance
is defined by the simulated number of individuals (n_sim
) divided by the number
of species (s_pool
). Therefore, for the log-normal model sim_sad
offers
also a simpler parameterization that just specifies the coefficient of
variation (cv_abund
) of the log-normal SAD.
abund2 <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", sad_coef = list("cv_abund" = 2)) summary(abund2)
Obviously, the simulated community includes less species than the user-defined
value of s_pool = 100
. This is a consequence of the stochastic sampling from the
relative abundance distribution. When some species have very low relative abundances,
they might not be sampled into the simulated community. However, sim_sad
offers
the option fix_s_sim = TRUE
, which results in the user-defined value of species
in the simulation. This is implemented by adding very rare species to the community,
while removing individuals from the common species. Please note that the constraint
fix_s_sim = TRUE
might result in deviations from the underlying theoretical
SAD model.
abund2a <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", sad_coef = list("cv_abund" = 2), fix_s_sim = T) summary(abund2a)
The function sim_sad
inherits all SAD models provided by sads::rsad
.
For a complete list see ?sim_sad
. Here, we show an example of how to simulate
a log-series SAD. It has to be noted that for some SAD models the species richness
is not a direct parameter, but emerges from the other parameters. This is also true
for the log-series model. Therefore, the parameter s_pool
is set to NULL
.
abund3 <- sim_sad(s_pool = NULL, n_sim = 10000, sad_type = "ls", sad_coef = list("N" = 1e5, "alpha" = 20)) head(abund3)
Of course the simulated number of species can be easily evaluated
length(abund3) summary(abund3)
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.
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.
class(comm1) summary(comm1) plot(comm1)
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)
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:
comm3 <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02) plot(comm3)
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) par(oldpar)
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) par(oldpar)
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) par(oldpar)
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)
Morlon et al. 2008. A general framework for the distance-decay of similarity in ecological communities. Ecology Letters 11, 904-917.
Wiegand and Moloney 2014. Handbook of Spatial Point-Pattern Analysis in Ecology. CRC Press
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