simecol (version 0.5-5)

neighbours: Count Number of Neighbours in a Rectangular Cellular Grid.

Description

This function is the base function for the simulation of deterministic and stochastic cellular automata on a rectangular grid.

Usage

neighbours(x, state=NULL, wdist=NULL, tol=1e-4)
  neighbors(x, state=NULL, wdist=NULL, tol=1e-4)

Arguments

x

Matrix. The cellular grid, in which each cell can have a specific state value, e.g. zero (dead cell) or one (living cell) or the age of an individual.

state

A value, whose existence is checked within the neighbourhood of each cell.

wdist

The neighbourhood weight matrix.

tol

Tolerance value for the comparision of state with the state of each cell. If tol is a large value, then more than one state can be checked simultaneously.

Value

• A matrix with the same structure as x with the weighted sum of the neigbours with values between state - tol and state + tol.

Details

See example for details.

See Also

seedfill, eightneighbours, conway

Examples

mycolors <- function(n) {
      col <- c("wheat","darkgreen")
      if (n>2) col <- c(col, heat.colors(n-2))
      col
    }

    # weight matrix for neighbourhood determination
    wdist <- matrix(c(0.5,0.5,0.5,0.5,0.5,
                      0.5,1.0,1.0,1.0,0.5,
                      0.5,1.0,1.0,1.0,0.5,
                      0.5,1.0,1.0,1.0,0.5,
                      0.5,0.5,0.5,0.5,0.5),nrow=5)

    pj <- 0.99  # survival probability of juveniles
    pa <- 0.99  # survival probability of adults
    ps <- 0.1   # survival probability of senescent
    ci <- 1.0   # "seeding constant"
    adult <- 5  # age of adolescence
    old   <- 10 # age of senescence

    ## Define a start population
    n<-80
    m<-80
    x<-rep(0, m*n)

    ## stochastic seed
    ## x[round(runif(20,1,m*n))] <- adult
    dim(x)<- c(n,m)

    ## rectangangular seed in the middle
    x[38:42,38:42] <- 5

    ## plot the start population
    image(x, col=mycolors(2))

    ## Simulation loop (hint: increase loop count)
    for (i in 1:10){

      ## rule 1: reproduction
      ## 1.1 which cells are adult? (only adults can generate)
      ad <- ifelse(x>=adult & x<old, x, 0)
      dim(ad) <- c(n,m)

      ## 1.2 how much (weighted) adult neighbours has each cell?
      nb <- neighbours(ad, wdist=wdist)

      ## 1.3 a proportion of the seeds develops juveniles
      ## simplified version, you can also use probabilities
      genprob <- nb * runif(nb) * ci
      xgen  <- ifelse(x==0 & genprob >= 1, 1, 0)

      ## rule 2: growth and survival of juveniles
      xsurvj <- ifelse(x>=1     & x < adult & runif(x) <= pj, x+1, 0)
      ## rule 2: growth and survival of adults
      xsurva <- ifelse(x>=adult & x < old   & runif(x) <= pa, x+1, 0)
      ## rule 2: growth and survival of senescent
      xsurvs <- ifelse(x>= old              & runif(x) <= ps, x+1, 0)

      ## make resulting grid of complete population
      x     <- xgen + xsurvj + xsurva + xsurvs
      dim(x)  <-c(n,m)

      ## plot resulting grid
      image(x, col=mycolors(max(x)+1), add=TRUE)
      if (max(x)==0) stop("extinction", call.=FALSE)
    }

    ## modifications:  pa<-pj<-0.9

    ## additional statistics of population structure
    ## with table, hist, mean, sd, ...