Tools for analysing and plotting genotype-phenotype maps

Description

The gpmap package deals with genotype-phenotype maps for biallelic loci underlying quantitative phenotypes. The package provides a class gpmaps, analysis functions and basic lineplots. The package is designed for studying the properties of GP maps without reference to any particular population, i.e. the physiological (Cheverud & Routman, 1995) or functional (Hansen, 2001) properties of the GP map. This is opposed to statistical effects underlying most of quantitative genetics, where the GP-map is analysed togehter with genotype frequencies in a given population (e.g. Lynch & Walsh, 1998).

In version 0.1 which is released as part of the publication of Gjuvsland et al. (2013) we have implemented functionality for studying monotonicity Gjuvsland et al. (2011) of GP maps. The package utilizes the isotone package for monotone regression, and the foreach package for parallel computation.

The package consists of the following high-level functions : enumerate_genotypes, generate_gpmap, degree_of_monotonicity, decompose_monotone and plot.gpmap

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Cheverud JM & Routman EJ (1995) Epistasis and Its Controbution to Genetic Variance Components. Genetics 139:1455-1461 [link]

Gjuvsland AB, Vik JO, Woolliams JA, Omholt SW (2011) Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance. Journal of Evolutionary Biology 24(10):2269-2279 [link]

Gjuvsland AB, Wang Y, Plahte E and Omholt SW (2013) Monotonicity is a key feature of genotype-phenotype maps. Front. Genet. 4:216. doi: 10.3389/fgene.2013.00216 [link]

Hansen T & Wagner GP (2001) Modeling genetic Architecture: A Multilinear Theory of gene Interaction. Theoretical Population Biology 59:61-86 [link]

Leeuw J, Hornik K and Mair P (2009) Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software 32(5) [link]

Lynch M & Walsh B (1998) Genetics and Analysis of Quantitative Traits, Sunderland, MA: Sinauer Associates

Dataset containing example GP maps

Description

Example GP maps with two loci including: The orthogonal GP maps A, D, AA, AD, DA and DD used in decomposition of genetic variance (Zeng et al. 2005). The GP map mouseweight for body weight studied by Cheverud et al. (1995).

Usage

data(GPmaps)

Format

Objects of class gpmap

References

Cheverud JM & Routman EJ (1995) Epistasis and Its Controbution to Genetic Variance Components. Genetics 139:1455-1461 [link]

Zeng ZB, Wang T, Zou W. (2005). Modelling quantitative trait loci and interpretation of models. Genetics 169: 1711-1725. [link]

Decompose genotype-phenotype map(s) using monotone regression

Description

Functions for decomposing genotype-phenotype (GP) maps with N biallelic loci using monotone regression from the isotone package.

Usage

decompose_monotone(gpmap)
decompose_monotone_single(gpmap)

Arguments

Details

decompose_monotone works for any gpmap object (values is (3^N)xK matrix of genotypic values) and calls the internal function decompose_monotone_single for each column. decompose_monotone_single takes a gpmap object with a single set of genotypic values (K=1), loops through all 2^N possible combinations of plusalleles, calls monotone_regression and identifies the best fit. The code uses the foreach package and will run in parallel if a parallel backend is registered (see foreach documentation).

Value

The input gpmap is returned with two added elements

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Leeuw J, Hornik K and Mair P (2009) Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software 32(5) [link]

Gjuvsland AB, Wang Y, Plahte E and Omholt SW (2013) Monotonicity is a key feature of genotype-phenotype maps. Front. Genet. 4:216. doi: 10.3389/fgene.2013.00216 [link]

Examples

data(GPmaps)

#Additive GP map is monotone so monoR2=1 and values.mono=values
decompose_monotone(A)

#Pure AxA epistasis map
decompose_monotone(AA)

#two-locus example in Cheverud & Routman (1995)
decompose_monotone(mouseweight)

#decompose four random 3-locus GP maps
set.seed(0)
randomGP <- rnorm(3^2*4)
dim(randomGP) <- c(9,4)
decompose_monotone(generate_gpmap(randomGP))

Degree of monotonicity of GP map

Description

Functions for computing degree of monotonicity m for gpmap objects.

