Field experiments were conducted in 2019 and 2020 at the E.V. Smith Research Center Field Crops Unit (32.4417° N, 85.8974° W) Shorter, Alabama. The soil characteristics at the research site were sandy loam, (coarse-loamy, siliceous, sub-active, thermic Paleudults) with pH 6.2 and 0.8% organic matter. The average temperature ranged from 18.1°C to 27.6°C and precipitation was 8.26 mm to 1.25 mm from April to August 2019. In 2020, the average temperature ranged from 17.27°C to 26.98°C and precipitation was 2.03 mm to 3.37 mm from April to August.

The study was conducted in a split-plot design with four replications. As previously stated, the three systems i.e., conservation tillage with a crimson clover cover crop (CT + CC), conservation tillage with winter fallow (CT + WF), and conventional tillage (CVT), were considered in the main plots. The durations of weedy plots described the beginning of weed removal (CTWR), and the durations of weed-free plots illustrated the end of weed control (CWFP). Hence, these durations in weedy and weed-free plots from 0 to 8 weeks after planting were considered in subplots.

Crimson clover cultivar “Dixie” was seeded at a rate of 22.4 kg ha^-1 using a grain drill. Termination of crimson clover was accomplished using a roller-crimper (Ashford and Reeves, 2003) followed by an application of glyphosate (Roundup Powermax^®, Monsanto Company, St. Louis, MO) plus glufosinate (Liberty^®, Bayer Crop Science, Research Triangle Park, NC) herbicides sprayed at the rate of 841 g ae ha^-1 and 492 g ae ha^-1 respectively. Within all plots, a KMC 4-row parabolic subsoiler (Kelly Manufacturing Company, Tifton, GA) was used to disrupt naturally occurring hard pans found at this location before planting corn in all treatments to prevent deep-tillage interaction. Subsequently, CVT plots were cultivated using three disks, and two field cultivator passes. Corn (Pioneer^® 1197 YHR) was planted using a precision planter with the population set at 12950 seeds ha^-1 on April 16, 2019, and April 27, 2020, respectively. A starter application of nitrogen, phosphorus, and potassium (NPK) fertilizer was applied at a rate of 45 kg ha^-1 after planting corn. A tank mixture of glyphosate plus acetochlor (Warrant, Monsanto Company, St. Louis, MO) herbicide sprayed at the rate of 841 g ae ha^-1 and 1682 g ae ha^-1, respectively, followed by hand hoeing, was utilized for weed control in a weed-free period and after weedy intervals using TDI 11004 nozzles. The corn was harvested on August 19, 2019, and August 27, 2019.

Crimson clover biomass samples were collected randomly from a 0.25 m² area per plot before termination. The collected samples were placed in a forced air drier for 72 h at 65°C, and then the weight was recorded. Weed biomass was collected from a randomly selected 0.25 m² quadrat from weedy plots (CTWR) immediately before applying herbicides. For example, W2, i.e., two weeks weedy; herbicides sprayed at two weeks after planting and weed biomass collected just before application. Additionally, weed biomass collected once at the end of the growing season in the weed-free duration plots. Weed species inside the randomly selected area were cut at the soil surface, placed in a forced air drier for 72 h at 65°C, and then weighed.

A sigmoidal logistic model was fitted for the weedy periods (i.e., CTWR), while the Gompertz model was fitted for the weed-free periods (i.e., CWFP) in each winter fallow (CT + WF), conventional tillage (CVT), and cover crop treatments (CT + CC). The inverse prediction method applied at 95% relative yield to estimate the CTWR and CWFP (i.e., weeks on the x-axis). The estimation of CPWC components were the next steps under which there were not a relative yield reduction greater than 5%, as the acceptable yield losses (AYL) were considered at 5% for both curves Gompertz and logistic as described by Knezevic et al. (2002); Blankenship et al. (2003), and Price et al. (2018). Regression of relative yield was performed as a function of time for both CTWR and CWFP, and then nonlinear regression models were fitted to assess the CPWC, as illustrated by Knezevic et al. (2002); Williams et al. (2007) and Korres and Norsworthy (2015).

For the weedy periods to estimate CTWR, a logistic model with three parameters was fitted to relative corn yield under all three treatments.

