Predicting Seedling Emergence of Three Canarygrass ( Phalaris ) Species under Semi-Arid Conditions Using Parametric and Non-Parametric Models

: The Phalaris genus includes annual weed species such as short-spiked canarygrass ( Phalaris brachystachys Link.), little-seed canarygrass ( Phalaris minor Retz.) and hood canarygrass (Phalaris paradoxa L.), which are especially problematic in Spain; as such, there is a need to develop models to predict the timing of their emergence. Field experiments were conducted at two different locations during two (2006/07 and 2007/08) and three (from 2005/06 to 2007/08) growing seasons. In both locations, 500 seeds of each Phalaris species were sown each growing season, simulating rain-fed cereal ﬁeld conditions. In addition, the models were validated with three, four and eight independent experiments for P. brachystachys , P. minor and P. paradoxa , respectively. The emergence period of the three Phalaris species lasted between 31 and 48 days after sowing (DAS), showing two main ﬂushes. The three cardinal points for parametric and non-parametric models were established to be between − 1 ◦ C and 1 ◦ C for base temperature, between 9.8 ◦ C and 11.8 ◦ C for optimal temperature and between 21.2 ◦ C and 23.4 ◦ C for ceiling temperature; base water potential was estimated to be between − 1 and − 1.1 MPa. Both parametric and non-parametric models obtained similar results and were successfully validated in 12 out of 15 independent experiments. four and eight of eight experimental locations for P. brachystachys , P. minor and P. paradoxa , respectively. Our ﬁndings demonstrate that parametric and non-parametric statistical tools can predict the emergence of seedlings under different agroclimatic conditions. These models, especially the non-parametric HTT models, are potentially applicable to actual ﬁeld situations by providing guidance for DSS to implement weed management tactics.


Introduction
Phalaris is a grass genus that includes annual weed species that are spread through the Mediterranean basin area [1,2], India [3,4], China [5] and the United States [6]. Similar to many problematic annual weeds, the success of this genus as a weed can be attributed to its high seed production, and hence, high rate of population growth [7].
The difficulty of their chemical control and the high cost of effective herbicides against these weeds are probably the main reasons these weed species are problematic in winter cereal crops [13]. In addition, the selection of herbicide-resistant biotypes has made their control even more complicated. There have been 11 and 8 cases of herbicide-resistant biotypes of P. minor and P. paradoxa that involve 22 and 12 active ingredients, respectively, of three modes of actions (ACCase inhibitors, ALS inhibitors and Photosystem II inhibitors) described so far. Further, there are four more cases for P. brachystachys, belonging to eight In the case of P. brachystachys and P. paradoxa, seeds were harvested in June 2005 from a commercial wheat field near Jerez, Cadiz, in southern Spain (37.15 N, 6.18 W); whereas seeds of P. minor were collected from a commercial wheat field of Cordoba (37.86 N, 4.83 W). For the three species, seeds were collected from more than 20 individuals. Once at the laboratory, seeds were cleaned and dry-stored in a refrigerator at 4 • C until the sowing date.
In both locations, four quadrates of 25 × 25 cm were sown with 500 seeds for each Phalaris species and each growing season. The sowing procedure varied between locations.
In Tomejil, commercial field soil was used without any previous replacement or sterilization. In this location, the upper 2 cm of soil layer was extracted, mixed with the corresponding seeds and then returned to the ground so that the seeds were evenly distributed in the top 2 cm of the soil. An additional control was introduced next to each plot to avoid the natural seed bank effect. In contrast, in the ETSIA experiments, the top 5 cm of soil was replaced by a mixture of 25% Kekkilä peat (Kekkilä Oy, Vantaa, Finland), 25% sand and 50% local soil. This mixture was oven-dried at 100 • C for 22 h to sterilize from pathogens and natural seed banks. Afterward, seeds were added to this mixture and were incorporated into the corresponding plot. In both locations, the date when the seeds were mixed with the soil was considered the sowing day. This procedure was followed each year and each newly sowed plot was placed next to that from the previous season, which was left undisturbed. This procedure allowed us to monitor seedling emergence over two growing seasons and to study the emergence under a tillage simulation (sowing season), in which the TT and HTT accumulation starting from the sowing date, and under non-tillage situation (second season), in which the initial moment was chosen at the first relevant rainfall. As a result, the models could be tested in eight different situations (Table 1). Seedling emergence was recorded weekly with destructive counts to avoid double counts, between October and May each season. A 2 mm mesh cage was placed over each plot to avoid seed or seedling losses by predators.

