Calculate Likelihoods for Alternative Relationships

For each specified pair of individuals, calculate the log10-likelihoods of being PO, FS, HS, GP, FA, HA, U (see Details). Individuals must be genotyped or have at least one genotyped offspring.

NOTE values $>0$ are various NA types, see 'Likelihood special codes' in 'Value' section below.

Usage

CalcPairLL(
  Pairs = NULL,
  GenoM = NULL,
  Pedigree = NULL,
  LifeHistData = NULL,
  AgePrior = TRUE,
  SeqList = NULL,
  Complex = "full",
  Herm = "no",
  Err = 1e-04,
  ErrFlavour = "version2.0",
  Tassign = 0.5,
  Tfilter = -2,
  quiet = FALSE,
  Plot = TRUE
)

Arguments

Pairs

dataframe with columns ID1 and ID2, and optionally

Sex1: Sex of ID1, 1=female, 2=male, 3=unknown, or NA to take from LifeHistData. The sex of individuals occurring as parent in Pedigree cannot be altered.
Sex2: Sex of ID2
AgeDif: Age difference in whole time units, BirthYear1 - BirthYear2 (i.e. positive if ID2 is born before ID1). If NA, calculated from LifeHistData. Use '999' to explicitly specify 'unknown'.
focal: relationship character abbreviation; PO, FS, HS, GP or U. See Details for its effect and explanation of abbreviations. Default: U
patmat: 1=maternal relatives, 2=paternal relatives. Only relevant for HS & GP, for which it defaults to Sex1, or 1 if Sex1=3, but is currently only predictably implemented for pairs of two genotyped individuals. Always equal to Sex2 for PO pairs when Sex2 is known.
dropPar1: Drop the parents of ID1 before calculating the pair likelihood, rather than conditioning on them; choose from 'none', 'dam', 'sire', or 'both'. See example. If e.g. the pair shares a common mother, 'none' and 'sire' will condition on this shared mother and not calculate the likelihood that they are maternal siblings, while dropPar1='dam' or 'both' will calculate that likelihood, and the other likelihoods as if the mother of ID1 were unknown.
dropPar2: as dropPar1, for ID2

GenoM

numeric matrix with genotype data: One row per individual, and one column per SNP, coded as 0, 1, 2 or -9 (missing). See also GenoConvert.

Pedigree

dataframe with columns id-dam-sire; likelihoods will be calculated conditional on the pedigree. May include non-genotyped individuals, which will be treated as dummy individuals.

LifeHistData

data.frame with up to 6 columns:

ID: max. 30 characters long
Sex: 1 = female, 2 = male, 3 = unknown, 4 = hermaphrodite, other numbers or NA = unknown
BirthYear: birth or hatching year, integer, with missing values as NA or any negative number.
BY.min: minimum birth year, only used if BirthYear is missing
BY.max: maximum birth year, only used if BirthYear is missing
Year.last: Last year in which individual could have had offspring. Can e.g. in mammals be the year before death for females, and year after death for males.

"Birth year" may be in any arbitrary discrete time unit relevant to the species (day, month, decade), as long as parents are never born in the same time unit as their offspring, and only integers are used. Individuals do not need to be in the same order as in `GenoM', nor do all genotyped individuals need to be included.

AgePrior

logical (TRUE/FALSE) whether to estimate the ageprior from Pedigree and LifeHistData, or a matrix as generated by MakeAgePrior and included in the sequoia output. The AgePrior affects which relationships are considered possible: only those where $P(A|R) / P(A) > 0$. When TRUE, MakeAgePrior is called using its default values. When FALSE, all relationships are considered possible for all age differences, except that parent-offspring pairs cannot have age difference zero, and grand-parental pairs have an age difference of at least two.

SeqList

list with output from sequoia. If input parameter Pedigree=NULL, SeqList$Pedigree will be used if present, and SeqList$PedigreePar otherwise. If SeqList$Specs is present, input parameters with the same name as its items are ignored. The list elements 'LifeHist', 'AgePriors', and 'ErrM' are also used if present, and override the corresponding input parameters.

Complex

Breeding system complexity. Either "full" (default), "simp" (simplified, no explicit consideration of inbred relationships), "mono" (monogamous).

Herm

Hermaphrodites, either "no", "A" (distinguish between dam and sire role, default if at least 1 individual with sex=4), or "B" (no distinction between dam and sire role). Both of the latter deal with selfing.

