300 on each calendar day, a specific seedbank fraction loses its dormant ... programming skills and sufficient level of expertise to develop its heuristics. .... CALVO HARO RM, GONZALEZ-ANDUJAR JL & PEREZ S (1994) Manual de modelos ...... 3; H aj Se ye d. H ad i & G on za le z-An du ja r, 2. 00. 9. M atric aria p erfo ra ta.
Weed Research
Predicting field weed emergence with empirical models and soft computing techniques
Journal: Manuscript ID
WRE-2015-0204.R1 Review Paper
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Manuscript Type:
Weed Research
Date Submitted by the Author:
Complete List of Authors:
n/a
Keywords:
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Gonzalez-Andujar, Jose Luis; Instituto de Agricultura Sostenible (CSIC), Crop Protection; Chantre, Guillermo; UNIVERSIDAD NACIONAL DEL SUR, AGRONOMIA; Morvillo, Claudia; University of Buenos Aires. Faculty of Agronomy, Crop production Blanco, Anibal; UNIVERSIDAD NACIONAL DEL SUR, Planta Piloto de Ingeniería Química Forcella, Frank; USDA-ARS, North Central Soil Conservation Research Lab.
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Artificial neural networks, genetic algorithms, predictive modelling, nonlinear regression, degree days, weed control
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Predicting field weed emergence with empirical models and soft computing
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techniques
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J. L. Gonzalez-Andujar1, G. R. Chantre2, C. Morvillo1,3, A. M. Blanco4, F. Forcella5 1
4 5 6 7 8 9 10
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Instituto de Agricultura Sostenible (CSIC), Aptdo. 4084, 14080 Córdoba, Spain Departamento de Agronomía/CERZOS, Universidad Nacional del Sur/CONICET, Bahía
Blanca, Buenos Aires, 8000, Argentina 3
Departamento de Producción Vegetal, Facultad de Agronomía, Universidad de Buenos
Aires, Av. San Martín 4453, (1417), Buenos Aires, Argentina 4
Planta Piloto de Ingeniería Química, Universidad Nacional del Sur/CONICET, Bahía
Blanca, Buenos Aires 8000, Argentina. 5
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USDA-ARS North Central Soil Conservation Research Laboratory, Morris, MN 56267,
USA
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Summary
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Seedling emergence is one of the most important phenological processes that influences
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the success of weed species. Therefore, predicting weed emergence timing plays a critical
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role in scheduling weed management measures. Important efforts have been made in the
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attempt to develop models to predict seedling emergence patterns for weed species under
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field conditions. Empirical emergence models have been the most common tools used for
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this purpose. They are based mainly on the use of temperature, soil moisture and light. In
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this review, we present the more popular empirical models, highlight some statistical and
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biological limitations that could affect their predictive accuracy and, finally, we present a
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new generation of modelling approaches to tackle the problems of conventional empirical
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models, focusing mainly on soft computing techniques. We hope that this review will
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inspire weed modellers and that it will serve as a basis for discussion and as a frame of
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reference when we proceed to advance the modelling of field weed emergence.
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Key words: Artificial neural networks, genetic algorithms, predictive modelling, nonlinear
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regression, weed control, degree days.
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Introduction Seedling emergence is one of the most important phenological processes that influences the success of weed species (Forcella et al., 2000) and, therefore, predicting
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weed emergence timing plays a critical role in scheduling weed management measures
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(Ghersa, 2000). For example, from the chemical control perspective, many POST
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herbicides will not control weeds that have not yet emerged at the time of application.
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Conversely, if control is applied too late, early emerged weeds may be too large for
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adequate control (Dalley et al., 2004). Moreover, if weeds are controlled too late, potential
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crop yield can be reduced. Organic (ecological) farming practices using mechanical weed
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control techniques also would benefit from weed emergence predictive tools to better
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define intervention times (Oriade & Forcella 1999; Forcella et al. 2012).
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Since the early 1990´s important efforts have been made in the attempt to develop models to predict seedling emergence patterns for several weed species (e.g. Dorado et al.,
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2009; Izquierdo et al., 2013; Werle et al., 2014; Zambrano-Navea et al., 2013) as a
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fundamental step in the development of IWM strategies. These efforts vary from empirical
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weed emergence models to more complex mechanistic models.
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Although mechanistic or reductionist models can help to provide a close description
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of the basic ecophysiological processes underlying weed emergence (i.e., seed dormancy,
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germination and pre-emergence shoot growth) (Batlla et al., 2004; Vleeshouwers &
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Kropff, 2000; Gardarin et al., 2012), they usually require a large amount of often
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unavailable or difficult to gather experimental information to be developed, calibrated and
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finally validated (Grundy, 2003). Conversely, empirical weather-based models aim to
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identify the relation between soil environmental variables and emergence data collected
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under field conditions with the final objective to provide real-time information on weed
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management programs.
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Empirical models simply describe the general shape of the data set to which the
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researcher is trying to fit a curve. They provide a simpler framework for practical support
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decisions regarding optimal time for intervention. The most common means of analyzing
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such relationships is some form of regression, which typically is nonlinear.
