Predictivity Method Tracks Dynamic Genetic Parameters in Large Livestock Populations Under Selection

A computational evaluation of a statistical framework called Genetic Parameters via Predictivity demonstrated that dynamic heritabilities and genetic correlations can be accurately tracked across successive time slices in very large genotyped livestock populations under intense genomic selection. Published in Genetics Selection Evolution, the study investigated how the GPP method performs when evaluating directional selection across multi-generation cohorts. Traditional parameter estimation techniques, including restricted maximum likelihood and Bayesian Markov chain Monte Carlo Gibbs sampling, face steep computational barriers as dense genomic relationship matrices expand to hundreds of thousands or millions of animals. The researchers established that GPP provides an accurate, scalable alternative by linking empirical predictivity within and across traits to deterministic formulas of genomic prediction accuracy, resolving a persistent computational bottleneck in modern quantitative genetics.

Animal breeding programs increasingly depend on genomic selection, which has expanded databases in commercial dairy and beef cattle to millions of genotyped individuals. As selection operates over successive generations, allele frequencies shift and gametic phase disequilibrium accumulates through the Bulmer effect, causing underlying additive genetic variances, heritabilities, and genetic correlations to change continuously over time. Other biological and operational factors, including evolving trait definitions, resource reallocation within individual animals, non-additive gene action, and non-linear associations, also cause genetic parameters to deviate from their ancestral states. While capturing these temporal shifts is vital for managing genetic trends and avoiding undesirable deterioration in correlated traits, classical mixed model equations become prohibitively dense, making standard variance component estimation across successive time slices mathematically or computationally intractable in industrial datasets.

To rigorously test whether GPP can monitor these continuous shifts without relying on computationally demanding base-population inversions, the investigators simulated multi-generation cattle populations using the AlphaSimR package and the Markovian Coalescent Simulator in R. The simulation constructed a historical base population from 100,000 founder haplotypes across 30 chromosomes, generating 60,000 segregating loci under a demographic model tailored to bovine coalescent properties. From these loci, 49,950 biallelic single nucleotide polymorphisms were designated as genetic markers, while 3,000 distinct, non-overlapping quantitative trait loci were selected to control simulated phenotypes. The mating structure maintained an effective population size of 50 animals across generations using controlled allocations of breeding males and females, producing controlled populations subjected to strong directional genomic selection over 10 consecutive generations.

The experimental architecture examined three distinct simulated phenotypes to reflect commercial breeding dynamics. Trait 1 was designated as a primary production trait exhibiting a baseline heritability of 0.40, serving as the sole target of directional genomic selection based on genomic estimated breeding values. Trait 2 was modeled with a baseline heritability of 0.10 and had no initial genetic correlation with the primary trait. From these underlying foundations, two dynamic composite traits were derived: Trait 3, mimicking a real fitness trait having an initial heritability of 0.10 and a declining genetic correlation with production over generations, and Trait 4, mimicking a secondary production trait that began with an initial heritability of 0.10 and exhibited an increasing positive genetic correlation with the primary trait. Selection was conducted across five independent replicates under two scale scenarios: Scenario A comprising 5,000 genotyped animals per generation, and Scenario B comprising 100,000 genotyped animals per generation.

The mechanics of the GPP method rely on partitioned validation cohorts evaluated across sequential overlapping generation intervals, specifically examining eight distinct three-generation time slices extending from generations 1 through 3 to generations 8 through 10. Within each time slice, the first two generations serve as the reference population to estimate genomic breeding values, while the third generation constitutes the focal validation group. For each trait, the predictivity parameter represents the Pearson correlation between the estimated genomic breeding values derived from the reference population and the adjusted phenotypes within the focal group. This observed predictivity is subsequently combined with the estimated number of independent chromosome segments to calculate both trait heritability and its accompanying standard error without constructing or inverting whole-population genomic relationship matrices.