Estimation of TT and HTT
Three biological parameters, T b , T o and T c , were used to estimate TT [24,25]. For the estimation of HTT, the accumulation of TT was only produced when soil moisture (soil water potential, Ψ) rose above a base water potential (Ψ b ). TT and HTT are the accumulated DTD and hydrothermal degrees (DHD), which were obtained via the following: where T is the daily temperature, T b is the base temperature, T o is the optimal temperature, T c is the ceiling temperature, Ψ is the daily water potential and Ψ b is the base water potential.
The three biological parameters of TT for each species were established through an iterative process until the best combinations were obtained for the most accurate models. This best combination was chosen by representing field emergence percentages against the different TT, then applying parametric and non-parametric regressions. The same procedure was used to set the biological parameters for HTT; however, in this case, we added Ψ b to the combination.
Daily maximum and minimum air temperatures and daily precipitation were obtained from the closest meteorological station in each location. In order to estimate the soil Ψ, Saxton and Rawls [26] equations were followed. We also used a procedure defined by Fuentes-Yagüe and García-Legaspi [27] to estimate the soil water content needed for these equations.

Development of the Parametric Model
The Weibull three parameters in Equation (1) were tested as a biological growth model in a parametric non-linear regression.
where Y is the cumulative emergence percentage from the total percentage of seedling emergence (A), which in this case was fixed to 100% each season, x is the TT or HTT and k is the slope of the curve at b, which is the inflection point.

Development of the Non-Parametric Model
For the non-parametric regression, observed data were aggregated using the next cumulated kernel density estimation (2) [19]: where K(t) is the integrated Gaussian kernel (3), t i is the TT or HTT at the middle of two consecutive inspections, W i is the percentage of emerged seedlings counted between two consecutive inspections and h is the bandwidth or the smoother parameter.
The bandwidth (h) was selected using the plug-in approach. This approach was conducted with the R software, using the function "hpi.kcde" from the "ks" package [28]. Then, the "kcde" function from the same package was used to apply the Gaussian kernel distribution explained before.

Model Accuracy
The accuracy of the models was tested with the root mean square error (RMSE, 4), where greater model accuracy, and thus the best combination of biological parameters, is indicated by lower RMSE values. As a reference, RMSE was evaluated with the scale proposed by Royo-Esnal et al. [29] for percentages of emergence; their model is as follows: excellent accuracy for values under 5, very good for values between 5 and 10, good for values between 10 and 15 and not successful for values over 15.
where x i represents the observed cumulative percentage emergence, y i is the predicted cumulative percentage of emergence and n is the number of observations.

Data Validation
The developed models were tested with independent data obtained from two locations ( Table 2), Seville-Garden and ETSIA, during three (from 2016/17 to 2018/19 season) and one season (2018/19), respectively. In Seville-Garden (37.35 N, 5.93 W), the experiment was conducted using 35 L pots containing a mixture of 50% sand and 50% peat moss, while in the ETSIA (same location as the experiment), the experiment was performed in 25 × 25 cm 2 quadrants, as in the original experiment. Data from five independent experiments for the emergence of P. paradoxa across Spain (Table 3) were used to validate the models. In these experiments, plots were also quadrates of 25 cm × 25 cm 2 . The sowing procedure for all validation experiments was the same. In each plot, the upper 2 cm of the soil layer was extracted, mixed with 1000 seeds and then returned to the ground so that the seeds were evenly distributed. Sowed seed density was between 500 and 1000; the percentage of emerged seedlings was used for validation, fixing the maximum number to 100%.
During the experiments, a temperature datalogger (digital thermometer DS18B20; Maxim, San José, CA, USA) was buried at a depth of 2 cm in each experimental location. Rainfall data were obtained from the closest meteorological station for each location.

