Modeling the emergence of North African knapweed (Centaurea diluta), an increasingly troublesome weed in Spain

Abstract North African knapweed (Centaurea diluta Aiton) is an annual weed that is widespread in southern Spain and is of increasing concern in dryland cropping systems. Despite its expanding range in Spain, there is limited information on the emergence timing and pattern of this species, knowledge of which is critical for developing more timely and effective management strategies. Therefore, there is a need to develop simple and reliable models to predict the timing and emergence of this annual weed under dryland conditions. A multi-location field experiment was established across Spain in 2016 to 2017 to assess the emergence of C. diluta. At each of 11 locations, seeds were sown in the fall, and emergence was recorded. Overall emergence averaged 39% in the first year across all sites and 11% in the second year. In both years, the main emergence flush occurred at the beginning of the growing season. A three-parameter Weibull function best described seedling emergence of C. diluta. Emergence models were developed based on thermal time (TT) and hydrothermal time (HTT) and showed high predictability, as evidenced by root mean-square error prediction values of 10.8 and 10.7, respectively. Three cardinal points were established for TT and HHT at 0.5, 10, and 35 C for base, optimal, and ceiling temperatures, respectively, while base water potential was estimated at −0.5 MPa.


Introduction
In recent years, legislation in the European Union has restricted the number and use of herbicides in cropping systems (Barzman and Dachbrodt-Saaydeh 2011;European Council 1991;European Parliament 2009) as well as tillage frequency (Kutter et al. 2011), thus limiting weed control options for growers. These restrictions have made it more difficult to control troublesome weeds and have led to an increase in the occurrence of lesser-known weeds, such as North African knapweed (Centaurea diluta Aiton) in southern Spain.
Centaurea is a genus in Asteraceae that has a worldwide distribution and comprises a diverse group of about 250 species (Susanna and Garcia-Jacas 2007). Some of the species, such as red star-thistle (Centaurea calcitrapa L.) and Iberian knapweed (Centaurea iberica Trevir. ex Spreng.) (Nosratti et al. 2017) are considered troublesome weeds, while others, including diffuse knapweed (Centaurea diffusa Lam.) and Maltese star-thistle (Centaurea melitensis L.), are of minor agronomic importance. Some Centaurea species have also evolved resistance to several herbicide families, including yellow star-thistle (Centaurea solstitialis L.) to acetolactate synthase inhibitors in the United States, spotted knapweed [Centaurea stoebe subsp. australis (Pančić ex A. Kern.) Greuter] to synthetic auxins in Canada, and garden cornflower (Centaurea cyanus L.) populations to both herbicide families in Poland (Heap 2018).
A total of 94 Centaurea species have been described in the Iberian Peninsula (Valdes et al. 1987), including the increasingly troublesome annual herb, C. diluta. This species is becoming a major agronomic weed, primarily because of its large size and high competitive ability (Saavedra et al. 2018). In recent years, it has spread into southern Spain and is of increasing concern to farmers in the region (Ortiz et al. 2015). The first reference to this species as a weed was in the early 1980s, when it was found in wheat (Triticum aestivum L.), sunflower (Helianthus annuus L.), pea (Pisum sativum L.), and beet (Beta vulgaris L.) fields (Castroviejo et al. 1980;Pujadas-Salvá and Hernández-Bermejo 1986;Saavedra 1997). Since then, its impact has increased, largely because its seeds can easily contaminate cereal grains at harvest and can also be mistakenly seeded with cereal grains at planting. These dispersal pathways (Domínguez-Borrero et al. 2015) may explain its irregular distribution in the region (Vázquez 2008).
Centaurea diluta is an annual dicot native to North Africa and southwestern Europe, including Spain. It is a vigorous plant that can reach up to 350 cm in height and produce a large number of capitula and hairy achenes (3 mm) that can be easily dispersed (Saavedra 1997;Valdes et al. 1987). To our knowledge, there are no published data on the number of seeds produced by C. diluta plants or their dormancy status. But stands of similar annual herb congeners such as C. solstitialis can produce nearly 28,000 seeds m −2 (Gutierrez et al. 2005). Anecdotal reports and studies from similar species suggest that seeds of C. diluta exhibit limited dormancy (Joley et al. 1997(Joley et al. , 2003 There is also relatively little published information on methods for controlling C. diluta, except for several technical reports (Saavedra et al. 2017(Saavedra et al. , 2018. The availability of such information is critical for the development of integrated weed management programs for this species. To develop and implement effective management strategies, a better understanding of its seedling emergence pattern and the ability to accurately predict emergence and growth are required. Seed germination is largely dependent on three key biological parameters related to temperature (Bradford 2002). The first is the base temperature (T b ), which is the minimum temperature for a seed of a given species to germinate such that thermal degrees are not accumulated below this temperature; the second is the ceiling temperature (T c ), which is the maximum temperature for germination, such that no thermal degrees above this temperature are accumulated; and the third is optimum temperature (T o ), which is the temperature at which seed germination occurs most rapidly. These parameters aid in estimating the thermal time (TT) and the hydrothermal time (HTT) for describing the emergence pattern of weeds. Thermal time models only use soil temperature to describe emergence, while HTT models correct TT accumulating degrees when soil moisture is above a base level (Grundy 2003). In dryland cropping systems, HTT-based models are more precise than TT models, because they also take into account the water content of soils (Royo-Esnal et al. 2012). However, accurately determining soil moisture within a field can be difficult, because many soil properties can vary widely within a single field (Finch-Savage 2004). For this reason, TT-based models with good accuracy may be more practical and useful. The ability to accurately predict the emergence pattern of a target weed or weeds can be valuable to crop managers, because it allows them to implement control tactics when weeds may be most vulnerable (Barros and Freixial 2010;Kropff and Spitters 1991;Zimdahl 2007). Increasing the efficacy of a given weed control strategy is likely to also result in improved economic and environmental outcomes, as lower quantities of herbicide or cultivations are needed to achieve the same level of control than later applications or cultivations when plants may be larger and more difficult to control (Shaner and Beckie 2014).
Certainly, knowledge of the phenological stages of target weeds is essential for implementing appropriate management tactics, particularly during early growth, as it can facilitate determining the critical period of weed control (Knezevic and Datta 2015), the most effective method of control (Royo-Esnal et al. 2012), and also potentially provides important information on whether a given species may be adapted to a particular habitat or region (Holt 1991).
Until recently, C. diluta was not considered a major agronomic weed in Spain and, as such, no research has been performed to determine or predict its emergence pattern. However, the increasing importance of this weed in southern Spain and the possibility of invasion into northern Spain as climate changes make C. diluta an important weed species to target for further study. Thus, the objective of this research was to develop a model to predict the emergence pattern of C. diluta and describe its early growth stages under Mediterranean semiarid conditions. This research is critical, because the ability of this species to expand its range into new regions will depend largely on the likelihood of its seeds germinating and its seedlings emerging and establishing in these novel environments.