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In this review we have restricted our attention to empirical models as they are the most common models used for modelling weed emergence under field conditions. We 2
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identify some statistical and biological limitations that could affect their predictive
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accuracy and, finally, we present briefly a new generation of algorithm modelling
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approaches to overcome their limitations, focusing mainly on soft computing techniques.
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Predicting weed emergence
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Empirical emergence models are tools for predicting the percentage of total weed emergence occurrence based mainly on the use of temperature and soil moisture (Forcella
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et al., 2000; Grundy, 2003;) and, more recently, light (Royo-Esnal et al. 2015). They are
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based on the thermal or hydrothermal time concepts (Gummerson, 1986; Roman et al.,
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2000; Martinson et al., 2007), which assume that seeds need to accumulate a certain
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amount of growing degree days (GDD) before completing germination and emergence.
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They link emergence with GDD and can be classified, in a general way, as thermal-time,
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hydrothermal-time, and photohydrothermal-time models. In thermal time models (TT),
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daily mean soil temperature (eventually air temperature) is accumulated above a specific
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threshold during the cropping season until weed emergence is completed. Thermal time
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accumulation can start at various times depending upon specific situations. These dates
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could be the last soil tillage event or burndown herbicide application; crop sowing; or an
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arbitrary date such as 1 January for summer-growing weeds in cold climates of the
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Northern Hemisphere, or winter-growing weeds in warm climates of the Southern
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Hemisphere.
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A more complex approach includes the integration of soil water potential with soil
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temperature into hydrothermal-time (HTT). These models can be better at predicting
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emergence than TT models (McGiffen et al., 2008), as they include soil water availability,
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which is an important factor for seed germination and shoot growth. In these models, GDD
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are accumulated when the daily average of soil water potential and soil temperature are
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above specified threshold values below which seedlings cannot emerge (Gummerson,
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1986). If experimental soil temperature and water potential data are missing, the weed
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modeler can easily and accurately estimate such variables using free access software (e.g.,
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Soil Temperature and Moisture Model (STM2); Spokas and Forcella, 2009). In
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photohydrothermal-time models (PhHTT), photoperiod is used to modify TT based upon
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daylength (Royo-Esnal et al. 2015). The rationale is that with longer day lengths, soil is
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irradiated longer and accumulates more heat than with shorter day lengths, even when
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maximum and minimum air temperatures are identical between days with long and short 3
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day lengths. The output for these models is percentage of the total annual emergence of a
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given species. A typical non-linear regression model (NLR) for weed emergence is like the
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following Y=f(x, φ)+ε
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(1)
where ε ≈ N(0,σ2), Y is cumulative emergence, x is cumulative GDD (TT, HTT, or
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PhHTT) and φ are specific function parameters. The term f(x, φ) is a non-linear S-shaped
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function. S-shaped curves start at some fixed point, then increase up to an inflection point,
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after which the slope of the curve decreases and the curve approaches the upper asymptote
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(Ratkowsky, 1983) (Fig. 1). Different parametric S-type models have been commonly
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fitted to emergence data (e.g. Schutte et al., 2008; Dorado et al., 2009) and, among these,
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the Logistic, Weibull and Gompertz have been used most widely in predicting weed
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emergence (Table S1).
Logistic:
! = #/%1 + ()*+−-+) − *))/
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Gompertz: ! = # ()*%−()*+−-+) − *))/
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(2)
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Figure 1 near here
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(3)
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Weibull ! = #%1 − ()*+−+-+) − *))1 )/
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(4)
In these expressions, ! and ) as in eqn 1, - is the slope parameter (emergence rate),
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* represents the inflection point on the ) axis, 5 is a shape factor that determines the
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skewness and kurtosis of the distribution, and # is the maximum emergence fraction of the
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model.
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Gompertz and Logistic are very similar functions. Both are special cases of a generalized
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logistic model (Calvo et al., 1994). The main differences between the Gompertz and
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Logistic functions is that the Gompertz function approaches the asymptote much more
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gradually, which often matches observations of late-emerging seedlings. The Weibull
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model is a more flexible function than the Logistic and Gompertz. It can acquire the
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characteristics of other types of distributions based on the value of the shape parameter c
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(eqn 4). It typically has been used for modelling seedling emergence patterns (Table S1).
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Comparison amongst models has been performed (e.g. Dorado et al., 2009). However, a clearly general favored model has not emerged. Even the same species (e.g.
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Chenopodium album and Avena fatua) fitted different models best under diverse crops (see
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Table S1).
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Statistical limitations
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Model limitations
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The aim of NLR models is to predict weed emergence easily and provide a practical tool to make informed management decisions. In this sense, NLR fitting presents several
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statistical limitations that could affect their predictive accuracy (Cao et al., 2011; Onofri et
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al., 2010). Some of these issues are briefly presented bellow:
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-Fitting nonlinear models requires good initial parameter estimates. Poor initial estimates
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could lead to wrong solutions or may yield no solutions at all (Holmström & Petersson,
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2002). The algorithm used to find the solutions of nonlinear equations may incorrectly
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pinpoint a local minima and thus only find local optima and, therefore, resulting parameter
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estimations are biased.
