Crop growth models dynamically simulate processes of C, N and water balance on daily or hourly time-steps to predict crop growth and development and at season-end, final yield. Their ability to integrate effects of genetics, environment and crop management have led to applications ranging from understanding gene function to predicting potential impacts of climate change. The history of crop models is reviewed briefly, and their level of mechanistic detail for assimilation and respiration, ranging from hourly leaf-to-canopy assimilation to daily radiation-use efficiency is discussed. Crop models have improved steadily over the past 30–40 years, but much work remains. Improvements are needed for the prediction of transpiration response to elevated CO2 and high temperature effects on phenology and reproductive fertility, and simulation of root growth and nutrient uptake under stressful edaphic conditions. Mechanistic improvements are needed to better connect crop growth to genetics and to soil fertility, soil waterlogging and pest damage. Because crop models integrate multiple processes and consider impacts of environment and management, they have excellent potential for linking research from genomics and allied disciplines to crop responses at the field scale, thus providing a valuable tool for deciphering genotype by environment by management effects.
Crop production models simulate plant and soil processes based on principles of plant physiology, soil science and climatology (Loomis, Rabbinge & Ng 1979). Using daily or hourly time-steps, they dynamically simulate how a community of plants responds to environment and management over time with given genetic traits (Fig. 1). Mathematically, they integrate a series of rate equations such as those described in Wilkerson et al. (1983). Their field-scale or community perspective is explicit in their quantification of solar radiation interception, photosynthesis, transpiration, respiration and growth on a land-area basis. Most models are source-driven, thus assuming that growth is limited by the supply of assimilate (Sinclair & Jamieson 2006). Crop carbon balance is enforced by balancing gains from assimilation against losses through respiration (as CO2) and abscission of plant tissues. Plant and soil N balances are similarly calculated. The integrated crop-soil models honour water balance on a land-area basis, considering inputs of water versus losses of water to transpiration, soil evaporation, runoff and deep drainage. Stomatal conductance and ‘trading’ of transpired water for CO2 uptake is an integral part of the process of water and energy balance. Lastly, crop models simulate crop phenology and partitioning, and integrate processes of C, N and water balance from planting to maturity, giving final yield and production as well as daily values of crop components over time to maturity.
Historical perspective and types of models
Crop modelling had its early origins with scientists such as C. T. de Wit (1965), J. L. Monteith (1965), W. G. Duncan (Duncan, 1971, Duncan et al. 1967) and R.S. Loomis (Loomis et al. 1979). Early models focused on leaf to canopy assimilation, with emphasis on light interception and canopy architecture. Subsequent modelling efforts progressed to develop whole crop models where life cycle prediction, life-long C balance and growth of different organs were emphasized (Hesketh, Baker & Duncan 1971, 1972; Baker, Hesketh & Duncan 1972). By 1974, Duncan had developed crop models for cotton, peanut, soybean and maize, and in 1978, de Wit and colleagues published a monograph describing the generic crop model BACROS (De Wit 1978).
The approaches to modelling growth of different organs varied from attempting to model individual sink strength of all organs on the plant along with mass flow through phloem, to simple fractional partitioning on a daily basis. The SOYMOD model (Meyer et al. 1979) was among the early mechanistic models. It contained detailed mechanisms for leaf-level photosynthesis, mass flow of phloem and individual sink-strength of organs. Phloem movement per se was easily simulated, but there were major problems and empiricisms in defining the sink strength of the different organs (leaves, petioles, roots, nodules, pods and seeds) on the unloading side of the mass flow phloem system. For example, root growth in the SOYMOD model persisted up to maturity when the expectation was that root growth should halt as rapid seed growth began. Several other early models, SIMCOT (Hesketh et al. 1971, 1972; Baker et al. 1972) and GOSSYM (Baker, Lambert & McKinion 1983; Reddy, Baker & Jenkins 1985) allocated assimilate based on sink strength of individual organs. The requirement to define sink strength of individual leaves, petioles, stem internode segments, roots, cotton bolls and individual seeds, led researchers to collect field samples of individual organs indexed by canopy position. The most vexing problem was how to prioritize allocation of assimilate to organs when vegetative and reproductive organs were present at the same time. Forty years later, accurate prediction of differentiation of tissues and resulting tissue sink strengths remains problematic. As a consequence, many models predict partitioning as an empirical function of crop developmental stage, mixed with simple logic such as giving reproductive organs highest priority for assimilate. For example, the SUCROS and MACROS family of crop models developed between 1981 and 1989 included tables of input parameters that quantified partitioning as a function of growth stage (Penning de Vries et al. 1989; Spitters, Keulen & Kraalingen 1989). This approach is continued in later, derived models such as WOFOST. The partitioning table approach requires collecting data on apparent fraction of dry matter partitioned to different organs as a function of crop life cycle but does not require tagging of individual organs in order to estimate growth rates. Other crop modellers (Wilkerson et al. 1983; Boote, Jones & Hoogenboom 1998) implemented hybrid approaches that used partitioning tables for vegetative growth, but tracked cohorts of reproductive structures (pods and seeds). The reproductive sites are assigned explicit sink strengths for C and N, they are given priority over vegetative tissues, and new sites continued to be added until the crop reaches its carrying capacity at which point vegetative growth completely ceases. Throughout that later phase, addition and growth of those reproductive structures can be co-limited by supply (source) and sink requirements (co-limited models) or just driven by assimilate supply (source-driven model). Most models describe pools of available N that can be mobilized to seed under defined rules, usually with requirement to maintain N concentration of seeds, and with acceleration of N mobilization linked to presence of reproductive sink demand for N.
Modelling Crop Development
Capturing the plant life cycle
Accurate prediction of temperature and daylength effects on development is essential for ensuring that key transitions of vegetative and reproductive growth phases occur at the correct time. Early models predicted crop development poorly, and it was well into the 1980s and 1990s before robust modules for phenology (Hadley et al. 1984; Ritchie, Godwin & Otter-Nacke 1985a, 1985b; Kiniry & Bonhomme 1991; Grimm et al. 1993, 1994; Ritchie et al. 1998; Jamieson et al. 2007) were created. Even now, the most important parameters to set when modelling a new cultivar are those affecting crop development and phenology.