Plant Material
Seeds of C. diluta were collected from more than 20 individual plants in June 2016 in Los Molares, Sevilla, in southern Spain (37.15°N, 5.72°W) from a commercial wheat field. Seeds were cleaned and dry-stored in a refrigerator at 4 C until needed for field trials in September 2016.

Experimental Design
The experiment was established in 2016 to 2017 in 11 locations across Spain (Figure 1), and in 7 of the locations, C. diluta emergence was monitored both in 2016 to 2017 and for a second season in 2017 to 2018 (Table 1). The experiment was conducted under rainfed conditions with no supplemental irrigation, similar to conditions in cereal fields where this weed species is problematic. Four 0.25 by 0.25 m quadrats were established as experimental replications in each location. In each quadrat, a total of 100 C. diluta seeds were sown in the top 2 cm of soil by gently mixing the soil. The same sowing procedure was followed in all locations, except at the Sevilla Garden site, where the experiment was conducted using 35-L pots containing a mixture of 50% sand and 50% peat moss. Seeds were only sown during the first season between October and November 2016, depending on field and weather conditions (Table 1). Seedling emergence in each quadrat was recorded weekly from October until May, except during emergence flushes, when data were collected every 2 to 3 d. In three northern sites and three southern sites during the first year, the first two seedlings to emerge from each replicate quadrat were recorded and allowed to grow until mid-February to assess establishment success and early growth under different environmental conditions. All other seedlings that emerged at these six sites as well as all seedlings emerging at the other six sites were recorded and removed from quadrats at each sampling. The BBCH scale (Meier 2001) was used to assess seedling phenology for the two plants per quadrat that were allowed to grow. In each location, a data logger with a thermometer DS18b20 sensor (Maxim, San José, California, USA) and conductivity LM393N sensor (ON Semiconductor, Phoenix, Arizona, USA) were placed at a 2-cm soil depth within the experimental area.

