rflan: The distribution of mutant cell counts

Description Usage Arguments Details Value See Also Examples

Description

Density, distribution function, quantile function and random generation for mutant cell counts.

Usage

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  dflan(m,mutations=1,fitness=1,death=0,model=c("LD","H"))
  pflan(m,mutations=1,fitness=1,death=0,model=c("LD","H"),lower.tail=TRUE)
  qflan(p,mutations=1,fitness=1,death=0,model=c("LD","H"),lower.tail=TRUE)
  rflan(n,mutations=1,mutprob=NULL,fitness=1,death=0,
        dist=list(name="lnorm",meanlog=-0.3795851,sdlog=0.3016223),
        mfn=1e9,cvfn=0) 

Arguments

m

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

mutations

mean number of mutations: positive integer. Ignored if mutprob is non-empty.

mutprob

mutation probability: numeric between 0 and 1. By default empty. See details.

fitness

fitness parameter: numeric positive.

death

death probability: numeric between 0 and 0.5.

dist

lifetime distribution for mutant cells. See Details.

model

statistical lifetime model. Must be one of "LD" (default) for Luria-Delbrück model (exponential lifetimes), or "H" for Haldane model (constant lifetimes).

mfn

mean final number of cells: numeric positive.

cvfn

coefficient of variation of final numbers of cells: numeric, default 0. If non-zero and if mutprob is empty, compute the sample with mutprob = mutations/mfn

lower.tail

logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > m]

Details

The argument dist is a list beginning with the distribution name followed by its parameters, and must be one the 4 following distributions: "dirac"(location), "exp"(rate), "lnorm"(meanlog, sdlog), "gamma"(shape, scale).

If cvfn is positive, the final numbers of cells are generated with the log-normal distribution with mean mfn and coefficient of variation cvfn.

If mutprob is non-empty if cvfn is zero, the sample is computed with mutations as the product of mutprob by mfn. If cvfn is non-zero, the sample is computed with mutations as

α = \mathcal{L}≤ft[π≤ft(1-\frac{δ}{1-δ}\right)\right]

whith π is the ratio of mutations by mfn, δ the death probability and \mathcal{L}(x) is the Laplace transform of the log-normal distribution with mean mfn and coefficient of variation cvfn.

Value

dflan gives the density, pflan gives the distribution function, qflan gives the quantile function, and rflan generates a random sample.

rflan returns a list with two arguments, each with length n: a vector of integers $mc (mutant counts), and a vector of numeric $fn (final numbers of cells).

See Also

link{draw.clone}

Examples

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#----------------------- distributions ----------------------------------

# Luria-Delbrück model, mean number of mutations 1, fitness parameter 1
dflan(0:10)
pflan(0:10)
qflan(c(0.95,0.99))

# Luria-Delbrück model, mean number of mutations 2, fitness parameter 0.5
qflan(c(0.95,0.99),mutations=2,fitness=0.5)
qflan(c(0.05,0.01),mutations=2,fitness=0.5,lower.tail=FALSE)

# Haldane model, mean number of mutations 2, fitness parameter 0.5
qflan(c(0.95,0.99),mutations=2,fitness=0.5,model="H")

#---------------------- random samples ----------------------------------
# lognormal lifetime distribution, lognormal final numbers
X <- rflan(100,cvfn=0.3)
X$mc              # mutant counts
X$fn              # final numbers

# mean number of mutations 2, fitness parameter 0.5 (realistic model, but slow)
rflan(1000,mutations=2,fitness=0.5)$mc

# exponential lifetimes (Luria-Delbrück model, fast)
rflan(1000,mutations=2,fitness=0.5,dist=list(name="exp",rate=1))$mc

# constant lifetimes (Haldane model, fast)
rflan(1000,mutations=2,fitness=0.5,dist=list(name="dirac",location=1))$mc

# specifying mutation probability and mean final number
rflan(1000,mutprob=2e-9,mfn=2e9,fitness=0.5,dist=list(name="dirac",location=1))$mc

# positive cell death probability
rflan(1000,mutprob=2e-9,mfn=2e9,death=0.1,fitness=0.5,dist=list(name="dirac",location=1))$mc

rcqls/flan documentation built on May 27, 2019, 3:05 a.m.

Related to rflan in rcqls/flan...