4. Pedigree Analysis and Population Genetics

This vignette summarizes a practical workflow for pedigree analysis with visPedigree, with emphasis on the interpretation of the main indicators used in breeding and conservation genetics.

The discussion is organized around five questions:

1. How complete and deep is the pedigree?
2. How long is the generation cycle?
3. Has genetic diversity been eroded by unequal founder use, bottlenecks, or drift?
4. How large is the effective population size under different definitions?
5. Are relationship, inbreeding, subpopulation structure, and gene flow under control?

1. Setup and Data Preparation

Different package datasets are used for different analytical tasks.

• deep_ped is useful for pedigree depth and diversity summaries.
• big_family_size_ped contains a Year column and is suitable for generation intervals.
• small_ped is convenient for relationship examples.
• inbred_ped is convenient for inbreeding and classification examples.

library(visPedigree)
library(data.table)

data(deep_ped, package = "visPedigree")
data(big_family_size_ped, package = "visPedigree")
data(small_ped, package = "visPedigree")
data(inbred_ped, package = "visPedigree")

tp_deep <- tidyped(deep_ped)
tp_small <- tidyped(small_ped)
tp_inbred <- tidyped(inbred_ped)

2. Pedigree Overview with pedstats()

pedstats() provides a compact structural summary with three components:

• $summary: pedigree size and parental structure.
• $ecg: pedigree completeness and ancestral depth.
• $gen_intervals: generation intervals, only when a usable time column is available.

Here deep_ped has no explicit birth-date column. Accordingly, pedstats() returns $summary and $ecg, whereas $gen_intervals remains NULL.

stats_deep <- pedstats(tp_deep)

stats_deep$summary
#>        N NSire  NDam NFounder MaxGen
#>    <int> <int> <int>    <int>  <int>
#> 1:  4399   483   554      138     13
tail(stats_deep$ecg)
#>         Ind      ECG FullGen MaxGen
#>      <char>    <num>   <num>  <num>
#> 1: K110997Q 7.616211       5     12
#> 2: K110997Z 6.722656       5     12
#> 3: K110998Q 4.606445       2     12
#> 4: K110998Z 6.417969       5     12
#> 5: K110999Q 7.345215       5     12
#> 6: K110999Z 6.875977       5     12
stats_deep$gen_intervals
#> NULL

Pedigree depth and pedigree time are related but distinct quantities. The former is addressed by pedecg(), whereas the latter is addressed by pedgenint().

3. Pedigree Completeness with pedecg()

Equivalent complete generations (ECG) summarize the amount of ancestral information available for each individual:

$$ECG_i = \sum_j \left(\frac{1}{2}\right)^{g_{ij}}$$

where $g_{ij}$ is the number of generations between individual $i$ and ancestor $j$. ECG increases with both pedigree depth and pedigree completeness.

In practice:

• ECG combines depth and completeness.
• FullGen counts how many fully known ancestral generations exist.
• MaxGen records the deepest known ancestral path.

ECG is especially useful because it provides the depth adjustment required by realized effective population size estimators based on inbreeding or coancestry.

ecg_deep <- pedecg(tp_deep)

ecg_deep[order(-ECG)][1:10]
#>          Ind      ECG FullGen MaxGen
#>       <char>    <num>   <num>  <num>
#>  1: K110034Q 9.078125       6     12
#>  2: K110052L 9.078125       6     12
#>  3: K110060H 9.078125       6     12
#>  4: K110069Z 9.078125       6     12
#>  5: K110097Q 9.078125       6     12
#>  6: K110118M 9.078125       6     12
#>  7: K110131M 9.078125       6     12
#>  8: K110138M 9.078125       6     12
#>  9: K110155M 9.078125       6     12
#> 10: K110165M 9.078125       6     12

4. Generation Intervals with pedgenint()

Generation interval is the age of a parent at the birth of its offspring:

$$L = t_{offspring} - t_{parent}$$

pedgenint() estimates this quantity for seven pathway summaries:

• SS, SD, DS, DD: sex-specific gametic pathways.
• SO, DO: sex-independent sire-offspring and dam-offspring pathways.
• Average: all parent-offspring pairs combined.

