Modelling selection response in plant breeding programs using crop models as mechanistic gene-
to-phenotype (CGM-G2P) multi-trait link functions
Cooper M
1*
, Powell O
1
, Voss-Fels KP
1
, Messina CD
2
, Gho C
2
, Podlich DW
2
, Technow F
3
, Chapman SC
4
,
Beveridge CA
5
, Ortiz-Barientos D
5
, Hammer GL
1
1
Queensland Alliance for Agriculture and Food Innovation (QAAFI), The University of Queensland,
Brisbane, Qld 4072, Australia
2
Corteva Agriscience, Johnston, Iowa 50131, USA
3
Corteva Agriscience, Tavistock, ON N0B, Ontario, Canada
4
School of Agriculture and Food Sciences, The University of Queensland, Brisbane, Qld 4072,
Australia
5
School of Biological Sciences, The University of Queensland, Brisbane, Qld 4072, Australia
* Corresponding Author: Mark Cooper, mark.cooper@uq.edu.au
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Abstract
Plant breeding programs are designed and operated over multiple cycles to systematically change
the genetic makeup of plants to achieve improved trait performance for a Target Population of
Environments (TPE). Within each cycle, selection applied to the standing genetic variation within a
structured reference population of genotypes (RPG) is the primary mechanism by which breeding
programs make the desired genetic changes. Selection operates to change the frequencies of the
alleles of the genes controlling trait variation within the RPG. The structure of the RPG and the TPE
has important implications for the design of optimal breeding strategies. The breeder’s equation,
together with the quantitative genetic theory behind the equation, informs many of the principles
for design of breeding programs. The breeder’s equation can take many forms depending on the
details of the breeding strategy. Through the genetic changes achieved by selection, the cultivated
varieties of crops (cultivars) are improved for use in agriculture. From a breeding perspective,
selection for specific trait combinations requires a quantitative link between the effects of the alleles
of the genes impacted by selection and the trait phenotypes of plants and their breeding value. This
gene-to-phenotype link function provides the G2P map for one to many traits. For complex traits
controlled by many genes, the infinitesimal model for trait genetic variation is the dominant G2P
model of quantitative genetics. Here we consider motivations and potential benefits of using the
hierarchical structure of crop models as CGM-G2P trait link functions in combination with the
infinitesimal model for the design and optimisation of selection in breeding programs.
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Introduction
Plant breeding programs are designed to develop improved cultivated varieties (cultivars) of crops
for use in agriculture. They have a long history and have served an important role in improving crop
productivity (Allard 1960, 1999, Wricke and Weber 1986, Fehr 1987a,b, Hallauer and Miranda 1988,
Blum 1988, Cooper and Hammer 1996, Bernardo 2002, Duvick et al. 2004, Fischer et al. 2014, Smith
et al. 2014, Hammer et al. 2019, Voss-Fels et al. 2019a). Through the iterative cycles of breeding
programs, plant breeders utilise the accessible genetic variation for traits, available through elite
germplasm and other genetic resources, to improve the genetics of multiple traits of crop cultivars
(Figure 1, Table 1). Today many technologies can be applied to change the genetic content of plants
and discover new pathways for trait improvements (Tester and Langridge 2010, Morrell et al. 2012,
Wallace et al. 2018, Bailey-Serres et al. 2019). Here we will focus our considerations on the genetic
improvement of traits by directional selection within the context of plant breeding programs (Figure
1; Cooper et al. 2014, Walsh and Lynch 2018). Selection for cultivar performance and breeding value
has been the foundation for long-term genetic improvement of crops (Duvick et al. 2004, Smith et al.
2014, Walsh and Lynch 2018, Voss-Fels et al. 2019a). For purposes of discussion, crop grain yield will
be considered as the ultimate trait of interest (Evans 1993, Fischer et al. 2014). Importantly, grain
yield is a multi-trait outcome of crop growth and development processes and responses to diverse
environmental conditions (Evans 1993, Cooper and Hammer 1996, Messina et al. 2009, Connor et al.
2011, Fischer et al. 2014). Within this context we argue that the crop sciences (Messina et al. 2020)
together with advances in plant and crop models have the potential for important new roles in
improving the design and effective operation of breeding programs within the context of the future
needs for crop improvement (Hammer et al. 2019, 2020). To realise these opportunities plant and
crop models will have to be designed to take advantage of advances in understanding of trait genetic
architecture and the principles of quantitative genetics (Cooper et al. 2002a,b, 2005, 2009, Hammer
et al. 2006, 2019). Here we introduce a quantitative genetics perspective of approaches for linking
trait genetic models with mechanistic crop models to enhance our understanding of the genetic
architecture of complex traits, such as grain yield of crops, and to explore new prediction
applications for breeding.