Estimation of Thermal and Hydrothermal Time
Temperature and moisture data from each location were used to estimate cardinal temperatures: base (T b ), optimum (T o ), and ceiling (T c ). These values were obtained through an iterative process using the following steps: several combinations of these three cardinal temperatures were used to develop the TT or HTT; then, a nonlinear regression between TT or HTT and observed data (field-emergence data) was tested using three biological growth equations (Equations 1 to 3); and finally, the best-fit combination for the initial parameters was selected. Base water potential (Ψ b ) was calculated using a similar procedure. In the first year, the sowing date was considered as the zero moment, while in the second year, the zero moment was considered the first day when >10 mm of rain were received.
Water content was estimated using conductivity values, given the high correlation between these two variables (Brevik and Fenton 2002), and then was used to calculate the water potential following the equations described in Saxton and Rawls (2006).
Once the cardinal temperatures were fixed, both cumulative thermal (TT) and hydrothermal times (HTT) were calculated by summing the daily TT and HTT as follows: Figure 1. Locations showed as circles indicate areas in Spain where Centaurea diluta is considered a troublesome weed, whereas locations showed as triangle indicate areas where this weed is present but currently not considered problematic. If the soil temperature was between T b and T o : TT = T − T b If the soil temperature was between T o and T c : TT = (T c − T) and if T < T b or T > T c , then TT = 0 where T is the mean daily temperature.
Hydrothermal time was estimated by including soil moisture in the TT calculations.
To develop this TT, a reduction in daily TT was established when the temperature was above T o , because a slight reduction between T o and T c makes more biological sense than a drastic reduction when the temperature is above T c . This approach to determining TT was used by Roman et al. (2000) and Sousa-Ortega et al. (2019) with good results. Moreover, as the three cardinal points were established by an iterative process using numerous combinations of them, a possible result with similar T o and T c would suggest that this slight reduction in TT is not necessary.

Modeling Seedling Emergence and Statistical Analysis
Three sigmoidal models were fit to the results: Gompertz (Equation 1), three-parameter log-logistic (Equation 2), and three-parameter Weibull (Equation 3) (Ritz et al. 2015): where Y is the cumulative emergence; b is the emergence rate; TT is the thermal time (HTT, if using this scale); and m is the inflection point, which is the time to reach 50% emergence (Onofri et al. 2010).
where Y is the cumulative emergence, d is the maximum emergence, b is the slope (emergence rate) at m, and m is the inflection point. The accuracy of these models was tested with the root meansquare error prediction (RMSEP) (Equation 4), where greater model accuracy is indicated by lower RMSEP values (Izquierdo et al. 2013).
where x i represents the actual cumulative percentage emergence, y i is the predicted cumulative percentage emergence, and n is the number of observations. Testing was performed for 13 of 18 data sets, because data from sites with low emergence percentages (<10%) were excluded, as they were considered not representative of the emergence behavior of this species (Guillemin et al. 2013).

Practical Use of the Model
The model selected was tested with independent data to evaluate its predictive ability. The independent validation was conducted in two additional experiments. The first of these experiments was carried out in Morón (37.26°N, 5.75°W) following the same procedure described earlier and sowing C. diluta seeds on December 17, 2018. The soil was a sandy loam (68% sand, 14% silt, and 18% clay), and weather data were recorded with the same data logger described earlier. In the second experiment, the model was fit to a natural seedbank of C. diluta in Montoro (38.01°N, 4.41°W) in 2019 to 2020. The soil at this site was a clay composed of 5% sand, 31% silt, and 62% clay. Weather data were collected from the nearest weather station (Adamuz), and water content was estimated using the equations described in Fuentes-Yaguë (1998).
To further evaluate the accuracy of the model under different weather conditions, temperature and rainfall data for two seasons from the past 10 yr at the Córdoba site were selected to run the model. The weather data were taken from a weather station (37.86°N, 4.80°W) adjacent to the Córdoba experimental site. The first season was selected, because of an early first rain event (September 8, 2013), while the second season was selected for its relatively late first rain event (October 27, 2011). A linear regression based on experimental years was used to estimate the soil temperature for these two seasons.

Statistical Analysis
Differences in total seedling emergence among locations were analyzed by one-way ANOVA for each season. Differences among means were determined using Tukey's test at P = 0.05.

Weather Conditions
Weather conditions differed substantially between locations and seasons. These differences should provide robustness to any mathematical model that fits the emergence pattern. According to the model, moisture levels were adequate for the accumulation of hydrothermal degrees in all cases, with the exception of Sevilla ETSIA (both years), Sevilla FTS, and Valladolid ( Figure 2).

