gregorius {genetics}

Probability of Observing All Alleles with a Given Frequency in a Sample of a Specified Size.

Description

Probability of observing all alleles with a given frequency in a sample of a specified size.

Usage

gregorius(freq, N, missprob, tol = 1e-10, maxN = 10000, maxiter=100, showiter = FALSE)

Arguments

freq

(Minimum) Allele frequency (required)

N

Number of sampled genotypes

missprob

Desired maximum probability of failing to observe an allele.

tol

Omit computation for terms which contribute less than this value.

maxN

Largest value to consider when searching for N.

maxiter

Maximum number of iterations to use when searching for N.

showiter

Boolean flag indicating whether to show the iterations performed when searching for N.

Details

If freq and N are provided, but missprob is omitted, this function computes the probability of failing to observe all alleles with true underlying frequency freq when N diploid genotypes are sampled. This is accomplished using the sum provided in Corollary 2 of Gregorius (1980), omitting terms which contribute less than tol to the result.

When freq and missprob are provide, but N is omitted. A binary search on the range of [1,maxN] is performed to locate the smallest sample size, N, for which the probability of failing to observe all alleles with true underlying frequency freq is at most missprob. In this case, maxiter specifies the largest number of iterations to use in the binary search, and showiter controls whether the iterations of the search are displayed.

Value

A list containing the following values:

call

Function call used to generate this object.

method

One of the strings, "Compute missprob given N and freq", or "Determine minimal N given missprob and freq", indicating which type of computation was performed.

retval$freq

Specified allele frequency.

retval$N

Specified or computed sample size.

retval$missprob

Computed probability of failing to observe all of the alleles with frequency freq.

Note

This code produces sample sizes that are slightly larger than those given in table 1 of Gregorius (1980). This appears to be due to rounding of the computed missprobs by the authors of that paper.

Author(s)

Code submitted by David Duffy [e-mail], substantially enhanced by Gregory R. Warnes [e-mail].

References

Gregorius, H.R. 1980. The probability of losing an allele when diploid genotypes are sampled. Biometrics 36, 643-652.

Examples

# Compute the probability of missing an allele with frequency 0.15 when
# 20 genotypes are sampled:
gregorius(freq=0.15, N=20)

# Determine what sample size is required to observe all alleles with true
# frequency 0.15 with probability 0.95
gregorius(freq=0.15, missprob=1-0.95)