Weather Conditions
During the three seasons between September to May, the mean temperature was similar in both locations, ranging from 13.5 • C to 14.9 • C. September was the hottest month with a monthly mean temperature between 22.4 • C and 24.2 • C, whereas January was the coldest month (8.2-10.8 • C). On the other hand, precipitation varied in quantity and in distribution across the three seasons, ranging from 363 mm to 539 mm, with the highest recorded rainfall occurring in October, November or April, depending on the year (Table 4 and Figure 1). However, moisture was not a limiting factor that prevented seedlings from emerging in any of the three seasons.

Description of the Emergence
In the years in which seeds were sowed, the emergence period (time required for 10% to 90% emergence) of the three Phalaris species lasted between 31 and 48 days after sowing (DAS); 10% of emergence was reached between 2 and 27 December , whereas 50% and 90% were achieved between 28 December and 1 February and between 9 and 29 January, respectively. In most cases, the emergence pattern showed two flushes, the first in December and the second in February. Despite the similarity of the emergence pattern between the three species, P. minor showed a longer emergence period, whereas it was shorter in P. brachystachys ( Table 5).
Seeds that did not emerge during the first season and remained in the soil began emergence earlier in the following season due to the rainfall during October. In 2006/07, 50% emergence was reached during December, but 90% emergence occurred in February; thus, the emergence period was approximately three months. On the contrary, during

Description of the Emergence
In the years in which seeds were sowed, the emergence period (time required for 10% to 90% emergence) of the three Phalaris species lasted between 31 and 48 days after sowing (DAS); 10% of emergence was reached between 2 and 27 December, whereas 50% and 90% were achieved between 28 December and 1 February and between 9 and 29 January, respectively. In most cases, the emergence pattern showed two flushes, the first in December and the second in February. Despite the similarity of the emergence pattern between the three species, P. minor showed a longer emergence period, whereas it was shorter in P. brachystachys (Table 5). Seeds that did not emerge during the first season and remained in the soil began emergence earlier in the following season due to the rainfall during October. In 2006/07, 50% emergence was reached during December, but 90% emergence occurred in February; thus, the emergence period was approximately three months. On the contrary, during 2007/08, the emergence period was similar or even shorter than that in newly sowed plots, except for P. brachystachys, which showed similar behavior to the previous season ( Figure 2 and Table 5).

Accuracy of the Parametric Model
The biological parameters established for Phalaris species were very similar, setting 1 °C as Tb for the three of them. Additionally, To and Tc were established at 9.9 °C and 22.4 °C, 10.0 °C and 21.2 °C and 11.8 °C and 22.8 °C for P. brachystachys, P. paradoxa and P. minor, respectively. On the other hand, the Ψb was established at −1.0 MPa for P. paradoxa

Accuracy of the Parametric Model
The biological parameters established for Phalaris species were very similar, setting 1 • C as T b for the three of them. Additionally, T o and T c were established at 9.9 • C and 22.4 • C, 10.0 • C and 21.2 • C and 11.8 • C and 22.8 • C for P. brachystachys, P. paradoxa and P. minor, respectively. On the other hand, the Ψ b was established at −1.0 MPa for P. paradoxa and P. minor, whereas it was established at −1.1 MPa for P. brachystachys.
The parameters of the Weibull equation are defined in Table 6. Regarding these equations, Phalaris species achieved 50% emergence between 24 and 30 cumulated daily thermal degrees (DTD) for TT and between 22 and 39 cumulated daily hydrothermal degrees (DTD) for HTT. According to the accuracy of the parametric models, TT models for each species presented average RMSE values between 10.9 and 14.5. The most accurate model was for P. minor, in which an excellent accuracy (RMSE ≤ 5) was achieved in one situation, good accuracy (5 < RMSE ≤ 10) in four more situations and sufficient accuracy (10 < RMSE ≤ 15) and unsuccessful accuracy (RMSE > 15) in one situation each (Table 7). On the other hand, P. paradoxa and P. brachystachys presented a good fit in two and three situations, sufficient in one and four situations and unsuccessful in four and one more situation, respectively (Table 7, Figure 3). Scarce seedling emergence did not allow fitting the models to the data from P. brachystachys and P. minor at Tomejil-S07YR08.
Regarding the HTT model, soil moisture did not improve the model accuracy for P. minor and P. brachystachys; however, it slightly increased the precision for P. paradoxa, reducing the RMSE value from 14.5 to 14.2 (Table 7, Figure 3).