Timing of key events such as floral initiation, anthesis and physiological maturity are usually predicted by integrating a developmental rate, R, over time. Models usually assume that a potential rate of development, Rpot, is modified by individual environmental factors,
where T is the primary temperature effect, P is the effect of photoperiod and V to Z optionally describe effects of vernalization or of specific abiotic stresses that may accelerate or delay development. The vernalization effect, if present, varies with temperature but operates independently of the main temperature effect. R is integrated over intervals defined by the two stages that delimit a given phase. The duration of the phase may be expressed in various types of units but most often is expressed in thermal time (TT) or a proxy such as leaf number. There remains large uncertainty over the shape of the temperature response functions (White et al. 2012b), correct values of cardinal temperatures, what temperature is most useful for predicting phenology (crown, shoot apical, canopy or air), and what time scale to use (daily versus hourly or less) (Porter & Gawith 1999). These uncertainties in shape, cardinal temperatures, tissue, and time scale are important because they affect crop life cycle progression under diverse and future climate conditions. Similar uncertainty is associated with functions for photoperiod, vernalization and other factors.
Improving predictions of crop development
While phenology is predicted surprisingly well using degree-day approaches based on mean air temperature and species cardinal temperatures (Ritchie et al. 1985a, 1985b; Ritchie 1998; Keating et al. 2003), the true physiological responses may be more complex. Furthermore, cardinal temperatures may differ for vegetative and reproductive development, as shown for soybean (Boote et al. 1998) and maize (Stewart, Dwyer & Carrigan 1998). Water deficit during vegetative growth can slow leaf appearance rate and delay onset of anthesis-reproductive in many crops, whereas water deficit during the reproductive phase accelerates maturation and senescence (Specht, Williams & Weidenbenner 1986; DeSouza, Egli & Bruening 1997). In faba bean (Vicia faba), water stress accelerates onset of reproductive growth as well as final maturity (Sau & Minguez 2000). In maize, excess soil moisture can delay flowering and increase anthesis-silking interval (Lizaso & Ritchie 1997; Zaidi et al. 2004). Nutrient deficiencies (N, P and K) and low irradiance can likewise prolong vegetative development, thus delaying onset of reproductive, while the same stresses may accelerate reproductive maturation (Singh et al. 1999).
Daylength is an important seasonal factor that influences reproductive development in photoperiod-sensitive plants. Photoperiod response is generally modelled with acceptable accuracy, but there is a need to improve the mechanisms to account for the level of actions at genes and gene expression. The present procedure of taking measurements in sowing date, latitude or phytotron experiments to estimate photoperiod response is inefficient for characterizing new cultivars, but gene-based estimation of cultivar responses is feasible (Hoogenboom et al. 1997; Messina et al. 2006; White et al. 2008).
Modelling Growth and Yield
Simulating leaf area
Early efforts to simulate leaf area index (LAI) and its decline were rather empirical, using polynomial (Hunt & Parsons 1974) or logistic-type functions (Baker, Horrocks & Goering 1975; Dale, Coelho & Gallo 1980) to describe canopy expansion. Nevertheless, a very detailed model of leaf growth was available as early as 1979 (Charles-Edwards 1979). Many crop simulation models, including CERES (Ritchie 1998), CropSyst (Stockle, Donatelli & Nelson 2003), STICS (Brisson et al. 1998) and Sirius (Jamieson et al. 1998) simulate leaf area per plant with allometric equations as a function of heat unit accumulation, but multiplied by plant density to scale to a canopy basis. Alternatively, a number of reports describe expansion and senescence of successively formed individual leaves (also scaling this up to whole plant and canopy leaf area), for maize (Stewart & Dwyer 1994; Birch, Hammer & Rickert 1998; Lizaso, Batchelor & Westgate 2003), wheat (Porter 1984), potato (Fleisher & Timlin 2006) and sunflower (Dosio et al. 2003). Figure 2 illustrates LAI simulations for irrigated and rainfed maize, employing simulation of leaf area of successively formed leaves with the IXIM-maize model (Lizaso et al. 2003, 2011). Tillering (e.g. new ‘plant units’) is considered in some of the models. Simulation approaches vary from those that assume leaf area is sink-limited, temperature-driven and scaled by potential leaf size (Stewart & Dwyer 1994), to those assuming a source limitation where daily leaf mass growth is converted to leaf area (Penning de Vries et al. 1989) using a constant or variable area-to-mass ratio (cm2 g−1), the specific leaf area. Other models describe the three dimensional (3-D) growth of organs (Fournier & Andrieu1998; Ruiz-Ramos & Minguez 2006) by applying concepts of Lindenmayer (1968) systems.
Effect of climatic factors, water, assimilate supply and N on leaf growth
Leaf expansion is highly sensitive to temperature (Rawson & Hindmarsh 1982; Fournier & Andrieu 1998), as studied under controlled temperatures in growth chambers (Thiagarajah & Hunt 1982) and under fluctuating air temperatures in the field (Robertson et al. 1998). From these studies emerge quite distinct responses of plant species in terms of optimum, maximum and minimum temperatures for leaf growth. Recently, Parent et al. (2010) unveiled a common pattern of temperature response for leaf area growth processes of 18 species, when responses are normalized to those rates at 20 °C. This strongly points to the possibility of simplifying modelled crop temperature effects on leaf area expansion.
No uniform consensus has emerged from research on the impact of elevated CO2 on leaf area. Kimball, Kobayashi & Bindi (2002) reviewing results of free air CO2 enrichment (FACE) experiments reported an increase in peak LAI in wheat, ryegrass and rice under good growing conditions (mean 11%), but no increase in LAI for sorghum. Masle (2000) reported an increase (39–82%) in wheat leaf area in response to 2.5-fold increase in CO2. Taylor et al. (2001) showed consistent increases in leaf area of poplar to elevated CO2 in FACE experiments. Accelerated senescence has been reported for maize (Manderscheid, Erbs & Weigel 2012) and sorghum (Ottman et al. 2001) in FACE conditions, possibly due to elevated canopy temperature.
