Computational Genetic Genealogy

Why Twins Require Special Handling

Twins create unique challenges for genetic genealogy algorithms due to their special genetic relationships:

Types of Twins and Their Genetic Signatures

• Monozygotic (Identical) Twins: Develop from a single fertilized egg that splits into two embryos
  • Share virtually 100% of their genetic material
  • Appear genetically indistinguishable using standard DNA tests
  • Same sex (both male or both female)
• Dizygotic (Fraternal) Twins: Develop from two separately fertilized eggs
  • Share approximately 50% of their DNA (like regular siblings)
  • Can be different sexes
  • Genetically similar to full siblings but born simultaneously

These unique genetic relationships create several challenges for pedigree reconstruction algorithms:

1. Identical Genetic Profiles: Standard algorithms may be unable to distinguish between identical twins
2. Relationship Ambiguity: The extremely high IBD sharing between identical twins can be confused with duplicate samples
3. Pedigree Placement: Algorithms must ensure both twins are consistently placed in family structures
4. Downstream Relationships: Children of twins have special genetic relationships that standard models don't capture

Specialized Twin Handling

Bonsai v3 includes a dedicated twins.py module that implements specialized algorithms for detecting and handling twin relationships:

from .constants import TWIN_THRESHOLD

def is_twin_pair(
    total_half: float,
    total_full: float,
    age1: int,
    age2: int,
    sex1: str,
    sex2: str,
):
    """
    Determine if a pair of individuals are twins.

    Args:
        total_half: The total length of half segments shared by the two individuals.
        total_full: The total length of full segments shared by the two individuals.
        age1: The age of the first individual.
        age2: The age of the second individual.
        sex1: Sex of the first individual.
        sex2: Sex of the second individual.

    Returns:
        True if the individuals are twins, False otherwise.
    """
    # handle unrelated people
    if total_half is None:
        return False
    if total_full is None:
        return False

    if total_half < TWIN_THRESHOLD:
        return False
    elif total_full < TWIN_THRESHOLD:
        return False
    elif sex1 != sex2:
        return False
    elif age1 and age2 and age1 != age2:
        return False

    return True

This module also provides functions for grouping twins into sets and integrating twin information into the pedigree reconstruction process:

def get_twin_sets(
    ibd_stat_dict: dict[frozenset, dict[str, int]],
    age_dict: dict[int, float],
    sex_dict: dict[int, str],
):
    """
    Find all sets of twins.

    Args:
        ibd_stat_dict: A dictionary of IBD statistics.
        age_dict: A dictionary mapping ID to age
        sex_dict: A dictionary mapping ID to sex ('M' or 'F')

    Returns:
        idx_to_twin_set: A dictionary mapping an index to a set of node IDs
            that form a twin set.
        id_to_idx: A dict mapping each twin ID to its index.
    """
    # Implementation details...

Key Features of the Module

• Twin Detection: Uses genetic and demographic criteria to identify potential twin pairs
• Twin Set Management: Groups twins into sets and maintains their relationships
• Integration with Pedigree Building: Ensures consistent placement of twins in pedigree structures
• Configuration Options: Provides tunable thresholds for twin identification

Identifying Twin Relationships

Bonsai v3 uses several criteria to identify potential twin relationships:

1. Genetic Criteria

• Extremely High IBD Sharing: Twins share exceptional amounts of DNA
  • Identical twins: Nearly 100% (all chromosomes)
  • Fraternal twins: ~50% (similar to regular siblings)
• IBD Pattern Analysis: Examining the pattern of half-identical and fully-identical regions
  • Identical twins show extensive fully-identical regions
  • Fraternal twins show patterns similar to full siblings

2. Demographic Criteria

• Identical Age: Twins are typically born on the same day
  • When age data is available, twins should have the same birth year
  • Small discrepancies might exist in reported ages
• Sex Compatibility: Sex information provides additional constraints
  • Identical twins must be the same sex
  • Fraternal twins can be the same or different sexes

Implementation in is_twin_pair Function

The is_twin_pair function implements these criteria, evaluating:

1. Total half-identical IBD sharing against the TWIN_THRESHOLD
2. Total fully-identical IBD sharing against the TWIN_THRESHOLD
3. Sex compatibility (requiring matching sex)
4. Age compatibility (requiring matching age if available)

Only if all these criteria are met does Bonsai classify a pair as twins.