Figure 3.
Predicted emergence for the three Phalaris species, using thermal (dotted line) and hydrothermal (black line) time-based Weibull models at each location and for the first and second seasons in each plot. Black dots-observed (mean) seedling emergence. Scarce seedling emergence did not allow fitting the models to the data in P. brachystachys and P. minor at Tomejil-S07YR08. Predicted emergence for the three Phalaris species, using thermal (dotted line) and hydrothermal (black line) time-based Weibull models at each location and for the first and second seasons in each plot. Black dots-observed (mean) seedling emergence. Scarce seedling emergence did not allow fitting the models to the data in P. brachystachys and P. minor at Tomejil-S07YR08.

Accuracy of the Non-Parametric Model
The best combinations of the three cardinal temperatures for the non-parametric models were different from those established with the parametric model. T b , T o and T c were established at 0 • C, 9.8 • C and 23.4 • C for P. brachystachys, at −1 • C, 9.8 • C and 22.5 • C for P. paradoxa and at 1 • C, 12.3 • C and 22.7 • C for P. minor. However, the Ψ b value for the non-parametric model was the same as for the parametric models.
With the non-parametric TT model, 50% emergence for P. paradoxa was reached at 42 cumulated DTD and 90% emergence at 75; whereas 30 and 62 total accumulated DHD were needed for HTT to reach 50% and 90% emergence, respectively. For P. minor, TT and HTT models required 32 and 23 accumulated DTD/DHD, respectively, to achieve 50% emergence and 61 accumulated DTD/DHD was required to reach 90% emergence. Finally, the non-parametric models for P. brachystachys, required 40 and 67 accumulated DTD/DHD to reach 50% and 90% emergence (Figure 4).

Accuracy of the Non-Parametric Model
The best combinations of the three cardinal temperatures for the non-parametric models were different from those established with the parametric model. Tb, To and Tc were established at 0 °C, 9.8 °C and 23.4 °C for P. brachystachys, at −1 °C, 9.8 °C and 22.5°C for P. paradoxa and at 1 °C, 12.3 °C and 22.7 °C for P. minor. However, the Ψb value for the non-parametric model was the same as for the parametric models.
With the non-parametric TT model, 50% emergence for P. paradoxa was reached at 42 cumulated DTD and 90% emergence at 75; whereas 30 and 62 total accumulated DHD were needed for HTT to reach 50% and 90% emergence, respectively. For P. minor, TT and HTT models required 32 and 23 accumulated DTD/DHD, respectively, to achieve 50% emergence and 61 accumulated DTD/DHD was required to reach 90% emergence. Finally, the non-parametric models for P. brachystachys, required 40 and 67 accumulated DTD/DHD to reach 50% and 90% emergence (Figure 4).  The RMSE values for the TT-based models of the three Phalaris species were between 10.9 and 15.8. The most accurate model was obtained for P. minor, which was excellent for one situation, good for four more situations and sufficient and unsuccessful in one situation each. The accuracy of the P. brachystachys model was good in three situations, sufficient in another three and insufficient in one situation; however, the models for P. paradoxa only obtained excellent accuracy in one situation, good in another, sufficient in two more and unsuccessful in four situations (Table 8, Figure 5).
Concerning the HTT models, the soil moisture had only slightly improved the precision for the P. paradoxa model, reducing the RMSE value from 15.8 to 14.4 (Table 8, Figure  5). The missing values of P. brachystachys and P. minor at Tomejil-S07YR08 are due to the lack of enough seedling emergence to apply the models. The RMSE values for the TT-based models of the three Phalaris species were between 10.9 and 15.8. The most accurate model was obtained for P. minor, which was excellent for one situation, good for four more situations and sufficient and unsuccessful in one situation each. The accuracy of the P. brachystachys model was good in three situations, sufficient in another three and insufficient in one situation; however, the models for P. paradoxa only obtained excellent accuracy in one situation, good in another, sufficient in two more and unsuccessful in four situations (Table 8, Figure 5). The missing values of P. brachystachys and P. minor at Tomejil-S07YR08 are due to the lack of enough seedling emergence to apply the models.  The missing values of P. brachystachys and P. minor at Tomejil-S07YR08 are due to the lack of enough seedling emergence to apply the models.
Concerning the HTT models, the soil moisture had only slightly improved the precision for the P. paradoxa model, reducing the RMSE value from 15.8 to 14.4 (Table 8, Figure 5).

