AlphaSimR is built upon the basics of genetics for the stochastic simulation of crop and animal breeding programmes. This vignette will provide an overview of the genome, it’s inheritance, and the tools used to read it with supporting examples and code.
What is a genome?
The genome is the complete set of genetic information within an organism. It is made up of deoxyribonucleic acid (DNA), consisting of sequences of four types of nucleotide bases: adenine (A), cytosine (C), guanine (G), and thymine (T). Within one DNA molecule, there are two strands joined by base-pairs: A binds with T and C binds with G. This forms a double helix structure which can be visualised as a spiral ladder. These DNA molecules are condensed around supporting protein to form a thread-like structure known as chromosomes. Due to the different demographic history across species, how the DNA is package can vary substantial including the number of chromosome and the number of chromosome copies (ploidy). For example, humans have 23 pairs of chromosomes (22 autosomnal, one non-autosomnal) for ~three billion base-pairs. Whereas cattle have 30 pairs of chromosomes for fewer base-pairs at ~2.7 billion. As these species are both diploid, in each chromosome pair, one has been inherited from the father (paternal) and one has been inherited from the mother (maternal).
Genes, alleles, loci, genotypes, and haplotypes.
Although similar, there are essential differences in the terminology used. This next section will provide a short glossary for genes, allele, loci, genotypes, and haplotypes.
Genes are segments of DNA that are translated to proteins. Typically they will contain a few hundred to more than two billion bases-pairs with a codon (triplet base-pair) coding for either an amino acid or to start/stop.
An allele in a gene is a gene variant. More generally, an allele represents a possible sequence of bases at a particular site on a genome (known as a locus). When biallelic (two variants per gene) the allele is either ancestral (denoted 0) or a mutant (denoted 1). Per the name, new alleles arise from mutation.
A genotype is the combination of alleles across chromosome copies that an organism has at a specified locus or across loci. For instance, there are three possible genotypes for a diploid at a biallelic locus with ancestral allele A and mutant allele a: ancestral homozygous (aa) with allele dosage 0, heterozygous (aA or Aa) with allele dosage 1, and mutant homozygous (AA) with allele dosage 2. Genotypes can differ between individuals due to random segregation in inheritance.
A haplotype (haploid genotype) describes the physical grouping of alleles along the same chromosome. This means that these group of alleles tend to be inherited together. New haplotypes are created through recombination.
What does this look like in AlphaSimR?
Let’s start with creating the founding genome using
runMacs. As mentioned, cattle have 30 pairs of chromosomes,
but for the purpose of this simulation we are only interested in three.
When we inspect the founderGenome we see that it has a ploidy of two
with 12 loci across three chromosomes (with four segregating sites on
each).
founderGenome = runMacs(nInd = 10,
nChr = 3,
segSites = 4,
species = "CATTLE")
# Set simulation parameters
SP = SimParam$new(founderGenome)
SP$setTrackRec(TRUE)
# Inspect the founderGenome
founderGenome
#> An object of class "MapPop"
#> Ploidy: 2
#> Individuals: 10
#> Chromosomes: 3
#> Loci: 12Then we can observe the genotypes with pullSegSiteGeno.
Each row represents one of the ten individuals and each column
represents a defined loci labelled as the Chromosome_Locus. All will
have a value of zero to two equivalent to the allele dosage. Commonly,
this would be homozygous ancestral (0), heterozygous (1), and homozygous
mutant (2). Since this is a diploid, we are observing these genotypes
across the pair of chromosomes. Where the ancestral allele is not known,
the allele dosage will be randomly assigned.
pullSegSiteGeno(founderGenome)
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 1 0 2 2 2 1 1 2 1 2 0 2 0
#> 2 0 0 2 2 0 0 2 0 1 0 0 0
#> 3 1 1 1 2 0 2 2 0 1 0 1 1
#> 4 0 2 2 2 0 1 2 1 2 0 1 1
#> 5 1 2 2 2 1 1 1 0 2 1 2 0
#> 6 0 1 2 2 1 2 1 0 1 0 2 0
#> 7 1 1 1 1 0 0 2 1 2 0 1 0
#> 8 0 1 2 2 1 1 2 2 1 1 1 0
#> 9 2 0 1 1 0 1 2 1 1 0 2 0
#> 10 1 1 1 2 1 2 2 1 1 0 2 0The haplotypes can be observed with pullSegSiteHaplo.