Usage

 
  degree_of_monotonicity(gpmap) 
  degree_of_monotonicity_single(gpmap) 

Arguments

Details

degree_of_monotonicity works for any gpmap object (values is (3^N)xK matrix of genotypic values) and calls the internal function degree_of_monotonicity_single for each column. degree_of_monotonicity_single computes substitution effect, locus weights and per-locus and overall degree of monotonicity as decribed in Gjuvsland et al. (2013).

Value

degree_of_monotonicity returns the input gpmap with the following added fields:

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Gjuvsland AB, Wang Y, Plahte E and Omholt SW (2013) Monotonicity is a key feature of genotype-phenotype maps. Front. Genet. 4:216. doi: 10.3389/fgene.2013.00216 [link]

Examples

data(GPmaps)

#Additive GP map is monotone 
degree_of_monotonicity(A)

#Pure AxA epistasis map
degree_of_monotonicity(AA)

#two-locus example in Cheverud & Routman (1995)
degree_of_monotonicity(mouseweight)

Function for enumerating genotypes for N biallelic loci

Description

Function for enumerating all 3^N genotypes for N biallelic loci. Optional specification of names of loci and alleles. genotypes. Generates a data frame of multilocus genotypes in the sequence used for objects of class gpmap.

Usage

 enumerate_genotypes(nloci=1, locinames=NULL, allelenames=NULL) 

Arguments

Details

Unless specified locinames default to "Locus 1", "Locus 2",..,"Locus N".

If allelenames is not specified then the alleles will be named "1" and "2".

Value

Returns a data frame with locinames as colnames, and with 3^N rows specifying all possible genotypes in the sequence used for all GP maps in the package (the same sequence as used in Gjuvsland et al.( 2011)), where the genotype at the first locus varies fastest, then the second locus, and so on:

  Locus_1 Locus_2
1      11      11
2      12      11
3      22      11
4      11      12
5      12      12
6      22      12
7      11      22
8      12      22
9      22      22

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Gjuvsland AB, Vik JO, Woolliams JA, Omholt SW (2011) Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance. Journal of Evolutionary Biology 24(10):2269-2279 [link]

Examples

#genotypes for a single locus
enumerate_genotypes()

#genotypes for two loci "A" and "B", with alleles named "H" and "L"
enumerate_genotypes(2,c("A","B"),c("H","L"))

#genotypes for the two-locus example in Cheverud & Routman (1995)
enumerate_genotypes(2,c("D7Mit17","D1Mit7"),rbind(c('A1','A2'),c('B1','B2')))

Function for creating genotype-phenotype (GP) maps

Description

Function for creating a gpmap object representing a genotype-phenotype (GP) map for N biallelic loci or more generally K such maps, from a matrix of genotypic values.

Usage

 generate_gpmap(y, locinames = NULL, allelenames = NULL, mapnames = NULL) 

Arguments

Details

Arguments locinames and allelenames are passed on to enumerate_genotypes, and the genotypic values in y should be given in the same sequence as the sequence of genotypes returned by enumerate_genotypes. If mapnames is not specified then the GP maps will be named "GPmap_1", "GPmap_2",..,"GPmap_K".

Value

The function returns an object of class gpmap containing the following components

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Gjuvsland AB, Vik JO, Woolliams JA, Omholt SW (2011) Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance. Journal of Evolutionary Biology 24(10):2269-2279 [link]

Examples

#inter- and intra-locus additive GPmap with two loci 
generate_gpmap(c(-2,1,0,-1,0,1,0,1,2),mapnames="Additive") 

#two-locus GP map with AxA epistasis for loci named A and B
generate_gpmap(c(-1,0,1,0,0,0,1,0,-1),locinames=c("A","B"),mapnames="AxA")

#random GP map with 3 loci
set.seed(0)
generate_gpmap(rnorm(27))

Perform monotone regression on a genotype-phenotype (GP) map

Description

The function uses partial_genotype_order and activeSet from the isotone package to do monotone regression (Leeuw et al., 2009) on a GP map.