In order to expand leaf tissue, plants must maintain adequate flows of water, energy, C skeleton, and nutrients. Given the key role of leaves in capturing radiant energy and providing new C, the question arises as to how restrictive is the assimilate supply upon leaf expansion. The issue may be complicated by day/night cycles (Salah & Tardieu 1997). Research on Arabidopsis sp. (Pantin et al. 2011), tomato (Bertin & Gary 1998) and wheat (Rodriguez, Andrade & Goudriaan 2000) suggests that C supply may limit leaf expansion mostly at night and in the early phases of leaf area expansion. The mechanism would allow maintaining leaf growth under low light conditions.
The expansion of new cells in leaf meristems results from the combined contributions of hydraulic and metabolic forces (Pantin et al. 2011). The hydraulic component balances the soil available water and the atmospheric demand (Chenu et al. 2008), while the metabolic processes rely on C supply (Pantin et al. 2011), cell wall enzyme activity (Bacon 1999) and biochemical signals such as ABA (Pantin et al. 2013). Crop models handle water dynamics in a much simpler way. Most models reduce leaf expansion under soil water deficit using several procedures to estimate the ratio of soil water supply to crop water demand (Ritchie et al. 1998). The same method is employed for the simulations in Figure 2, which show water deficit effects on LAI as well as biomass and yield. Some models incorporate the effect of vapour pressure deficit (VPD) to account for atmospheric demand (Stockle et al. 2003).
The response of leaf expansion to N nutrition and N stress may exhibit differences across species. Vos identified contrasting behaviour between the ‘potato strategy’ where leaf size is reduced to maintain N concentration and photosynthetic capacity per unit leaf area (Vos & van der Putten 1998), compared to the ‘maize strategy’ where leaf size and light capture are prioritized at the expense of N concentration and photosynthetic capacity (Vos, van der Putten & Birch 2005). These differences are relevant considering that many simulation models reduce leaf growth in a similar way, by computing a ratio of soil N supply to crop N demand (Godwin & Singh 1998; Stockle et al. 2003).
Radiation use efficiency (RUE)-based methods for assimilation
Because of the complexities inherent in predicting leaf-to-canopy assimilation as well as growth and maintenance respiration, many models predict net dry matter assimilation as a function of RUE and light interception (Monteith 1977, Monteith, 1994), thus avoiding photosynthesis, growth and maintenance respiration issues (Ritchie et al. 1985b; Sinclair & Amir 1992; Jamieson et al. 1998; Ritchie 1998; Brisson et al. 2003; Jones et al. 2003; Keating et al. 2003; Nendel et al. 2011). The approach is based on work by John Monteith (1977) who found that for C-3 crops grown without stress in Britain, seasonal aboveground biomass accumulation increased linearly with intercepted solar radiation, the slope of the relation thus being RUE in g MJ−1.
RUE-based models typically model leaf area development as a function of TT (expressed as rate of leaf appearance and increase in size of successive leaves until a given leaf position). The resulting LAI (from leaf area per plant and plant density) is then used to calculate light interception. Daily dry matter accumulation is the daily radiation integral multiplied by fraction light interception and RUE. The simplicity of this approach is attractive, as is the easy capability to measure rate of leaf tip appearance, light interception and total dry matter accumulation in field studies. A reference RUE is considered to be constant (Sinclair & Muchow 1999). The actual daily RUE is adjusted for non-optimum temperatures, limiting water and limiting N (Ritchie et al. 1985b; Sinclair & Amir 1992; Jamieson et al. 1998; Ritchie 1998). In addition, models may increase RUE of C-3 species under low light conditions to account for higher fraction of diffuse light with lower intensity (Ritchie et al. 1985b). Other aspects such as life cycle, partitioning and yield formation are often similar across all crop models whether using RUE or more mechanistic leaf-to-canopy scaling of assimilation.
Scaling up from leaf to canopy assimilation
Efforts to scale leaf-based assimilation to the crop canopy commenced with de Wit (1965) and Duncan et al. (1967), but the accuracy and correct methodologies were difficult to assess because of limited field data on leaf and canopy-scale CO2 fluxes. The first limitation is the requirement for detailed gas exchange data to parameterize the models. Another requirement is the accurate prediction of LAI over time, and degree of linkage to photosynthesis as the driver. Parameterization issues have been partly resolved by an explosion of measurements of leaf photosynthesis and enzyme responses to environment, as well as characterizations of leaf biochemistry and canopy architecture/light intercepting structures. This was facilitated by increased numbers of scientists and improved instrumentation. In addition, ground-breaking physiological research led to more universal ways to describe basic C-3 and C-4 photosynthesis (Farquhar & Caemmerer 1982; Caemmerer 2000). Their theories along with experimental measurements illustrated that leaf photosynthesis is a relatively conserved process (across plant species) that originates with electron transport efficiency of the photosystems and the nature of rubisco enzyme function, such that quantum efficiencies of C-3 and C-4 photosynthesis are highly predictable and, in the absence of stresses, are nearly constant at defined temperature, oxygen and atmospheric CO2 levels. While there are many methods and equations for predicting light-saturated rate of leaf photosynthesis, the basic question comes down to how to predict the amount of rubisco enzyme and electron transport system per unit leaf area as a function of leaf N concentration and leaf mass per unit leaf area and how these relations change with leaf age. This will capture the majority of the photosynthetic response to leaf N, although there are variations in the partitioning of N among leaf proteins attributed to species variation, to photosynthetic acclimation to CO2 and to shade acclimation.