The function accepts Date/POSIXct columns, date strings, or numeric years. When only an integer year is available, it is converted internally to YYYY-07-01 as a mid-year approximation.

tp_time <- tidyped(big_family_size_ped)

genint_year <- pedgenint(tp_time, timevar = "Year", unit = "year")
#> Numeric time column detected. Converting to Date (YYYY-07-01). For finer precision, convert to Date beforehand.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
genint_year
#>    Pathway      N     Mean         SD
#>     <char>  <int>    <num>      <num>
#> 1: Average 280512 1.001093 0.03770707
#> 2:      DD    607 1.164398 0.37080261
#> 3:      DO 140256 1.001093 0.03770714
#> 4:      DS    507 1.196959 0.39776787
#> 5:      SD    607 1.164398 0.37080261
#> 6:      SO 140256 1.001093 0.03770714
#> 7:      SS    507 1.196959 0.39776787

The optional cycle parameter adds GenEquiv, which compares the observed mean interval with a target breeding cycle:

$$GenEquiv_i = \frac{\bar{L}_i}{L_{cycle}}$$

Values larger than 1 indicate that the realized generation interval exceeds the target cycle.

genint_cycle <- pedgenint(tp_time, timevar = "Year", unit = "year", cycle = 1.2)
#> Numeric time column detected. Converting to Date (YYYY-07-01). For finer precision, convert to Date beforehand.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.

genint_cycle[Pathway %in% c("SS", "SD", "DS", "DD", "Average")]
#>    Pathway      N     Mean         SD  GenEquiv
#>     <char>  <int>    <num>      <num>     <num>
#> 1: Average 280512 1.001093 0.03770707 0.8342445
#> 2:      DD    607 1.164398 0.37080261 0.9703321
#> 3:      DS    507 1.196959 0.39776787 0.9974660
#> 4:      SD    607 1.164398 0.37080261 0.9703321
#> 5:      SS    507 1.196959 0.39776787 0.9974660

5. Subpopulation Structure with pedsubpop()

Before interpreting diversity or relationship metrics, it is useful to check whether the pedigree forms a single connected population or a mixture of separate components.

pedsubpop() has two modes:

• by = NULL: summarize disconnected pedigree components.
• by = "...": summarize the pedigree by an existing grouping variable.

ped_demo <- data.table(
  Ind = c("A", "B", "C", "D", "E", "F", "G", "H"),
  Sire = c(NA, NA, "A", NA, NA, "E", NA, NA),
  Dam  = c(NA, NA, "B", NA, NA, NA, NA, NA),
  Sex = c("male", "female", "male", "female", "male", "female", "male", "female"),
  Batch = c("L1", "L1", "L1", "L1", "L2", "L2", "L3", "L3")
)

tp_demo <- tidyped(ped_demo)

pedsubpop(tp_demo)
#>       Group     N N_Sire N_Dam N_Founder
#>      <char> <int>  <num> <num>     <int>
#> 1:      GP1     3      1     1         2
#> 2:      GP2     2      1     0         1
#> 3: Isolated     3      0     0         3
pedsubpop(tp_demo, by = "Batch")
#>     Group     N N_Sire N_Dam N_Founder
#>    <char> <int>  <int> <int>     <int>
#> 1:     L1     4      1     1         3
#> 2:     L3     2      0     0         2
#> 3:     L2     2      1     0         1

This is a compact summary tool. When the actual split pedigree objects are needed for downstream analysis, use splitped().

6. Diversity Indicators with pediv()

pediv() is the integrated diversity summary. It combines:

• founder and ancestor contributions (fe, fa),
• founder genome equivalents (fg),
• three effective population size estimates (Ne).

All of these quantities depend on the definition of the reference population. In the present example, the reference population is defined as the most recent two generations in deep_ped.

ref_pop <- tp_deep[Gen >= max(Gen) - 1, Ind]
length(ref_pop)
#> [1] 3471

div_res <- pediv(tp_deep, reference = ref_pop, top = 10, seed = 42L)
#> Calculating founder and ancestor contributions...
#> Calculating founder contributions...
#> Calculating ancestor contributions (Boichard's iterative algorithm)...
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Calculating Ne (coancestry) and fg...
#> Calculating Ne (inbreeding)...
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Calculating Ne (demographic)...
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.

