A hydrothermal model to predict Russian thistle (Salsola tragus) seedling emergence in the dryland of the Pacific Northwest (USA)

Abstract Russian thistle (Salsola tragus L.) is among the most troublesome weeds in cropland and ruderal semiarid areas of the Pacific Northwest (PNW). Predicting S. tragus emergence timing plays a critical role in scheduling weed management measures. The objective of this research was to develop and validate a predictive model of the seedling emergence pattern of S. tragus under field conditions in the PNW to increase the efficacy of control measures targeting this species. The relationship between cumulative seedling emergence and cumulative hydrothermal time under field conditions was modeled using the Weibull function. This model is the first to use hydrothermal time units (HTT) to predict S. tragus emergence and showed a very good fit to the experimental data. According to this model, seedling emergence starts at 5 HTT, and 50% and 90% emergence is completed at 56 HTT and 177 HTT, respectively. For model validation, independent field experiments were carried out. Cumulative seedling emergence was accurately predicted by the model, supporting the idea that this model is robust enough to be used as a predictive tool for S. tragus seedling emergence. Our model can serve as the basis for the development of decision support systems, helping farmers make the best decisions to control S. tragus populations in no-till fallow and spring wheat systems.


Introduction
Russian thistle (Salsola tragus L.; syn.: Salsola kali) is among the most troublesome weeds in cropland and ruderal semiarid areas in the Pacific Northwest (PNW) (Beckie and Francis 2009).In dryland, this summer annual species is one of the most abundant broadleaf weeds in crops such as spring wheat (Triticum aestivum L.) (Young 1988), camelina [Camelina sativa (L.) Crantz] (Schillinger 2019), pulses, canola (Brassica napus L.), and mustard (Brassica spp.) (Nakka et al. 2019).In spring wheat, yield losses can range from 11% to 50%, depending on the amount of rainfall (Young 1988).This summer annual species emerges from March to May (Schillinger 2007), coinciding with the planting dates of spring crops or even preceding them in the region (Ogg and Dawson 1984).Salsola tragus is less problematic in winter crops, because they are already established when S. tragus emerges, reducing weed competitiveness, weed growth, and wheat yield losses (Fahad et al. 2015).Weeds that escape herbicide applications or emerge late may not be a problem for current crops but can become a severe weed problem during and after harvest (Young and Whitesides 1987), as they consume water and nutrients needed for the next crop.Furthermore, S. tragus control after wheat harvest in the PNW can be complicated and expensive.At that time, herbicides may be less effective due to factors like reduced active ingredient per biomass, thicker cuticles and higher wax accumulation than in younger plants (Harbour et al. 2003;Kirkwood 1999), or inadequate environmental conditions (high temperatures, low precipitation and air humidity) (Oreja et al. 2023).Therefore, the accurate daily prediction of seedling emergence is crucial for making successful management decisions regarding this weed.
For annual plants, successful establishment is critical to guarantee reproductive success (Forcella et al. 2000) and determines the intensity of the weed-crop interaction.A long emergence period with several flushes guarantees some individuals will escape from postemergence applications and mechanical controls, as well as from the effect of some residual herbicides.The late-emerging individuals are not the most important in terms of causing yield loss, but they will contribute to replenishing the seedbank for future seasons (Grundy 2003;Soltani et al. 2009).Therefore, predicting S. tragus emergence is critical to optimizing in-crop herbicide applications to reduce yield loss in the present season as well as potentially reduce the number of late-emerging individuals that replenish the seedbank.
Seedling emergence is the final step of several processes involving seed dormancy release, germination, and preemergence seedling growth (Forcella et al. 2000).Once S. tragus seeds are fully mature, they require an afterripening period to avoid germination in fall and so being killed by frost in winter.Following the afterripening period, if environmental conditions are favorable, seeds will germinate (Thorne et al. 2007).Temperature and water availability are the most important factors driving seed germination (Soltani et al. 2022).Empirical models based on accumulation of either thermal or hydrothermal time have been developed for many weed species to predict the time course of seedling emergence in crop fields.These models consider that seeds need to accumulate a certain amount of growing degree days independent of soil water availability (thermal models) or including information about soil water potential (hydrothermal models).
Effective weed management relies on applying control measures at the right time.Postemergence herbicides are most effective when applied at an early seedling stage before the plant becomes tolerant.This goal can be accomplished with the aid of predictive models of weed emergence.The objective of this research was to develop a predictive model of the seedling emergence pattern of S. tragus in the dryland PNW that can provide precise information to farmers and crop advisors in order to increase the efficacy of control measures targeting this species.