Current crop models with leaf-to-canopy assimilation modules are now generally stable in prediction and function, and parameters for single leaf assimilation can be scaled up to accurately predict canopy assimilation. The successes have revealed important principles that include (1) use of sunlit and shaded leaf approaches for allocation of light distribution to multilayered leaves, because ‘big-leaf’ models are not adequate, (2) use of single leaf-light-response equations that capture the rubisco-kinetics and have definable parameters connected to light-and-CO2-saturated leaf photosynthesis (Amax) and initial quantum efficiency (QE), and (3) connection of rubisco and electron transport capacity to leaf N concentration (and content) in such a way that crop N nutrition status, leaf vertical position in canopy, leaf aging, and crop aging have the correct effects on leaf photosynthesis and canopy assimilation (Boote & Pickering 1994; dePury & Farquhar 1997; Lizaso et al. 2005a, 2005b, 2011; Alagarswamy et al. 2006; Bondeau et al. 2007; Müller, Braune & Diepenbrock 2009; Tao, Yokozawa & Zhang 2009). Required model parameterization includes leaf-level photosynthesis response to photosynthetic photon flux density, temperature, CO2, leaf N and leaf age. Parameters such as QE in low light can be considered constants (Ehleringer & Bjorkman 1977), and rubisco competitiveness for CO2 versus O2 is considered conservative and repeatable for C-3 versus C-4 species (Farquhar & Caemmerer 1982). The Ball-Berry leaf conductance model (Ball 1987; Collatz et al. 1991) is often used to link stomatal conductance to CO2 to leaf-level conductance to water vapour. There are additional complexities to scale this to prediction of canopy conductance and temperature, especially considering the plant water status relative to root water uptake.
Experimental measurements are essential for developing, parameterizing and testing of the scaling from leaf-level processes to canopy assimilation. Testing simulations of canopy assimilation requires canopy assimilation measurements with controlled-environment chambers (Jones et al. 1984; Baker et al. 1990), field-portable systems (Bourgeois & Boote 1992; Pickering, Jones & Boote 1993) or non-invasive, field eddy-flux experiments (Rochette et al. 1996; Lizaso et al. 2005b; Bernacchi et al. 2007). These flux measurements require interpretation of what is being measured because there are multiple fluxes of CO2 to and from the crop and soil in the field. Total crop dry matter accumulation over time is an important secondary test of the correctness of scaling from leaf to canopy assimilation, but such tests still require assumptions concerning crop respiration and the composition of organs being grown.
For mechanistically detailed models, carbon gains through photosynthesis must balance losses from respiration and abscission. The metabolic cost of growing new tissue is usually simulated as ‘growth respiration,’ whose magnitude is a function of the biochemical composition of the new tissue. Costs of biosynthesis for lipid or protein-rich tissue are much larger than for tissues composed mainly of lignocellulose or starch (Penning De Vries, Brunsting & Van Laar 1974). Growth respiration efficiency is considered insensitive to temperature and other environmental factors (McCree 1974, McCree, 1982, McCree & Silsbury 1978). Amthor (2003) used a detailed analysis of alternative lignin synthesis pathways to argue that genetic differences might be exploited to improve growth efficiency.
The other component of respiration that models recognize is maintenance respiration, which concerns the metabolic cost of maintaining basic tissue integrity over time (Penning de Vries 1975) and involves turnover of proteins and lipids, maintenance of ion gradients across membranes, and processes of acclimation, all of which require metabolism but do not involve dry matter gain. There is much uncertainty in the magnitude of maintenance respiration, especially for high lignin-high cellulose tissues in vegetative organs versus high starch, oil or protein compounds in seeds. Early research demonstrated that maintenance respiration increased with temperature and that less active, mature or senescing tissues exhibited lower maintenance respiration than younger tissues (McCree 1974, McCree, 1982, McCree & Silsbury 1978).
Crop modelling will benefit from additional research and interpretation of measurements of total crop respiration, and the solving of maintenance respiration as a degree of freedom left while predicting dry matter accumulation. Experience with soybean, peanut and maize models (Bovi 1983; Boote & Pickering 1994; Lizaso et al. 2005b, 2011) indicates that the crop C balance is predictable and agrees within about 10% of observed dry matter growth for those case comparisons, starting with leaf-to-canopy assimilation, combining growth respiration methods of Penning de Vries et al. (1974) with general approaches of maintenance respiration.
Crop models as tools for integrating effects of many processes upon growth and yield
A strength of crop models is that they integrate multiple physiological processes to account for many important influencing factors. With the level of maturation of current models, most of these processes are at least already covered, albeit somewhat superficially in some cases. This is an advantage in evaluating genetic trait effects, as the models become tools that allow an individual discipline scientist to improve models for the processes they are interested in, while assuming that the other processes are addressed by other scientists. Crop model improvement in this sense can be uneven, with improvement in some processes but not in others, often depending on interests of participating scientists. From an overall crop systems viewpoint, neglected topics for modelling include root systems, soil fertility and waterlogging. Notice that these are below-ground and soils-related issues. Another insufficiently explored area involves effects of diseases and insects. Model improvement in these two areas will require expertise of soil scientists, pathologists and entomologists, but this is of increasing interest as research concerns have begun to shift towards understanding how low soil fertility and greater disease and pest pressure impact crop growth. By contrast, crop physiology-related mechanisms are reasonably well represented in crop models.
One of the advantages of mechanistic models is that they predict intermediate outputs of various processes, which can then be compared to intermediate measurements. For example, with an hourly time-step model, one can evaluate leaf-level photosynthesis as well as canopy assimilation and transpiration as illustrated by Lizaso et al. (2005a, 2005b) who included a leaf to canopy level assimilation module in the IXIM-Maize model (Lizaso et al. 2011), thus replacing the RUE approach of CERES-Maize. Figure 3 shows diurnal simulation by the IXIM-Maize model of canopy assimilation throughout a day by comparison to field-measured canopy assimilation. This illustrates the concept of improving individual processes in a model without losing ability to predict the overall season-long growth, as IXIM is actually better than CERES-Maize in predicting time-course of dry matter in biomass and grain and its carbon balance (Lizaso Oñate et al. 2008; Lizaso et al. 2011). See root mean squared error and maize model comparisons in Figure 2. In another example, Boote et al. (2009) tested the N-fixation aspects of the CSM-CROPGRO-Soybean model by comparison to instantaneous acetylene reduction estimates of N-fixation, and showed generally accurate prediction of N-fixation sensitivity to water deficit, increased light, shading, depodding and life cycle.
