# Introduction

This vignette demonstrates analytic methods for determining relatedness in a pedigree. The relatedness coefficient is a measure of the genetic overlap between two individuals. In the simplest terms, it quantifies the genetic overlap between two individuals. The relatedness coefficient ranges from 0 to 1, with 1 indicating a perfect genetic match (which occurs when comparing an individual to themselves, their identical twin, or their clone), whereas 0 indicates no genetic overlap. We introduce two functions: calculateRelatedness and inferRelatedness, which allow users to compute and infer the relatedness coefficient, respectively.

library(BGmisc)

## Calculating Relatedness Coefficient

The calculateRelatedness function offers a method to compute the relatedness coefficient based on shared ancestry, as described by Wright (1922). This function utilizes the formula:

$r_{bc} = \sum \left(\frac{1}{2}\right)^{n+n'+1} (1+f_a)$

Where $$n$$ and $$n'$$ represent the number of generations back of common ancestors the pair share.

# Example usage:
# For full siblings, the relatedness coefficient is expected to be 0.5:
calculateRelatedness(generations = 1, full = TRUE)
#> [1] 0.5
# For half siblings, the relatedness coefficient is expected to be 0.25:
calculateRelatedness(generations = 1, full = FALSE)
#> [1] 0.25

# Inferring Relatedness Coefficient

The inferRelatedness function is designed to infer the relatedness coefficient between two groups based on the observed correlation between their additive genetic variance and shared environmental variance. This function leverages the ACE framework.

# Example usage:
# Infer the relatedness coefficient:
inferRelatedness(obsR = 0.5, aceA = 0.9, aceC = 0, sharedC = 0)
#> [1] 0.5555556