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-The parameters are estimated by NLR fitting routine using algorithms such Marquardt-
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Levenberg (ML) or Gauss–Newton (GN) (Ratkowsky, 1983). There is a wide range of
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statistical software to fit NLR models, which likely is the cause of NLR’s popularity.
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Choice of the appropriate fitting algorithm is very important. For instance, ML is more
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robust than GN, which means that in many cases it finds a solution even if it starts very far
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from the global minimum. Unfortunately, the algorithms used in the fitting procedures may
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not be selected adequately and users often rely on their statistical software´s default
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options.
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- Observations are censored. When we make periodic seedling counts, the “new
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emergence” events could have occurred at any time in the interval between the last and
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current counts. Neglecting the existence of censored data may lead to biased results.
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- Observed cumulative emergence values obtained from consecutive monitoring are not
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statistically independent, resulting in positive autocorrelation of the residuals and,
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therefore, which leads to erroneous predictions.
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Biological/ecological limitations
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Because TT, HTT, and PhHTT models are developed based on environmental conditions, they might be used to predict weed emergence across different years and
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geographical regions. Nevertheless, validation results show that empirical models may not
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be accurate if environmental conditions vary significantly from the original conditions in
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which the experiment was conducted (e.g., Izquierdo et al., 2013). Many reasons can
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explain these differences. For instance, different soil management (e.g., cultivation
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operation) may reduce the accuracy of the model by varying the vertical distribution of the
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seeds within the soil profile (Grundy et al., 1996). As a result, seeds will have different
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temperature, soil moisture and light conditions, and the rate of dormancy release and
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germination will be different (Cao et al., 2011). In addition, deeply buried seeds need more
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time to emergence than seeds near the soil surface, thereby delaying and/or extending the
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emergence flush. Also, model accuracy may be limited by possible population
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differentiation at diverse geographic locations as a result of different selection pressures in
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different environmental conditions (Dorado et al., 2009).
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In addition, the use of microclimate indices (TT, HTT, PhHTT) as single
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explanatory variables is based on the following assumptions: (i) the seedling emergence
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process is considered as “a whole” without proper discrimination between seed dormancy,
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germination and post-germination growth subprocesses, and (ii) population-based thermal
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(Tb = base temperature) and hydric (Ψb = base water potential) parameters are assumed
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independent of soil microclimatic variables (soil water potential and soil temperature,
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respectively). As suggested by Dahal and Bradford (1994) and Kebreab and Murdoch 6
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(1999) interactions between Tb and Ψ, as well as between Ψb and T are to be expected,
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mainly when estimated parameters are not constant within the population (Bradford 2002).
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Further developments Recently, a new generation of modelling approaches is beginning to tackle the statistical problems of conventional NLR models. For instance, Davis et al. (2013) used
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nonlinear mixed-effect models, which can reduce the number of restrictive assumptions
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presented by NLR models. Onofri et al. (2010; 2011; 2014) presented new developments
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that maintain the positive features of parametric approaches; and Cao et al. (2013)
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described a non-parametric approach as a very flexible tool to model weed emergence.
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Other new conceptual approaches come from the algorithmic modelling culture
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(sensu Breiman, 2001). Algorithmic modelling departs from the concept of an “ideal
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system” described by complete-and-precise information, and heads toward a real, uncertain
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and complex system where precise and deterministic models hardly apply. As highlighted
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by Bonissone (1997) “as we attempt to solve real-world problems we realize that they are
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typically ill-defined systems, difficult to model and with large-scale solution spaces.” In
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this context, Soft Computing Techniques (also called computational intelligence) are
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capable of dealing with complex systems because it does not require strict mathematical
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definitions. Unlike conventional computing (i.e. hard computing), Soft computing is
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tolerant of uncertainty, imprecision and partial truth providing a better rapport with reality
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(Das et al., 2013). Among Soft Computing Techniques (SCTs), Artificial Neural Networks
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(ANNs) (Chantre et al., 2012; 2014) and Genetic Algorithms (GAs) (Haj Seyed Hadi &
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Gonzalez-Andujar 2009; Blanco et al., 2014) have been proposed as promising tools for
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weed emergence prediction.
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Artificial neural networks (ANNs)
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Artificial neural networks are machine learning computer techniques that provide a
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practical and flexible modelling framework for multivariate nonlinear mapping (Lek &
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Guégan 1999). Such models are inspired by the operation of biological neural networks,
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specifically the animal brain. ANNs are generally represented as a system of
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interconnected processing units (also called nodes or neurons), which exchange signals
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(i.e., information) between each other. The connections have numeric weights that are 7
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adjusted during the training process using a given learning algorithm. Therefore, an ANN
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model is characterized by (1) its architecture (i.e. the pattern of connections among nodes),
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(2) its method of determining the weights on the connections (i.e., learning or training
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process), and (3) its activation functions (i.e. mathematical functions that process input
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data). Briefly, a feed-forward neural network (also called multilayer perceptron) consists of
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input variables (xn), output variables (Yn) and a given number of hidden layers containing
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n nodes (for further details on ANN architectures the reader is referred to Fausett (1994)).