Inclusion of other nutrients, such as P uptake and response to P-deficient soils and P fertilization into APSIM (Keating et al. 2003) and the DSSAT crop models (Daroub et al. 2003; Dzotsi et al. 2010) are examples of adding new features to existing crop models, where the modelling framework was already in place. The dynamic P processes in the soil also required, in DSSAT, the use of the CENTURY soil organic matter model (Gijsman et al. 2002) as well as soil chemistry related to inputs of soil test P-values. Addition of sensitivity of growth and transpiration of common bean to soil salinity in the CROPGRO model (Webber et al. 2010) or waterlogging to the soil water routine in APSIM (Asseng et al. 1997) are additional examples of adding new features to existing models.
Improvement of root growth response to edaphic conditions of soil is another potential area for model improvement. Most models have functions to predict root growth and distribution in the soil, but few of these models mechanistically represent responses to soil conditions (e.g. soil impedance or O2 levels) (Pages et al. 2000). The feedback effects of root signals (from drying soil or impedance or poorly growing roots) first shown 20 years ago by Davies & Zhang (1991) to reduce photosynthesis, transpiration and growth of shoots needs to be incorporated into crop models. Of course, soil impedance, soil temperature and other soil-related processes must be accurately predicted by the model's soil module before effects on plant growth can be simulated.
Another area for improvement concerns more mechanistic representations of reproductive growth. Few models explicitly account for stresses affecting pollination, fertilization or early embryo development effects, which not only affect yield per se but seed quality. The daily flower, pod and seed cohort structure of the CROPGRO model provides a framework for describing such responses, including (1) effects of periods of thermal stress on flower fertility, (2) individual fruit and seed growth rate, and (3) competition between early versus late-set reproductive sites that affect final seed size distribution (Batchelor, Jones & Boote 1996). Grain protein content and protein components as a function of grain growth, N translocation and temperature are considered in the SIRIUS model (Martre et al. 2006).
Improving Modelled Growth and Yield Response to Climatic Factors
Correct model responses to weather and climatic factors are important both for accurate prediction of present-day production under weather variability as well as prediction of future impacts of climate change. For these reasons, it is important that we test crop models as thoroughly as possible against observed data on crop response to climatic factors. Such multimodel comparison testing is vigorously encouraged by the Agriculture Model Intercomparison and Improvement Project (AgMIP; Rosenzweig et al. 2013). Readers are referred to the reviews by Boote, Pickering & Allen (1997) and which evaluated advances and gaps in the capability of crop models to predict future crop growth and yield under climate change. Approaches and methodologies for testing crop models against climate change data were suggested by Boote et al. (2010).
Testing and improving modelled assimilation and growth response to rising CO2
More data on crop response to CO2 are becoming available with continued research in chamber-based and field-based FACE systems, as well as meta-data analyses for soybean (Ainsworth et al. 2002), wheat (Amthor 2001) and other crops (Kimball et al. 2002; Hatfield et al., 2008, 2011). Concerns have been raised that crop models may overestimate crop response to CO2 as compared to responses observed in field experiments (Long et al. 2006), despite extensive testing of models against field data (Ewert, Porter & Rounsevell 2007). However, recent experiments indicate that crop responses in FACE field experiments may underestimate the true response to elevated CO2 due to inhibitory effects of fluctuations of elevated CO2 that are inherent in FACE experiments (Bunce 2012, Bunce, 2013).
CO2 response is well defined by the theories of C-3 and C-4 photosynthesis responses to CO2 (Farquhar & Caemmerer 1982; Caemmerer 2000). Nevertheless, many crop models, especially those with RUE approaches, use simple modifiers for incorporating the CO2 effect on RUE as well as CO2 effect on transpiration (Tubiello et al. 1999, 2007; White et al. 2011). For many crops, these model comparisons have been shown to reproduce measured data with elevated CO2 (Grant et al. 1995; Kartschall et al. 1995; Ewert, van Oijen & Porter, 1999; Tubiello et al. 1999; Asseng et al. 2004).
There are several important issues relative to CO2 effects. First, how do the models address photosynthetic acclimation and second order effects of elevated CO2 (decreased rubisco activity, decreased conductance, increased LAI). For example, the leaf N concentration should be reduced with CO2 increase (Sinclair et al. 2000) as shown with APSIM-Nwheat (Asseng et al. 2004), recognizing that species also differ for this [see discussion in Boote et al. (1997)]. The legume soybean shows much less decline in leaf N concentration and less shift in protein allocated to rubisco than does rice (Baker & Allen 1993). Linking acclimation to leaf N concentration is a simple approach that mimics acclimation for less complex models. Drewry et al. (2010) used a mechanistic multilayer canopy-soil-root system model to test simulations against canopy assimilation of soybean in FACE and found that 5% down-regulation of rubisco had a negligible effect on leaf and canopy assimilation, and that the LAI effect was unimportant at high LAIs. Leakey et al. (2006) reported that the reduction in stomatal conductance with elevated CO2 was similar under short-term versus long-term open-field enrichment, a finding that is useful for crop modelling. Another issue is whether respiration is modified by CO2 level (Drake et al., 1999). Properly accounting for composition shift of leaf and grain tissues under climate change (less protein but higher carbohydrate concentration) may be sufficient to address this effect. The third and most important secondary effect of CO2 is the extent of reduction in canopy transpiration (Grant et al. 1995; Kartschall et al. 1995) discussed next.
Transpiration response to rising CO2
A common misconception is that a 40% reduction in leaf stomatal conductance (under doubled CO2) should reduce canopy transpiration by 40%. With reduced leaf-level conductance, however, the canopy energy balance feedback causes the foliage temperature to rise, pushing leaf and canopy transpiration up, thus giving only 10–12% reduction in canopy transpiration with a 40% reduction in leaf conductance for doubled CO2 for C-3 species (Boote et al. 1997; Bernacchi et al. 2007; Hatfield et al. 2008, 2011). C-4 photosynthesis species, with their lower stomatal conductance and greater stomatal sensitivity to CO2, have a larger reduction in canopy transpiration with doubled CO2. A 22% reduction in transpiration was reported for maize by Kim et al. (2006) and Chun et al. (2011), and 18% and 20% reductions were reported for sorghum and maize, respectively, by Allen et al. (2011). Increasing CO2 from 368 to 561 μmol mol-1 resulted in a 13% reduction in evapotranspiration (ET) of sorghum under FACE in Arizona (Triggs et al. 2004), a value that is comparable considering the smaller CO2 increment used. The extent of modelled reduction in canopy transpiration with rising CO2 has not been tested sufficiently in most crop models.