Err

estimated genotyping error rate, as a single number, or a length 3 vector with P(hom|hom), P(het|hom), P(hom|het), or a 3x3 matrix. See details below. The error rate is presumed constant across SNPs, and missingness is presumed random with respect to actual genotype. Using Err >5% is not recommended, and Err >10% strongly discouraged.

ErrFlavour

function that takes Err (single number) as input, and returns a length 3 vector or 3x3 matrix, or choose from inbuilt options 'version2.9', 'version2.0', 'version1.3', or 'version1.1', referring to the sequoia version in which they were the default. Ignored if Err is a vector or matrix. See ErrToM for details.

Tassign

minimum LLR required for acceptance of proposed relationship, relative to next most likely relationship. Higher values result in more conservative assignments. Must be zero or positive.

Tfilter

threshold log10-likelihood ratio (LLR) between a proposed relationship versus unrelated, to select candidate relatives. Typically a negative value, related to the fact that unconditional likelihoods are calculated during the filtering steps. More negative values may decrease non-assignment, but will increase computational time.

quiet

logical, suppress messages

Plot

logical, display scatter plots by PlotPairLL.

Value

The Pairs dataframe including all optional columns listed above, plus the additional columns:

xx: Log10-Likelihood of this pair having relationship xx, with xx being the relationship abbreviations listed below.
TopRel: Abbreviation of most likely relationship
LLR: Log10-Likelihood ratio between most-likely and second most likely relationships. Other LLRs, e.g. between most-likely and unrelated, can easily be computed.

Relationship abbreviations:

PO: Parent - offspring
FS: Full siblings
HS: Half siblings
GP: Grandparent
FA: Full avuncular
HA: Half avuncular and other 3rd degree relationships
U: Unrelated
2nd: Unclear which type of 2nd degree relatives (HS, GP, or FA)
??: Unclear which type of 1st, 2nd or 3rd degree relatives

Likelihood special codes:

222: Maybe (via) other parent (e.g. focal="GP", but as likely to be maternal as paternal grandparent, and therefore not assignable)
333: Excluded from comparison (shouldn't occur)
444: Not implemented (e.g. would create an odd double/triple relationship in combination with the provided pedigree)
777: Impossible (e.g. cannot be both full sibling and grandparent)
888: Already assigned in the provided pedigree (see dropPar arguments)
999: NA

Details

The same pair may be included multiple times, e.g. with different sex, age difference, or focal relationship, to explore their effect on the likelihoods. Likelihoods are only calculated for relationships that are possible given the age difference, e.g. PO (parent-offspring) is not calculated for pairs with an age difference of 0.

Non-genotyped individuals can be included if they have at least one genotyped offspring and can be turned into a dummy (see getAssignCat); to establish this a pedigree must be provided.

Warning 1: There is no check whether the input pedigree is genetically sensible, it is simply conditioned upon. Checking whether a pedigree is compatible with the SNP data can be done with CalcOHLLR.

Warning 2: Conditioning on a Pedigree can make computation orders of magnitude slower.

Why does it say 777 (impossible)?

This function uses the same machinery as sequoia, which will to save time not calculate the likelihood when it is quickly obvious that the pair cannot be related in the specified manner.

For PO (putative parent-offspring pairs) this is the case when:

the sex of the candidate parent, via Pairs$Sex2 or LifeHistData, does not match Pairs$patmat, which defaults to 1 (maternal relatives, i.e. dam)
a dam is already assigned via Pedigree and Pairs$dropPar1 ='none', and Pairs$patmat = 1
Pairs$focal is not 'U' (the default), and the OH count between the two individuals exceeds MaxMismatchOH. This value can be found in SeqList$Specs), and is calculated by CalcMaxMismatch
the age difference, either calculated from LifeHistData or specified via Pairs$AgeDif, is impossible for a parent-offspring pair according to the age prior. The latter can be specified via AgePrior, or is taken from SeqList, or is calculated when both Pedigree and LifeHistData are provided.

For FS (putative full siblings) this happens when e.g. ID1 has a dam assigned which is not dropped (Pairs$dropPar1='none' or 'sire'), and the OH count between ID1's dam and ID2 exceeds MaxMismatchOH. The easiest way to 'fix' this is by increasing the presumed genotyping error rate.