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A basic three layer feed-forward ANN was implemented successfully by Chantre et
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al. (2014) for Avena fatua field emergence prediction in different temperate regions of the
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United States, Canada and South Australia (Fig. 2).
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As observed in Fig. 2, each of the input nodes of the model receives a given input
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variable (note that cumulative thermal-time and hydro-time are considered independent
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variables) and broadcasts it to each one of the hidden neurons. Hidden neurons compute
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their activation functions and broadcast their results (z1, z2, z3) to the single output neuron
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that finally produces the response of the network (Y). The output signal of each hidden
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neuron (zj) is calculated as:
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j=1, …, 3
while the output of the network is given by: y = f ∑ w jz j + w 0 j=1,3
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z j = f ∑ vij x i + v 0j i =1,2
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(5)
(6)
In Eqns (5) and (6), f(.) is the activation function of the network, xi is the
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corresponding input variable, vij are the weights of the connections between the input and
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hidden neurons, and v0j is the bias of hidden neuron j. Similarly, wj represents the weights
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of the connections between hidden and output neurons and w0 is the bias of the output
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neuron.
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From a statistical point of view, ANNs have many positive features that should be
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highlighted. They: (i) effectively implement a wide range of nonlinear mapping problems
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due to their excellent potential for data interpolation, (ii) admit multivariate input/output
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mapping, (iii) have no requirements for a given a priori shape fitting function (i.e., ANNs
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can easily generate an outcome in the form of a polynomial function of degree n), and (iv) 8
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for certain cases involving complex emergence patterns, ANNs require fewer adjustable
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parameters than conventional multivariate techniques to obtain a similar parsimony.
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Among the negative aspects of ANNs implementation we might cite the following:
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First, they have very low extrapolation capacity. Thus to adequately optimize a given
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objective function (e.g., error minimization), a wide range of observed scenarios is needed
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to exploit ANN interpolation capability. Second, ANNs employ a “black-box” model
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approach with limited explanatory power from a mechanistic biological perspective. Third,
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it is usually required trial and error to identify the network that renders the largest
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parsimony.
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Although ANNs have been used intensively to solve highly complex non-linear mapping problems in agronomic and biological systems (Saberali et al., 2007; Fortin et al.,
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2010; Dai et al., 2011), their application for modelling weed emergence remains largely
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unexplored. Recent studies performed by Chantre et al. (2012) and Chantre et al. (2014)
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have shown that ANNs are able to outperform conventional NLR models. As discussed by
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Chantre et al. (2014), the adoption of two independent input variables (i.e., thermal-time
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and hydro-time) instead of a single explanatory variable (i.e., hydrothermal-time) weighted
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differently within the neural network which produced better results. This possibly was due
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to a more intimate discrimination of the germination and post-germination growth
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processes. In other words, the use of two (or more) independent variables instead of a
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single aggregated variable enhances the statistical power of ANNs compared to NLR.
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Thus, additional variables such as (i) seed burial depth (tillage system), (ii) dispersal or
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seeding date, (iii) photoperiod, or (iv) seedbank dormancy level might be included.
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However, overparameterization my occur by increasing the number of input variables thus
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generating less parsimonious models.
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Genetic Algorithms (GAs) Genetic algorithms are stochastic optimization techniques based on the evolution of
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sets of potential solutions (also called individuals or phenotypes) following natural
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selection rules (i.e., selection, crossover, mutation). Each individual has a set of specific
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properties (chromosomes in a biological sense), which can suffer crossover and mutation.
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Basically, from an initial population of randomly generated individuals the GA algorithm
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iteratively performs a stochastic search in which successive generations (i.e., populations)
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are obtained. The fitness (i.e. the value of the objective function in the optimization
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problem) of every individual in successive populations is evaluated, and the evolutionary 9
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process proceeds until the best fitness value (i.e. solution) is obtained. These techniques
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have demonstrated good performance in non-linear unconstrained models (Michalewicz,
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1996; Rangaiah, 2010; Blanco et al., 2014). In fact, GAs show a good balance between
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exploration and exploitation of the search space increasing the probability of convergence
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to global optima (i.e., expected solutions) instead of reaching local minima (Blanco et al.,
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2014). In addition, stochastic techniques only use objective function (e.g., by minimizing
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an error function) values in the calculation compared to deterministic algorithms which
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also require calculation of derivatives). This feature facilitates their computational
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implementation and robustness of the search, due to a higher convergence speed. Either,
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GA or ANN approaches can be implemented with average computing time of 15 to 20
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minutes (personal observation). For more information on GAs the interested reader is referred to Michalewicz
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(1996). Based on the mentioned strengths, Haj Seyed Hadi and Gonzalez-Andujar (2009)
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suggested that GAs are more appropriate to deal with ill-conditioned optimization
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problems than the deterministic optimization algorithms usually used in the NLR
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approach. The authors compared GAs with NLR for fitting emergence data of six weed
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species and found that GAs often provided a better fit than NLR.