Most crop models have a daily time step for ET and do not include true energy balance component or feedback effects of stomatal closure on canopy temperature in a mechanistic manner. There is a need to improve crop models in this respect, even if via a simple methodology. Mechanistic models with instantaneous energy balance generally use the Farquhar and Caemmerer (1982) leaf photosynthesis method with Ball-Berry stomatal conductance versus VPD (Ball 1987; Collatz et al. 1991), in which there is energy balance iteration on transpiration, intercellular CO2 (Ci), stomatal conductance and foliage temperature. Drewry et al. (2010), using a mechanistic multilayer canopy-soil-root system model with all these features, simulated 7% and 19% reductions in transpiration for soybean and maize, respectively, under Illinois FACE conditions, with species differences associated with (higher) LAI compensation for soybean and greater reduction of conductance for maize. Reductions of 5.4% and 8.6% in seasonal evapotranspiration for soybean and maize under doubled CO2 were simulated by Wilson, Carlson & Bunce (1999) using a coupled soil-vegetation-atmosphere model that simulated feedbacks of microclimate, soil evaporation and rising LAI effect. Crop models with instantaneous energy balance that predict all the way to grain yield, include ECOSYS (Grant & Baldocchi 1992), MAIZSIM (Yang et al. 2009a,b; Kim et al. 2012), and an early effort with the CROPGRO model (Pickering, Jones & Boote 1995). Simulated reduction in canopy evapotranspiration was 11–12% for irrigated soybean for CO2 increase from 350 to 700 μmol mol-1, using the CROPGRO-soybean model adapted by Pickering (Boote et al. 1997), which concurs with reported reductions of 12% of soybean ET in sunlit controlled-environment chambers (Jones, Jones & Allen 1985) and in FACE systems (Bernacchi et al. 2007). Several global land-surface models include the energy balance feedback on transpiration, but these models greatly simplify crop phenology, assimilation and partitioning to yield (Bondeau et al. 2007). Some land-surface models also include detailed leaf-level biochemistry photosynthesis following Farquhar and von Caemmerer along with Ball-Berry stomatal conductance. Presumably, those models should accurately predict transpiration, since the primary goal of most of the global land-surface models is to provide sensible and latent heat feedbacks to general circulation models, rather than to accurately predict growth and yield.
Testing and improving models for stresses of elevated temperature on reproductive growth and yield
While there has been considerable emphasis on photosynthesis and vegetative growth response to elevated temperature, reproductive growth and grain yield are actually more affected by elevated temperature than is vegetative (Prasad et al. 2003; Boote et al. 2005; Prasad, Boote & Allen 2006). For this reason and because food production depends more on grain, there is a new urgency to understanding heat stress effects on reproductive growth and improving models for heat stress effects on yield and reproductive fertility. There are four effects of above-optimum temperature on crop yields: the foremost mechanism is the gradual reduction in yield associated with a shorter grain-filling period, the second is a gradual reduction in grain growth/size, the third is reduction in crop photosynthesis, and the fourth is progressively more failures of grain-set (via floral infertility and embryo abortion), which occur at very high temperatures (Kim et al. 1996; Matsui et al. 1997; Porter & Gawith 1999; Prasad et al. 2003, 2006). Effects of adversely low or high temperatures on formation of reproductive sites (fertility-sterility) may not be sufficiently well predicted by current crop models, and this is a major concern with use of crop models for response to climate change (Asseng, Foster & Turner 2011; Lobell, Sibley & Ivan Ortiz-Monasterio 2012). Rice, for example, is sensitive to air temperatures less than 18 °C, below which spikelet generation is poor and spikelets are sterile or poorly formed. The ORYZA 2000 model incorporates this effect (Bouman 2001; Bouman & van Laar 2006). Rice also is very sensitive to supraoptimal temperature during the anthesis phase. Daily maximum temperatures above 32 °C progressively reduce spikelet fertility (less pollen production and less viable pollen) for rice, with total sterility at 41–42 °C (Kim et al. 1996; Matsui et al. 1997; Boote et al. 2005). This translates to a gradual reduction in rice grain yields from optimum at mean daily temperature of 25 °C to zero yield at 35 °C (Baker & Allen 1993; Baker, Boote & Allen 1995). Few rice models adequately account for this effect, and most have not been tested. The ORYZA model is sensitive to both low and high temperature extremes, and its simulations have been compared qualitatively by Matthews et al. (1995) to the elevated temperature literature cited above. Sorghum, a cereal often thought to be heat-tolerant, has the same grain yield sensitivity to supraoptimal temperatures as rice, with total failure of grain formation at 40/30 °C diurnal temperature cycle (Prasad et al. 2006) and the causes are the same as rice (reduced pollen amount and reduced pollen viability). Data documenting the sensitivity of maize, the dominant C-4 grain crop, to elevated temperatures are relatively few (Cicchino et al. 2010; Rattalino Edreira et al. 2011), although its cereal-nature similarity to rice and sorghum leads us to assume that maize likely has the same heat-sensitivity. Sorghum and maize simulation models seldom consider effects of elevated temperature on grain-set per se, and they rely mainly on the shortening of vegetative growth and grain-filling phases to reduce grain yield with rising temperature. We lack data to test whether this assumption is adequate. The models may give the right answer but for the wrong reason, as too much shortening of grain-fill may compensate for lack of effect of supraoptimal temperature on grain-set. Shortening the life cycle may give insufficient yield reduction under an acute heat stress that occurs around anthesis. Existing sorghum and maize models need to be tested for accurate response to elevated temperatures. Soybean and peanut are more tolerant of elevated temperatures than rice or sorghum, as those two legumes have a similar optimum mean temperature of 24–25 °C for yield, but they have a more gradual yield reduction and have a higher failure temperature at 39–40 °C (thus 5 °C more tolerant than the rice and sorghum crops) (Pan 1996; Prasad et al. 2003; Boote et al. 2005). A possible mechanism relates to pollen being shed in the legumes near sunrise, whereas pollen-shed of rice, sorghum and maize occurs later in the morning, possibly because the anthers must desiccate in order to release pollen. Screening germplasm and land-races of all of these crops will hopefully reveal mechanisms of heat tolerance, the degree of genetic variation, and provide data for parameterization of crop models for response to heat-stress during the critical anthesis and grain-set phases.
