From Prediction to Decision: Breeding Models in an Age of Biological Complexity

For decades, plant breeding has rested on a deceptively simple equation:

P = G + E + G×E + ε

Phenotype as the combined result of genetics, environment, their interaction, and a residual term representing everything left unexplained.

This framework has driven remarkable genetic gains across crops worldwide and remains one of the foundations of modern breeding. Yet the traits that matter most to breeding programmes (yield, drought tolerance, disease resistance, nutrient-use efficiency, and adaptation) remain among the most difficult to understand.

Not because the equation is wrong, but because many of the processes shaping phenotype were historically unmeasured, poorly understood, or simply inaccessible to observation.

Viewed through this lens, the history of modern breeding can be interpreted as a gradual process of making ε smaller. Not by eliminating uncertainty, but by transforming previously unexplained phenomena into biological knowledge that supports better selection decisions.

From a statistical perspective, many advances in modern breeding can be viewed as the progressive structuring of genetic and residual sources of variation, transforming what was once treated as unexplained error into interpretable biological information.

Environmental covariates, spatial analyses, genomic prediction, high-throughput phenotyping, crop growth models, and increasingly sophisticated mixed models all contribute to that process. Each has helped reveal structure where breeders once saw noise.

From Noise to Signal

Environmental variation provides one of the clearest examples.

Traditionally, environments were represented as locations, years, or management scenarios. Today, they can be described through detailed information on weather patterns, soil characteristics, water availability, and management history.

This shift has changed more than predictive performance; it has changed the kinds of questions breeders can answer. Enviromic approaches have improved the prediction of genotype performance in environments that have never been phenotyped directly [1,2]. As a result, breeders can make more informed decisions even when field information is incomplete.

A similar transition has occurred within field trials themselves. Fertility gradients, drainage patterns, and countless other sources of heterogeneity influence plant performance independently of genetics. Traditional experimental designs sought to minimise these effects. Spatial mixed models allow them to be quantified and accounted for directly, separating genetic signal from local field variation that would otherwise inflate residual error [3].

The underlying genetics remained the same. What changed was our ability to distinguish genetic signal from environmental and experimental noise.

The transition from description to interpretation is equally evident in multi-environment trials. Factor analytic models have transformed the way genotype-by-environment interaction is analysed. By decomposing G×E into a small number of latent factors, these approaches often reveal biologically meaningful patterns of adaptation that would remain hidden in simpler analyses [4,5].

What was once absorbed into residual variation increasingly becomes information that can guide selection.

When Better Models Change Outcomes

The strongest evidence for this transformation appears when additional information changes which genotypes are selected.

Yield provides a compelling example. In wheat breeding, integrating high-throughput phenotyping with genomic prediction has generally improved prediction and selection accuracy compared with genomic information alone [6–8]. More important than the improvement itself is what it represents.

Additional biological information can reveal meaningful differences among candidate lines that would otherwise remain hidden. Rather than simply increasing predictive performance, these approaches strengthen confidence that advancement decisions are being made on the most promising material.

This distinction is critical. The value of additional information lies not in generating more complex models, but in improving the quality of the decisions derived from them.

Drought tolerance tells a similar story. Multi-environment prediction models that incorporate dominance effects and genotype-by-environment interactions outperform simpler approaches because they more accurately reflect how genotypes respond across contrasting environments [9].

In practical terms, this reduces the risk of advancing material that performs well under one set of conditions but fails under another.

Although these examples involve different crops, traits, and analytical approaches, they point towards the same conclusion: progress occurs when previously hidden biological processes become measurable and interpretable.

From Factors to Systems

For decades, breeding models focused on estimating the contribution of individual factors to performance. Genetic effects, environmental effects, and genotype-by-environment interactions remain fundamental concepts.

Increasingly, however, complex traits are being understood as emergent properties of interconnected systems rather than isolated factors.

Yield is not produced by genetics alone, nor by environment alone. It emerges from interactions among crop development, resource acquisition, stress responses, and environmental conditions throughout the life of the plant. The same applies to drought tolerance, nutrient-use efficiency, and many forms of disease resistance.

This perspective is reflected in approaches that integrate physiological understanding directly into prediction frameworks, treating adaptation as a biological process rather than simply a statistical pattern [10].

The question is therefore no longer simply which factor contributed how much. The more important question is whether our analytical framework captures enough of the underlying system to support a confident decision.

Not all sources of uncertainty are equally informative. Some improve our understanding of biological processes, others influence which materials are advanced, retained, or discarded. Those are the sources of uncertainty that matter most.

Beyond G, E and G×E?

Perhaps the most intriguing developments are emerging from areas that challenge the boundaries of the traditional framework itself.

Plants do not experience the environment alone. Their roots exist within complex biological communities composed of bacteria, fungi, and countless other microorganisms interacting continuously with both the plant and the surrounding soil.

Evidence increasingly suggests that different genotypes recruit different microbial communities, while soil characteristics influence which interactions become possible. In some cases, the same genotype can assemble markedly different microbiomes depending on where it is grown.

The significance of these findings extends beyond microbiome research itself.

Their importance lies in the fact that they challenge a long-standing assumption: that phenotype can always be decomposed cleanly into genetic and environmental components.

Consider a future breeding programme evaluating two lines with similar field performance. If one genotype consistently establishes more beneficial biological partnerships across environments, should both lines be considered equivalent?

Traditional breeding frameworks might suggest so.

Increasingly, biology suggests otherwise.

Whether these effects ultimately become routine components of breeding models remains uncertain. Regardless of how they are incorporated into breeding programmes, they remind us that the boundaries of biological explanation are not fixed.

As new processes become measurable, phenomena once absorbed into residual variation become open to investigation.

What Does This Mean for a Breeder?

