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Calculate Founder and Ancestor Contributions

Source: R/pedanalysis.R
pedcontrib.Rd

Calculates genetic contributions from founders and influential ancestors. Implements the gene dropping algorithm for founder contributions and Boichard's algorithm for ancestor contributions to estimate the effective number of founders ($f_e$) and ancestors ($f_a$).

Usage

pedcontrib(
  ped,
  reference = NULL,
  mode = c("both", "founder", "ancestor"),
  top = 20
)

Arguments

ped

A tidyped object.

reference

Character vector. Optional subset of individual IDs defining the reference population. If NULL, uses all individuals in the most recent generation.

mode

Character. Type of contribution to calculate:

  • "founder": Founder contributions ($f_e$).

  • "ancestor": Ancestor contributions ($f_a$).

  • "both": Both founder and ancestor contributions.

top

Integer. Number of top contributors to return. Default is 20.

Value

A list with class pedcontrib containing:

  • founders: A data.table of founder contributions (if mode includes "founder", or "both").

  • ancestors: A data.table of ancestor contributions (if mode includes "ancestor", or "both").

  • summary: A list of summary statistics including:

    • f_e: Classical effective number of founders (\(q=2\), Lacy 1989).

    • f_e_H: Information-theoretic effective number of founders (\(q=1\), Shannon entropy): \(f_e^{(H)} = \exp(-\sum p_i \ln p_i)\).

    • f_a: Classical effective number of ancestors (\(q=2\), Boichard 1997).

    • f_a_H: Information-theoretic effective number of ancestors (\(q=1\)): \(f_a^{(H)} = \exp(-\sum q_k \ln q_k)\).

Each contribution table contains:

  • Ind: Individual ID.

  • Contrib: Contribution to the reference population (0-1).

  • CumContrib: Cumulative contribution.

  • Rank: Rank by contribution.

Details

**Founder Contributions ($f_e$):** Calculated by probabilistic gene flow from founders to the reference cohort. When individual ancestors with one unknown parent exist, "phantom" parents are temporarily injected correctly conserving the probability mass.

**Ancestor Contributions ($f_a$):** Calculated using Boichard's iterative algorithm (1997), accounting for:

  • Marginal genetic contribution of each ancestor

  • Long-term contributions through multiple pathways

The parameter $f_a$ acts as a stringent metric since it identifies the bottlenecks of genetic variation in pedigrees.

References

Boichard, D., Maignel, L., & Verrier, É. (1997). The value of using probabilities of gene origin to measure genetic variability in a population. Genetics Selection Evolution, 29(1), 5-23.

Examples

# \donttest{
library(data.table)
# Load a sample pedigree
tp <- tidyped(small_ped)

# Calculate both founder and ancestor contributions for reference population
ref_ids <- c("Z1", "Z2", "X", "Y")
contrib <- pedcontrib(tp, reference = ref_ids, mode = "both")
#> Calculating founder contributions...
#> Calculating ancestor contributions (Boichard's iterative algorithm)...

# Print results including f_e, f_e(H), f_a, and f_a(H)
print(contrib)
#> Founder and Ancestor Contributions
#> ===================================
#> Reference population size: 4
#> 
#> Founders: 9 (reported top 9)
#>   f_e(H) = 7.672  |  f_e = 6.585
#> 
#> Top 10 Founder Contributions:
#>       Ind  Contrib CumContrib  Rank
#>    <char>    <num>      <num> <int>
#> 1:      N 0.281250   0.281250     1
#> 2:     J2 0.125000   0.406250     2
#> 3:      R 0.125000   0.531250     3
#> 4:      A 0.109375   0.640625     4
#> 5:      B 0.109375   0.750000     5
#> 6:      F 0.093750   0.843750     6
#> 7:      I 0.062500   0.906250     7
#> 8:     J1 0.062500   0.968750     8
#> 9:      O 0.031250   1.000000     9
#> 
#> Ancestors: 3 (reported top 3)
#>   f_a(H) = 2.828  |  f_a = 2.667
#> 
#> Top 10 Ancestor Contributions:
#>       Ind Contrib CumContrib  Rank
#>    <char>   <num>      <num> <int>
#> 1:      X    0.50       0.50     1
#> 2:      N    0.25       0.75     2
#> 3:      Y    0.25       1.00     3

# Access Shannon-entropy effective numbers directly
contrib$summary$f_e_H   # Information-theoretic effective founders (q=1)
#> [1] 7.671504
contrib$summary$f_e     # Classical effective founders (q=2)
#> [1] 6.585209
contrib$summary$f_a_H   # Information-theoretic effective ancestors (q=1)
#> [1] 2.828427
contrib$summary$f_a     # Classical effective ancestors (q=2)
#> [1] 2.666667

# Diversity ratio rho > 1 indicates long-tail founder value
contrib$summary$f_e_H / contrib$summary$f_e
#> [1] 1.16496
# }