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Recently, Blanco et al. (2014) developed an emergence model for Avena fatua
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based on the disaggregation of seed dormancy release (i.e., after-ripening process) and
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germination/pre-emergence growth processes. Logistic functions (eq. 2) were adopted to
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model separately (i) seedbank dormancy release as a function of after-ripening thermal-
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time accumulation, and (ii) germination/pre-emergence growth as a function of
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hydrothermal-time accumulation (Fig. 3A). In such work, a GA optimization approach was
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implemented for parameter estimation. The logic of the model illustrated in Fig. 3A is that
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on each calendar day, a specific seedbank fraction loses its dormant condition due to after-
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ripening thermal-time accumulation (θAT). The accumulated dormancy release function
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(AcDr) is obtained by integrating such fractions over time following a logistic distribution
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(Fig. 3A). Thereafter, each specific non-dormant fraction undergoes the germination/post-
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germination process by accumulating hydrothermal-time (θHTG). Finally, accumulated
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emergence (AcG) is obtained by integrating each day the germinated/post-germinated
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fractions corresponding to the different portions of the seedbank that lost dormancy during
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the previous days.
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The scheme of the model (i.e. Genetic Algorithm block) is shown in Fig. 3B. Model input consist of the soil microclimatic data (daily mean soil temperature and soil
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water potential). Thereafter, θAT and θHTG (cumulative time variables) constitute the input
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of the dormancy release (AcDr) and accumulated emergence (AcG) logistic functions,
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respectively. In the present example, the solutions are represented by individuals, each one
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constituted by the parameters of the logistic functions = adr, ag, pdr, pg) (see Fig. 3). The
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GA algorithm performs selection, crossover and mutation operations (Forrest, 1993) on
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such individuals (i.e., optimization variables) from a randomly selected initial population
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along a pre-specified number of generations or until some convergence criterion is met.
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The main output of the model is the accumulated emergence function, which is obtained by
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integrating the daily germinated fraction of A. fatua corresponding to each non-dormant
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seed bank fraction which, in turn is finally represented by the cumulative dormancy release
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curve (Fig 3A).
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As discussed by Blanco et al. (2014), the GA optimization approach provided enough flexibility to closely represent complex A. fatua emergence patterns in the semiarid
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region of Argentina. In this case, the possibility to quantify separately dormancy release
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requirements (after-ripening thermal-time accumulation) from hydrothermal-time needs for
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germination and emergence clearly outperformed the prediction accuracy of previously
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developed NLR and ANN models. Although the model proposed by Blanco et al. (2014) is
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rather simple in terms of the equations used (logistics) and parameters interpretation, a
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negative aspect of such a modelling approach is the fact that it requires moderate
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programming skills and sufficient level of expertise to develop its heuristics.
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Conclusion Models based on SCTs can provide enough flexibility to represent weed seedling
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emergence patterns better than NLR models and, therefore, offer more reliable results. An
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important feature of these new modelling alternatives is the lack of substantial conceptual
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drawbacks observed in NLR models (Cao et al., 2011), such as the requirement for initial
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parameter estimates to start the optimization process that conditions the final solution.
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Failure to provide an accurate prediction has practical consequences for weed emergence
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models. Economic losses may occur if control measures do not coincide with the seasonal 11
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dynamics of the weed populations, not only in terms of crop/weed competition, but harvest
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efficiencies, and production of seeds by escaped weeds as well.
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From a practical point of view, the implementation of SCT models for use by farmers and technicians can be done effectively. A good example of a successful
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implementation is the AVEFA-Bordenave model developed by Blanco et al. (2014), which
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was described previously. Output from this model can accessed freely on line at
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http://www.meteobahia.com.ar/productoavefa.php. Extension of this system to multiple
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sites within a region as well as multiple regions can be envisioned easily. The
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implementation of these techniques can also be seen as sub-models integrated within
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operational planning of herbicide-based (Lodovichi et al. 2013) or strategic IWM programs
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(Beltran et al. 2012).
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Despite their advantages, some caveats of ANNs and GAs should be mentioned: (i) To obtain reliable model predictions a good pool of input data (i.e., series of cumulative
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field emergence data with their corresponding soil microclimatic data) are required. These
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should be representative of a wide range of observed field scenarios and to take advantage
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of the maximum interpolation capacity of both ANNs and GAs during the training process;
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(ii) Although SCTs are relatively simple to develop and implement, they require a
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minimum degree of familiarity with specific programming platforms. For example, the
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MatLab environment (MathWorks, Inc.) provides well developed toolboxes for modeling
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ANNs and implementing GA optimization. Nevertheless, SCT models are a valuable
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alternative to the classical parametric non-linear regression models to describe and predict
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weed emergence. However, further research is required to establish more generally the
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usefulness of these approaches.
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Acknowledgments
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J. L. Gonzalez-Andujar was supported by FEDER (European Regional Development
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Funds) and the Spanish Ministry of Economy and Competitiveness funds (Projects
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AGL2012-33736). G. R. Chantre was supported by grants from Consejo Nacional de
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Investigaciones Cientificas y Tecnicas (CONICET) and Universidad Nacional del Sur
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(PGI-UNS).