Validation of the Models with Independent Data Sets
Although the validation of the parametric and non-parametric models with the independent data was similar, the consideration of the soil moisture increased the precision of the parametric and non-parametric HTT-based models for P. minor and P. paradoxa with respect to the TT-based ones; however, this did not happen for P. brachystachys (Table 9, Figure 6). Table 9. Root mean square error (RMSE) values obtained from thermal (TT) and hydrothermal (HTT) times of parametric and non-parametric models at each validation location. Numbers in bold show the lowest RMSE value in each location and season.

Emergence Pattern
Similar to the observations of Jiménez-Hidalgo [11] and Taylor et al. [30], the emergence patterns of the three Phalaris species were similar, with the first seedlings observed in November and the last ones in March or even April, depending on the season, but in The models for P. brachystachys showed lower accuracy than the models of the other two Phalaris species for the description of the independent data. In this case, the P. brachystachys model only achieved sufficient accuracy at one location out of three and was best with the non-parametric TT model. On the contrary, P. minor and P. paradoxa models were successfully validated with the independent data. In the case of P. minor, the RMSE values were successful at three of the four studied locations (Table 9, Figure 6), with the parametric HTT model obtaining the highest accuracy. Further, HTT reduced the RMSE values for parametric and non-parametric models at all validation locations. Concerning P. paradoxa, the models were successfully validated at the eight locations, where the non-parametric HTT model was the most accurate; in this case, the soil moisture reduced the RMSE values at five out of eight locations.

Emergence Pattern
Similar to the observations of Jiménez-Hidalgo [11] and Taylor et al. [30], the emergence patterns of the three Phalaris species were similar, with the first seedlings observed in November and the last ones in March or even April, depending on the season, but in all cases with two flushes during the emergence season, the first one in December and the second in February. Both flushes occurred when the mean air temperature was close to the optimum temperature, between 9 • C and 13 • C, and was separated by a period when the mean air temperature dropped below 9 • C.
When we compared the emergence of the Phalaris species to that of other problematic winter weeds in the south of Spain, we found that they were similar to that of winter wild oat (Avena sterilis subsp. ludoviciana (Durieu) Gillet and Magne), of which the emergence period also lasts from November to March [31]. On the contrary, Phalaris showed more staggered emergence periods than north African knapweed (Centaurea diluta Aiton), which emerges between late October and early January [25], or ryegrass (Lolium rigidum Gaudin), which emerges from November to February [24]. The wide emergence period of the Phalaris species could also contribute to their presence as problematic weeds in summer crops.

