# R/popdynfun.r In PopGenReport: A Simple Framework to Analyse Population and Landscape Genetic Data

```################################################################################
##### function to convert cost distances into dispersal probabilities
################################################################################
#'Function to calculate dispersal distances based on cost distances
#'
#'@param x Cost (Euclidean) distance matrix
#'@param d0 dispersal distance
#'@param p of all individuals in a population
#'@return a dispersal probability matrix
#'@description converts cost distances to probabilities: to reach a certain patch[ d0 average distance of p of all individuals, for example d0=100, p =0.5 -> 50\% procent of all migrating individuals go up to 100 m.
#' @export
#' @importFrom data.table rbindlist

p2p <- function(x, d0, p)
{
return (exp(((x/d0)*log(p))))
}

################################################################################
######landscape creation functions
################################################################################

#'Function to add lines to landscape
#'
#'@param r raster that represents the landscape
#'@param x1 from coordinates
#'@param x2 to coordinates
#'@param val resistance value 1 is no resistance
#'@param plot switch if landscape should be plotted
#'@return returns modified raster layer
#'@description adds a line from x1 to x2 to a raster layer
#' @export

{
ll <- Line(rbind(x1,x2))
S1 = Lines(list(ll), ID="a")
lin <- SpatialLines(list(S1))
r1 <-rasterize(lin, r, field=val, fun='last', background=NA,  mask=FALSE, update=T, updateValue='all', filename="", na.rm=TRUE)
if (plot==TRUE) plot(r1)
r1
}

#'Function to add a polygon to a landscape
#'
#'@param r raster that represents the landscape
#'@param pol coordinates of the polygon
#'@param val resistance value, One equals no resistance
#'@param plot switch if landscape should be plotted
#'@return returns modified raster layer
#'@description adds a polygon to a raster layer
#' @export

addpoly <- function(r, pol, val, plot=T)
{
r1 <- rasterize(addpoly, r, field=val, update=TRUE, updateValue='all')
if (plot==T) plot(r1)
r1
}

################################################################################
##### functions  of popdynamics
################################################################################
#mutation
#'Function to execute mutation on a pop data.frame
#'
#'@param x a pop object
#'@param n.allels number of alleles
#'@param mutrate the mutation rate
#'@param mtype the mutation process (currently on n.all is implemented. (=Choose any allel from 1:n.allels))
#'@param n.cov (number of covariates, default  )
#'@return a dispersal probability matrix
#'@description mutation subprocess on single populations
#' @export

mutation <- function(x, n.allels, mutrate, mtype="n.all", n.cov)
{

n.indp <- nrow(x)
n.loci <-  ( ncol(x)-n.cov)  / 2
p.mut = mutrate
noffset = n.cov

if (!is.null(n.indp) )    #some populations might have gone extinct...
{
mut.ind <- which(matrix(as.logical( rbinom(n.indp*n.loci,1,p.mut)), ncol=n.loci, nrow=n.indp)==TRUE,arr.ind=T )

if (nrow(mut.ind)>0) #are there any mutations in this population?