Model Development Experiment
In 2020, one experiment (hereafter referred as Site A) was established in a completely randomized block design with four replications.Each replication had 10 plots, each measuring 3 m by 4.5 m.Four hundred S. tragus seeds were sprinkled in the center of each plot on March 23, with 200 seeds (86% viability) spread in two separate 1 m 2 areas within each plot.Seeds came from S. tragus plants collected on October 2019 from a grower's field south of Ione, OR (45.3867°N, −119.8436°W).Seeds were stored in paper bags at room temperature (20 to 25 C) until use.Seed germination was tested in germination chambers at constant temperature (25 C) and 12-h interval of light and darkness, arranged in five replicates with 25 seeds per replicate each year.Initially, petri dishes were set up with a filter paper and water was added as required later.Germination was recorded regularly until no further seeds germinated (the incubation period did not exceed 15 d).After S. tragus seeds were sprinkled, spring wheat ('Ryan') was planted on March 24 in the experimental area using a no-till drill (Great Plains 606NT, Salinas, KS, USA) with 25 cm of interrow space at a seeding rate of 120 kg ha −1 .The experimental area was fenced to prevent tumbleweed S. tragus plants from blowing across the research plots.Spring wheat fertilization was conducted following standard recommendations for the region (Wysocki et al. 2007).The number of emerged seedlings was recorded every 15 d from April 7 until July 29.Data from the 10 plots per replicate were averaged, and the cumulative emergence percentage was calculated at the end of the season.

Model Validation Experiments
Also, in 2020 but in a no-till fallow field, one experiment (hereafter referred to as Site B) was conducted in a completely randomized block with four replications.Plot size was 3 m by 4.5 m.Salsola tragus seeds (from the same seed lot as those used in Site A) were sprinkled in the center of each plot in two 1 m 2 areas on March 5.In 2021, two experiments were conducted in fallow and spring wheat following the same experimental design and plot size as Sites A and B. Again, S. tragus seeds were sprinkled in the center of each plot in two 1 m 2 areas on March 13 in the fallow site (hereafter referred to as Site C) and on March 10 in the spring wheat site (hereafter referred to as Site D), at a seeding rate of 400 seeds (56% viability) per plot (200 seeds in each 1 m 2 area).Seeds came from S. tragus plants collected on October 2020 from a different grower's field south of Ione, OR (45.4409°N, 119.8791°W).After S. tragus seeds were sprinkled, spring wheat (Ryan) was planted in Site C on March 11 using the same no-till drill described for Site A at a seeding rate of 120 kg ha −1 .Sites B, C, and D were fenced to prevent S. tragus plants from rolling across the experiments and dispersing seeds across the experimental area.Fertilization of spring wheat in Site D was conducted following standard recommendations for the region (Wysocki et al. 2007).The number of emerged seedlings was recorded every 15 d in 2020, from March 31 to July 4 in site B, and weekly in 2021, from March 23 to July 13 in sites C and D, until no further seedlings were observed.

Soil Environmental Measures
Daily soil temperature and moisture were measured with 24 sensors per site located in a range of shallow soil depths varying from 0 up to 2.5 cm.Temperature was measured with calibrated thermistors, and water potential was measured with Decagon MPS6 water potential sensors (Meter Group, 2365 NE Hopkins Ct., Pullman, Washington 99163, US).Four sets of sensors (north, south, east, west) were established in each experimental site, with each set having two thermistors and four MPS6 sensors.
Soil temperature and water potential were used to calculate the hydrothermal time (θ HT ), expressed as C • kPa • d (degrees Celsius × kilopascal × days), being a function of hydro time (θ H = Ψ -Ψ b ) (kPa) and thermal time (θ T = T -T b ) (C), where Ψ is daily average soil water potential, Ψ b is base water potential for seed germination expressed in kPa, T is daily average temperature at the soil surface, and T b is base temperature for seed germination expressed in C, according to Equation 1: where θ H = 1 when Ψ > Ψ b , otherwise θ H = 0; and θ T = T -T b when T > T b , otherwise θ T = 0.The Ψ b and T b considered for S. tragus were −1,000 kPa (Yousefi et al. 2020) and 4 C (Dwyer and Wolde-Yohannis 1972), respectively.The cumulative hydrothermal time (HTT) was estimated from March 28 according to Equation 2, where d is the time period in days when HTT was computed: Weed Science

Model Development
To describe the pattern of seedling emergence, percent of cumulative emergence, E, was related to the cumulative hydrothermal time (HTT) with a Weibull model (Gonzalez-Andujar et al. 2016; Martinson et al. 2007): where k is the maximum emergence fraction, b is the slope (emergence rate), and p is the inflection point on the x axis.Model performance was assessed by calculating the root mean-square error (RMSE), sum of the residuals (SRES), and sum of the absolute residuals (SARES) (Bastida et al. 2021).These measures are defined by Equations 4 to 6, where x i and y i are the observed and predicted cumulative percentage emergence, respectively: ABS is absolute value of the number within parentheses and n is the number of observations.A scale of RMSE meaning is (Royo-Esnal et al. 2010): < 5 = excellent prediction, 5 to 10 = very good prediction, 10 to 15 = good prediction, and >15 = insufficient prediction.The SRES and SARES determine how errors in the model cancel out.If SRES is small compared with SARES, errors in the model will tend to cancel out.If SRES and SARES are large and SRES is positive, the model will tend to underestimate the observed value.However, if SRES is negative and large in comparison to SARES, then the model will tend to overestimate the observed value.Model parameters and goodness of fit were estimated by nonlinear least-squares regression using GraphPad Prism 6.0 (GraphPad Software, San Diego, CA, USA).