Each row represents the sequence of alleles on each chromosome per
individual. Since this is diploid, we observe two for each individual:
one maternal (id_1) and the other paternal (id_2). All will have a value
of 0 or 1 for either ancestral or mutant allele respectingly. As before,
each column represents a defined loci.
pullSegSiteHaplo(founderGenome)
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 1_1 0 1 1 1 1 1 1 1 1 0 1 0
#> 1_2 0 1 1 1 0 0 1 0 1 0 1 0
#> 2_1 0 0 1 1 0 0 1 0 1 0 0 0
#> 2_2 0 0 1 1 0 0 1 0 0 0 0 0
#> 3_1 0 0 0 1 0 1 1 0 0 0 1 0
#> 3_2 1 1 1 1 0 1 1 0 1 0 0 1
#> 4_1 0 1 1 1 0 1 1 0 1 0 1 0
#> 4_2 0 1 1 1 0 0 1 1 1 0 0 1
#> 5_1 1 1 1 1 0 0 1 0 1 0 1 0
#> 5_2 0 1 1 1 1 1 0 0 1 1 1 0
#> 6_1 0 1 1 1 1 1 0 0 1 0 1 0
#> 6_2 0 0 1 1 0 1 1 0 0 0 1 0
#> 7_1 0 1 1 1 0 0 1 1 1 0 0 0
#> 7_2 1 0 0 0 0 0 1 0 1 0 1 0
#> 8_1 0 0 1 1 1 0 1 1 0 1 0 0
#> 8_2 0 1 1 1 0 1 1 1 1 0 1 0
#> 9_1 1 0 0 0 0 1 1 0 1 0 1 0
#> 9_2 1 0 1 1 0 0 1 1 0 0 1 0
#> 10_1 0 0 0 1 0 1 1 0 0 0 1 0
#> 10_2 1 1 1 1 1 1 1 1 1 0 1 0How are genomes inherited?
Genetic code is inherited from an individuals mother and father. This involves cells known as gametes: eggs (from mother) and sperm (from father). These cells have half the number of chromosomes to other cells in the species. For example, in diploid species like humans gametes are haploid cells. These have been developed through interphase (DNA replication) and meiosis (cell division). The mechanism of interphase and meiosis are outside the scope of this vignette, however is important due to their contribution to genetic variation.
Genetic Variation: the DNA lottery
Broadly speaking, there are three contributions to genetic variation: mutation, crossing over (or recombination), and independent assortment.
Mutation occurs during DNA replication in interphase. Although the rate is very small (~2.5x10-8 mutation per nucleotide), when considering the whole genome mutation is not negligible.
Both crossing over and independent assortment occurs in the first part of meiosis known as the reductional division. Crossing over refers to the swapping of genetic material at random between chromatids resulting in variation. Independent Assortment refers to the random orientation of homologous chromosome pairs resulting in gametes with many different assortments of chromosomes. (recall there are 23 pairs in a human).
Within genetics, albeit quantitative or population, we are interested in how individual’s genomes differ to the next. Thus, it is this variation we wish to capture to understand how genetics influence desired (or undesired) traits in crop and animal breeding.
