The role of miscarriage and sororal birth order in male same-sex orientation: Theoretical predictions and empirical data

This study combines theoretical modeling and empirical data from eight populations to demonstrate that while the Fraternal Birth Order Effect is robustly supported, the observed Sororal Birth Order Effect and higher prevalence of male same-sex orientation among only-children suggest that maternal miscarriages and potentially additional mechanisms beyond the Maternal Immune Hypothesis play a significant role in the development of male sexual orientation.

The Gist

The Big Question: Why Do Some Men Prefer Men?

Scientists have long known a strange fact: Men who are attracted to other men (androphilic men) tend to have more older brothers than men who are attracted to women. This is called the Fraternal Birth Order Effect (FBOE).

The leading theory for why this happens is the Maternal Immune Hypothesis (MIH). Imagine a mother's immune system as a security guard.

• When a mother carries a boy, her body sees "male" proteins (like a specific uniform) and builds antibodies against them.
• If she has a second boy, her guard is already on high alert. The antibodies attack the developing brain of the second boy, slightly altering how his brain wires up for attraction.
• The more older brothers she has, the stronger the "security guard" gets, and the higher the chance the next boy will be attracted to men.

But here is the puzzle: Recent studies show that having older sisters also seems to increase the odds of a man being gay, even if he has no older brothers. This is the Sororal Birth Order Effect (SBOE).

The problem? The "Security Guard" theory (MIH) says sisters shouldn't matter because they don't wear the "male uniform." So, why do sisters seem to matter?

The Study's Mission

The authors of this paper wanted to solve a mystery: Is the "older sister" effect real, or is it just a trick of the numbers?

They used two tools:

1. Computer Simulations: They built a virtual world to test how the "Security Guard" theory works.
2. Real Data: They looked at actual family trees from 8 different countries (including France, Canada, Indonesia, and Samoa).

The "Trick" of the Numbers (Spurious Correlation)

Imagine a classroom. If you pick a student who has 3 older brothers, it is statistically very likely they also have 2 or 3 older sisters. Why? Because big families usually have a mix of boys and girls.

The researchers found that the "older sister effect" is partly a statistical illusion. Because older brothers and older sisters usually come in the same families, the math makes it look like sisters are causing the effect, when really it's just the brothers doing the work.

The Analogy:
Imagine you are studying why people get wet. You find that people with umbrellas are wetter than people without them.

• The Trick: You realize that people with umbrellas are also the ones who are standing in the rain.
• The Reality: The umbrella didn't make them wet; the rain did. But because umbrellas and rain go together, the umbrella looks like the cause.
• In this study: "Older Sisters" are the umbrellas, and "Older Brothers" are the rain.

The Twist: The "Ghost" Brothers (Miscarriages)

The researchers thought they had solved it: "It's just a statistical trick!" But then they added a new variable to their computer model: Miscarriages.

They realized that a mother might have had a pregnancy that ended early (a miscarriage) before the baby was born.

• The "Ghost" Brother: Even if a male fetus is miscarried, the mother's immune system might still see the "male uniform" and build antibodies.
• The Problem: In family records, we only count the babies who were born. We don't know about the "ghost" brothers who were miscarried.

The Analogy:
Imagine a security guard who gets a report of a "suspicious person" (a male fetus) but the person never actually enters the building (the baby is miscarried). The guard still gets nervous and builds up a defense.

• Later, the guard meets a real person (a born baby).
• If you only count the people who entered the building, you might think the guard is reacting to the wrong person.
• In this case, the "Ghost Brother" (miscarriage) makes the mother's immune system stronger, which affects the next baby. But because we can't see the ghost, the math gets messy.

What They Found in Real Life

When the researchers looked at real data from 8 countries, they found two surprising things:

1. The Sister Effect is Real (and Strong): Even after they mathematically "controlled" for the number of older brothers, having more older sisters still increased the odds of a man being gay.
2. The "Only Child" Mystery: The study found that only-children (men with no siblings at all) are more likely to be gay than men who are the firstborn but have younger siblings.