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MCGIFFEN M, SPOKAS K, FORCELLA F, ARCHER D, POPPE S & FIGUEROA R
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ROYO-ESNAL A, NECAJEVA J, TORRA J, RECASENS J & GESCH RW (2015)
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Emergence of field pennycress (Thlaspi arvense L.): Comparison of two accessions and
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FORCELLA F (2008) A hydrothermal seedling emergence model for giant ragweed
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SPOKAS K & FORCELLA F (2009) Software tools for weed seed germination modeling.
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VLEESHOUWERS L & KROPFF M (2000) Modelling field emergence patterns in arable
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weeds. New Phytologist 148, 445-457.
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WERLE R, SANDELL LD, BUHLER DD, HARTZLER RG & LINDQUIST JL (2014)
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Predicting Emergence of 23 Summer Annual Weed Species. Weed Science 62, 267-279.
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ZAMBRANO-NAVEA C, BASTIDA F & GONZALEZ-ANDUJAR JL (2013) A
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hydrothermal seedling emergence model for Conyza bonariensis. Weed Research 53, 213-
505
220.
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506 507
Figure captions
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Figure 1. Typical S-type model fitted to emergence data.
509 510
Figure 2. A three layer feed-forward ANN. The network has two inputs thermal-time (ϴT=
511
(T - Tb)tg) and hydro-time (ϴH = (ψ - ψb)tg), three neurons in the hidden layer and a single
512
output variable (y = cumulative emergence). The term f(.) = the activation function of the
513
network; vij = connection weights between input-hidden layer neurons and wj = connection
514
weights between hidden and output layer neurons; v0j = bias on hidden neuron j, w0 =
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output neuronbias (adapted from Chantre et al., 2014).
516 17
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Figure 3. Genetic Algorithm based model for Avena fatua field emergence prediction
518
(adapted from Blanco et al., 2014). (A) Schematic representation of the model showing
519
that accumulated dormancy release (dashed line) is obtained by integrating daily dormancy
520
release (bars). Dotted lines represent accumulated germination/pre-emergence growth of
521
each non-dormant fraction. Note that as time increases, the dotted line reaches the height of
522
the bar, meaning that each non-dormant seedbank fraction germinates during the following
523
days according to a specific distribution. Accumulated emergence (solid line) is obtained
524
by integrating each day the germinated/post-germinated fraction corresponding to each
525
non-dormant seedbank fraction. (B) Genetic algorithm based parameter estimation scheme.
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Em ergence (% )
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100 90 80 70 60 50 40 30 20 10 0
300
600
900
1200
1500
1800
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Soil Therm al Tim e (C)
Figure 1. Typical S-type model fitted to emergence data
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v01
v11
f z1
w1
ϴT
v02 v12 v21
z2
w0
w2
f
f
y
v22
ϴH
w3
v13
z3
v23 v03
f
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Re Figure 2. A three layer feed-forward ANN. The network has two inputs (thermal-
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time= ϴT and hydro-time=ϴH), three neurons in the hidden layer and a single output variable (y = cumulative emergence) (adapted from Chantre et al., 2014).
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6
Figure 3. Genetic algorithm based model for Avena fatua field emergence prediction
7
(adapted from Blanco et al.,2014). (A) Schematic representation of the model showing
8
that accumulated dormancy release (dashed line) is obtained by integrating daily
9
dormancy release (bars). Dotted lines represent accumulated germination/pre-emergence
10
growth of each non-dormant fraction. Note that as time increases, the dotted line reaches
11
the height of the bar, meaning that each non-dormant seedbank fraction germinates
12
during the following days according to a specific distribution. Accumulated emergence
13
(solid line) is obtained by integrating each day the germinated/post-germinated fraction
14
corresponding to each non-dormant seed bank fraction. (B) Genetic algorithm based
15
parameter estimation scheme.
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Table S1. Empirical and soft computing based models for weed emergence published from 1996 to 2015. This list does not pretend to be exhaustive, but only gives a sample of the multitude of empirical weed emergence models developed in the last 20 years. Abbreviations: RH: Chapman-Richards; CSP: Cubic Splines; POL: Polynomial; NLME: Nonlinear mixed-effect models. !
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X
X
Apocynum androsaemifolium L.
turf Turf
X
Datura stramonium L.
X
X
X
X
X
X
X
Digitaria sanguinalis (L.) Scop.
Echinocloa colonum (L.) Link
Echinocloa cruss-galli (L.) Beauv.
Echinochloa ssp.
Eleusine indica (L.) Gaertn.
Eriochloa villosa (Thunb.) Kunth
X
X
X
X
X
Galium spp
Galium spurium L.
Galium tricornutum Dandy
Heliotropium europaeum L.,
Hibiscus trionium L.
X
X
Galinsoga parviflora Cav.
X
X
Galinsoga ciliate Raf. Blake
Galium aparine L.
X
Fallopia convolvulus (K.) A. Löve
X
X
X
Digitaria ischaemum (Schreb.) Schreb. ex Muhl.
X
X
X
X
X
X
X
X
Datura ferox L.
X
X
Cyperus rotundus L.
