🧬 genetics

Two-tower models for genomic prediction of reproductive outcomes and sex-specific fertility liabilities: simulation insights

This study demonstrates that two-tower machine learning architectures, particularly TT-LASSO and TT-MLP, effectively predict binary reproductive outcomes and recover latent sex-specific fertility liabilities from genotypic data, offering a powerful framework for modeling the joint genetic contributions of mates in reproductive traits.

Original authors: Pappas, F., Palaiokostas, C., Debes, P. V., Johnsson, M.

Published 2026-07-09

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CC BY 4.0

Original authors: Pappas, F., Palaiokostas, C., Debes, P. V., Johnsson, M.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are trying to predict whether a specific couple will have a successful relationship. You can't just look at the man's personality or the woman's personality in isolation; the success of the relationship depends on both of them. If one person is unwilling or unable to commit, the relationship fails, no matter how great the other person is.

This paper tackles a similar problem in animal breeding (like fish or farm animals). The goal is to predict reproductive success (having babies). The authors realized that fertility isn't just a trait of one animal; it's a "team sport." For a pregnancy to happen, both the male and the female must be fertile. If either one fails, the result is zero.

Here is a simple breakdown of what they did and what they found:

The Problem: The "Two-Door" Puzzle

Traditional computer models often try to predict fertility by looking at an animal's DNA as if it were a solo act. But biology doesn't work that way. It's like a security system with two doors: Door A (Male) and Door B (Female). Both doors must be unlocked for the treasure (a baby) to be found. If Door A is locked, it doesn't matter how open Door B is; the treasure remains hidden.

The researchers wanted to build a computer model that understands this "two-door" rule. They needed a system that could:

Predict if a specific pair will reproduce successfully.
Figure out individually how fertile the male is and how fertile the female is, even though the model only sees the final "Yes/No" result of the pair.

The Solution: The "Two-Tower" Machine

To solve this, they built special AI models called "Two-Tower" models.

The Analogy: Imagine a factory with two separate assembly lines (Towers).
- Tower 1 looks only at the Male's DNA.
- Tower 2 looks only at the Female's DNA.
- Each tower produces a single score: "How fertile is this individual?"
- Finally, a "Manager" multiplies these two scores together. If both scores are high, the result is a "Success." If one is zero, the result is "Failure."

They tested three different types of "Managers" (algorithms) to see which one worked best:

The Linear Manager (TT-LASSO): A simple, rule-based calculator that looks for the strongest patterns.
The Deep Thinker (TT-MLP): A complex neural network that tries to find hidden, non-linear connections.
The Pattern Spotter (TT-CNN): A model designed to find local patterns in the DNA sequence (like looking for specific words in a book).

What They Discovered

1. The Simple Manager Often Wins
Surprisingly, the Linear Manager (TT-LASSO) was the best at predicting whether a pair would succeed or fail. It was like a sharp, no-nonsense accountant who got the binary answer (Success/Fail) right more often than the complex deep-learning models.

2. The Deep Thinker is Better at Fairness
While the Linear Manager was great at the final prediction, it sometimes got "lazy." If the female had very strong genetic signals for fertility, the Linear Manager would ignore the male's data and just guess based on the female.
The Deep Thinker (TT-MLP), however, was better at being fair. It managed to figure out the fertility scores for both the male and the female accurately, even when one sex had much weaker genetic data than the other. It didn't just lean on the "loud" signal; it listened to both.

3. The "Compatibility" Twist
The researchers also tested a scenario where the couple's success depended on a specific "chemistry" between their genes (like a lock and key that only fit if they are a specific match).

The Two-Tower models (which keep the male and female separate) struggled a bit here because they couldn't see the direct interaction between the two DNA strands.
A Fully Connected Model (which smashes the male and female DNA together into one big pile before analyzing) was much better at catching these specific "chemistry" matches.

The Bottom Line

This paper shows that to predict animal fertility, you need a model that respects the "team" nature of reproduction.

If you just want to know "Will this pair have babies?", a simple, linear two-tower model is very effective.
If you want to know "How fertile is the dad?" and "How fertile is the mom?" individually, a more complex neural network (the Deep Thinker) gives a more balanced and accurate answer.

The study proves that by splitting the problem into two separate "towers" and then combining them, we can get a clear picture of both the team's performance and each player's individual contribution.

Technical Summary: Two-Tower Models for Genomic Prediction of Reproductive Outcomes

Problem Statement
Reproductive success in sexually reproducing species is an "extended phenotype," a joint biological outcome requiring the fertility of both mates. Unlike individual traits, fertilization success cannot be expressed as a simple linear combination of male and female liabilities; it is inherently non-linear, as success requires both individuals to be fertile. Traditional predictive models often struggle to simultaneously predict the aggregate pair-level outcome while recovering interpretable, sex-specific genetic contributions (liabilities) from high-dimensional genomic data. This study addresses the challenge of modeling these joint phenotypes to enable genomic prediction of binary reproductive outcomes and the recovery of sex-specific fertility liabilities.