div_res$summary
#>     NRef NFounder     feH       fe NAncestor     faH       fa     fafe       fg
#>    <int>    <int>   <num>    <num>     <int>   <num>    <num>    <num>    <num>
#> 1:  3471      157 92.0943 64.73344        94 60.1444 44.12033 0.681569 19.17965
#>     MeanCoan NSampledCoan NeCoancestry NeInbreeding NeDemographic
#>        <num>        <int>        <num>        <num>         <num>
#> 1: 0.0260693         1000     124.5124     98.00425      374.2021
div_res$ancestors
#>          Ind    Contrib CumContrib  Rank
#>       <char>      <num>      <num> <int>
#>  1: K500I804 0.05248848 0.05248848     1
#>  2: K60GXQ91 0.04525893 0.09774741     2
#>  3: K60NXQ91 0.04525893 0.14300634     3
#>  4: K600532I 0.04445765 0.18746399     4
#>  5: K700S069 0.03927182 0.22673581     5
#>  6: K900D251 0.03622875 0.26296456     6
#>  7: K700S011 0.02906223 0.29202679     7
#>  8: K700U416 0.02890017 0.32092697     8
#>  9: K700U650 0.02890017 0.34982714     9
#> 10: K500I869 0.02831497 0.37814211    10

6.1 fe, fa, and fg: what do they measure?

These three indicators describe diversity loss from complementary angles.

Effective number of founders (fe)

$$f_e = \frac{1}{\sum_{i=1}^{f} p_i^2}$$

where $p_i$ is the expected contribution of founder $i$ to the reference population. fe answers the question: if all founders had contributed equally, how many founders would generate the same diversity?

Use fe when the main concern is unequal founder representation.

Effective number of ancestors (fa)

$$f_a = \frac{1}{\sum_{j=1}^{a} q_j^2}$$

where $q_j$ is the marginal contribution of ancestor $j$ after removing the contributions already explained by more influential ancestors. fa is usually smaller than fe when bottlenecks occurred.

Use fa when the main concern is genetic bottlenecks caused by a limited set of influential ancestors.

Founder genome equivalents (fg)

In its simplest interpretation,

$$f_g = \frac{1}{2\bar{C}}$$

where $\bar{C}$ is the mean coancestry of the reference population. In visPedigree, fg is estimated from a diagonal-corrected mean coancestry:

$$\hat{\bar{C}} = \frac{N-1}{N}\cdot\frac{\bar{a}_{off}}{2} + \frac{1 + \bar{F}_s}{2N}$$

$$f_g = \frac{1}{2\hat{\bar{C}}}$$

where $N$ is the size of the full reference cohort, $\bar{a}_{off}$ is the mean off-diagonal additive relationship among sampled individuals, and $\bar{F}_s$ is their mean inbreeding coefficient.

Use fg when the main concern is the amount of founder genome still surviving after unequal use, bottlenecks, and drift. In practice, fg is often the most conservative diversity indicator.

6.2 Shannon-entropy effective numbers: feH and faH

The classical fe and fa are based on $\sum p_i^2$ (Hill number order $q = 2$), which is disproportionately influenced by a few large contributions. visPedigree also reports the information-theoretic counterpart at order $q = 1$, derived from Shannon entropy:

$$ f_e^{(H)} = \exp\!\Bigl(-\sum_{i=1}^{f} p_i \ln p_i\Bigr), \qquad f_a^{(H)} = \exp\!\Bigl(-\sum_{j=1}^{a} q_j \ln q_j\Bigr) $$

These are the exponentials of Shannon entropy, which give a diversity measure that counts all contributors — including rare ones — more equitably than the classical $q = 2$ metric. They appear in the pediv() summary as feH and faH, and in the pedcontrib() summary as f_e_H and f_a_H.

The three diversity orders satisfy a monotone ordering:

$$N_f \ge f_e^{(H)} \ge f_e, \qquad K \ge f_a^{(H)} \ge f_a$$

where $N_f$ is the total number of founders and $K$ is the number of ancestors considered. When $f_e^{(H)} / f_e$ is much larger than 1, many minor founders still carry genetic material into the reference population but are invisible to the classical metric.