While we focus on plant breeding programs, it is understood that they do not operate in isolation to
achieve sustainable improvements in on-farm crop productivity. Successful crop improvement
programs combine the genetic improvement outcomes from breeding programs with the
recommendations from agronomy research to deliver on-farm improvements in crop productivity
(e.g., Duvick et al. 2004, Hammer et al. 2014, Fischer et al. 2014, Messina et al. 2020, Cooper et al.
2020). Thus, breeding programs and agronomy research programs are strongly interdependent.
However, within the dominant crop improvement paradigm of today they operate sequentially,
typically with limited or loosely coupled levels of integration. Within this sequential approach,
breeding programs first develop new crop cultivars, arguably with limited attention to sampling the
full range of agronomic management possibilities used by farmers. Then agronomic research
programs follow, focussing on the development and optimisation of crop management strategies for
the new cultivars. Both plant breeders and agronomists are interested in traits and how they
contribute to on-farm crop productivity through improved yield, yield stability, grain nutrition for
human and animal consumption and grain quality for many commercial uses. However, they differ in
the types of models they use to study traits for such common objectives. We consider how
mechanistic crop models can be developed to connect the modelling objectives of plant breeding
and quantitative genetics with those of crop agronomy for important traits contributing to grain
yield potential and yield stability (Cooper et al. 2009, Hammer et al. 2019, Messina et al. 2020).
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Mechanistic crop models have a long history of development (Holzworth et al. 2014, Jones et al.
2016) and have been used for many applications to support agronomy research. However, in
contrast, for plant breeding there has been much less consideration of the potential applications of
mechanistic crop models to study traits. Nevertheless, given the long-term nature of breeding
programs, there has been parallel interest in applications of simulation methods for modelling plant
breeding programs (Podlich and Cooper 1998, Cooper et al. 2002a,b, Li et al. 2012, Bernardo 2020).
Here, the statistical gene-to-phenotype (G2P) models of quantitative genetics are used to study and
represent the genetic architecture of traits and the effects of genes on trait variation (Falconer and
Mackay 1996, Lynch and Walsh 1998, Walsh and Lynch 2018). However, to date these quantitative
genetic models of trait genetic architecture have received little attention in agronomy research and
in the development of mechanistic crop models. These differences in trait modelling approaches can
create barriers to their integration for accelerated crop improvement. However, understanding their
potential connections creates new opportunities (e.g., Cooper et al. 2002a,b, 2005, 2016, Chapman
et al. 2002, 2003, Hammer et al. 2006, 2019, Chenu et al. 2009, 2017, 2018, Messina et al. 2011,
2018, Technow et al. 2015, Onogi et al. 2016, Bustos-Korts et al. 2019a,b, Peng et al. 2020). Here we
provide an overview of the progression from the trait G2P models of quantitative genetics to
applications using mechanistic crop models (CGM-G2P). The review is orientated from a perspective
of seeking opportunities to use crop models with quantitative genetics to integrate plant breeding
and agronomy to enhance prediction of crop improvement outcomes.
The overarching objective of the manuscript is to demonstrate how an integrated crop improvement
strategy, based on trait genetics, crop physiology, breeding and agronomy, can be enabled if we can
use CGM-G2P multi-trait link functions within the framework of quantitative genetics for design and
operation of plant breeding programs. The manuscript provides: (1) an introduction to the breeder’s
equation and the infinitesimal G2P model of trait genetic architecture that are widely applied in
quantitative genetic theory to model plant breeding programs, (2) possible extensions of the
infinitesimal model of quantitative genetics using the hierarchical structure of crop growth models
(CGM-G2P), (3) demonstration of applications of the hierarchical CGM-G2P models to plant
breeding, and (4) discussion of the implications CGM-G2P models for plant breeding.
Modelling Plant Breeding Programs
The objectives of breeding programs are defined in terms of trait targets for genetic improvement
(Figure 1a). The targets are based on the required combinations of plant traits for superior
performance of a new cultivar and also the current levels of the traits possessed by the cultivars that
are to be replaced by the new products of breeding programs (e.g., Hallauer and Miranda 1988, Fehr
1987a,b, Bernardo 2002). The trait targets for a new cultivar may be defined in terms of specific
levels of expression of the trait phenotype. For example, a specific threshold level of disease
resistance, drought tolerance and grain quality may be required for a cultivar to be useful for the
production systems of farmers. Alternatively, the targets can be defined in terms of levels of trait
phenotypes that are superior to those of the dominant cultivars currently in use by farmers.