Why is this weird?
If the "Security Guard" theory is right, the firstborn should be the least likely to be gay because the guard hasn't seen any "male uniforms" yet. But the data shows only-children are more likely to be gay than firstborns with siblings.

The Conclusion: The Math Doesn't Add Up

The researchers tried to explain these findings using the "Miscarriage" theory. They calculated: "How many miscarriages would we need to have to explain why sisters seem to matter and why only-children are more gay?"

The Result: The math required a 37% to 57% miscarriage rate to make the numbers work.

• The Reality: In the real world, miscarriage rates are usually around 10% to 30%.

The Verdict:
The "Ghost Brother" theory (miscarriages) explains some of the mystery, but not all of it. The required number of "ghosts" is too high to be realistic.

This suggests one of two things:

1. There is a hidden mechanism: There might be a different biological reason why older sisters influence sexual orientation that we haven't discovered yet.
2. The theory needs an upgrade: The "Security Guard" theory might need to be expanded to include other factors we don't understand.

Summary in One Sentence

While having older brothers definitely increases the chance of a man being gay due to a mother's immune system, the fact that older sisters also seem to matter (and that only-children are surprisingly gay) suggests that our current understanding of biology is missing a piece of the puzzle—perhaps involving miscarriages we can't see, or a completely new biological rule we haven't found yet.

Technical Summary

1. Problem Statement

The study addresses the Fraternal Birth Order Effect (FBOE), a robust phenomenon where androphilic (gay) men have significantly more older brothers than heterosexual men. The prevailing explanation is the Maternal Immune Hypothesis (MIH), which posits that mothers develop antibodies against male-specific antigens (e.g., NLGN4Y) during successive male pregnancies, altering the neurodevelopment of subsequent sons.

However, the MIH faces three critical challenges that this study aims to resolve:

1. The Sororal Birth Order Effect (SBOE): Some studies report that older sisters also increase the likelihood of male androphilia, independent of older brothers. The MIH predicts no effect from sisters, as they do not trigger male-specific immune responses. It is debated whether this SBOE is "spurious" (a statistical artifact of the correlation between older brothers and sisters) or "real" (indicating a distinct biological mechanism).
2. The Role of Miscarriage: It has been hypothesized that miscarried male fetuses contribute to maternal immunization. If true, this could explain androphilia in firstborns (who have no living older brothers) and potentially create a spurious SBOE if miscarriage rates differ or affect the correlation between sibling sexes.
3. The Only-Child Paradox: Empirical data suggests a higher prevalence of male androphilia among only-children compared to firstborns with younger siblings. The MIH struggles to explain this, as firstborns in larger sibships should theoretically have the same baseline risk as only-children unless specific maternal conditions or miscarriage dynamics are at play.

2. Methodology

The authors employed a dual approach combining mathematical modeling/simulation and empirical data analysis.

A. Simulation Modeling

• Framework: They constructed a formal model of the MIH where the maternal immune response ($imr$) increases additively with each male birth ($b$) and follows a Gamma distribution for initial variation. Sexual orientation is determined by a logistic function of $imr$.
• Variables:
  • FBOE & SBOE: Simulated populations to derive explicit functions for the effects of older brothers ($ob$) and older sisters ($os$).
  • Correlation Control: Generated datasets with and without the natural correlation between $ob$ and $os$ to isolate spurious effects.
  • Miscarriage ($f_m$): Introduced a miscarriage probability affecting both sexes. Crucially, they modeled whether miscarried male fetuses contribute to $imr$ (parameter $\alpha$).
• Statistical Analysis: Used Generalized Linear Models (GLM) and ABZ regression to test for SBOE while controlling for FBOE. They utilized WAIC (Watanabe-Akaike Information Criterion) to determine the best-fitting mathematical function for the SBOE.
• Estimation: Developed a function to estimate the required miscarriage frequency ($f_m$) that would generate an observed SBOE slope in simulated data.

