# Internal Functions in polysat The internal functions `G`, `INDEXG`, `GENLIST`, `RANMUL`, and `SELFMAT` are used for calculating genotype probabilities under partial selfing. The internal function `.unal1loc` finds all unique alleles at a single locus. The internal function `fixloci` converts locus names to a format that will be compatible as column headers for allele frequency tables. ```r G(q, n) INDEXG(ag1, na1, m2) GENLIST(ng, na1, m2) RANMUL(ng, na1, ag, m2) SELFMAT(ng, na1, ag, m2) .unal1loc(object, samples, locus) fixloci(loci, warn = TRUE) ``` ## Arguments - `q`: Integer. - `n`: Integer. - `ag1`: A vector representing an unambiguous genotype. - `na1`: Integer. The number of alleles, including a null. - `m2`: Integer. The ploidy. - `ng`: Integer. The number of genotypes. - `ag`: An array of genotypes such as that produced by `.genlist`. - `object`: A `"genambig"` object. - `samples`: Optional, a numeric or character vector indicating which samples to use. - `locus`: A character string or number indicating which locus to use. - `loci`: A character vector of locus names. - `warn`: Boolean indicating whether a warning should be issued if locus names are changed. ## Returns `G` returns $$ \frac{(n+q)!}{(q+1)! * (n-1)!}(n+q)!/((q+1)! * (n-1)!) $$ `INDEXG` returns an integer indicating the row containing a particular genotype in the matrix produced by `GENLIST`. `GENLIST` returns an array with dimensions `ng, m2`, containing all possible unambiguous genotypes, one in each row. The null allele is the highest-numbered allele. `RANMUL` returns a list. The first item is a vector of polynomial coefficients for calculating genotype frequencies under random mating. The second is an array showing how many copies of each allele each genotype has. `SELFMAT` returns the selfing matrix. Parental genotypes are represented in rows, and offspring genotypes in columns. The numbers indicate relative amounts of offspring genotypes produced when the parental genotypes are self-fertilized. `.unal1loc` returns a vector containing all unique alleles, not including `Missing(object)`. `fixloci` returns a character vector of corrected locus names. ## References De Silva, H. N., Hall, A. J., Rikkerink, E., and Fraser, L. G. (2005) Estimation of allele frequencies in polyploids under certain patterns of inheritance. **Heredity** 95 , 327--334 ## See Also `deSilvaFreq`, `meandistance.matrix2`, `genotypeProbs`, `genambig.to.genbinary`, `alleleDiversity` ## Examples ```r # Calculation of genotype probabilities in a tetraploid with four # alleles plus a null, and a selfing rate of 0.5. This is a translation # of code in the supplementary material of De Silva et al. (2005). m2 <- 4 m <- m2/2 na1 <- 5 self <- 0.5 ng <- na1 for(j in 2:m2){ ng <- ng*(na1+j-1)/j } ag <- polysat:::GENLIST(ng, na1, m2) temp <- polysat:::RANMUL(ng, na1, ag, m2) rmul <- temp[[1]] arep <- temp[[2]] rm(temp) smat <- polysat:::SELFMAT(ng, na1, ag, m2) smatdiv <- (polysat:::G(m-1,m+1))^2 p1 <- c(0.1, 0.4, 0.2, 0.2, 0.1) # allele frequencies # GPROBS subroutine rvec <- rep(0,ng) for(g in 1:ng){ rvec[g] <- rmul[g] for(j in 1:m2){ rvec[g] <- rvec[g]*p1[ag[g,j]] } } id <- diag(nrow=ng) smatt <- smat/smatdiv s3 <- id - self * smatt s3inv <- solve(s3) gprob <- (1-self) * s3inv %*% rvec # gprob is a vector of probabilities of the seventy genotypes. ``` ## Author(s) Lindsay V. Clark

polysat-internal function