In AlphaSimR:
- Random mutations can be added to individuals in populations with
mutate. For the purpose of demonstration, the mutation is at a much higher rate than would be expected.
basePop = newPop(founderGenome)
mutatedBasePop = mutate(basePop, mutRate = 0.1, simParam = SP)
pullSegSiteGeno(basePop)
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 1 0 2 2 2 1 1 2 1 2 0 2 0
#> 2 0 0 2 2 0 0 2 0 1 0 0 0
#> 3 1 1 1 2 0 2 2 0 1 0 1 1
#> 4 0 2 2 2 0 1 2 1 2 0 1 1
#> 5 1 2 2 2 1 1 1 0 2 1 2 0
#> 6 0 1 2 2 1 2 1 0 1 0 2 0
#> 7 1 1 1 1 0 0 2 1 2 0 1 0
#> 8 0 1 2 2 1 1 2 2 1 1 1 0
#> 9 2 0 1 1 0 1 2 1 1 0 2 0
#> 10 1 1 1 2 1 2 2 1 1 0 2 0
pullSegSiteGeno(mutatedBasePop)
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 1 0 2 1 1 1 2 2 1 1 1 2 0
#> 2 0 1 2 2 0 0 2 0 1 1 0 1
#> 3 1 1 1 1 0 2 2 0 2 0 1 1
#> 4 1 2 1 1 0 0 2 2 2 0 1 2
#> 5 1 2 2 2 0 1 1 0 2 1 2 0
#> 6 0 2 2 1 2 2 1 0 1 1 2 0
#> 7 1 1 1 1 0 0 2 1 2 0 1 0
#> 8 0 1 2 2 1 1 1 2 1 1 1 1
#> 9 2 0 1 0 0 1 1 1 1 0 2 0
#> 10 1 1 1 2 1 1 2 1 0 0 2 1- Independent assortment and recombination can be observed across generations.
The first step is to make the cross in the base population to produce
the second generation. For this, randCross can be used to
create one cross, producing a pair of full siblings.
secondGenPop = randCross(pop = basePop, nCrosses = 1, nProgeny = 2, simParam = SP)
str(secondGenPop)
#> Formal class 'Pop' [package "AlphaSimR"] with 18 slots
#> ..@ id : chr [1:2] "11" "12"
#> ..@ iid : int [1:2] 11 12
#> ..@ mother : chr [1:2] "4" "4"
#> ..@ father : chr [1:2] "6" "6"
#> ..@ sex : chr [1:2] "H" "H"
#> ..@ nTraits: int 0
#> ..@ gv : num[1:2, 0 ]
#> .. ..- attr(*, "dimnames")=List of 2
#> .. .. ..$ : NULL
#> .. .. ..$ : NULL
#> ..@ pheno : num[1:2, 0 ]
#> .. ..- attr(*, "dimnames")=List of 2
#> .. .. ..$ : NULL
#> .. .. ..$ : NULL
#> ..@ ebv : num[1:2, 0 ]
#> ..@ gxe : list()
#> ..@ fixEff : int [1:2] 1 1
#> ..@ misc : list()
#> ..@ miscPop: list()
#> ..@ nInd : int 2
#> ..@ nChr : int 3
#> ..@ ploidy : int 2
#> ..@ nLoci : int [1:3] 4 4 4
#> ..@ geno :List of 3
#> .. ..$ : raw [1, 1:2, 1:2] 0e 0e 0e 0c
#> .. ..$ : raw [1, 1:2, 1:2] 04 03 0c 06
#> .. ..$ : raw [1, 1:2, 1:2] 09 05 09 05
# Collect the iid for mother and father
mother = as.integer(secondGenPop@mother[1])
father = as.integer(secondGenPop@father[1])Then, the haplotypes can be extracted for the mother, father, and two progeny to observe the inheritance. Recall that id_1 is the maternal haplotype (inherited from mother) and id_2 is the paternal haplotype (inherited from father). For clarity, no mutation is included in this example. All variation observed is due to independent assortment and/or recombination.