B. Empirical Data Analysis

• Datasets: Analyzed individual-level family data from eight diverse populations: Indonesia, France, French Polynesia, Greece, Canada, Czech Republic, Samoa, and Iran.
• Sample Size: Included thousands of participants, with specific focus on distinguishing androphilic vs. gynephilic men and controlling for bisexual/ambiphilic categories.
• Statistical Approach:
  • Applied ABZ regression (sexual orientation ~ $ob$+$os$ + total siblings).
  • Tested for SBOE significance after controlling for $ob$.
  • Estimated the miscarriage frequency ($f_m$) required to explain the observed SBOE slopes in real populations.
  • Compared the prevalence of androphilia in only-children vs. firstborns with younger siblings.

3. Key Contributions

1. Quantification of Spurious SBOE: The study mathematically demonstrates that a "spurious" SBOE arises naturally from the positive correlation between the number of older brothers and older sisters in populations with high fertility.
2. The Miscarriage Mechanism: The authors provide the first quantitative evidence that miscarriage disrupts statistical controls. Even when controlling for the number of living older brothers, the presence of miscarried brothers (which are unobserved in standard datasets) creates a residual correlation that generates a significant, spurious SBOE.
3. The Only-Child Effect: The study identifies a counter-intuitive mechanism where miscarriage increases the prevalence of androphilia in only-children relative to firstborns with younger siblings. This occurs because "only-children" in the dataset include those with miscarried older brothers (who boosted maternal immunity), whereas "firstborns with younger siblings" are a mixed group where the presence of a younger sibling dilutes the specific immunological history of the firstborn.
4. Empirical Validation: Confirmed a significant SBOE across eight global populations even after controlling for FBOE, and confirmed the higher prevalence of androphilia in only-children.

4. Key Results

• Spurious vs. Real SBOE: In simulations without miscarriage, controlling for older brothers eliminated the SBOE. However, when miscarriage was introduced, a significant SBOE persisted even after controlling for living older brothers.
• Estimated Miscarriage Rates: To explain the magnitude of the observed SBOE in empirical data, the model required estimated miscarriage rates between 37% and 57%.
  • Significance: These rates are significantly higher than typical reported human miscarriage rates (10–30%).
• Only-Children vs. Firstborns: Empirical data showed a significantly higher frequency of androphilia in only-children ($f_H \approx 0.46$) compared to firstborns with younger siblings ($f_H \approx 0.36$). This aligns with the simulation prediction that miscarriage creates this disparity.
• Correlation Dynamics: The correlation between older brothers and sisters ($\tau_{ob-os}$) was found to be driven by mean fertility and over-dispersion of family size.

5. Significance and Implications

• Refining the MIH: The study suggests that the Maternal Immune Hypothesis may need extension. While MIH explains the FBOE, the persistence of a significant SBOE and the specific patterns in only-children suggest that miscarriage plays a critical, previously under-quantified role.
• The "Spurious" vs. "Real" Debate: The findings imply that a significant portion of the observed SBOE is likely spurious, driven by the statistical artifact of unobserved miscarried brothers. However, the estimated miscarriage rates required to explain the entirety of the effect are unrealistically high.
• Future Directions: The discrepancy between estimated (37–57%) and reported (10–30%) miscarriage rates suggests two possibilities:
  1. Under-reporting: Actual miscarriage rates (especially early ones triggering immunity) are much higher than currently recorded.
  2. Additional Mechanisms: There may be a non-spurious (real) SBOE driven by mechanisms outside the classic MIH (e.g., autosomal antigens or other biological factors) that operates alongside the spurious effect.
• Methodological Impact: The paper highlights that standard statistical controls for birth order are insufficient in the presence of unobserved miscarriages, necessitating new analytical frameworks for studying sexual orientation and birth order.

In conclusion, the paper provides a rigorous theoretical and empirical framework showing that miscarriage is a key confounding variable in birth order studies. It challenges researchers to reconsider whether the Sororal Birth Order Effect is entirely an artifact of unobserved male pregnancies or if it signals a distinct, yet-to-be-identified biological mechanism.