# Shannon metrics are included in pediv() output
div_res$summary[, .(NFounder, feH, fe, NAncestor, faH, fa)]
#>    NFounder     feH       fe NAncestor     faH       fa
#>       <int>   <num>    <num>     <int>   <num>    <num>
#> 1:      157 92.0943 64.73344        94 60.1444 44.12033

# The ratio feH/fe reveals long-tail founder diversity
div_res$summary[, .(rho_founder = feH / fe, rho_ancestor = faH / fa)]
#>    rho_founder rho_ancestor
#>          <num>        <num>
#> 1:     1.42267      1.36319

# pedcontrib() provides the same metrics via its summary
contrib_res <- pedcontrib(tp_deep, reference = ref_pop, mode = "both")
#> Calculating founder contributions...
#> Calculating ancestor contributions (Boichard's iterative algorithm)...
contrib_res$summary[c("n_founder", "f_e_H", "f_e", "n_ancestor", "f_a_H", "f_a")]
#> $n_founder
#> [1] 157
#> 
#> $f_e_H
#> [1] 92.0943
#> 
#> $f_e
#> [1] 64.73344
#> 
#> $n_ancestor
#> [1] 94
#> 
#> $f_a_H
#> [1] 60.1444
#> 
#> $f_a
#> [1] 44.12033

7. Effective Population Size with pedne() and pediv()

pediv() reports three complementary effective population size definitions. Each addresses a distinct biological question.

7.1 Demographic Ne

$$N_e = \frac{4 N_m N_f}{N_m + N_f}$$

where $N_m$ and $N_f$ are the numbers of contributing males and females. This is the easiest estimate to understand, but it ignores realized pedigree structure, inbreeding, and drift. It is therefore often optimistic.

7.2 Inbreeding Ne

$$\Delta F_i = 1 - (1 - F_i)^{1/(ECG_i - 1)}$$

$$N_e = \frac{1}{2\overline{\Delta F}}$$

This estimator uses the realized rate of inbreeding. ECG standardizes individuals with different pedigree depths. Use this estimate when the primary concern is the rate of inbreeding accumulation.

7.3 Coancestry Ne

$$\Delta c_{ij} = 1 - (1 - c_{ij})^{1/(\frac{ECG_i + ECG_j}{2})}$$

$$N_e = \frac{1}{2\overline{\Delta c}}$$

This estimator is based on the rate of coancestry among members of the reference population. Because it captures the accumulation of relatedness before it is fully expressed as realized inbreeding, it is often the strictest and most sensitive warning signal in managed breeding populations.

8. Average Relationship Trends with pedrel()

pedrel() summarizes the mean off-diagonal additive relationship within groups:

$$MeanRel = \frac{1}{n(n-1)} \sum_{i \ne j} a_{ij}$$

where $a_{ij} = 2f_{ij}$. A higher MeanRel means that individuals within the group are, on average, more related by descent.

This summary is useful for tracking relatedness by generation or year.

tp_small$BirthYear <- 2010 + tp_small$Gen

rel_by_gen <- pedrel(tp_small, by = "Gen")
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
rel_by_gen
#>      Gen NTotal NUsed   MeanRel
#>    <int>  <int> <int>     <num>
#> 1:     1      9     9 0.0000000
#> 2:     2      5     5 0.2000000
#> 3:     3      7     7 0.1547619
#> 4:     4      3     3 0.1145833
#> 5:     5      2     2 0.0468750
#> 6:     6      2     2 0.5507812

The reference argument lets you focus on a subset of interest inside each group, such as candidate breeders.

ref_ids <- c("Z1", "Z2", "X", "Y")

pedrel(tp_small, by = "Gen", reference = ref_ids)
#> Warning in FUN(X[[i]], ...): Group '1' has less than 2 individuals after
#> applying 'reference', returning NA_real_.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning in FUN(X[[i]], ...): Group '2' has less than 2 individuals after
#> applying 'reference', returning NA_real_.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning in FUN(X[[i]], ...): Group '3' has less than 2 individuals after
#> applying 'reference', returning NA_real_.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning in FUN(X[[i]], ...): Group '4' has less than 2 individuals after
#> applying 'reference', returning NA_real_.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#> Warning: Subsetting removed parent records. Result is a plain data.table, not a tidyped.
#> Use tidyped(tp, cand = ids, trace = "up") to extract a valid sub-pedigree.
#>      Gen NTotal NUsed   MeanRel
#>    <int>  <int> <int>     <num>
#> 1:     1      9     0        NA
#> 2:     2      5     0        NA
#> 3:     3      7     0        NA
#> 4:     4      3     0        NA
#> 5:     5      2     2 0.0468750
#> 6:     6      2     2 0.5507812

MeanRel and coancestry-based Ne are conceptually linked, but they are not identical summaries. MeanRel is an average additive relationship within a group, whereas coancestry-based Ne is derived from the rate of increase in coancestry across pedigree depth.

