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Introduction

Coop & Edge (2019) use a population genetics approach to estimate the likelihood of finding a genetic relative in a database. They assumes that two individuals are related if they share a certain number of genetic blocks, which is determined by the degree of relatedness (e.g. first cousin, second cousin, etc.). Using this assumption, they calculates the expected number of blocks shared between two individuals of a given degree of relatedness based on the size of the genetic database and the population size. They then uses the Poisson distribution to estimate the probability of finding at least one relative of a given degree of relatedness in a database of a certain size.

The original code can be found here.

Below is an adaptation of the code for demonstration purposes with annotations for clarification.

# Load necessary packages
library(wesanderson) # for color palettes

# Set path to the data file
path <- "/Users/tinalasisi-usc/GitHub/PODFRIDGE/data/"
savepath <- "/Users/tinalasisi-usc/GitHub/PODFRIDGE/output/"

# Set up vector for cousin degree
p <- c(1:8) 

# Set up initial population size
N <- 76e6 

# Read in data on US population sizes by year
US_pop <- read.csv(paste(path, "US_popsize.csv", sep = ""))

# Calculate number of grandparents by generation
p_grandpar_gen <- 1950 - 30 * (p + 1)

# Determine which years match the grandparents' generation
these.years <- match(p_grandpar_gen, US_pop$year)

# Get population sizes by year for grandparents' generation
US_Ns <- US_pop$Population[these.years]

# Scale population size down by 50% to account for sex and age
N <- US_Ns
N <- N * 0.5 * 0.9 

# Set minimum population size for small populations
N[US_Ns < 1e6] <- 1e6 

# Set up vector of database sizes to test
DB.sizes <- c(1e6, 5e6, 10e6)

# Set color palette for graphs
my.cols <- wes_palette("Darjeeling1")


# Plot probability of having at least one p-th cousin in database
plot(c(1, 8), c(0, 1), type = "n", ylab = "Probability of at least one p-th cousin in database", xlab = "p (degree of cousin)")
sapply(1:length(DB.sizes), function(i) {
  DB.size <- DB.sizes[i]
  prob.no.rellys <- exp(-2^(2*p - 2) * DB.size / N)
  points(p, 1 - prob.no.rellys, type = "b", col = my.cols[i], pch = 19, lwd = 1.5)
})
[[1]]
NULL

[[2]]
NULL

[[3]]
NULL
legend(x = "bottomright", legend = c("Database size (Millions) =", format(DB.sizes / 1e6, dig = 1)), col = c(NA, my.cols), pch = 19)

# Plot of expected number of p-th cousins in sample
plot(c(1,8),c(0,1000),type="n",ylab="Expected number of p-th cousins in database",xlab="p.(degree of cousin)")
sapply(1:length(DB.sizes),function(i){

    num.cousins<-4^(p)*DB.sizes[i]/(N/2)
    points(p,num.cousins,type="b",col=my.cols[i],lwd=1.5,pch=19)
   # points(p,4^(p),type="b",col="black")
})

[[1]]
NULL

[[2]]
NULL

[[3]]
NULL

sessionInfo()
R version 4.2.2 (2022-10-31)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Ventura 13.0.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] wesanderson_0.3.6 workflowr_1.7.0  

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.9       highr_0.9        compiler_4.2.2   pillar_1.8.1    
 [5] bslib_0.4.1      later_1.3.0      git2r_0.30.1     jquerylib_0.1.4 
 [9] tools_4.2.2      getPass_0.2-2    digest_0.6.30    jsonlite_1.8.3  
[13] evaluate_0.18    lifecycle_1.0.3  tibble_3.1.8     pkgconfig_2.0.3 
[17] rlang_1.0.6      cli_3.4.1        rstudioapi_0.14  yaml_2.3.6      
[21] xfun_0.35        fastmap_1.1.0    httr_1.4.4       stringr_1.5.0   
[25] knitr_1.41       fs_1.5.2         vctrs_0.5.1      sass_0.4.4      
[29] rprojroot_2.0.3  glue_1.6.2       R6_2.5.1         processx_3.8.0  
[33] fansi_1.0.3      rmarkdown_2.18   callr_3.7.3      magrittr_2.0.3  
[37] whisker_0.4      ps_1.7.2         promises_1.2.0.1 htmltools_0.5.3 
[41] httpuv_1.6.6     utf8_1.2.2       stringi_1.7.8    cachem_1.0.6