RH-CSP
NLME
RH-CSP
NLME
X
turf
Cucumber
winter cereals
winter cereals
winter cereals
winter cereals; No indicated
No indicated
No indicated
No indicated
turf
maize, soybean, turf
Rice
corn, soybean,rice, cotton, turf
Maize, Soybean
Maize; soybean, turf
Maize; Soybean
Cucumber
Rice
sunflower; cucumber
No indicated
Cyperus difformis L.
RH-CSP
Cucumber
Wheat
No indicated
turf; cucumber
corn/Soybean, No indicated
turf
No indicated
cereals
winter cereals, No indicated
cereals
cereals, canola
Garcia et al., 2013; Cao et al., 2013
Haj Seyed Hadi & Gonzalez-Andujar, 2009; Leguizamon et al., 2005
Page et al., 2006; Bullied et al., 2003
Martinson et al., 2007; Gonzalez-Diaz et al., 2007
Graziani & Steinmaus, 2009 Chantre et al., 2014; Blanco et al., 2014; Chantre et al., 2012;
Webster & Cardina, 1999
Wu et al., 2013
Blackshaw, 2003
Schutte et al., 2008; Werle et al., 2014
Davis et al., 2013; Schutte et al., 2012;
Myers et al., 2004; Werle et al. 2014
Otto et al., 2007
Co
py
Werle et al., 2014
Tursun et al., 2015
Royo-Esnal, 2010
Royo-Esnal, 2010
Royo-Esnal, 2010
Royo-Esnal, 2010; Benjamin et al., 2010
Otto et al., 2007
Otto et al., 2007
Otto et al., 2007
Werle et al., 2014
Leguizamon et al. 2009; Masin et al., 2005
Lundy et al., 2014
Dorado et al., 2009; Werle et al., 2014
Masin et al., 2014; Bagavathiannan et al, 2011;
Leguizamon et al. 2009
Leguizamon et al. 2009; Masin et al., 2005;Myers et al., 2004
Masin et al., 2014; Masin et al., 2010;
Fidanza et al., 1996
Werle et al., 2014
Dorado et al., 2009; Vitta & Satorre, 1999
Tursun et al., 2015
Lundy et al., 2014
Satorre et al., 1996; Tursun et al., 2015
Zambrano-Navea et al., 2013
Tursun et al., 2015
Donald, 2000
Otto et al., 2007
Roman et al., 2000; Werle et al., 2014; Tursun et al., 2015
Bullied et al., 2003;Grundy & Mead, 2000;
Otto et al., 2007;Myers et al., 2004; Leblanc et al., 2004;
Grundy et al., 2010;Masin et al., 2010;
Werle et al., 2014 Masin et al., 2014; Schutte et al. 2014: Masin et al., 2012;
Otto et al., 2007; Grundy & Mead, 2000
Haj Seyed Hadi & Gonzalez-Andujar, 2009
w
vie
No indicated
non crop
Blueberry
no indicated
X
X
No indicated; corn/soybean, turf
corn, soybean;turf
No indicated
Werle et al., 2014
Masin et al., 2010; Haj Seyed Hadi & Gonzalez-Andujar, 2009
Vitta & Satorre, 1999
Myers et al., 2004
Haj Seyed Hadi & Gonzalez-Andujar, 2009
Bullied et al., 2003; Werle et al. 2014; Tursun et al., 2015
turf
X
X
X
Dorado et al., 2009; Myers et al., 2004; Werle et al., 2014 Ekeleme et al., 2005 Benjamin et al., 2010; Otto et al., 2007
canola; no indicated, cucumber
X
X
X
Reference Masin et al., 2014;Masin et al., 2010;
Maize; cereals, canola,
Soybean
corn, Soybean
cereals
Re X
X
X
wheat; No indicated
corn, cassava
Maize; Soybean; turf
Nonparametric ANNs GAs Crop/s
Cynodon dactylon L. Pers.
RH-CSP
RH-CSP
RH
Other
Conyza bonariensis (L.) Cronquist
X
X
Convolvulus arvensis L.
X
X
X
X
X
X
X
Cirsium arvense ( L.) Scop.
X
X
Chenopodium polyspermum L.
X
Chenopodium album L.
X
Capsella bursa-pastoris L. (Medicurs)
Cenchrus spinifex Cav.
X
X
Bromus spp.
Bromus diandrus Roth
Avena sterilis L.
X
Avena fatua L.
X
X
X
Apocynum cannabinum L.
X
X
X
Arundo donax L.
X
X
Ambrosia trifida L.
Androsace septentrionalis L.
X
Ambrosia artemisiifolia L
X
X
Amaranthus rudis Sauer
Amaranthus spp.
X
X
Amaranthus retroflexus L.
X
X
X
Amaranthus quitensis Kunth
X
X
Amaranthus hibridus L.
Amaranthus blitoides S. Wats
X
LOGISTIC
X
X
Ageratum conyzoides L.
X
GOMPERTZ
Alopecurus myosuroides L
X
WEIBULL
Abutilon teophrasti Medik.
Species
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Page 24 of 40
X
Kochia scoparia (L.) Schrad.
X
Portulaca oleracea L.
X
Solanum ptychanthum Dunal
X
Xanthium strumarium L.
