# Age Priors

`MakeAgePrior.Rd`

Estimate probability ratios \(P(R|A) / P(R)\) for age differences A and five categories of parent-offspring and sibling relationships R.

## Usage

```
MakeAgePrior(
Pedigree = NULL,
LifeHistData = NULL,
MinAgeParent = NULL,
MaxAgeParent = NULL,
Discrete = NULL,
Flatten = NULL,
lambdaNW = -log(0.5)/100,
Smooth = TRUE,
Plot = TRUE,
Return = "LR",
quiet = FALSE
)
```

## Arguments

- Pedigree
dataframe with id - dam - sire in columns 1-3, and optional column with birth years. Other columns are ignored.

- LifeHistData
dataframe with 3 or 5 columns: id - sex (not used) - birthyear (optional columns BY.min - BY.max - YearLast not used), with unknown birth years coded as negative numbers or NA. "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. It may include individuals not in the pedigree, and not all individuals in the pedigree need to be in LifeHistData.

- MinAgeParent
minimum age of a parent, a single number (min across dams and sires) or a vector of length two (dams, sires). Defaults to 1. When there is a conflict with the minimum age in the pedigree, the pedigree takes precedent.

- MaxAgeParent
maximum age of a parent, a single number (max across dams and sires) or a vector of length two (dams, sires). If NULL, it will be set to latest - earliest birth year in

`LifeHistData`

, or estimated from the pedigree if one is provided. See details below.- Discrete
discrete generations? By default (NULL), discrete generations are assumed if all parent-offspring pairs have an age difference of 1, and all siblings an age difference of 0, and there are at least 20 pairs of each category (mother, father, maternal sibling, paternal sibling). Otherwise, overlapping generations are presumed. When

`Discrete=TRUE`

(explicitly or deduced),`Smooth`

and`Flatten`

are always automatically set to`FALSE`

. Use`Discrete=FALSE`

to enforce (potential for) overlapping generations.- Flatten
logical. To deal with small sample sizes for some or all relationships, calculate weighed average between the observed age difference distribution among relatives and a flat (0/1) distribution. When

`Flatten=NULL`

(the default) automatically set to TRUE when there are fewer than 20 parents with known age of either sex assigned, or fewer than 20 maternal or paternal siblings with known age difference. Also advisable if the sampled relative pairs with known age difference are non-typical of the pedigree as a whole.- lambdaNW
control weighing factors when

`Flatten=TRUE`

. Weights are calculated as \(W(R) = 1 - exp(-lambdaNW * N(R))\), where \(N(R)\) is the number of pairs with relationship R for which the age difference is known. Large values (>0.2) put strong emphasis on the pedigree, small values (<0.0001) cause the pedigree to be ignored. Default results in \(W=0.5\) for \(N=100\).- Smooth
smooth the tails of and any dips in the distribution? Sets dips (<10% of average of neighbouring ages) to the average of the neighbouring ages, sets the age after the end (oldest observed age) to LR(end)/2, and assigns a small value (0.001) to the ages before the front (youngest observed age) and after the new end. Peaks are not smoothed out, as these are less likely to cause problems than dips, and are more likely to be genuine characteristics of the species. Is set to

`FALSE`

when generations do not overlap (`Discrete=TRUE`

).- Plot
plot a heatmap of the results?

- Return
return only a matrix with the likelihood-ratio \(P(A|R) / P(A)\) (

`"LR"`

) or a list including also various intermediate statistics (`"all"`

) ?- quiet
suppress messages.

## Value

A matrix with the probability ratio of the age difference between two individuals conditional on them being a certain type of relative (\(P(A|R)\)) versus being a random draw from the sample (\(P(A)\)). Assuming conditional independence, this equals the probability ratio of being a certain type of relative conditional on the age difference, versus being a random draw.

The matrix has one row per age difference (0 - nAgeClasses) and five columns, one for each relationship type, with abbreviations:

- M
Mothers

- P
Fathers

- FS
Full siblings

- MS
Maternal half-siblings

- PS
Paternal half-siblings

When `Return`

='all', a list is returned with the following elements:

- BirthYearRange
vector length 2

- MaxAgeParent
vector length 2, see details

- tblA.R
matrix with the counts per age difference (rows) / relationship (columns) combination, plus a column 'X' with age differences across all pairs of individuals

- PA.R
Proportions, i.e.

