# Estimation of neutral and non-neutral parameters of community assembly using Approximate Bayesian Computation (ABC) Estimates parameters of neutral migration-drift dynamics (through migration rate m and parameters of environmental filtering (through a filtering function `filt.abc()`) from the composition of a local community and the related regional pool. ```r coalesc_abc(comm.obs, pool = NULL, multi = "single", traits = NULL, f.sumstats, filt.abc = NULL, params = NULL, theta.max = NULL, nb.samp = 10^6, parallel = TRUE, tol = NULL, pkg = NULL, method="rejection") do.simul(J, pool = NULL, multi = "single", nb.com = NULL, traits = NULL, f.sumstats = NULL, filt.abc = NULL, params, theta.max = NULL, nb.samp = 10^6, parallel = TRUE, tol = NULL, pkg = NULL, method = "rejection") ``` ## Arguments - `comm.obs`: the observed community composition. If `multi = FALSE` (default), should be a matrix or data.frame of individuals on rows with their individual id (first column), and species id (second column). - `pool`: composition of the regional pool to which the local community is hypothesized to be related through migration dynamics with possible environmental filtering. Should be a matrix of individuals on rows with their individual id (first column), species id (second column), and (optionally) the trait values of the individuals. - `multi`: structure of the community inputs: * if `multi = "single"`, `comm.obs` contains a single community * if `multi = "tab"`, the user provides a site-species matrix (sites in rows and species in columns ) * if `multi = "seqcom"`, `comm.obs` contains a list of communities - `traits`: the trait values of species in the regional pool. It is used if trait information is not provided in `pool`. In this case, intraspecific trait variation is assumed to be null. - `f.sumstats`: a function allowing to calculate the summary statistics of local community composition. Will be used to compare observed and simulated community composition in the ABC estimation. It should take a community as input and output a list of summary statistics. - `filt.abc`: the hypothesized environmental filtering function. It is a function of individual trait values and additional parameters to be estimated. - `params`: a matrix of the bounds of the parameters used in `filt.abc`. The row names of `params` provide the parameter names used in ABC calculation and output. First column contains minimum values and second column contains maximum values. - `theta.max`: if `pool = NULL`, regional abundances will be simulated following a log-series distribution. The function will estimate the `theta` parameter of this distribution. `theta.max` then provides the upper bound for this estimation. - `nb.samp`: the number of parameter values to be sampled in ABC calculation. Random values of parameters of environmental filtering (see `filt.abc` and `params`) and of migration (denoted as `m`) are drawn from a uniform distribution between minimum and maximum values provided in `params` (and between 0 and 1 for m). - `parallel`: boolean. If `parallel = TRUE`, the function will perform parallel processing using the `parLapply()` function of package `parallel`. - `tol`: the tolerance value used in ABC estimation (see help in `abc()` function of package `abc` for further information). - `pkg`: packages needed for calculation of `filt.abc` and/or `f.sumstats`. - `method`: the method to be used in ABC estimation (see help on `abc()` function of package `abc` for further information). - `J`: local community size. - `nb.com`: number of communities. ## Details `coalesc_abc()` performs ABC estimation for one (if `multi = FALSE`, default) or several communities (if `multi = TRUE`) related to the same regional pool. `do.simul()` provides the simulated communities used in ABC estimation, and is not intended to be used directly. ## Returns - **par**: parameter values used in simulations. - **obs**: observed summary statistics. - **obs.scaled**: observed summary statistics standardized according to the mean and standard deviation of simulated values. - **ss**: standardized summary statistics of the communities simulated with parameter values listed in `par`. - **abc**: a single (if `multi = FALSE`, default) or a list of abc objects including ABC estimation information for each community provided in input (`comm.obs`). ## See Also `abc()` in `abc` package, `parLapply()` in `parallel` package. ## References Jabot, F., and J. Chave. 2009. Inferring the parameters of the neutral theory of biodiversity using phylogenetic information and implications for tropical forests. Ecology Letters 12:239-248. Csillery, K., M. G. B. Blum, O. E. Gaggiotti, and O. Francois. 2010. Approximate Bayesian computation (ABC) in practice. Trends in Ecology & Evolution 25:410-418. Csillery, K., O. Francois, and M. G. Blum. 2012. abc: an R package for Approximate Bayesian Computation (ABC). Methods in Ecology and Evolution 3:475-479. ## Author(s) F. Munoz ## Examples ```r # Trait-dependent filtering function filt_gaussian <- function(t, params) exp(-(t-params[1])^2/(2*params[2]^2)) # Definition of parameters and their range params <- data.frame(rbind(c(0, 1), c(0.05, 1))) row.names(params) <- c("topt", "sigmaopt") # Number of values to sample in prior distributions nb.samp <- 10^6 # Should be large ## Not run: # Basic summary statistics f.sumstats <- function(com) array(dimnames=list(c("cwm", "cwv", "cws", "cwk", "S", "Es")), c(mean(com[,3]), var(com[,3]), e1071::skewness(com[,3]), e1071::kurtosis(com[,3]), vegan::specnumber(table(com[,2])), vegan::diversity(table(com[,2])))) # An observed community is here simulated (known parameters) comm <- coalesc(J = 400, m = 0.5, theta = 50, filt = function(x) filt_gaussian(x, c(0.2, 0.1))) # ABC estimation of the parameters based on observed community composition ## Warning: this function may take a while res <- coalesc_abc(comm$com, comm$pool, f.sumstats = f.sumstats, filt.abc = filt_gaussian, params = params, nb.samp = nb.samp, parallel = TRUE, pkg = c("e1071","vegan"), method = "neuralnet") plot(res$abc, param = res$par) hist(res$abc) # Cross validation ## Warning: this function is slow res$cv <- abc::cv4abc(param = res$par, sumstat = res$ss, nval = 1000, tols = c(0.01, 0.1, 1), method = "neuralnet") plot(res$cv) # Multiple community option # When the input is a site-species matrix, use argument multi="tab" # See vignette Barro_Colorado for more details # When the input is a list of communities, use argument multi="seqcom" comm.obs <- list() comm.obs[[1]] <- cbind(rep(1,400), coalesc(J = 400, m = 0.5, filt = function(x) filt_gaussian(x, c(0.2, 0.1)), pool = comm$pool)$com)) comm.obs[[2]] <- cbind(rep(2,400), coalesc(J = 400, m = 0.5, filt = function(x) filt_gaussian(x, c(0.5, 0.1)), pool = comm$pool)$com)) comm.obs[[3]] <- cbind(rep(3,400), coalesc(J = 400, m = 0.5, filt = function(x) filt_gaussian(x, c(0.8, 0.1)), pool = comm$pool)$com)) comm.obs <- lapply(comm.obs, as.matrix) res <- coalesc_abc(comm.obs, comm$pool, multi="seqcom", f.sumstats=f.sumstats, filt.abc = filt_gaussian, params = params, nb.samp = nb.samp, parallel = TRUE, pkg = c("e1071","vegan"), tol = 0.1, method = "neuralnet") lapply(res$abc, summary) ## End(Not run) ```

coalesc_abc function