{
for (i in 1:nrow(mut.ind))
{

if (mtype=="n.all")
{
mf <- rbinom(1,1,0.5)
x[mut.ind[i,1], noffset+mut.ind[i,2]*2-mf] <- sample(1:n.allels,1)
}
}
}
}
x
}

####################################################################################
#reprodution
#'Function to execute reproduction on a pop data.frame
#'
#'@param x a pop object
#'@param type type of density dependence K.limit only yet
#'@param K Kapacity of a subpoplation
#'@param n.off number of offspring per female
#'@param n.cov (number of covariates, default 3 )
#'@return an updated pop object
#'@description reproduction subprocess on single populations
#' @export

reproduction <- function(x, type="K.limit",K=n.ind, n.off, n.cov)
{
noffset <- n.cov
n.loci <-  ( ncol(x)-n.cov)  / 2
n.ind <- nrow(x)

index.male <- x\$sex=="male"
index.female <- x\$sex=="female"
n.female <- sum(index.female)
n.male <-  sum(index.male)
#offsprings  <- data.frame(cbind(pop=NA, sex=NA, age=NA,matrix(NA,ncol=n.loci*2,nrow=1)) )

if (n.male>0 & n.female>0)
{
loci.cols <- (noffset+1):(n.loci*2+noffset)

genes.females <- (x[index.female,loci.cols])

#for (i in 1:(n.off-1)) genes.females <- rbind(genes.females,)

genes.females <- genes.females[rep(1:nrow(genes.females),n.off),]

pick.femall <-sample(c(T,F),n.female*n.off*n.loci,replace=T)
all.fem <-  matrix(as.vector(rbind(pick.femall,!pick.femall)),nrow=n.female*n.off, ncol=n.loci*2, byrow=T)

genes.off.fem <- matrix(t(genes.females)[t(all.fem)], ncol=n.loci, nrow=n.female*n.off, byrow=T)

breeding.males <- sample(which(index.male),n.female*n.off, replace=T)
genes.males <- x[breeding.males,loci.cols]
pick.malall <-sample(c(T,F),n.female*n.off*n.loci,replace=T)

all.mal <-  matrix(as.vector(rbind(pick.malall,!pick.malall)),nrow=n.female*n.off, ncol=n.loci*2, byrow=T)
genes.off.mal <- matrix(t(genes.males)[t(all.mal)], ncol=n.loci, nrow=n.female*n.off, byrow=T)

popn <- x\$pop[1]
off.sex <- factor( ifelse(runif(n.female*n.off)<0.5,"male","female"))
off.age <- 1

all.seq<- NA

for (i in seq(1,(2*n.loci-1),2))
{

if (i==1) all.seq[i] <- 1 else all.seq[i] <- all.seq[i-2]+1
all.seq[i+1] <- all.seq[i]+n.loci
}

off.loci <- cbind(genes.off.mal, genes.off.fem)[,all.seq]

colnames(off.loci) <-paste("locus", rep(seq(1,n.loci,1),each=2),rep(c("A","B"),n.loci),sep="")

offsprings <- data.frame(pop=popn, sex=off.sex , age=off.age, off.loci)

x <- rbind(x, offsprings)
#x<- (rbindlist(list(x,offsprings)))

#cut off at K

npop <- nrow(x)
x<- x[sample(1:npop,K, replace=F),]

} else x<- NULL    #return NULL if only males or only females....

return(x)
#return(data.frame(x))

}

#survival   (cut of at K)
#surv <- function(x, s=t.surv) {
#
#x<- x[runif(dim(x)[1])< s,]
#}
#lapply(pops, surv, s=0.1)

################################################################################
#emigration (for all populations at once xp=pops)
#'Function to execute emigration on a pops object
#'
#'@param xp all pops combined in a list
#'@param perc.mig percentage if migrating individuals
#'@param emi.m emigration probability (normally based on cost dispersal distance)
#'@param emi.table a fixed number of migrating individuals can be specified (overrides emi.m)
#'@return a list, first entry are updated pops, second entry the number of disperserin a matrix
#'@description emigration process on all population in one go
#' @export

emigration <- function(xp, perc.mig, emi.m, emi.table=NULL)
{
n.pops = length(xp)
migs <- matrix(0,nrow=n.pops, ncol=n.pops)
migrants<- NA

if (is.null(emi.table))
{
for (i in 1:n.pops)
{
pop.size <-nrow(xp[[i]])

if (!is.null(pop.size))
{
#how many migrants
migrants[i] <- sum(ifelse(runif(pop.size)<perc.mig,1,0))
#where do they go to (depends on emis)
fromto <- table(sample(1:n.pops,migrants[i],replace=T, prob=emi.m[,i]))

to <- as.numeric(names(fromto))
for (ii in 1:length(to)) migs[i,to[ii ]] <- migs[i,to[ii ]] + fromto[ii]
#migs[i, unique(to)] <- migs[i,unique(to)] + table(to)

}
}
} else migs <- emi.table #end emi.type

#deterministic emigration (needs to be passed by emi.table

#let them move (at the moment an individual can migrate more than once, need to be fixed)

for (from in 1:n.pops)
{

for (to in 1:n.pops)
{
#update population size during migration events!!!