Double relationships & focal relationship

Especially when Complex='full', not only the seven relationship alternatives listed above are considered, but a whole range of possible double and even triple relationships. For example, mother A and offspring B (PO) may also be paternal half-siblings (HS, A and A's mother mated with same male), grandmother and grand-offspring (GP, B's father is A's son), or paternal aunt (B's father is a full or half sib of A).

The likelihood reported as 'LL_PO' is the most-likely one of the possible alternatives, among those that are not impossible due to age differences or due to the pedigree (as reconstructed up to that point). Whether e.g. the likelihood to be both PO & HS is counted as PO or as HS, depends on the situation and is determined by the variable 'focal': During parentage assignment, it is counted as PO but not HS, while during sibship clustering, it is counted as HS but not PO -- not omitting from the alternative relationship would result in a deadlock.

Examples

CalcPairLL(Pairs = data.frame(ID1='i116_2006_M', ID2='i119_2006_M'),
           GenoM = Geno_griffin, Err = 1e-04, Plot=FALSE)
#>           ID1         ID2 Sex1 Sex2 AgeDif focal patmat dropPar1 dropPar2
#> 1 i116_2006_M i119_2006_M    3    3     NA     U      1     none     none
#>        PO     FS      HS      GP      FA      HA       U TopRel LLR
#> 1 -379.69 -336.6 -329.03 -329.03 -329.03 -329.03 -334.64    2nd   0

## likelihoods underlying parent LLR in pedigree:
# Example: dams for bottom 3 individuals
tail(SeqOUT_griffin$PedigreePar, n=3)
#>              id         dam        sire LLRdam LLRsire LLRpair OHdam OHsire
#> 140 i198_2010_M i166_2009_F        <NA>  10.42      NA      NA     0     NA
#> 141 i199_2010_F i165_2009_F i141_2008_M   9.55    2.73   17.03     0      0
#> 142 i200_2010_F i166_2009_F i142_2008_M   9.98   10.22   16.97     1      0
#>     MEpair
#> 140     NA
#> 141      0
#> 142      1
# set up dataframe with these pairs. LLRdam & LLRsire ignore any co-parent
Pairs_d <- data.frame(ID1 = SeqOUT_griffin$PedigreePar$id[140:142],
                      ID2 = SeqOUT_griffin$PedigreePar$dam[140:142],
                      focal = "PO",
                      dropPar1 = 'both')

# Calculate LL's, conditional on the rest of the pedigree + age differences
CalcPairLL(Pairs_d, GenoM = Geno_griffin, Err = 1e-04,
           LifeHistData = LH_griffin, Pedigree = SeqOUT_griffin$PedigreePar)
#> Ageprior: Pedigree-based, overlapping generations, flattened, MaxAgeParent = 99,99


#>           ID1         ID2 Sex1 Sex2 AgeDif focal patmat dropPar1 dropPar2
#> 1 i198_2010_M i166_2009_F    2    1      1    PO      1     both     none
#> 2 i199_2010_F i165_2009_F    1    1      1    PO      1     both     none
#> 3 i200_2010_F i166_2009_F    1    1      1    PO      1     both     none
#>        PO  FS      HS  GP      FA      HA       U TopRel   LLR
#> 1 -289.23 777 -299.18 777 -297.85 -300.15 -310.28     PO  8.62
#> 2 -279.66 777 -295.41 777 -294.33 -297.09 -310.77     PO 14.67
#> 3 -283.94 777 -298.42 777 -298.35 -299.93 -312.93     PO 14.41

# LLR changes when ignoring age and/or pedigree, as different relationships
# become (im)possible
CalcPairLL(Pairs_d, GenoM = Geno_griffin, Err = 1e-04)

#>           ID1         ID2 Sex1 Sex2 AgeDif focal patmat dropPar1 dropPar2
#> 1 i198_2010_M i166_2009_F    3    3     NA    PO      1     both     none
#> 2 i199_2010_F i165_2009_F    3    3     NA    PO      1     both     none
#> 3 i200_2010_F i166_2009_F    3    3     NA    PO      1     both     none
#>        PO      FS      HS      GP      FA      HA       U TopRel  LLR
#> 1 -308.78 -314.22 -312.81 -311.20 -313.25 -312.81 -329.70     PO 2.42
#> 2 -304.43 -310.40 -311.86 -309.98 -313.78 -311.86 -335.69     PO 5.54
#> 3 -303.14 -309.52 -310.47 -307.39 -311.26 -310.47 -332.35     PO 4.24

