Estimation & Prediction

Not a Sum: Modelling Nonlinear Probabilistic Interactions in the Genetic Prediction of Fertility

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Abstract

Reproductive success arises from complex interactions between sex-specific factors that are usually naturally masked and thus difficult to capture using traditional selective breeding frameworks. To address this, we developed complementary statistical and computational approaches to estimate and predict the heritable components of fertility in two farmed Arctic charr (Salvelinus alpinus) populations. Within a quantitative genetics context, we formulated a Bayesian latent fertility model that represents realized fertilization success as the multiplicative outcome of unobserved maternal and paternal liabilities, each mapped to the [0, 1] range through a probit link to represent their respective probabilistic contributions. This analytical framework enables sex-specific estimation of variance components and correlations from aggregate mating data, providing interpretable insights into the genetic architecture of reproductive success while remaining compatible with standard animal-model concepts. In both breeding nuclei studied, posterior heritabilities on the latent scale ranged at low-moderate levels for female and male fertility. Building on the same conceptual foundation, we designed a machine learning framework employing a two-tower multilayer perceptron (MLP) architecture, where male and female relationships-to-pedigree-founders inputs are processed through parallel subnetworks before joint prediction of fertilization outcomes. Applied to multi-generational breeding records, the two-tower model captured biologically meaningful structure, achieving a Receiver-Operator-Characteristic Area Under the Curve (ROC AUC) of 0.65 and a Precision-Recall Area Under the Curve (PR AUC) of 0.95 on a held-out test. Sex-specific tower outputs demonstrated a moderate positive correlation (Pearson's r = 0.42-0.44) with estimated breeding values, confirming a meaningfully aligned ranking between the two approaches. Simulation experiments confirmed that two-tower architectures can also recover distinct sex-specific liabilities given genotypic information and achieve predictive performance proportional to the underlying heritable component present in the data. Collectively, these developments bridge classic quantitative-genetic inference with modern computational methods, providing a unified framework for disentangling sex-specific contributions to reproductive outcomes. Overall, this analytical machinery offers a flexible and generalizable pathway for modelling interactive biological processes where outcomes emerge from the joint expression of latent individual effects.

Keywords: 2026

How to Cite:

Debes, P., Johnsson, M., Palaiokostas, C. & Pappas, F., (2026) “Not a Sum: Modelling Nonlinear Probabilistic Interactions in the Genetic Prediction of Fertility”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2286350. doi: https://doi.org/10.31274/wcgalp.23947

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