# pr.next.alleles: Probability of seeing next alleles (Dirichlet sampling) In DNAprofiles: DNA Profiling Evidence Analysis

## Description

Probability of seeing next alleles (Dirichlet sampling)

## Usage

 `1` ```pr.next.alleles(ij, seen, fr, theta = 0) ```

## Arguments

 `ij` integer matrix with allele numbers `seen` integer matrix with alleles already seen `fr` numeric vector with allelic proportions `theta` numeric background relatedness

## Details

When a population is subdivided into subpopulations, consecutively sampled alleles are not independent draws. This function implements the Dirichlet formula which states that after sampling n alleles, of which m are of type A_i, the probability that the next allele is of type A_i equals:

(m*θ+(1-θ)*p_i)/(1+(n-1)*θ)

The alleles already sampled are passed as the rows of the matrix `seen`, while the corresponding row of `ij` specifies for which alleles the probability of sampling is computed. The numer of rows of `ij` has to be equal to the number of rows of `seen`.

## Value

numeric (vector) of probabilities

`pr.next.allele`, `rmp`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# compute the pr. of seeing 1,1 after 1,1,1,1 # when theta=0 this is simply p_1^2 pr.next.alleles(t(c(1,1)),seen=t(c(1,1,1,1)),fr=c(1/4,3/4),theta=0) # but when theta>0, the pr. of seeing more 1's increases slightly pr.next.alleles(t(c(1,1)),seen=t(c(1,1,1,1)),fr=c(1/4,3/4),theta=0.05) # pr. distribution of (ordered!) genotypes after seeing 1,1,1 ij=matrix(c(1,1,1,2,2,2),ncol=2,byrow=TRUE) seen=matrix(1,nrow=3,ncol=3,byrow=TRUE) pr.next.alleles(ij,seen,fr=c(1/4,3/4),theta=0) # theta=0 pr.next.alleles(ij,seen,fr=c(1/4,3/4),theta=0.1) # theta=0.1 p0 <- pr.next.alleles(ij,seen,fr=c(1/4,3/4),theta=0) stopifnot(all.equal(p0[1]+2*p0[2]+p0[3],1)) p1 <- pr.next.alleles(ij,seen,fr=c(1/4,3/4),theta=0.05) stopifnot(all.equal(p1[1]+2*p1[2]+p1[3],1)) ```