9. Inbreeding Trends with inbreed() and pedfclass()

Wright’s inbreeding coefficient $F$ is the probability that the two alleles of an individual are identical by descent. A practical starting point is to inspect the mean trend by generation.

tp_inbred_f <- inbreed(tp_inbred)

f_trend <- tp_inbred_f[, .(MeanF = mean(f, na.rm = TRUE)), by = Gen]
f_trend
#>      Gen  MeanF
#>    <int>  <num>
#> 1:     1 0.0000
#> 2:     2 0.0000
#> 3:     3 0.2500
#> 4:     4 0.2500
#> 5:     5 0.4375

For classification by inbreeding severity, pedfclass() can be applied directly to the pedigree object. If the inbreeding coefficient is not yet present, the function computes it internally.

pedfclass(tp_inbred)
#> Calculating inbreeding coefficients...
#> Key: <FClass>
#>                 FClass Count Percentage
#>                  <ord> <int>      <num>
#> 1:               F = 0     4   57.14286
#> 2:     0 < F <= 0.0625     0    0.00000
#> 3: 0.0625 < F <= 0.125     0    0.00000
#> 4:   0.125 < F <= 0.25     2   28.57143
#> 5:            F > 0.25     1   14.28571

Custom reporting thresholds can be supplied through breaks.

pedfclass(tp_inbred, breaks = c(0.03125, 0.0625, 0.125, 0.25))
#> Calculating inbreeding coefficients...
#> Key: <FClass>
#>                   FClass Count Percentage
#>                    <ord> <int>      <num>
#> 1:                 F = 0     4   57.14286
#> 2:      0 < F <= 0.03125     0    0.00000
#> 3: 0.03125 < F <= 0.0625     0    0.00000
#> 4:   0.0625 < F <= 0.125     0    0.00000
#> 5:     0.125 < F <= 0.25     2   28.57143
#> 6:              F > 0.25     1   14.28571

The default thresholds correspond approximately to familiar pedigree scenarios:

• $F = 0.0625$: half-sib mating.
• $F = 0.125$: avuncular or grandparent-grandchild mating.
• $F = 0.25$: full-sib or parent-offspring mating.

10. Gene Flow and Partial Inbreeding

10.1 pedancestry(): founder-line proportions

pedancestry() tracks how founder groups contribute to later descendants. This is useful when founders are labeled by line, strain, or geographic origin.

ped_line <- data.table(
  Ind = c("A", "B", "C", "D", "E", "F", "G"),
  Sire = c(NA, NA, NA, NA, "A", "C", "E"),
  Dam  = c(NA, NA, NA, NA, "B", "D", "F"),
  Sex = c("male", "female", "male", "female", "male", "female", "male"),
  Line = c("Line1", "Line1", "Line2", "Line2", NA, NA, NA)
)

tp_line <- tidyped(ped_line)

anc <- pedancestry(tp_line, foundervar = "Line")
anc
#>       Ind Line1 Line2
#>    <char> <num> <num>
#> 1:      A   1.0   0.0
#> 2:      B   1.0   0.0
#> 3:      C   0.0   1.0
#> 4:      D   0.0   1.0
#> 5:      E   1.0   0.0
#> 6:      F   0.0   1.0
#> 7:      G   0.5   0.5

10.2 pedpartial(): which ancestors explain inbreeding?

pedpartial() decomposes total inbreeding into contributions from selected ancestors. It is useful for identifying which ancestors are most responsible for the observed inbreeding.

partial_f <- pedpartial(tp_inbred, ancestors = c("A", "B"))
#> Calculating partial inbreeding for 2 ancestors...
partial_f
#>       Ind       A       B
#>    <char>   <num>   <num>
#> 1:      A 0.00000 0.00000
#> 2:      B 0.00000 0.00000
#> 3:      C 0.00000 0.00000
#> 4:      D 0.00000 0.00000
#> 5:      E 0.12500 0.12500
#> 6:      F 0.00000 0.25000
#> 7:      G 0.15625 0.28125

11. Practical Interpretation

One useful interpretation order is:

1. Check pedigree depth and completeness with pedecg().
2. Check generation timing with pedgenint().
3. Quantify diversity loss with fe, fa, and fg; compare with feH and faH to assess long-tail founder value.
4. Compare demographic, inbreeding, and coancestry-based Ne.
5. Monitor MeanRel and MeanF over time.
6. Use pedsubpop(), pedancestry(), and pedpartial() to diagnose structure, introgression, and bottlenecks.

References

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