Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, i.e. ideal values of a set of plant traits resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of a performance criteria (e.g. yield, light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi-objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process-based crop model of sunflower and a functional-structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modeling approach, which identified paths for desirable trait modification, including direction and intensity. 1This is the post-print version of the manuscript published in Plant, Cell, and Environment (10.1111/pce.13001) 1 ar X iv :1 60 3. 03 23 8v 3 [ qbi o. Q M ] 1 9 Ju n 20 17 Introduction Using simulation models to optimize phenotype Global demand for agricultural products to supply food, feed, and fuel is rapidly increasing (Edgerton, 2009). One option to meet this growing agriculture need is to continue improving plant productivity per unit of cultivated land area. However, after decades of increase, many major crops have recently shown slower rates of yield improvement, stagnation, or even loss of productivity (Ray et al., 2012). This situation likely results from the negative effects of global climate change and societal prejudice that perceives environmental costs and limits agricultural resources, for example, public policies to reduce the use of chemicals in disease management programs (Sutton, 1996). Overcoming these challenges will require that breeders continue the genetic improvement of major crops accounting for changing agricultural practices towards sustainable production systems (Vanloqueren and Baret, 2009). In general, selecting plant traits associated with improvements in crop yield is difficult. Improvements at the organ or plant level must scale to the field level and these increases must not be gained at the expense of other traits that may ultimately offset yield advances (Sinclair et al., 2004). In addition, the specific environment where the crop is grown has a significant effect on yield. These genotype × environment (G × E) interactions require considerable experimental effort to identify the persistent traits that contribute to yield increases across many environments. The effort required is redoubled in pluri-annual crops where data, collected over changing environments, are difficult to interpret for complex phenotypes or at a fine scale. Computer-based modeling approaches have recently emerged as a method to save time, labor, and resources and to infer traits value beyond field experiments (Casadebaig, Zheng, et al., 2016 ; David Da Silva et al., 2014; Martre, He, et al., 2015). This computer-based strategy has been developed over the past two decades using a number of simulation models. These software models derive from mathematical equations that represent the biological processes that influence plant growth and development as a function of time, environment (climate, soil, and management), and genotype-dependent parameters. Those parameters are expected to be more heritable than complex traits, less prone to G x E interactions and to have a less complex genetic architecture (Heslot et al., 2014). These parameters also represent a range of functional traits, i.e any morphological, physiological, phenological or behavioral feature that is measurable at the individual level (Violle et al., 2007). In this case, simulation is used as a tool to predict trait × trait and trait × environment interactions when scaling from the individual plant to the field level. Depending on their structure, simulation models can be referred to as process-based crop models or functional-structural plant models. Process-based models are defined at the plot scale, often without an explicit representation of individual plants and focus on predicting crop performance, mainly harvestable organ yield or quality. Differences in the physiological framework (e.g radiation-based or water-based biomass production) lead to distinct families of process-based model that have been used worldwide (Brisson et al., 2003; Keating et al., 2003; Ritchie and Otter, 1985; Stockle et al., 2003). Such models are used to explore the G × E landscape and assist breeding programs by taking advantage of genetic and environmental resources (e.g. Chapman et al., 2003; Hammer et al., 2006; Jeuffroy et al., 2014). By contrast, functional-structural plant models particularly represent the plant structure (i.e. its topology and geometry) linked with the functions that allow the plant to interact with its environment, i.e. light interception, photosynthesis, carbon allocation, etc. (DeJong et al., 2011). Depending on the objectives, these models focus on specific plant structure such as trunk and wood (Nikinmaa et al., 2003) vegetative development (Costes et al., 2008; Fournier and Andrieu, 1999; Lopez et al., 2008), or fruit development (Allen et al., 2005). The concept of ideotype describes the idealized realization of a plant phenotype, “a biological model which is expected to perform or behave in a predictable manner within a defined environment” (Donald, 1968). This definition provides the breeder with a guide for characterization of cultivar by identifying and selecting for particular features in progenies. Model-assisted phenotyping and ideotype design is a research domain with recent developments (Martre, Bénédicte Quilot-Turion, et al., 2015). These advances formulates ideotype design as an optimization of model inputs related to plant traits (David Da Silva et al., 2014; Ding et al., 2016; Paleari et al., 2015; Quilot-Turion et al., 2012; Semenov et al., 2014; Semenov and Stratonovitch, 2013), allelic combinations (e.g. Letort et al., 2008; Quilot-Turion et al., 2016), or management options (Grechi et al., 2012; Wu et al., 2012). These approaches have been used for different goals, including understanding crop adaptation to climate change (Paleari et al., 2015;