Few models have been extensively tested for their response to elevated temperatures. Boote et al. (2010) evaluated the CSM-CROPGRO Peanut and Soybean models for response to elevated temperature data of Prasad et al. (2003) and Pan (1996), respectively, and concluded that the two models adequately predicted the effect of elevated temperature on grain yield of peanut and soybean. The APSIM N-Wheat model has a high-temperature routine that accelerates leaf senescence when maximum daily temperature is above 34 °C. This response has been qualitatively compared with meta-data showing general agreement; however, the model lacks interactions of heat stress and canopy temperature, which could be critical under varying water supply (Asseng et al. 2011). While there are many wheat models, few have addressed effects of near-freezing temperatures on reproductive fertility or effects of supraoptimal temperature on grain-set and grain growth.
Modelling Cultivars: the Genetic Component
Are current crop models ready to link to genetics and G × E on growth and yield
In molecular genetics, research often focuses on single gene effects, ignoring the possibility of compensation by other genes and processes during plant growth over its life cycle to produce final yield. Crop models have the potential ability to modify single processes, one trait at a time, to assess the effect on growth and final yield. More importantly, they can simulate the degree of additivity of traits or cancelling compensation of the traits (Hammer et al. 1996; Boote et al. 2003; Singh et al. 2012). The models have the advantage of being able to test those genetic traits in crops grown in different simulated environments, to illustrate when the trait will have positive or negative effects (Asseng et al. 2002). Admittedly, the crop models need improvement in their level of mechanism and may need increased ability to link gene effects to what is currently called a genetic coefficient in a crop model. Adding increased complexity to models may be needed, but this is also a hazard because models with many additional parameters may increase the potential model error and the uncertainty in parameter estimation (Thornley & Johnson 1990; Passioura 1996).
Future challenges for crop modelling to create linkage to genes
There will be a long and slow path for modelling full effects of genes upon the integrated processes of the whole plant organism, but some efforts have begun. Progress will be slow for several reasons. First, many crop models lack sufficient mechanistic detail for representing the action of individual genes unless they have very large effects such as on plant height or phenology. Secondly, there is incomplete understanding of how complexes of multiple genes respond differentially to environment to give different phenotype. Knowing that a gene results in a different gene product or plant morphology does not mean that the integrated outcome from a specific phenotype is clearly understood. Field phenotyping is a major limitation to linkage of genes to crop model function (White et al. 2012a), and one that is insufficiently addressed by the simple phenotyping done on seedling plants in greenhouses. In addition, there is insufficient understanding of what causes genotype by environment interactions (see next paragraph).
Advances in modelling genotype by environment by management (G × E × M) effects
Crop model simulations have shown that G × E × M interactions can be an outcome when the same genetic trait (result of genes controlling a process) gives an advantage in one environment but a disadvantage in a second environment (Hammer & Vanderlip 1989; Sinclair et al. 2000; Yin et al. 2000b; Sinclair & Muchow 2001; Asseng et al. 2002; Boote et al. 2003; Hammer et al. 2004; Boote 2011). In other words, the same gene may have different effects on yield in different environments. This is strongly illustrated in Table 1 for simulation of genetic traits of chickpea when grown either under fully irrigated conditions or under water-limited terminal drought. Chickpea in India is typically sown at the end of the monsoon and depends on residual soil water on high-clay soils. This genetic sensitivity analyses indicates the importance of the target environment (including irrigation management), because the responses to genotypic traits were frequently opposite and large for contrasting soil water availability [e.g. when specific leaf weight (SLW) was increased, simulated yield was about 11% lower in irrigated but 18% higher under water-limitation]. Increased SLW was negative for yield under irrigation because it reduced LAI and light interception. But the trait was very beneficial under rainfed conditions because it reduced LAI, light interception and transpiration (thus conserving water for subsequent grain yield later in the life cycle). Later flowering (which increases LAI) was very beneficial (15.4% increase) under irrigation, but very negative (13.5% decrease) under the terminal drought. The common factor was the amount of LAI produced and amount of soil water extracted (or left) before seed growth began. Faster root depth progression was important only under rainfed conditions, resulting in 2.3% yield increase. Increasing Amax was unimportant (1.3% increase) under rainfed conditions, but gave a large (13.3%) increase under irrigated production. Increased seed size and faster pod addition were beneficial under irrigation, but not under terminal drought. These simulated genetic traits showed differential responses depending on water environment (Singh & Virmani 1996) also shown in other studies (Singh et al. 2012).