psize <- nrow(xp[[from]])
m <- migs[from, to]
if (m>0)
{
ind.from <- sample(1:psize,m,replace=F)
xp[[to]] <- rbind(xp[[to]], xp[[from]][ind.from,])
xp[[from]] <- xp[[from]][-ind.from,]
xp[[to]][,"pop"] <- to
}
}
}
#output number of migrants to a population
#diag(migs) <- 0
#cat(paste("Migrants: ",colSums(migs),"\n"))
results <- list(xp, migs)
return(results)
}

################################################################################
#combines all pops into a single genind object.
#'Function converts pops to a genind object
#'
#'@param x pops object (a list of pop)
#'@param locs named coordinates of locations
#'@param n.cov number of covariates (defaults to 3)
#'@return a spatial genind object
#'@description converts pops into genind (to calculate Fst etc.)
#' @export

pops2genind <- function(x, locs=NULL, n.cov=3)
{
n.pops <- length(x)
n.loci <- (ncol(x[[1]])-n.cov )/2 #only diploid currently
noffset <- n.cov

##### convert pops to data.frame
#combine <-do.call(rbind.data.frame,x)
#combine <- do.call(rbind.data.frame,x)
combine <- as.data.frame(rbindlist(x))

#convert to genind
allele <-combine[,-(1:noffset)]
pop.size <- table(combine[,"pop"] )
res <- data.frame(matrix(NA, nrow=nrow(allele), ncol=n.loci))#rep(NA,sum(pop.size)))
for (i in seq(1, 2*n.loci, 2))
res[, ceiling(i/2)] <- paste(allele[, i], allele[, i + 1], sep = "/")
pops.genind <- df2genind(res,pop=combine\$pop, sep="/", ind.names= rownames(res))
if (!is.null(locs))
{
x <- rep(locs[,1], pop.size)
y <- rep(locs[,2], pop.size)
pops.genind@other\$xy <- cbind(x=x,y=y)
popNames(pops.genind) <- row.names(locs)
}
return(pops.genind)
}

################################################################################
### sim functions
################################################################################
#'Run a time-forward popgen simulation
#'
#'performs a time-forward, agent-based and spatiallly explicit genetic population simulation
#'
#'A pops object created via \code{init.popgensim} is used as input. The function simulates time forward individual-based spatially explicit population dynamics. Subpopulations are linked by dispersal that can be specified via a pairwise distance matrix between subpopulations [cost.mat]. Distances are converted to a probability. Currenlty the function used is the p2p function, where dispersal is modeled using an exponential function, that can be specified via disp.max and disp.rate. disp.max specifies the maximal distance that are achieved by the proportion of disp.rate individuals in a subpopulation. The number of dispersers per generation is set to round(mig.rate * n.ind). A simple mutation rate can be specified (the probability of a mutation per loci) using mut.rate. The maximal allowed number of alleles per loci need to be specified. Currently the mutation model is a simple Kmax-allele model [n.alleles]. As before n.cov is the number if covariates in the data.frame (currenlty fixed to n.cov=3). To track emigration events between subpopulations (be aware output is then a list instead of a simple pops object) rec can be set to "emi", which provides a matrix that shows the actual emigrations between subpopulations during the simulation. Emigration can also be determistic (instead of using disp.max and disp.rate) to a specified number of dispersal events per subpopulations. Over each generation events are occuring in that order: 1. dispersal, 2. reproduction, 3. mutation. For convinience the simulation can be run a specified number of generations [steps]. In case extra dynamics need to be modelled (e.g. one population is increased in number be a managment action or population are affected by environmental factors) simulations can also run only in single time steps [steps=1]. See example.