Calculating genetic correlations within GPP involves evaluating cross-trait predictivity by comparing the genomic breeding values predicted for one trait against the adjusted phenotypic values recorded for another trait within the focal generation. Because the formulation allows the designations of the two traits to be exchanged, the method naturally produces two separate, non-symmetric estimates of genetic correlation depending on which trait supplies the adjusted phenotypic benchmark. The study revealed that when tracking dynamic traits whose underlying composition changes due to correlated selection responses, estimating adjusted phenotypes for the secondary or fitness trait using breeding values calculated from the primary production trait yielded superior accuracy and minimized estimation lag compared to the inverse formulation.

In the large-scale population scenario comprising 100,000 genotyped animals per generation, GPP estimates of heritability and genetic correlation closely matched the realized parameters across all evaluated time slices. For the primary production trait, where realized heritability declined from 0.35 down to 0.30 as a consequence of directional selection and the Bulmer effect, GPP accurately tracked this downward trajectory with minimal bias. Standard pedigree-based restricted maximum likelihood evaluations were restricted to single-generation subsets because multi-generation datasets exceeded computational capabilities, whereas genomic restricted maximum likelihood was entirely infeasible in the large population. Even under these constrained single-generation comparisons, pedigree REML slightly overestimated heritability, while GPP maintained consistent fidelity to the realized population parameters.

The performance of GPP on the simulated fitness and secondary production traits in the large dataset further confirmed its capacity to track indirect selection responses across varying correlation strengths. As realized genetic correlations between primary production and fitness dropped from 0 in generation 1 to negative 0.54 in generation 10, GPP accurately captured both weak early-generation correlations and strong late-generation negative associations. Similarly, for the secondary production trait, where the realized correlation rose from 0 to positive 0.51, GPP estimates remained stable and aligned with realized values. In contrast, pedigree-based REML suffered from inflation during time slices with low correlation and exhibited slight overestimations during time slices with strong positive correlations, highlighting the stability of GPP under shifting genetic architectures.

Computational benchmarking demonstrated that GPP requires substantially fewer computing resources than classical variance component estimation methods, operating with an approximately linear scaling cost relative to the number of genotyped animals. Within the large-scale dataset of Scenario B, executing a single time-slice evaluation of GPP required 55 minutes and 11 seconds. Classical genomic restricted maximum likelihood could not run at this scale due to memory limits, while alternative Bayesian Gibbs sampling procedures scale quadratically with sample size, rendering repeated multi-slice evaluations impractical for commercial datasets. Additionally, sensitivity tests demonstrated that deliberately introducing incorrect variance components during the initial estimation of genomic breeding values prior to GPP had negligible impact on final heritability estimates, eliminating the necessity for iterative recalculation cycles.

Despite its computational efficiency, the investigation identified specific constraints and structural boundaries for the GPP methodology. When applied to the smaller dataset of 5,000 animals per generation, GPP produced inflated heritability estimates for the low-heritability fitness and secondary production traits, which in turn attenuated the corresponding genetic correlation estimates toward zero. The authors determined that for GPP to deliver reliable estimates, the number of individuals within the focal validation group must equal or exceed the effective number of independent chromosome segments. Furthermore, the mathematical formulation is directly adapted to populations where all phenotyped individuals are genotyped under genomic BLUP assumptions, leaving the handling of ungenotyped animals in single-step evaluations, maternal effects, and random regression models as subjects for future research.

Subject of Research: Evaluation of the GPP method for dynamic genetic parameter estimation in large genotyped populations

Article Title: Genetic parameters via predictivity in large populations under strong genomic selection

Article References: Gowane, G., Hidalgo, J., Hollifield, M. K., Misztal, I., & Lourenco, D. (2026). Genetic parameters via predictivity in large populations under strong genomic selection. Genetics Selection Evolution, 58(1), Article 39. https://doi.org/10.1186/s12711-026-01054-9

Image Credits: AI Generated

DOI: 10.1186/s12711-026-01054-9

Keywords: genomic selection, GPP method, heritability estimation, genetic correlation, livestock breeding, computational genetics, restricted maximum likelihood, BLUPF90, AlphaSimR, Bulmer effect, predictivity, genomic estimated breeding values, simulation study, additive genetic variance, quantitative genetics, population genetics