Model Validation
The model was validated using independent data from the described sites (B, C, and D) by comparing the observed seedling emergence and the predicted seedling emergence according to HTT, based on soil temperature and water potential measured on the sites and modeled by the Weibull function.Finally, the accuracy of the model was assessed by comparing the predicted and observed values through linear regression.

Results and Discussion
This work establishes for the first time a model for accurate prediction of S. tragus field emergence in the inland PNW.Our model can serve as the basis for the development of decision support systems, helping farmers to make the best decisions to control this troublesome weed in the future (Gonzalez-Andujar 2020).
The relationship between S. tragus cumulative emergence and cumulative hydrothermal time was well described by the Weibull model (Figure 1; Table 1).This model showed no significant bias, as indicated by SRES and SARES values (Table 1).The Weibull model has been widely used to model weed emergence due to its flexibility (Gonzalez-Andujar et al. 2016).Leguizamón et al. (2009) found a good fit of this model to describe the emergence of six summer annual grass weeds in maize (Zea mays L.) and soybean [Glycine max (L.) Merr.].
Our model was based on 7,212 S. tragus seedlings, counting an average of 1,803 seedlings per replication.It was validated with independent data sets and was in good agreement with the observed seedling emergence pattern in Site B (R 2 = 0.96), Site D (R 2 = 0.95), and Site C (R 2 = 0.81) (Figure 2).According to the model, the onset of emergence takes place at 5 HTT, and 50% and 90% emergence is reached at 56 and 177 HTT, respectively, indicating a rapid establishment of S. tragus in comparison with other species infesting cereals.Bastida et al. (2021) found that 50% and 90% emergence of shortspike canarygrass (Phalaris brachystachys Link) in wheat takes place at 108 and 160 HTT, respectively.The present model can be used to design herbicide programs for wheat-fallow rotations that high proportions of S. tragus seedlings in fallow fields with fewer herbicide applications than the current standard practice (three or four applications) (Kumar et al. 2017).Decreasing the number of herbicide applications will reduce the herbicide-resistance pressure and the risk of selecting for new herbicide-resistant populations (Neve et al. 2009), as well as environmental pollution (Rashid et al. 2010) and costs.Additionally, S. tragus has a short seed longevity.Burnside (1996) and Ogg and Dawson (1984) indicated that >99% of the seeds germinate in the first year; hence, the predictive model could help reduce the seedbank faster, by increasing the herbicide efficacy, than if the species had longer seed longevity.However, the annual emergence of S. tragus seedlings in calendar days can vary significantly among sites depending on environmental conditions, which can impact the effectiveness of residual herbicides in no-till fallow systems (Lyon et al. 2021).Particularly, the period between the 50% and 90% germination (more than 120 HTT units) can be wide for cool and/or dry seasons.Therefore, the model can estimate the proportion of emerged seedlings and assist in management decisions.
On the other hand, in spring wheat, no-till growers apply glyphosate before planting wheat to control emerged weeds, but in the case of S. tragus, most seedlings emerge after planting, thus escaping the herbicide application.Most S. tragus seedlings will emerge with the crop and compete for resources during and after the wheat harvest.To control S. tragus seedlings that emerge after seeding in spring wheat, this model can be used to apply selective herbicides in crop at the optimal HTT to minimize the number of plants competing with the crop and plants present at harvest (Young and Whitesides 1987).Salsola tragus can regrow after harvest, producing hundreds or thousands of seeds per plant.Consequently, reducing S. tragus plants present at harvest will reduce the number of seeds re-entering the soil seedbank (Oreja et al. 2023).
In recent years, there has been an increase in social demand for more sustainable management of agrosystems.In response, farmers are putting more emphasis on improving the efficiency of herbicide applications.In this study, our hydrothermal model describes the emergence of S. tragus with an accuracy of 81% to 96%, as demonstrated by validation tests at three different sites representing different field conditions (fallow vs. spring wheat) over two years.Future research should focus on wider model validation under different weather and soil management conditions (e.g., conventional tillage, where seeds are buried at deeper soil layers) to fine-tune the timing of control measures targeting this species (Egea-Cobrero et al. 2020).Table 1.Weibull model parameters (Equation 1) (SEs in parentheses), root mean-square error (RMSE), coefficient of determination (R 2 ), sum of the residuals (SRES), and sum of the absolute residuals (SARES) from the model performance.Weed Science 111

Figure 1 .
Figure 1.Observed (solid circles) and predicted (solid line) cumulative emergence (%) of Salsola tragus as a function of hydrothermal time (HTT) unit accumulation.Predictions are the result of the fit Weibull model to the experimental data set.Error bars on symbols are the SDs from the four replications.RMSE, root mean-square error.