Moreover, for the weed-free periods to evaluate CWFP, a Gompertz model with three parameters was fitted to relative corn yield under all three treatments.

Where y is the relative corn yield, α is the asymptote, b is the slope of the curve, x₀ is the point of inflection, and x is time (i.e., weeks after planting).

Hence, the difference between CWFP and CTWR components described the CPWC estimation with a 5% acceptable corn yield loss in CT + CC, CT + WF, and CVT systems. As described previously, weed control experiments estimate the relation between weed interference timings and relative crop yield and then determine the CPWC.

The collected weed biomass was quantified as a function of critical timing of weed removal (CTWR) and the critical weed-free period (CWFP) for each CT + CC, CT + WF, and CVT system using equations 1 and 2 mentioned above, in which y represents weed biomass. A sigmoidal logistic model was fitted for various weed-free periods, while the Gompertz model was fitted for the weedy periods in CT + CC, CT + WF, and CVT systems to assess weed biomass.

The ANOVA was applied to estimate treatment effects on actual and relative (percentage of long season weed-free period) corn yield data, and means were separated through Fisher’s LSD at α=0.05. The CPWC was estimated separately for each year due to significant treatments × year interaction. Sigma Plot 14.0 (Systat Software, San Jose, CA) and JMP Pro v. 13 (SAS Institute, Cary, NC) was used for the estimation of ANOVAs, inverse predictions, curve fitting regressions, and significance model parameters. The model parameters were utilized to support the predicted values of an explanatory variable (i.e., type of independent variable) CTWR and CWFP based on the response variable of relative corn yield. Coefficient of determination (R²) was used to check the fitness of the regression model to the observed data. The comparisons between model parameters were used to evaluate the effect of experimental treatments, including CT + CC, CT + WF, and CVT, on weed biomass production.

At clover termination, the cover crop biomass was 4,204 kg ha^-1 and 3,890 kg ha^-1 in 2019 and 2020, respectively. The average yield following crimson clover was 7,575 kg ha^-1, winter fallow 6,478 kg ha^-1, and conventional tillage 7,400 kg ha^-1 in 2019. The average yield following crimson clover was 8,253 kg ha^-1, winter fallow 7,224 kg ha^-1, and conventional tillage 7,280 kg ha^-1 in 2020.

Again, 5% acceptable yield loss (AYL) was considered to estimate the values of CTWR and CWFP as described by Blankenship et al. (2003) and Knezevic et al. (2002). In 2019, the predicted value of CTWR equals 2.5, 2.8, and 1.5 weeks after planting (WAP) for CT + CC, CT + WF and CVT systems, respectively ( Figure 1 and Tables 1 , 2 ). In addition, the predicted value of CWFP equals 5.3, 6.3, and 6.4 weeks after planting for CT + CC, CT + WF, and CVT, respectively ( Figure 1 and Tables 1 , 3 ). In 2019, based on the predicted values of CTWR for each system individually, the CTWR following the CT + CC system was delayed approximately 1.0 weeks compared with CVT system, while the beginning of CTWR under both CT + WF and CT + WF systems was in between second to third weeks ( Figure 1 and Tables 1 , 2 ). Additionally, comparing CT + CC system with CT + WF and CVT systems, the presence of crimson clover caused the early ending of CWFP at about 1.0 and 1.1 weeks respectively. However, the ending of CWFP under CT + WF and CVT systems were almost same during the weeks of 6 WAP.

In 2020, the predicted value of CTWR equals 3.8 WAP for CT + CC system. While the relative yield was above the threshold level of 95% for 8 weeks, so the model did not predict the CTWR value for CT + WF and CVT systems because curves were fitted only for 8 weeks ( Figure 1 and Tables 1 , 2 ). Moreover, the predicted values of CWFP equals 5.1, and 5.7 WAP for CT + WF and CVT, respectively, whereas for CT + CC system, the model did not predict the value due to greater than 95% relative yield during most of growing season ( Figure 1 and Tables 1 , 3 ). Hence, comparing the CVT system with CT + WF system, conventional tillage and winter fallow had almost same ending period during 5th weeks of timing ( Figure 1 and Tables 1 , 3 ).