#'@param simpops pops object (a list of pop)
#'@param steps the number of steps (generations)
#'@param cost.mat a cost matrix (e.g. calculated via costDistance)
#'@param n.offspring number of offsprings per female
#'@param n.ind number of individuals
#'@param mig.rate migration rate
#'@param disp.max dispersal distance of disp.rate individuals
#'@param disp.rate percentage of individuals achieving disp.max
#'@param n.allels number of maximal alleles at a loci
#'@param mut.rate mutation rate
#'@param n.cov number of covariates (defaults to 3)
#'@param rec switch if emigration matrix should be recorded, either "none" or "emi"
#'@param emi.table a emigration matrix, if provide a fixed number of migration events will take place otherwise based on disp.max, mig.rate and disp.rate,
#'@return an updated pops object after steps time steps or a list that includes the pops object and the emigration matrix [rec="emi"].
#'@examples
#'\dontrun{
#'set.seed(1)
#'locs <- cbind(x=round(runif(5,5,45)), y=round(runif(5,5,45)) )

#'cm <- as.matrix(dist(locs))
#initialise pops
#'pops <- init.popgensim(n.pops = 5, n.ind=20, sex.ratio = 0.25, n.loci = 5, n.allels = 10, n.cov = 3)
#'#run pops
#'pops <- run.popgensim(pops, steps = 200, cost.mat= cm, n.offspring = 2, n.ind = 20,
#'mig.rate = 0.125, disp.max = 30, disp.rate =0.1, n.allels = 10, mut.rate = 0)
#'#convert to genind object
#'pops.gi <-pops2genind(pops)
#'#calculate pairwise fsts using pairwise.fstb
#'fsts <- pairwise.fstb(pops.gi)
#'#plot
#'plot(locs, xlim=c(0,50), ylim=c(0,50), pch=16,cex=4, col="darkgrey")

#'for (i in 1:4)
#'for (ii in (i+1):5)
#'lines(c(locs[i,1], locs[ii,1]), c(locs[i,2], locs[ii,2]), lwd=fsts[i,ii]*30, col="darkgreen")
#'text(locs+0.5, labels=1:5, col="white", font=2)
#'}
#' @export

run.popgensim <- function(simpops, steps, cost.mat, n.offspring , n.ind,  mig.rate, disp.max, disp.rate, n.allels, mut.rate, n.cov=3, rec = "none", emi.table=NULL)
{
pops <- simpops
distances <- cost.mat
disdis <- p2p(distances,d0=disp.max, p=disp.rate)
stdemi.table= disdis/rep(colSums(disdis), each=ncol(disdis))
emi.tableint=NULL
#cl<- makePSOCKcluster(6)

for (year in 1:steps)
{

if (!is.null(emi.table))
{
emi.table <- stdemi.table * mig.rate * n.ind +  emi.table
emi.tableint <- floor(emi.table)
emi.table <- emi.table - emi.tableint
}

#emigration
emi<- emigration(pops, mig.rate, emi.m=disdis, emi.table=emi.tableint)
pops <- emi[[1]]
#emi[[2]] table of migrants....

#reproduction
pops <- lapply(pops, reproduction,K=n.ind, n.off=n.offspring, n.cov=n.cov)
# pops <- parLapply(cl, pops, reproduction, K=n.ind, n.off=n.offspring, n.cov=n.cov)
#mutation
pops <- lapply(pops, mutation, n.allels, mutrate=mut.rate, n.cov=n.cov)
}  #end of every year....   time loop

#stopCluster(cl)

out <- pops #list(pops=pops)
if (rec=="emi")
{
out <- list()
out[[1]] <- pops
out[[2]] <- emi[[2]]
}
return (out)
} #end of simpop function

################################################################################
#initialise populations
################################################################################
#'Initialise a spatial meta-population for a popgen simulation
#'
#'This functions initialises a time-forward, agent-based and spatiallly explicit genetic meta-population simulation
#'
#'To set up a population we have to specify the following parameters: n.pops defines the number of subpopulations and n.ind the number of individuals within subpopulations (carrying capacity). In the current implementaiton all subpopulations have the same number of individuals. sex.ratio determines the proportion of females in a subpopulation. finaly the number of loci and number of alleles need to be specified. locs is used to name the populations. For simplicity the names are provided via a data.frame of x and y coordinates (as they normally come from a genind object)
#'@param n.pops number of subpopulations
#'@param n.ind number of individuals per subpopulation
#'@param sex.ratio sex ratio of males and females
#'@param n.loci number of loci
#'@param n.allels number of maximal alleles per loci
#'@param locs coordinates of the subpopulations, provided as a row named data.frame(x=, y=) with n.pops rows.[Only used to name the subpopulations by row.names(locs). If not provided subpopulations are simply numbered.