`tblA.R`

divided by its`colSums`

, with full-sibling correction applied if necessary (see vignette).- LR.RU.A.raw
Proportions

`PA.R`

standardised by global age difference distribution (column 'X');`LR.RU.A`

prior to flattening and smoothing- Weights
vector length 4, the weights used to flatten the distributions

- LR.RU.A
the ageprior, flattend and/or smoothed

- Specs.AP
the names of the input

`Pedigree`

and`LifeHistData`

(or`NULL`

),`lambdaNW`

, and the 'effective' settings (i.e. after any automatic update) of`Discrete`

,`Smooth`

, and`Flatten`

.

## Details

\(\alpha_{A,R}\) is the ratio between the observed counts of pairs with age difference A and relationship R (\(N_{A,R}\)), and the expected counts if age and relationship were independent (\(N_{.,.}*p_A*p_R\)).

During pedigree reconstruction, \(\alpha_{A,R}\) are multiplied by the genetic-only \(P(R|G)\) to obtain a probability that the pair are relatives of type R conditional on both their age difference and their genotypes.

The age-difference prior is used for pairs of genotyped individuals, as well as for dummy individuals. This assumes that the propensity for a pair with a given age difference to both be sampled does not depend on their relationship, so that the ratio \(P(A|R) / P(A)\) does not differ between sampled and unsampled pairs.

For further details, see the vignette.

## CAUTION

The small sample correction with `Smooth`

and/or `Flatten`

prevents errors in one dataset, but may introduce errors in another; a
single solution that fits to the wide variety of life histories and
datasets is impossible. Please do inspect the matrix, e.g. with
`PlotAgePrior`

, and adjust the input parameters and/or the output
matrix as necessary.

## Single cohort

When all individuals in `LifeHistData`

have the same birth year, it is
assumed that `Discrete=TRUE`

and `MaxAgeParent=1`

. Consequently,
it is assumed there are no avuncular pairs present in the sample; cousins
are considered as alternative. To enforce overlapping generations, and
thereby the consideration of full- and half- avuncular relationships, set
`MaxAgeParent`

to some value greater than \(1\).

When no birth year information is given at all, a single cohort is assumed, and the same rules apply.

## Other time units

"Birth year" may be in any arbitrary time unit relevant to the species (day, month, decade), as long as parents are always born before their putative offspring, and never in the same time unit (e.g. parent's BirthYear= 1 (or 2001) and offspring BirthYear=5 (or 2005)). Negative numbers and NA's are interpreted as unknown, and fractional numbers are not allowed.

## MaxAgeParent

The maximum parental age for each sex equals the maximum of:

the maximum age of parents in

`Pedigree`

,the input parameter

`MaxAgeParent`

,the maximum range of birth years in

`LifeHistData`

(including BY.min and BY.max). Only used if both of the previous are`NA`

, or if there are fewer than 20 parents of either sex assigned.1, if

`Discrete=TRUE`

or the previous three are all`NA`

If the age distribution of assigned parents does not capture the maximum
possible age of parents, it is advised to specify `MaxAgeParent`

for
one or both sexes. Not doing so may hinder subsequent assignment of both
dummy parents and grandparents. Not compatible with `Smooth`

. If the
largest age difference in the pedigree is larger than the specified
`MaxAgeParent`

, the pedigree takes precedent (i.e. the largest of the
two is used).

@section grandparents & avuncular
The agepriors for grand-parental and avuncular pairs is calculated from
these by `sequoia`

, and included in its output as
`AgePriorExtra`.

## See also

`sequoia`

and its argument `args.AP`

,
`PlotAgePrior`

for visualisation. The age vignette gives
further details, mathematical justification, and some examples.