# LLRpair is calculated conditional on co-parent, and min. of dam & sire LLR
Pairs_d$dropPar1 <- 'dam'
Pairs_s <- data.frame(ID1 = SeqOUT_griffin$PedigreePar$id[141:142],
                      ID2 = SeqOUT_griffin$PedigreePar$sire[141:142],
                      focal = "PO",
                      dropPar1 = 'sire')
CalcPairLL(rbind(Pairs_d, Pairs_s), GenoM = Geno_griffin, Err = 1e-04,
           LifeHistData = LH_griffin, Pedigree = SeqOUT_griffin$PedigreePar)
#> Ageprior: Pedigree-based, overlapping generations, flattened, MaxAgeParent = 99,99


#>           ID1         ID2 Sex1 Sex2 AgeDif focal patmat dropPar1 dropPar2
#> 1 i198_2010_M i166_2009_F    2    1      1    PO      1      dam     none
#> 2 i199_2010_F i165_2009_F    1    1      1    PO      1      dam     none
#> 3 i200_2010_F i166_2009_F    1    1      1    PO      1      dam     none
#> 4 i199_2010_F i141_2008_M    1    2      2    PO      2     sire     none
#> 5 i200_2010_F i142_2008_M    1    2      2    PO      2     sire     none
#>        PO  FS      HS      GP      FA      HA       U TopRel   LLR
#> 1 -289.23 777 -299.18  777.00 -297.85 -300.15 -310.28     PO  8.62
#> 2 -239.97 777 -262.19  777.00 -259.82 -266.02 -282.76     PO 19.85
#> 3 -245.87 777 -265.52  777.00 -266.47 -271.87 -287.07     PO 19.64
#> 4 -235.68 777 -361.87 -251.85 -254.73 -263.57 -275.37     PO 16.17
#> 5 -240.97 777 -263.38 -256.61 -258.66 -263.96 -279.04     PO 15.63


## likelihoods underlying LLR in getMaybeRel output:
MaybeRel_griffin$MaybePar[1:5, ]
#>           ID1         ID2 TopRel  LLR OH BirthYear1 BirthYear2 AgeDif Sex1 Sex2
#> 1 i091_2005_F i118_2006_M     PO 8.55  0         NA         NA     NA    3    3
#> 2 i127_2007_M i197_2010_F     PO 7.90  0         NA         NA     NA    3    3
#> 3 i121_2007_M i175_2009_M     PO 7.85  0         NA         NA     NA    3    3
#> 4 i030_2002_F i061_2004_F     PO 7.75  0         NA         NA     NA    3    3
#> 5 i041_2003_F i080_2004_M     PO 7.71  0         NA         NA     NA    3    3
#>   SNPdBoth
#> 1      392
#> 2      392
#> 3      392
#> 4      392
#> 5      392
FivePairs <- MaybeRel_griffin$MaybePar[1:5, c("ID1", "ID2", "Sex1", "Sex2")]
PairLL <- CalcPairLL(Pairs = rbind( cbind(FivePairs, focal = "PO"),
                                    cbind(FivePairs, focal = "HS"),
                                    cbind(FivePairs, focal = "GP")),
                     GenoM = Geno_griffin, Plot=FALSE)
PairLL[PairLL$ID1=="i121_2007_M", ]
#>            ID1         ID2 Sex1 Sex2 AgeDif focal patmat dropPar1 dropPar2
#> 3  i121_2007_M i175_2009_M    3    3     NA    PO      1     none     none
#> 8  i121_2007_M i175_2009_M    3    3     NA    HS      1     none     none
#> 13 i121_2007_M i175_2009_M    3    3     NA    GP      1     none     none
#>         PO      FS      HS      GP      FA     HA       U TopRel  LLR
#> 3  -313.21 -324.46 -321.90 -321.51 -323.01 -321.9 -337.98     PO 8.30
#> 8  -313.21  222.00 -321.09 -321.09 -323.01 -321.9 -337.98     PO 7.88
#> 13 -313.21 -324.46 -321.09 -321.09 -322.83 -321.9 -337.98     PO 7.88
# LL(FS)==222 : HSHA, HSGP, FAHA more likely than FS
# LL(GP) higher when focal=HS: GP via 'other' parent also considered
# LL(FA) higher when focal=PO: FAHA, or FS of 'other' parent