Methodology
The authors employed a simulation-based approach using the AlphaSimR package to generate datasets under diverse genetic architectures. The study evaluated three distinct Two-Tower (TT) machine learning architectures designed to process sex-specific genomic inputs (SNP genotypes) through separate sub-models ("towers") before fusing them multiplicatively to predict pair-level success.

Simulation Design:
- Data Generation: Simulated populations with 10 chromosomes and 5,000 SNPs, derived from a founding population of 4,000 individuals.
- Scenarios: Fourteen scenarios were created to test model robustness against varying parameters:
  - Heritability (HER): Sex-specific heritabilities ( $h^2$ ) ranging from 0.1 to 0.7, including balanced and unbalanced cases.
  - Genetic Correlation (COR): Inter-sexual genetic correlations of -0.7, 0, and 0.7.
  - Prevalence (PREV): Different infertility case/control ratios (0.1, 0.25, 0.4).
  - Mating Structure (MATE): Varying sire-to-dam ratios (1:2, 1:1, 2:1).
  - Sex-Specific Infertility (SEX): Unbalanced infertility rates between sexes.
  - Mate Compatibility: An additional scenario introducing genotype-dependent incompatibility (non-additive interactions) between specific sire-dam genotypes.
Model Architectures:
- TT-MLP: A Multilayer Perceptron with three hidden layers, ReLU activations, and dropout.
- TT-CNN: A 1D Convolutional Neural Network processing chromosomes with padding, followed by batch normalization, pooling, and an MLP head.
- TT-LASSO: An L1-regularized linear model designed to drive less-contributing features to zero.
- Fully-Connected MLP (Baseline): A standard MLP where sire and dam genotype vectors were concatenated to capture non-additive interactions directly, serving as a comparison for the compatibility scenario.
Training and Evaluation:
- Models were trained using class-weighted binary cross-entropy loss in log space.
- Hyperparameters were tuned via Optuna using 5-fold cross-validation on a separate dataset.
- Metrics: Performance was evaluated using ROC-AUC for binary classification (pair-level success) and Pearson's correlation coefficients between tower outputs and True Genetic Values (TGV) for the recovery of sex-specific liabilities.

Key Results

Classification Performance: Prediction accuracy (ROC-AUC) scaled linearly with the Euclidean norm of the sex-specific heritabilities. TT-LASSO consistently achieved the highest overall classification performance across most scenarios, followed by TT-MLP. TT-CNN generally demonstrated the lowest performance.
Recovery of Sex-Specific Liabilities: All models successfully recovered latent fertility liabilities despite being trained only on joint outcomes.
- TT-LASSO showed superior recovery for the sex with the higher heritability (stronger signal-to-noise ratio) but often under-recovered the liability for the sex with lower heritability, particularly in unbalanced scenarios.
- TT-MLP provided more balanced and consistent recovery of genetic values across both sexes, regardless of heritability imbalances.
Impact of Data Structure:
- Prevalence: Higher infertility prevalence (more cases) improved learning and classification accuracy, while rare cases (low prevalence) destabilized performance.
- Mating Structure: Varying sire:dam ratios had minor effects on overall accuracy but influenced the recovery of specific sex liabilities in TT-LASSO.
- Mate Compatibility: In the scenario introducing genotype-dependent incompatibility, the Fully-Connected MLP (which concatenates inputs) outperformed the Two-Tower models, achieving the highest predictive accuracy. This suggests that standard TT architectures, which process sexes independently, struggle to capture complex non-additive interactions between mates without specific architectural modifications.

Significance and Claims
The paper claims that Two-Tower frameworks offer a powerful approach for modeling extended phenotypes like reproductive success. The primary contribution is the demonstration that these architectures can simultaneously predict aggregate reproductive outcomes and disentangle sex-specific genetic liabilities from genotypic information.

The authors emphasize that while TT-LASSO offers superior classification accuracy, TT-MLP provides more robust and balanced recovery of genetic values across varying genetic architectures. The study highlights that the choice of architecture depends on the specific goal: maximizing binary classification accuracy versus obtaining interpretable, balanced estimates of individual breeding values. Furthermore, the results indicate that while TT models are effective for additive genetic effects, capturing non-additive mate compatibility effects may require fully connected architectures that jointly model genotype interactions. The authors suggest these frameworks could be extended to other extended phenotypes, such as infectious disease susceptibility, and that the tower outputs could serve as efficient, low-dimensional representations for large-scale genomic evaluations.

The Problem: The "Two-Door" Puzzle

The Solution: The "Two-Tower" Machine

What They Discovered

The Bottom Line

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