X
X
X
Veronica hederifolia L.
Veronica persica Poir.
X
X
X
X
Maize; Soybean; turf
No indicated
No indicated
Maize, Soybean
Cucumber
canola, No indicated
X
X
X
Thlaspi arvense L.
Tribulus terrestris L. Urochloa platyphylla (Munro ex C.Wright) R.D.Webster
Maize; soybean
turf
No indicated
turf, corn, soybean
Wheat; No indicated
X
X
Cucumber
turf
X
X
X
X
Sorghum halepense (L.) Pers
X
Stellaria media (L.) Vill.
X
Sorghum bicolor (L.)
Sonchus oleraceus L.
X
RH-CSP
canola No indicated
X
RH-CSP
X
X
X
Sisymbrium irio L.
Solanum nigrum L.
Sinapis arvensis L.
X
Maize, turf, canola
Maize; turf
Sicyos angulatus L.
X
X
X
X
X
Turf, corn, soybean
Maize, Soyberan
Bullied et al., 2003; Werle et al., 2014
Masin et al., 2010; Masin et al., 2005a
Masin et al., 2010; Werle et al., 2014
Masin et al., 2005;Myers et al., 2004
Leguizamon et al. 2009
Myers et al., 2004;Werle et al., 2014
McGiffen et al., 2008
Harris et al., 1998
Tursun et al., 2015
Werle et al., 2014
Bullied et al., 2003
Co
Werle et al., 2014
Dorado et al., 2009; Norsworthy & Oliveira, 2007;
Otto et al., 2007
Grundy & Mead, 2000
Leguizamon et al. 2009
Tursun et al., 2015
Bullied et al., 2003; Werle et al., 2014;Royo-Esnal et al., 2015
Benjamin et al., 2010; Grundy et al., 2010; Grundy & Mead, 2000
Leguizamon et al. 2009;Dorado et al., 2009
Masin et al., 2012;Masin et al., 2010;
Werle et al., 2014
Otto et al., 2007
Werle et al., 2014; Myers et al., 2004
Tursun et al., 2015
Ray et al., 2005
Bullied et al., 2003
Werle et al., 2014
py
Otto et al., 2007; Calado et al., 2009; Tursun et al., 2015; Royo-Esnal et al., 2015
w
vie
corn, Soybean; turf
berries,ornmaentals, vegetables
forages, cereals, mint,
non crop
Cucumber
Re
No indicated
canola
Izquierdo et al., 2009
Werle et al., 2014
Grundy & Mead, 2000 Eizenberg et al. 2012
Izquierdo et al.,2013; Haj Seyed Hadi & Gonzalez-Andujar, 2009
Otto et al., 2007
Blackshaw et al. 2002
Schwinghamer & Van Acker, 2008; Werle et al., 2014
Werle et al., 2014
Haj Seyed Hadi & Gonzalez-Andujar, 2009
Ekeleme et al., 2003
Weed Research
No indicated; cucumber; cereal
cereals
turf
Sunflower
No indicated
cereals
No indicated
No indicated
Grassland; turf
turf
Setaria viridis (L.) Beauv.
X
X
RH-CSP
corn, cassava cereals
Setaria pumila (Poir.)
X
Setaria geniculata (Lam) Beauv.
X
X
RH-CSP-POL
X
X
X
X
Setaria faberi Herrm.
X
X
X
X
X
X
X
X
Setaria glauca (L.) Beauv.
X
Senecio vulgaris L.
Ranunculus repens L.
X
Polygonum pensylvanicum L.
X
X
Polygonum convolvulus L.
Polygonum aviculare L.
X
X
X
Papaver rhoeas L.
X
X
Matricaria perforata Merat
Orobanche cumana wallr.
X
Panicum dichotomiflorum Michx.
X
X
Lolium rigidum L.
X
Lamium purpureum L.
Lamium amplexicaule L.
X
X
Ipomoea hederacea Jacq.
Ipomoea purpurea (L.) Roth
Imperata cylindrica (L.) Beauv.
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REFERENCES BAGAVATHIANNAN MV, NORSWORTHY JK, SMITH KL & BURGOS N (2011) Seedbank size and emergence pattern of barnyardgrass (Echinochloa crus-galli) in Arkansas. Weed Science 59, 359-365. BENJAMIN LR, MILNE AE, PARSONS DJ & LUTMAN PJ (2010) A model to simulate yield losses in winter wheat caused by weeds, for use in a weed management decision support system. Crop Protection 29, 1264-1273. BLACKSHAW RE (2003) Soil temperature and soil water effects on pygmyflower (Androsace septentrionalis) emergence. Weed Science 51, 592-595.
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BLACKSHAW RE, BRANDT RN & ENTZ T (2002) Soil temperature and soil water effects on henbit emergence. Weed Science 50, 494-497.
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BULLIED WJ, MARGINET AM & VAN ACKER RC (2003) Conventional-and conservationtillage systems influence emergence periodicity of annual weed species in canola. Weed
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Science 51, 886-897.
CALADO JM, BASCH G & DE CARVALHO M (2009) Weed emergence as influenced by soil
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