Usage

monotone_regression(gpmap, plusallele)

Arguments

Details

Element i in plusallele specifies the ordering of the genotypes at locus i, if the element is 1 then 11 < 12 < 22 and conversely if it is 2 then 22 < 12 < 11. monotone_regression calls partial_genotype_order to obtain the partial ordering of genotypic values for the given plusalleles. This partial ordering is then used together with the GP map itself as input to the activeSet function from the package isotone.

Value

monotone_regression returns the output from activeSet directly.

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Leeuw J, Hornik K and Mair P (2009) Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software 32(5) [link]

Gjuvsland AB, Wang Y, Plahte E and Omholt SW (2013) Monotonicity is a key feature of genotype-phenotype maps. Front. Genet. 4:216. doi: 10.3389/fgene.2013.00216 [link]

Examples

data(GPmaps)

#Additive GP map is monotone 
monotone_regression(A,c(2,2))

#Pure AxA epistasis map
monotone_regression(AA,c(2,2))

#two-locus example in Cheverud & Routman (1995)
monotone_regression(mouseweight,c(1,1))

Generate partial ordering of genotype space based from allele content of genotypes

Description

Generate the strict partial order on genotype space specified in eq. (13) in Gjuvsland et al. (2011). For a genotype space with N biallelic loci a minimal description of this partial order is given by 2N*3^{(N-1)} inequalities.

Usage

 partial_genotype_order(plusallele) 

Arguments

Details

In short a partial order on a set is a binary relation defining a parwise ordering of some pairs of elements in the set, for a formal definiton see https://en.wikipedia.org/wiki/Partial_order. In the partial order on the set of genotypes defined in Gjuvsland et al. (2011) the comparable pairs of genotypes are equal at every locus except one, while all other pairs of genotypes are incomparable. This partial ordering of genotype space is implicit in the regression on gene content (the number of alleles with a given index in each genotype) used for decomposition of tne genotypic value in quantitative genetics (see e.g. Lynch and Walsh page 65).

Value

Returns a (2N*3^{(N-1)}) \times 2 matrix of genotype indexes. The genotype indexes refer to row number in the genotype sequence set up in enumerate_genotypes. Each row vector in the matrix contains the genotype indexes of one comparable pairs, and if the first index is k and the second is l then genotype[k] < genotype[l].

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

References

Gjuvsland AB, Vik JO, Woolliams JA, Omholt SW (2011) Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance. Journal of Evolutionary Biology 24(10):2269-2279 [link]

Lynch M & Walsh B (1998) Genetics and Analysis of Quantitative Traits, Sunderland, MA: Sinauer Associates

Functions for creating lineplots of genotype-phenotype (GP) maps

Description

Function for creating lineplots for genotype-phenotype (GP) map (an object of class gpmap) with 1-3 biallelic loci.

Usage

 
## S3 method for class 'gpmap'
plot(x, show=1, decomposed=FALSE, ...)

Arguments

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

Examples

data(GPmaps)

#plot additive gpmap
plot(A)

#plot decomposition of GPmap from Cheverud & Routman (1995)
decomp <- decompose_monotone(mouseweight)
plot(decomp, decomposed=TRUE)

Print function for gpmap objects

Description

Print a summary of a genotype-phenotype (GP) map (an object of class gpmap) with 1-3 N biallelic loci.

Usage

## S3 method for class 'gpmap'
print(x, ...)

Arguments

Details

Prints name(s) of GP map(s) and loci, a summary of genotypic values. Monotonicity measures are printed if available.

Author(s)

Arne B. Gjuvsland <arne.gjuvsland@nmbu.no> and Yunpeng Wang <yunpeng.wng@gmail.com>

Examples

data(GPmaps)
print(A)