A useful way to evaluate any new source of information is to ask a simple question:

Would it change what we do?

• Environmental covariates changed how breeders evaluate adaptation.
• Spatial models changed how field performance is interpreted.
• High-throughput phenotyping changed how crop responses are measured through time.
• Multi-environment prediction changed how stability and adaptation are assessed.
• Emerging microbiome research may eventually change how adaptation itself is understood.

Their value lies less in technical sophistication than in their ability to change how breeders interpret evidence.

Because breeding is not fundamentally an exercise in prediction for its own sake; it is an exercise in selection.

The value of an analytical framework lies not in the proportion of variance it explains, but in whether it improves the quality of the decisions derived from it.

The ultimate goal is not to explain more variation. It is to identify the information capable of changing a decision.

Those decisions accumulate across breeding cycles, where even modest improvements in selection accuracy contribute directly to long-term genetic gain.

Analytical advances do not create genetic gain directly. They improve the probability that the right genotypes are selected, advanced, and ultimately delivered as products.

Imagine two breeding lines entering the final stage of selection: 

1. both perform well across environments; 
2. both exhibit similar yield potential; 
3. both appear equally promising.

Yet one ranking is supported by analyses that account for environmental covariates, spatial effects, genotype-by-environment structure, and other biologically meaningful sources of information. The other is not.

In practice, that difference may determine which line receives years of additional testing, commercial investment, and ultimately reaches farmers’ fields.

Beyond Prediction

Richer datasets, more sophisticated sensors, and increasingly powerful analytical tools will continue to reshape plant breeding. Yet the most important advances may not come from generating more information. They may come from understanding which observations truly improve our understanding of performance and which simply accompany it.

Viewed collectively, the developments discussed here, from enviromics and spatial analysis to phenomics, crop growth modelling, and microbiome research, represent successive efforts to convert uncertainty into biological understanding.

In many ways, the history of modern breeding can be interpreted as a continuing effort to understand what belongs inside ε and what does not.

The objective is not to eliminate ε. Biology will always contain processes that remain unknown, unmeasured, or inherently unpredictable. The objective is to ensure that the uncertainty that remains contains as little actionable information as possible.

Farmers never see variance components, prediction accuracies or covariance structures; what they experience are cultivars.

Breeding programmes are not ultimately judged by the datasets they generate or the models they deploy. They are judged by the cultivars that create value in farmers’ fields through improved productivity, resilience, quality, and adaptation.

Ultimately, the success of a breeding programme is not determined by the amount of information it can collect or model.

It is determined by how confidently it can identify the small fraction of information that truly matters.

Because, in the end, breeding is not the science of eliminating uncertainty.

It is the science of making better decisions despite it.

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References

[1] Jarquín, D., Crossa, J., Lacaze, X., Du Cheyron, P., Daucourt, J., Lorgeou, J., et al. (2014). A Reaction Norm Model for Genomic Selection Using High-Dimensional Genomic and Environmental Data. Theoretical and Applied Genetics, 127, 595–607. DOI: 10.1007/s00122-013-2243-1

[2] Costa-Neto, G., Fritsche-Neto, R., Crossa, J., et al. (2021). Enviromic Assembly Increases Accuracy and Reduces Costs of Genomic Prediction for Yield Plasticity in Maize. Frontiers in Plant Science, 12, 717552. DOI: 10.3389/fpls.2021.717552

[3] Smith, A.B., Cullis, B.R., & Thompson, R. (2005). The Analysis of Crop Cultivar Breeding and Evaluation Trials: An Overview of Current Mixed Model Approaches. Journal of Agricultural Science, 143, 449–462. DOI: 10.1017/S0021859605005587

[4] Smith, A.B., Cullis, B.R., & Thompson, R. (2001). Analyzing Variety by Environment Data Using Multiplicative Mixed Models and Adjustments for Spatial Field Trend. Biometrics, 57, 1138–1147. DOI: 10.1111/j.0006-341X.2001.01138.x

[5] Kelly, A.M., Smith, A.B., Eccleston, J.A., & Cullis, B.R. (2007). The Accuracy of Variety Selection Using Factor Analytic Models for Multi-Environment Plant Breeding Trials. Crop Science, 47, 1063–1070. DOI: 10.2135/cropsci2006.08.0540

[6] Crain, J., Mondal, S., Rutkoski, J., Singh, R.P., & Poland, J. (2018). Combining High-Throughput Phenotyping and Genomic Information to Increase Prediction and Selection Accuracy in Wheat Breeding. The Plant Genome, 11(1), 170043. DOI: 10.3835/plantgenome2017.05.0043

[7] Sandhu, K.S., Lozada, D.N., Zhang, Z., et al. (2021). Combining Genomic and Phenomic Information for Predicting Grain Protein Content and Grain Yield in Wheat. Frontiers in Plant Science, 12, 613300. DOI: 10.3389/fpls.2021.613300

[8] Guo, J., et al. (2020). Increased Prediction Accuracy Using Combined Genomic and Physiological Trait Information in Soft Wheat. Scientific Reports, 10, 4481. DOI: 10.1038/s41598-020-63919-3

[9] Dias, K.O.G., Guimarães, C.T., Schaffert, R.E., et al. (2018). Improving Accuracies of Genomic Predictions for Drought Tolerance in Maize by Joint Modeling of Additive and Dominance Effects in Multi-Environment Trials. Heredity, 121, 24–37. DOI: 10.1038/s41437-018-0053-6

[10] Cooper, M., Technow, F., Messina, C., Gho, C., & Totir, L.R. (2016). Use of Crop Growth Models with Whole-Genome Prediction: Application to a Maize Multi-Environment Trial. Crop Science, 56, 2141–2156. DOI: 10.2135/cropsci2015.08.0512