Emergence Pattern
During the first season, the average percentage of emergence among all locations was 38.9% (Table 2), with significant differences between locations (P < 0.0001). Emergence of C. diluta was higher (52% to 63%) in Valladolid, Sevilla Garden, Madrid, Zaragoza, and Sevilla 2H than in Barcelona, Sevilla FTS, and Toledo. The average percentage of C. diluta emergence based on all locations during the first year was lower than that reported for other Centaurea species. The highest emergence values of 52% to 63% are below emergence values reported for other Centaurea species, including C. cyanus (68% to 79%) (Guillemin et al. 2017) and C. iberica (>75%) (Nosratti et al. 2017). However, these studies were conducted under controlled environmental conditions and under more ideal germination and emergence conditions than likely occurred under the variable field conditions in our study.
During the second season, the average total emergence (11%) at the seven sites where data were collected was lower than during the first year. Significant differences in total emergence were only found between the Córdoba and Madrid locations (P-value < 0.031) ( Table 2). An average 48.2% of C. diluta seeds sown in this study did not result in the production of seedlings. The percentage of seeds not producing seedlings ranged between 39.3% and 71.3% depending on location. This trend of decreasing seedling emergence (Table 2) was also observed in C. cyanus, for which seed viability was found to decrease at the end of the first year (Guillemin et al. 2017). However, the fate of seedlings that did not emerge (i.e., seeds remained dormant in the soil, died, or were predated) was not determined in our study. The emergence observed during the second season was on average less than one-third (11%) of that in the first year (39%), and this tendency is likely to continue in the forthcoming seasons; thus, if the seed rain of C. diluta can be curtailed during two seasons, the seedbank of this species is likely to be substantially reduced. Certainly a more in-depth understanding of the fate and viability of C. diluta seeds in the soil would be most valuable for accurately assessing the soil seedbank and resulting seedling emergence levels.
The emergence pattern of C. diluta in 2016 to 2017 was similar in all locations, with a single main flush (50% of the emergence) Figure 2. Precipitation (vertical bar) and daily mean soil temperature (line) at the locations where more than 10 Centaurea diluta seedlings were recorded. The horizontal black bar at the top of each graph represents the period for adequate hydrothermal degree accumulation according to the model.  occurring within 20 d after sowing (DAS), except at the Toledo site, where a drastically different emergence pattern was observed. The low proportion of seedlings emerging at this site (8.8%; Table 2), may not be representative of the typical emergence levels for this species (Guillemin et al. 2013). In general, emergence patterns across experimental locations were similar for the first 13 DAS, but differences were observed after 75% emergence was achieved. Centaurea diluta emergence flushes occurred early in the season and were concentrated over a few days (Figures 3 and 4). Thus, control of these seedlings is likely to be easier and more effective at these early growth stages than at later stages (Cardina et al. 2007). Moreover, this timing is also likely to be more cost-effective as 80% to 90% of the weed management effort in this region occurs early in the growing season.

Early Plant Growth
Interestingly, emergence levels of C. diluta were not only similar for the northern and southern locations in Spain (Table 2), but plants survived the relatively cooler winter conditions at the northern sites. Centaurea diluta plants survived winter conditions in all locations where early seedling growth was monitored (i.e., three northern and three southern sites). Seedlings of C. diluta that emerged between the end of October and beginning of November produced more than 9 leaves (BBCH scale = 19) by mid-February with the exception of the Zaragoza site, where temperatures were lower, reducing the growth of plants ( Figure 5). The lowest monthly mean temperature that C. diluta was able to survive was 6.2 C recorded at the Zaragoza site in December (Supplementary Data). Hence, C. diluta has the potential to establish and possibly become a problematic weed in northern regions of Spain.

Development and Accuracy of Emergence Model
T b , T o , and T c were established at 0.5, 10, and 35 C for thermal time (TT), while base water potential (Ψ b ) was estimated at −0.5MPa, for hydrothermal time (HTT), maintaining the same values for T b , T o , and T c as the TT estimation.
The three-parameter Weibull model fit best and explained the emergence of C. diluta with higher accuracy than the Gompertz or the three-parameter log-logistic models. For the TT model, the parameter values were 98.30 for d, −2.08 for b, and 235.40 for c; while the parameter values for the HTT model were: d = 98.86, b = −1.73, and m = 189.78. Both TT and HTT had similar RMSEP values when assessed using field-emergence observations (Table 3; Figure 3).
Both the HT and HTT models successfully predicted the emergence patterns across the various field locations in Spain, with variations (RMSEP) ranging from 4.8 to 23.9 for the TT model and from 5.5 to 26.8 for the HTT model, depending on the location. The lack of differences in the accuracy of the TT and HTT models could be explained by the weather conditions, where water stress was only evident in Sevilla and Valladolid (< −0.5 MPa) (Figure 2).  Córdoba and Sevilla 2H sites from a poor to a good fit (Table 3). Seed counting at Valladolid finished earlier, so later emergence could not be accounted for, which could reduce the accuracy of the model at this site.

