Instead of fixing bottleneck size for CompartmentType, draw from distribution

[ArtPoon]

So each Compartment of that Type is assigned a random deviate from the distribution, e.g., Poisson with Type-specific mean \lambda.

[ArtPoon]

I think this can be accomplished by modifying this line:

twt/R/simInnerTree.R

Line 244 in ae05f46

bottleneck.size <- comp$get.type()$get.bottleneck.size()

If we let the class bottleneck.size represent the mean, we can draw a Poisson variate instead of directly assigning this value:

mean.size <- comp$get.type()$get.bottleneck.size() 
bottleneck.size <- rpois(n=1, lambda=mean.size)

For example, this lets us assign a mean bottleneck size of 1.2 to a CompartmentType, and then the realized bottleneck size for a given event has some probability of being 1, 2 or more, conditional on being more than zero.

[ArtPoon]

We want to use a zero-truncated Poisson or negative binomial distribution:
https://en.wikipedia.org/wiki/Zero-truncated_Poisson_distribution

[ArtPoon]

We should use a negative binomial distribution because the number of transmitted-founders is probably not Poisson-distributed:
https://jvi.asm.org/content/83/8/3556.short

[ArtPoon]

https://rdrr.io/rforge/countreg/man/ztnbinom.html
https://r-forge.r-project.org/scm/viewvc.php/pkg/R/ztnbinom.R?view=markup&root=countreg
Released under GPLv3.

## ztnbinom: Zero-truncated negative binomial
dztnbinom <- function(x, mu, theta, size, log = FALSE) {
  if(!missing(theta) & !missing(size)) stop("only 'theta' or 'size' may be specified")
  if(!missing(size)) theta <- size
  rval <- dnbinom(x, mu = mu, size = theta, log = TRUE) - pnbinom(0, mu = mu, size = theta, lower.tail = FALSE, log.p = TRUE)
  rval[x < 1] <- -Inf
  rval[mu <= 0] <- 0
  if(log) rval else exp(rval)
}

pztnbinom <- function(q, mu, theta, size, lower.tail = TRUE, log.p = FALSE) {
  if(!missing(theta) & !missing(size)) stop("only 'theta' or 'size' may be specified")
  if(!missing(size)) theta <- size
  rval <- log(pnbinom(q, mu = mu, size = theta, lower.tail = lower.tail, log.p = FALSE) - dnbinom(0, mu = mu, size = theta)) -
    pnbinom(0, mu = mu, size = theta, lower.tail = FALSE, log.p = TRUE)
  rval[q < 1] <- if(lower.tail) -Inf else 0
  if(log.p) rval else exp(rval)
}

qztnbinom <- function(p, mu, theta, size, lower.tail = TRUE, log.p = FALSE) {
  if(!missing(theta) & !missing(size)) stop("only 'theta' or 'size' may be specified")
  if(!missing(size)) theta <- size
  p_orig <- p
  p <- if(log.p) p else log(p)
  p <- p + pnbinom(0, mu = mu, size = theta, lower.tail = FALSE, log.p = TRUE)
  p <- exp(p) + dnbinom(0, mu = mu, size = theta)
  rval <- qnbinom(p, mu = mu, size = theta, lower.tail = lower.tail, log.p = FALSE)
  if(lower.tail) rval[p_orig < dztnbinom(1, mu = mu, theta = theta, log = log.p)] <- 1
  rval
}

rztnbinom <- function(n, mu, theta, size) {
  if(!missing(theta) & !missing(size)) stop("only 'theta' or 'size' may be specified")
  if(!missing(size)) theta <- size
  qztnbinom(runif(n), mu = mu, theta = theta)
}

[ArtPoon]

This needs testing before we can close this issue

[ArtPoon]

Re-implemented in refactored code but not tested yet