pullSegSiteHaplo(basePop[basePop@iid == mother,])
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 4_1 0 1 1 1 0 1 1 0 1 0 1 0
#> 4_2 0 1 1 1 0 0 1 1 1 0 0 1
pullSegSiteHaplo(basePop[basePop@iid == father,])
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 6_1 0 1 1 1 1 1 0 0 1 0 1 0
#> 6_2 0 0 1 1 0 1 1 0 0 0 1 0
pullSegSiteHaplo(secondGenPop)
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 11_1 0 1 1 1 0 0 1 0 1 0 0 1
#> 11_2 0 1 1 1 1 1 0 0 1 0 1 0
#> 12_1 0 1 1 1 0 0 1 1 1 0 0 1
#> 12_2 0 0 1 1 0 1 1 0 1 0 1 0In the above, independent assortment will always be observed. This is
clear since despite being full siblings they inherit a different
arrangement of haplotypes from the mother and the father. We may observe
changes to the haplotypes via recombination between the four sites
across a chromosome (either chromosome one, two, and/or three). However,
this depends on the rate of recombination. Nevertheless, even if present
it can be hard or even impossible to observe through the haplotypes
alone, even in this small sample size. Instead we can use the
pullIbdHaplo to observe this. For further details on
recombination, please see the vignette on Recombination.
pullIbdHaplo(basePop[basePop@iid == mother,])
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 4_1 7 7 7 7 7 7 7 7 7 7 7 7
#> 4_2 8 8 8 8 8 8 8 8 8 8 8 8
pullIbdHaplo(basePop[basePop@iid == father,])
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 6_1 11 11 11 11 11 11 11 11 11 11 11 11
#> 6_2 12 12 12 12 12 12 12 12 12 12 12 12
pullIbdHaplo(secondGenPop)
#> 1_1 1_2 1_3 1_4 2_1 2_2 2_3 2_4 3_1 3_2 3_3 3_4
#> 11_1 8 8 7 7 8 8 7 7 7 7 8 8
#> 11_2 11 11 12 12 11 11 11 11 11 11 12 12
#> 12_1 8 7 7 7 8 8 7 8 7 7 8 8
#> 12_2 12 12 12 12 12 12 12 12 11 11 12 12How are genomes read?
For a genome to be read, first it needs to be sequenced. The techniques for this include Sanger sequencing or next-generation sequencing. These are then used to identify single nucleotide polymorphisms (SNPs). SNPs highlight variation at specific loci; equivalent to markers. Other terminology include traits and QTL: Quantitative Trait Locus. Traits are characteristics of interest such as milk yield or growth rate that have a genetic component. QTL are a region of DNA that’s associated with a specific trait that varies in the population. This could be identifiable by a marker (eg. SNP) or could only be correlated.
In AlphaSimR:
Let’s start a new population.
founderGenome = runMacs(nInd = 10,
nChr = 3,
segSites = 4,
species = "CATTLE")
# Set simulation parameters
SP = SimParam$new(founderGenome)Then, add an additive trait with three QTLs per chromosome using
SP$addTraitA and one SNP per chromosome with
SP$addSnpChip.
SP$addTraitA(nQtlPerChr = 3)
SP$addSnpChip(nSnpPerChr = 1)After, create a base population.
basePop = newPop(founderGenome, simParam = SP)
# Inspect basePop
basePop
#> An object of class "Pop"
#> Ploidy: 2
#> Individuals: 10
#> Chromosomes: 3
#> Loci: 12
#> Traits: 1The SNPs can be read with pullSnpGeno or, if the
location in the genome is known, pullMarkerGeno can be
used.