Practical Use of the Model
The tested sites showed a different behavior. At the Morón site, where 125 seedlings of C. diluta were recorded, TT-and HTTbased models provided very good accuracy ( Figure 5A). On the other hand, at the Montoro site, where 525 seedlings were recorded, the accuracy of the TT-based model was poor, while that of the HTT-based model provided very good accuracy ( Figure 5B). This difference was likely due to the water stress experienced at the Montoro site from October 23 to November 23. The ability of the HTT model to accurately predict the emergence of both sown seeds of C. diluta and those emerging from the resident seedbank, using the first significant rainfall (> 10 mm) as the zero moment, is to be highlighted ( Figure 5). Moreover, the TT model provided good fit of the independent data when moisture was not limiting. This situation becomes important in a typical wet autumn in this region because of the difficulty in measuring soil moisture, a key parameter required for the HTT model (Finch-Savage 2004).
Centaurea diluta is a troublesome agronomic weed primarily in the southern region of Spain. For this reason, its emergence pattern at the Córdoba site is considered typical for this weed ( Figure 6B). The emergence rate of C. diluta was relatively fast, with an important emergence flush occurring at 400 growing degree days

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Sousa-Ortega et al.: Centaurea diluta emergence ( Figure 6A). Based on this model, the emergence pattern of this species was highly influenced by the timing of the first rain event (>10 mm). If this rain event occurrs at the beginning of September, then 90% emergence could be achieved by October 20; whereas if rain is delayed until the end of October, 90% emergence could be achieved by March 26 ( Figure 6B). Similarly, Joley et al. (2003) reported that emergence of C. solstitialis was promoted by an 11-mm rainfall event before typical autumn rainfall. In both our simulated scenarios, the main seedling emergence flush occurred quickly after the first rainfall. If the first rain event occurs at the beginning of September, C. diluta will have attained 95% emergence before the typical wheat-sowing period in the region (December 1 to 15). Thus, emergence of the remaining 5% of seedlings may be low enough not to significantly affect wheat yield. This is especially the case in sunflower, which is sown during the second half of February in many regions of Spain, by which time 96% of C. diluta seedlings will have emerged. If the rain event is delayed until the end of October, emergence will be more staggered, attaining a 68% to 72% and 74% to 78% emergence at the time of typical wheat and sunflower sowing, respectively. Hence,  For the Sevilla Garden site, only the TT model was tested, because water potential could not be estimated using the equations described in Saxton and Rawls (2006).
depending on the timing of the first rain event, weed management options would vary. For example, if the first rains occurred early in the season, delaying sowing of wheat would be an effective strategy for managing C. diluta ( Figure 6B). Even if the first rain event is delayed, C. diluta emergence at wheat or sunflower planting would be greater than expected. So the presence of a large C. diluta seedbank in these crops could explain why this weed is present at high densities and causes substantial crop yield reductions. As mentioned earlier, almost 50% of the seeds sown apparently did not germinate, and hence emerge, in the two seasons of our study. It is possible that the viability of C. diluta seeds in the soil may be longer (>2 yr) than expected, at least for a certain proportion of the seed population, which could also explain the persistence of this species in arable crops of southern Spain. However, because of differences in the timing of soil disturbance in our experiment relative to that in commercial fields, the emergence patterns we observed and modeled for this weed may vary to some degree from those observed in commercial fields. That is, tillage occurring before the planting of both crops may have stimulated additional C. diluta emergence. Nosratti et al. (2017) and Joley et al. (2003) reported the stimulatory influence of light on the germination of the congeners, C. iberica and C. solstitialis. Thus, further research is needed to more fully understand the emergence behavior of C. diluta and to modify the models developed in our study to better reflect actual practices of growers in Spain.
The emergence of Centaurea diluta was effectively described in a large experiment that included data from 13 locations across Spain for one or two consecutive growing seasons. Moreover, the models developed showed good accuracies predicting the emergence of C. diluta from the natural seedbank. Our findings are potentially applicable to actual field situations by providing guidance on the optimal timing to implement weed control tactics or for crop sowing. However, additional experiments must be performed to integrate the possible effect of timing of soil disturbance before crop sowing on the emergence pattern of C. diluta.