#'@param n.cov number of covariates (currenlty do not change, defaults to 3. In future versions covariates such as age etc. will be implemented)
#'@return a simpops object (to be used in run.popgensim ), which is a list of subpopulations. Each subpopulation consists of a data.frame with a row for each individual (coding the covariates and genetic make-up).
#'@examples
#'init.popgensim(n.pops = 5, n.ind=8, sex.ratio = 0.25, n.loci = 4, n.allels = 7, n.cov = 3)
#' @export
init.popgensim <- function(n.pops, n.ind, sex.ratio, n.loci, n.allels, locs=NULL, n.cov=3)
{
noffset <- n.cov #number of covariates before the loci

#initialise populations
empty.loci <- matrix(NA,ncol=n.loci*2,nrow=n.ind)
colnames(empty.loci) <-paste("locus", rep(seq(1,n.loci,1),each=2),rep(c("A","B"),n.loci),sep="")
pops <- list( )
for (i in 1:n.pops)
{
pops[[i]]<- data.frame(cbind(pop=NA, sex=NA, age=NA,empty.loci))
#population number
pops[[i]][,"pop"] <- i
#sex
pops[[i]][,"sex"] <- "male"
pops[[i]][1:(round(n.ind*sex.ratio,0)),"sex"] <- "female"

pops[[i]][,"sex"] <- factor(pops[[i]][,"sex"])

#uniform allel distribution
pops[[i]][,(noffset+1):(n.loci*2+noffset) ]  <- sample(1:n.allels,n.loci*2*n.ind, replace=T)
}
if (is.null(locs)) names(pops)<- 1:n.pops else names(pops) <- row.names(locs)   #or from genind object....
return (pops)
}

################################################################################
### faster pairwise fst
################################################################################
#'Calculates pairwise fsts using a genind object (very fast)
#'
#'@param gsp a genind object
#'@return a pairwise fst matrix (same as hierfstat pairwise.fst)
#'@description for simulation the original pairwise.fst was too slow. The fast version works only with genind objects without NAs and diploid data (so to be save do not use it on non-simulated data)
#' @export
pairwise.fstb <- function(gsp)
{
n.pops <- length(popNames(gsp))
allPairs <- combn(1:n.pops, 2)
gen.mat2<- matrix(0, nrow=n.pops, ncol=n.pops)
allfreq <- function (x) 1-sum((x/2)^2)

for (i in 1:ncol(allPairs)){

np1 <- allPairs[1,i]
np2 <- allPairs[2,i]
p1 <- gsp@tab[gsp@pop==popNames(gsp)[np1],]
p2 <- gsp@tab[gsp@pop==popNames(gsp)[np2],]
p12 <- rbind(p1,p2)

lf <- gsp@loc.fac

n1 <- nrow(p1)
n2 <- nrow(p2)
n12 <- nrow(p12)

Hs1 <- mean( tapply(colSums(p1)/n1, lf, allfreq))
Hs2 <- mean( tapply(colSums(p2)/n2, lf, allfreq))
Hs12 <- mean( tapply(colSums(p12)/n12, lf, allfreq))
fst <- (Hs12-weighted.mean(c(Hs1, Hs2), c(n1,n2))) / Hs12
gen.mat2[np1,np2] <- fst
gen.mat2[np2,np1] <- fst

}
la <- popNames(gsp)
colnames(gen.mat2) <- rownames(gen.mat2) <- la
return(gen.mat2)
}
```

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PopGenReport documentation built on May 29, 2017, 9:09 p.m.