Ensuring Consistent Treatment of Twins

Once twins are identified, Bonsai must place them correctly in pedigree structures, maintaining biological consistency:

Key Principles of Twin Placement

1. Common Parentage: Twins must share the same parents in the pedigree
2. Generational Consistency: Twins must be placed in the same generation
3. Relationship Consistency: Twins must have consistent relationships with all other individuals

Bonsai enforces these principles through specialized pedigree construction logic when twins are present:

# Pseudocode for twin-aware pedigree construction
for each twin_set in all_twin_sets:
    # Identify the best placement for one twin in the set
    primary_twin = select_representative_twin(twin_set)
    best_parents = identify_best_parents(primary_twin, pedigree, ibd_data)
    
    # Place all twins in the set with the same parents
    for twin in twin_set:
        add_individual_to_pedigree(twin, parents=best_parents)
        
    # Ensure consistent relationships with others
    for relative in all_individuals:
        if is_related(primary_twin, relative):
            relationship = get_relationship(primary_twin, relative)
            # Apply same relationship to all twins in the set
            for twin in twin_set:
                ensure_relationship(twin, relative, relationship)

Implementation Challenges

Several practical challenges arise when implementing twin placement:

• Evidence Conflicts: Different twins may have slightly different IBD patterns with other relatives due to testing or analysis variation
• Priority Decisions: When evidence conflicts, the algorithm must decide which relationships to prioritize
• Computational Efficiency: Handling twins can increase the complexity of pedigree construction algorithms

Bonsai addresses these challenges through a combination of evidence pooling, confidence-weighted decision making, and specialized optimization strategies.

Beyond Simple Twin Relationships

Twins are just one example of special genetic relationships that require specialized handling. Bonsai v3 also addresses several other scenarios involving very close relatives:

1. Double First Cousins

Double first cousins occur when two siblings from one family marry two siblings from another family. Their children are related through both parents:

• Share approximately 25% of their DNA (similar to half-siblings)
• Can be confused with half-siblings in genetic analysis
• Require pedigree context to correctly identify

2. Parent-Child Incest Cases

Children resulting from parent-child relationships have unusual genetic patterns:

• Share 75% of their DNA with the parent who is also their grandparent
• Have elevated homozygosity due to consanguinity
• Present special ethical considerations in reporting

3. Compound Relationships

Individuals can be related through multiple pathways, creating complex genetic signatures:

• Half-siblings who are also first cousins
• Double cousins through multiple family connections
• Relationships in endogamous communities with multiple connections

Special Handling Implementation

Bonsai implements several strategies to handle these complex cases:

1. Multi-Pathway Analysis: Evaluating how multiple relationship paths contribute to observed IBD
2. Pattern Recognition: Identifying characteristic patterns of complex relationships
3. Model Adjustment: Modifying likelihood models to account for unusual sharing patterns
4. Consistency Enforcement: Ensuring pedigree structures maintain biological consistency

Fundamental Limitations of Genetic Differentiation

Identical twins present a fundamental challenge for genetic genealogy because standard DNA tests cannot reliably distinguish between them. This creates what we call "The Identical Twin Problem":

Key Aspects of the Problem

• Genetic Indistinguishability: Standard autosomal DNA tests show effectively identical results
• Algorithmic Ambiguity: Algorithms cannot determine which twin is which based solely on genetic data
• Downstream Propagation: Ambiguity affects relationships with all descendants

Strategies for Handling Identical Twins

While perfect genetic differentiation is generally not possible with standard tests, several approaches can help manage the identical twin problem:

1. Incorporating Non-Genetic Information
   • Birth order and birth dates
   • Names and other identifying information
   • Known relationships from documentary sources
2. Special Notation and Visualization
   • Explicit twin labeling in pedigrees
   • Visual elements showing potential ambiguity
   • Alternative pedigree representations
3. Advanced Genetic Techniques (beyond standard tests)
   • Rare somatic mutations that differ between twins
   • Epigenetic markers that diverge over lifetime
   • Specialized testing targeting post-zygotic mutations

Communicating Twin Relationships

Effective visualization and reporting of twin relationships is critical for user understanding. Bonsai implements several specialized approaches:

1. Visual Representation of Twins

• Node Styling: Special visual markers for twin nodes in pedigree diagrams
• Connection Styling: Special edges connecting twins to each other
• Color Coding: Visual distinction between identical and fraternal twins

2. Confidence Reporting

• Twin Confidence Metrics: Quantitative measures of confidence in twin identification
• Explanation Codes: Notation explaining the evidence supporting twin classification
• Alternative Relationship Scores: Showing scores for competing hypotheses

3. Communicating Ambiguity

• Explicit Uncertainty Notation: Clear indication when twins cannot be distinguished
• Alternative Placement Visualization: Showing multiple possible pedigree configurations
• Confidence Intervals: Visualizing confidence in twin-related predictions

Special Genetic Relationships Through Twin Parents

Children of twins have unique genetic relationships that require special modeling:

Children of Identical Twins

• Genetic Half-Siblings: Children of identical twins are genetically equivalent to half-siblings, even though they are legally cousins
• Expected Sharing: ~25% of their DNA (similar to half-siblings)
• Pedigree Representation: Requires specialized notation to accurately represent the genetic relationship

Children of Fraternal Twins

• Enhanced First Cousins: Genetically similar to standard first cousins, but may have slightly different age patterns
• Expected Sharing: ~12.5% of their DNA (typical for first cousins)
• Age Considerations: Often much closer in age than typical first cousins

Implementation Approaches

Bonsai implements several strategies to correctly model relationships involving children of twins:

1. Twin-Aware Relationship Inference: Adjusting relationship likelihoods based on twin status of parents
2. Special Relationship Categories: Defining specialized categories for twin-specific relationships
3. Modified Age Models: Adjusting age-based constraints for relationships through twin parents
4. Consistency Enforcement: Ensuring all relationships through twins maintain biological consistency

# Pseudocode for handling children of twins
def infer_relationship_with_twin_awareness(id1, id2, ibd_data, twin_sets):
    # Check if either individual is a child of a twin
    parent1 = get_parents(id1)
    parent2 = get_parents(id2)
    
    for twin_set in twin_sets:
        # If parents are identical twins, adjust relationship model
        if parent1 in twin_set and parent2 in twin_set:
            # These individuals are genetic half-siblings through identical twin parents
            return {
                "legal_relationship": "first_cousins",
                "genetic_relationship": "half_siblings",
                "expected_sharing": 0.25,
                "notes": "Parents are identical twins"
            }
        
        # Other twin-specific relationship checks...
    
    # If no twin-specific condition applies, use standard inference
    return standard_relationship_inference(id1, id2, ibd_data)

Handling twins and other very close relatives is a crucial aspect of computational genetic genealogy. Bonsai v3's specialized algorithms in the twins.py module provide robust mechanisms for detecting twin relationships, ensuring consistent pedigree placement, and correctly modeling complex genetic relationships involving twins.

By understanding the unique challenges posed by twins and implementing tailored solutions, Bonsai can create more accurate and biologically consistent pedigree reconstructions, even in the presence of these special cases.

In the next lab, we'll explore how Bonsai v3 handles complex relationship patterns through specialized logic in the relationships.py module, building on the foundation of twin handling to address an even broader range of special relationship scenarios.