## Examples

```
# without pedigree or lifehistdata:
MakeAgePrior(MaxAgeParent = c(2,3))
#> Ageprior: Flat 0/1, overlapping generations, MaxAgeParent = 2,3
#> M P FS MS PS
#> 0 0 0 1 1 1
#> 1 1 1 1 1 1
#> 2 1 1 0 0 1
#> 3 0 1 0 0 0
#> 4 0 0 0 0 0
MakeAgePrior(Discrete=TRUE)
#> Ageprior: Flat 0/1, discrete generations, MaxAgeParent = 1,1
#> M P FS MS PS
#> 0 0 0 1 1 1
#> 1 1 1 0 0 0
#> 2 0 0 0 0 0
# single cohort:
MakeAgePrior(LifeHistData = data.frame(ID = letters[1:5], Sex=3,
BirthYear=1984))
#> Ageprior: Flat 0/1, discrete generations, MaxAgeParent = 1,1
#> M P FS MS PS
#> 0 0 0 1 1 1
#> 1 1 1 0 0 0
#> 2 0 0 0 0 0
# overlapping generations:
# without pedigree: MaxAgeParent = max age difference between any pair +1
MakeAgePrior(LifeHistData = SeqOUT_griffin$LifeHist)
#> Ageprior: Flat 0/1, overlapping generations, MaxAgeParent = 10,10
#> M P FS MS PS
#> 0 0 0 1 1 1
#> 1 1 1 1 1 1
#> 2 1 1 1 1 1
#> 3 1 1 1 1 1
#> 4 1 1 1 1 1
#> 5 1 1 1 1 1
#> 6 1 1 1 1 1
#> 7 1 1 1 1 1
#> 8 1 1 1 1 1
#> 9 1 1 1 1 1
#> 10 1 1 0 0 0
#> 11 0 0 0 0 0
# with pedigree:
MakeAgePrior(Pedigree=Ped_griffin,
LifeHistData=SeqOUT_griffin$LifeHist,
Smooth=FALSE, Flatten=FALSE)
#> Ageprior: Pedigree-based, overlapping generations, MaxAgeParent = 3,3
#> M P FS MS PS
#> 0 0.000 0.000 5.043 4.316 3.862
#> 1 3.476 1.967 2.798 2.636 2.971
#> 2 2.011 3.167 0.077 0.691 0.583
#> 3 0.340 0.959 0.000 0.000 0.000
#> 4 0.000 0.000 0.000 0.000 0.000
# with small-sample correction:
MakeAgePrior(Pedigree=Ped_griffin,
LifeHistData=SeqOUT_griffin$LifeHist,
Smooth=TRUE, Flatten=TRUE)
#> Ageprior: Pedigree-based, overlapping generations, flattened, smoothed, MaxAgeParent = 5,5
#> M P FS MS PS
#> 0 0.000 0.000 2.761 3.574 2.918
#> 1 2.698 1.655 1.783 2.270 2.321
#> 2 1.693 2.467 0.598 0.760 0.721
#> 3 0.548 0.972 0.299 0.380 0.360
#> 4 0.274 0.486 0.001 0.001 0.001
#> 5 0.001 0.001 0.000 0.000 0.000
#> 6 0.000 0.000 0.000 0.000 0.000
# Call from sequoia() via args.AP:
Seq_HSg5 <- sequoia(SimGeno_example, LH_HSg5, Module="par",
args.AP=list(Discrete = TRUE), # non-overlapping generations
CalcLLR = FALSE, # skip time-consuming calculation of LLR's
Plot = FALSE) # no summary plots when finished
#> Genotype matrix looks OK! There are 214 individuals and 200 SNPs.
#> There are 106 females, 108 males, 0 individuals of unknown sex, and 0 hermaphrodites.
#> Exact birth years are from 2000 to 2001
#> Ageprior: Flat 0/1, discrete generations, MaxAgeParent = 1,1
#>
#> ~~~ Duplicate check ~~~
#>
#> ~~~ Parentage assignment ~~~
#> Assign parents ...
#> Initial total LL :
#> [1] -18301.9
#> Post-parentage total LL :
#> [1] -13690.07
#> Estimating birth years ...
#> assigned 126 dams and 165 sires to 214 individuals
#> Possibly not all parents were assigned, consider running GetMaybeRel() conditional on this pedigree to check
```