Threshold Parameters (T b , T o , T c and Ψ b )
The three cardinal temperatures (T b , T o and T c ) were similar between models and species. The T b ranged from −1 • C to 1 • C, which is a similar to that used by González-Andújar et al. [20] for P. paradoxa, who established this parameter at 0.8 • C; lower than that established by Mesgaran et al. [32] and Derakhshan et al. [22] for P. minor (3.5 • C and 4.7 • C, respectively), but the latter were estimated for germination under controlled conditions in germination chambers and might vary from required field conditions for emergence.
The established T o , between 9.9 • C and 12.3 • C, was also lower than that set under controlled conditions by Derakhshan et al. [22], who established them between 22.6 and 29.6 • C. The differences between the results observed in the present manuscript and those from Derakhshan et al. [22] might be explained because the authors established a T o for germination, and because seeds belong to a population growing at a completely different climate (north of Iran) and temperature requirements could easily be different. However, the T o estimated in the present work is in agreement with values estimated in field conditions by Jiménez-Hidaldo [11] and Taylor et al. [30], who describe an optimum range between 10-15 • C and 10-17 • C, respectively. Similar to T b and T o , T c was also lower than that established under controlled conditions [22,33], but this parameter has not been previously estimated in field conditions for Phalaris species in any other work, and thus, no comparison is possible.
Concerning Ψ b , no significant differences were found between the three Phalaris species: it was set to −1.1 MPa for P. brachystachys and −1 MPa for the other two species. Despite this, P. brachystachys was shown to be a little more tolerant to drought conditions for the emergence; this is in agreement with observations from Alcantara et al. [34], who described a higher drought tolerance by P. brachystachys than P. minor during growth stages.
Apart from soil temperature and moisture, other factors are known to affect the start of the emergence process, considering this process from dormancy release to the emergence of cotyledons on the soil surface. Light is known to promote the release of dormant seeds of Phalaris species, such as P. paradoxa [35] and P. minor [36]; however, in the present study, light could only have been a relevant variable at the sowing date, as no further soil disturbance was performed. An interesting future experiment could be established to study the effect of tillage at different dates on the emergence of these Phalaris species and the suitability of the models developed in the present manuscript to those emergence patterns.

Parametric vs. Non-Parametric Models
Although the non-parametric model could have slightly improved the accuracy of the parametric TT-based model for P. brachystachys and the HTT-based model for P. minor, in practice, both parametric and non-parametric models showed very similar accuracy (Tables 3 and 7, Figures 3 and 5), as is shown by the validation results, which show similar precision to those of the parametric model, with improved accuracy at 9 of 15 experimental locations (Table 8). These results show that non-parametric models have the same capacity to describe and predict weed emergence as classical parametric models, which is somehow in disagreement with the observations from Gonzalez-Andújar et al. [20], who concluded that non-parametric models were only useful for describing and not for predicting weed emergence. These differences could be explained by the fact that Gonzalez-Andújar et al. [20] developed a model for P. paradoxa using only data from a single location and year to predict its emergence at the same locations during the next two years. The present work used data from two locations and three seasons; thus, its conclusions are more reliable than those obtained from a single season.

Applicability of the Models
In this work, emergence models were successfully developed to describe the emergence of three Phalaris species, with both parametric and non-parametric statistical tools. Emergence models frequently present limited application due to within-species variation. Very often, models developed in one location cannot be applied to other locations with different agroclimatic conditions because models tend to fail when environmental conditions vary from where they were developed [37]. Moreover, the mother plant effect promotes differences in the dormancy and germination characteristics of the offspring, even in the same population [38]. This has been the case of L. rigidum, whose emergence model could successfully be applied in central and north-east Spain, but not in the south [24]. However, in the present work, the three models could be validated with independent data from the same (Guadalcázar, Seville, Tomejil) and from different agroclimatic locations (Burgos, Huesca, and Valladolid) within Spain. This result suggests that the applicability of these models is wider than for other weed species, and that they could be applied with fair accuracy, at least in the whole Iberian Peninsula with a Mediterranean climate. Despite this promising result, the applicability of these models for the emergence of Phalaris species in other Mediterranean climatic zones should be checked and be calibrated if necessary.
Ideally, these models should be implemented in software tools together with other already developed models. There already are several models for the emergence of winter weeds in Spain, such as those for Papaver rhoeas [37], L. rigidum [24], A. sterilis [31] or Bromus diandrus [39], among others, and an effort should be made to integrate them into a DSS tool, such as AlertInf [40,41], which is being applied in the Venetto region (Italy) with considerable success.

Conclusions
The parametric and non-parametric models successfully described the emergence of P. brachystachys, P. minor and P. paradoxa. In addition, both models presented similar results at independent validation data, obtaining good accuracy at one of three, three of four and eight of eight experimental locations for P. brachystachys, P. minor and P. paradoxa, respectively. Our findings demonstrate that parametric and non-parametric statistical tools can predict the emergence of seedlings under different agroclimatic conditions. These models, especially the non-parametric HTT models, are potentially applicable to actual field situations by providing guidance for DSS to implement weed management tactics.