# From SNP
SNP = pullSnpGeno(pop = basePop, snpChip =1)
print(SNP)
#> 1_2 2_2 3_4
#> 1 2 1 1
#> 2 2 0 0
#> 3 2 1 1
#> 4 2 2 0
#> 5 2 1 1
#> 6 1 1 0
#> 7 1 1 0
#> 8 1 2 0
#> 9 2 1 1
#> 10 2 0 1
# From marker
location = colnames(SNP)
pullMarkerGeno(basePop, markers = location)
#> 1_2 2_2 3_4
#> 1 2 1 1
#> 2 2 0 0
#> 3 2 1 1
#> 4 2 2 0
#> 5 2 1 1
#> 6 1 1 0
#> 7 1 1 0
#> 8 1 2 0
#> 9 2 1 1
#> 10 2 0 1The defined trait (Trait 1) can be inspected via the genetic values calculated for each individual.
basePop@gv
#> Trait1
#> [1,] 0.67763080
#> [2,] -0.50739888
#> [3,] 0.88013470
#> [4,] -0.20293014
#> [5,] -0.30383140
#> [6,] 0.16827305
#> [7,] -2.06067306
#> [8,] 1.92008559
#> [9,] -0.63964190
#> [10,] 0.06835126The genetic map for the QTLs can be retrieved via
getQtlMap. Here the site of each QTL is identified per
chromosome. The pos notes the position of the QTL on each chromosome in
Morgans.
getQtlMap(trait = 1, simParam = SP)
#> id chr site pos
#> 1_1 1_1 1 1 0.0000000
#> 1_3 1_3 1 3 0.4738446
#> 1_4 1_4 1 4 0.5179529
#> 2_1 2_1 2 1 0.0000000
#> 2_3 2_3 2 3 0.1559803
#> 2_4 2_4 2 4 0.4044692
#> 3_1 3_1 3 1 0.0000000
#> 3_2 3_2 3 2 0.1965774
#> 3_3 3_3 3 3 0.3314247What is a genetic map?
A genetic map (also known as linkage map) provides the genetic
distance in Morgans between genetic markers, QTLs, and/or segregating
sites on a chromosome. This differs from a physical map which gives the
physical distance in the DNA sequence by the number of nucleotides.
Thus, is based on the actual structure of the genetic material. Although
AlphaSimR can import a physical map for all loci
through the lociMap-class, it can only output genetic maps
of defined segregating sites, including QTLs, SNPs, and all defined
loci. For this, the observed recombination frequencies between loci are
used to show how genetic information is shuffled in chromosomes. Thus,
highlighting how markers are inherited.
For a genetic map of all defined loci (or segregating sites),
getGenMap is used. getSnpMap can be used for
the genetic map of the SNP(s) on each chromosome. As hinted previously,
getQtlMap can be used for the genetic map of the
QTL(s).
getGenMap(SP)
#> id chr pos
#> 1 1_1 1 0.00000000
#> 2 1_2 1 0.38038081
#> 3 1_3 1 0.47384462
#> 4 1_4 1 0.51795289
#> 5 2_1 2 0.00000000
#> 6 2_2 2 0.01723463
#> 7 2_3 2 0.15598034
#> 8 2_4 2 0.40446916
#> 9 3_1 3 0.00000000
#> 10 3_2 3 0.19657736
#> 11 3_3 3 0.33142468
#> 12 3_4 3 0.60763015
getSnpMap(snpChip = 1, simParam = SP)
#> id chr site pos
#> 1_2 1_2 1 2 0.38038081
#> 2_2 2_2 2 2 0.01723463
#> 3_4 3_4 3 4 0.60763015How is this used in plant and animal breeding?
By understanding the genome, breeders can produce crop and livestock with desirable traits for use in specific production systems. For example, a breeder may desire to have polled cattle to increase animal welfare and human safety. When considering the breeding design for a species, breed, and or system, there are many factors to consider with potential to introduce unintended consequences. These include balancing the trade off between short-term genetic gain and long-term loss in genetic variation as well as antagonistic relationships between desired traits commonly observed between production and functional traits in animals. AlphaSimR provides a fast and inexpensive way to explore and test a wide range of breeding designs for long term genetic improvement across plants and animals through forward-in-time stochastic simulations.
For a more detailed overview of AlphaSimR in plant and animal breeding with exercises, please see the edx course: Breeding Programme Modelling with AlphaSimR. Available at: https://learning.edx.org/course/course-v1:EdinburghX+ISB001+1T2021/home