Table 1. Grain yield response to 10% change in cultivar coefficients, simulated for 22 years for Annigeri chickpea grown rainfed or irrigated at Patancheru, India. Sown on day 302 on a very fine montmorillonitic clay soil, starting at field capacity. Simulated with the CSM-CROPGRO model as adapted for chickpea by Singh & Virmani (1996)
Cultivar coefficient modified
Standard simulation (Annigeri)
+10%, rate of root depth progression
+10% leaf photosynthesis (Amax)
+10% specific leaf weight (SLW)
Life cycle traits
10% longer from emergence to anthesis
10% longer seed-fill (first seed to maturity)
10% larger potential seed size
10% faster pod addition
Further examples are given here of simulating additivity of traits and responsiveness of genetic traits under climate change scenarios. Singh et al. (2012) conducted a model sensitivity analysis of genetic traits towards designing improved ideotypes of peanut for regions in India under climate change scenarios. They found that a 2 °C greater temperature tolerance of reproductive processes (flower fertilization, pod-addition and partitioning) gave greater benefit in warm locations and under future warmer climate scenarios. Likewise, they found that the benefit of varying SLW was positive or negative depending on location because rainfall and soil water were site-dependent, similar to the chickpea example above and another study with wheat (Asseng et al. 2003). Singh et al. (2012) also reported that individual traits when placed into combinations of three to five traits together gave additive effects to improve peanut yield by 12% to 23%, and the additivity was as great or larger (15% to 29%) under future climate change (Ludwig & Asseng 2010) compared to the baseline climate. This gives some optimism that genetic improvement can be part of adaptation to climate change. Boote (2011) reported that traits of determinacy, higher SLW and earlier pod addition were of minimal value for soybean under ambient CO2, because those traits resulted in smaller LAI and less light interception. But those same traits had greater benefit under elevated CO2, because CO2 stimulation of vegetative growth recovers the LAI and light interception while allowing the other attendant benefits of those traits for higher leaf photosynthesis and longer grain-fill. Individual traits when placed in combinations for soybean were mostly additive with 15% yield improvement easily achieved with only three example traits whether under baseline or elevated CO2.
Associating genes and markers with genetic coefficients in crop models
There is a need to understand better how actual genes or genetic markers relate to the cultivar-specific coefficients (in Fig. 1, for example) used to represent genetic differences and cultivars in crop models. Presently, few model coefficients correspond in any direct way to known genetic mechanisms. Efforts to create such linkages (Hammer et al. 1996, 2004; White & Hoogenboom 1996; Yin et al. 2000a; Messina et al. 2006; White et al. 2008) have primarily expressed the cultivar coefficients as simple functions of one or more genes, with scalars to represent allelic effects (e.g. 0 for absence of the allele, 1 for presence of the allele). The equation below from Messina et al. (2006) illustrates this for daylength sensitivity in soybean where the critical short day length (CSDL) effect is expressed in terms of specific E loci and number of loci (NLOCI). Six other cultivar coefficients influencing life cycle phase durations and their sensitivity to daylength were also functions of E loci and NLOCI.
In a test case, Messina et al. (2006) used quantitative trait loci (QTL) markers to characterize an independent set of seven public soybean cultivars evaluated for maturity date and yield in the U.S. Midwest Regional Soybean Trials for 5 years over eight sites. The E loci input to the model accounted for 75% of the variation in maturity and 54% of the variation in yield.
The soybean example is obviously simple, as most of the yield effects were expressed via variation in crop life cycle. But the example illustrates the need for crop modellers to consider more detailed mechanisms to account for genetics in the crop models and for geneticists to explore the phenotyping that must be done to characterize the field expression of the genes. See White et al. (2012a) for proposed approaches to use models to assist field phenotyping and detection of QTL markers.
Improving Mechanisms in Crop Models: What Needs to Be Done
There are many climate-sensitive processes of plant growth not discussed above that are worthy of model improvement: these include leaf appearance rate, root growth, onset of flowering-anthesis, setting of reproductive sites, growth of reproductive or harvestable organs (e.g. potato, sugarcane), leaf senescence and crop maturation. But in all respects, model improvement must be matched with good experimentation and collection of data for developing and testing of the model improvements. Our suggested priorities are:
More intensive testing of crop response to elevated CO2. Crop models have been insufficiently tested with experimental data of increased temperature and CO2 by temperature treatments, a critical area for model improvement considered in the AgMIP (Rosenzweig et al. 2013).
More mechanistic methods are needed for predicting allocation of C and N assimilates among plant organs, that is determining what has priority.
A better understanding and simulating of source-sink relationships under changing source-sink conditions with climate change is required.
Climate change is also likely to impact yield quality (e.g. protein and oil content) which is often poorly simulated in crop models.
Canopy energy balance is needed to properly account for the feedback effects of reduced stomatal conductance on transpiration and canopy temperature under elevated CO2. These involve canopy aerodynamics and canopy energy balance, not just leaf-level stomatal conductance processes. This would allow modellers to use foliage temperature effects on processes, rather than air temperature.
Better root growth algorithms are needed to account for static and dynamic soil properties (aluminum saturation, pH, soil temperature, soil impedance, soil fertility, soil water deficit as well as hypoxia stresses). Of course, that has the problem of requiring more inputs for doing simulations. Feedback effects from poor root growth or root signals (from drying soil or impedance) are needed to reduce shoot growth.
Better linkage to soil nutrients and soil fertility beyond nitrogen is needed. There are few soil scientists conducting research on root nutrient uptake mechanisms of the Barber (1995) style. More realistic mechanisms are needed that account for reduction in nutrient uptake when root energy status is low (reduced assimilate supply) or when root activity is limited by cool soil temperature.
Better prediction of elevated temperature effects on reproductive fertility, sink formation, grain-filling and senescence are needed in the models.
With climate change, regions in the tropics may experience increased rainfall, leading to water-logged anaerobic soils and coastal regions may experience greater incursions of saline water. Thus, there is a need to simulate root-level responses to waterlogged soils and salinity (Asseng et al. 1997; Lizaso, Melendez & Ramirez 2001; Webber et al. 2010). This is a complex problem that begins with insufficient modelling of the soil-waterlogging itself, continues with inadequate simulation of short-term and long-term crop responses, and also includes the need to predict genetic variation in tolerance of waterlogging. This will also require addressing uncertainties such as the C investment in exudates and root turnover, the progression of rooting and root length density with soil depth, and the effects of specific soil stresses on root elongation.
We conclude that there is great potential for using crop models in combination with experimental studies to improve crop models and to use crop models for many applications which include crop management, evaluation of genetic improvement over environments, climate change impacts and adaptations, and extrapolating and integration of research findings. Model improvement in mechanisms is needed and will be ongoing. Model linkage to genetics is a new area with good potential but it will continue for many years due to the complexity of understanding and integrating genotype by phenotype interactions into simulation models.