Combinations of both approaches are common; e.g. create cultivars with new combinations of
disease resistance genes, 5% improved grain yield under defined drought conditions and 5% reduced
post-harvest storage and processing costs compared to a given cultivar. To achieve these objectives
plant breeders design and operate breeding programs over multiple cycles (Figure 1b). The breeding
programs use selection, in combination with segregation and recombination of the alleles of the
genes controlling the traits, to create the targeted change in genetic control of traits. The genetic
basis of the change enabled by selection is achieved by increasing the frequencies of favourable
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alleles and creating new combinations of the favourable alleles across all of the genes that
contribute to the control of variation for the target traits and which are polymorphic within the
reference population of genotypes (RPG). The genetic changes required to move from the current
genotypes to the improved target genotypes can be modelled in terms of genetic trajectories in
multi-dimensional G2P space (Podlich and Cooper 1998, Gavrilets 2004, Walsh and Lynch 2018).
Based on selection theory, a genetic trajectory is achieved by changing the frequencies of the
favourable alleles of the genes within the RPG, which in turn enables the creation of new genotypes
through assembling new combinations of the alleles across many genes (e.g., Falconer and Mackay
1996, Podlich and Cooper 1998, Hammer et al. 2006, Messina et al. 2011, Walsh and Lynch 2018).
Depending on the trait and structure of the RPG, the numbers of genes, or Quantitative Trait Loci
(QTL), involved in the genetic architecture of a trait have been estimated to range from few to many
hundreds (e.g., Barton and Keightley 2002, Cooper et al. 2005, Boer et al. 2007, Buckler et al. 2009,
Mace et al. 2019, Wang et al. 2020). Quantitative genetics provides the theoretical framework and
methods for modelling the genetic trajectories that underlie the genetic improvement enabled
through a breeding program (Falconer and Mackay 1996, Lynch and Walsh 1998, Walsh and Lynch
2018, Wisser et al. 2019). Thus, to model breeding programs it is necessary to be able to model trait
genetic architecture, trait G2P relationships, and how selection brings about genetic change for
traits within the context of the structured RPG of the breeding program.
To assess contributions of allele effects to the selection response for a trait in breeding applications
requires consideration of the breeder’s equation in combination with three breeding concepts
(Figure 1, Table 1): Germplasm, the Target Population of Environments (TPE), and Trait Product
Profiles. Germplasm represents the structured pools of genetic resources that are available to the
breeder, and the organisation of the genetic diversity available through the germplasm (standing
genetic diversity) into the RPG used in the breeding program. The TPE represents the mixture of
environment-types for which cultivar performance is evaluated and targeted. Trait Product Profiles
represent the important trait targets required by cultivars to achieve improved performance within
the TPE. This “breeding trinity” sets the scene for the operation of the breeding program. Together
the germplasm and the TPE determine the biophysical properties and genotype-by-environment-by-
management (GxExM) context of the agricultural system within which the breeding program
operates (Messina et al. 2009, Cooper et al. 2020). The Trait Product Profiles identify the targets for
genetic improvement of crops. The breeder’s equation quantifies the speed with which the Trait
Product Profiles can be achieved by the breeding program using selection applied to the standing
genetic variation that is accessible to the breeder within the RPG.
New genotypes are created over breeding program cycles by manipulating, selecting and
recombining trait genetic variation within the context of the genetic diversity for a RPG (Figure 1b).
Trait performance for the new genotypes is measured and evaluated within the context of the range
of environmental conditions expected for a TPE (Figure 1b). Breeding programs are conducted for
multiple cycles (Figure 1b). Each cycle produces a new cohort of cultivars. The Target Product
Profiles are rarely achieved in one cycle of a breeding program. Thus, the products of the breeding
program cycles provide a continuous sequence of new cultivars with progressively improving trait
performance for the TPE, moving towards the Target Product Profiles (e.g., Duvick et al. 2004, Smith
et al. 2014, Atlin et al. 2017, Voss-Fels et al. 2019a). When the new cultivars are widely grown by
farmers throughout the TPE they can contribute to improved crop productivity (Fischer et al. 2014,
Atlin et al. 2017, McFadden et al. 2019). We also note that the Target Product Profiles of a breeding
program are rarely static. They change as the conditions of agricultural systems and needs of society
change.
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