We observed yield loss increased with the extent in time of weed infestation, and Gantoli et al. (2013) reported the same in the estimation of corn CPWC. Although our points of estimated critical period were not exact same among two years because of different weed pressure in two years ( Figure 2 ). Some previous publications indicated that the CPWC differed remarkably when estimated in respect of days after planting or days after germination (Gantoli et al., 2013). Moreover, several corn studies have estimated the critical period of weed control, and there was great variability in the CPWC. The starting of the corn CPWC was more variable (3-14 leaf stage) than the end (14-leaf stage) in Canada (Hall et al., 1992). In contrast, Halford et al. (2001) illustrated that starting of the CPWC was more stable (around 6-leaf stage) than the end period (9-13 leaf stage or 24 to 46 DAE) in corn. Results reported by Evans et al. (2003) described that the starting of CPWC was estimated from germination up to the seven-leaf stage, while the end of the CPWC was estimated from seven-leaf stage up to anthesis in corn crop. A field experiment was conducted in Canada to compare the CPWC between conventional and no-till corn and summarized that the CPWC starting and ending period was earlier under a no-till system than in conventional tillage systems (Halford et al., 2001). In addition, the previous study concluded that the estimated value of CPWC in narrow-row spacing was different than wide rows spacing in corn due to higher competition for late-germinating weeds (Murphy et al., 1996). Thus, high-density corn planted in narrow row spacing would most likely decrease the end of the CPWC (Teasdale, 1998). However, Norsworthy and Oliveira (2004) concluded that there was no significant difference between light interception in narrow and wide row spacing of corn; hence CPWC and competition of late germination weeds were almost the same in these two systems.

The most common and troublesome weed species found in the southeastern United States cropping systems are Palmer amaranth (Amaranthus spp.), sicklepod [Senna obtusifolia (L.)], large crabgrass [Digitaria sanguinalis (L.) Scop.], morning glory (Ipomoea spp.), and nutsedges (Cyperus spp.) (Van Wychen, 2016). In 2019, weed removal needed to start before 150-200 kg ha^-1 of weed biomass for all systems ( Figure 2 ), based on the predicted values CTWR that started at approx. 3 WAP under CT + CC and CT + WF systems while approx. 1.5 WAP following the CVT system to prevent a yield loss greater than 5% in each system ( Figure 2 and Table 4 ). In 2020 the recorded dry weight of weed biomass based on prediction value of CTWR (3.8 WAP) for CT + CC treatment was 30 kg ha^-1 approximately. Although weed biomass of CT + WF and CVT systems were approx. 60 and 400 kg ha^-1 respectively ( Figure 2 and Table 4 ) in between 3 to 4 WAP in 2019. In both years, the weed biomass increased as the critical timing of weed removal (CTWR) increased. However, results showed differences in point estimates between slope and inflection points under each system for both years due to difference in weed pressure among both years. It has been observed that weed density was lower in 2020 than in 2019 ( Figures 2 , 3 and Tables 4 , 5 ).

The same strategy was followed in the case of the critical weed-free period (i.e., CWFP) following CT + CC, CT + WF, and CVT systems in both years ( Figure 3 and Table 5 ). In 2019 the weed biomass was recorded during the predicted value of CWFP (5.3 WAP) following CT + CC treatment was approx. 100 kg ha^-1. However, in case of CT + WF and CVT systems, the recorded dry weight was approx. 50-60 kg ha^-1 at 6 WAP ( Figure 3 and Table 5 ). In 2020, the recorded weed biomass level at predicted value of CWFP following CT + WF treatment (i.e., 5.1 WAP) and CVT treatment (i.e., 5.7 WAP) was 50 kg ha^-1 approximately.

Moreover, the recorded maximum production of weed biomass level in both weedy and weed-free plots following CT + CC (cover crop) treatment was lower as compared to CT + WF and CVT systems under both years ( Figures 2 and 3 , Tables 4 and 5 ). This is likely due to the cover crop inhibiting weed seed (mainly small, seeded weeds) germination and decreased growth through physical suppression and allelopathy in the conservation tillage system (Akemo et al., 2000; Haramoto and Gallandt, 2004; Korres and Norsworthy, 2015). The practical application for this research is to understand the critical period of weed control (CPWC) in row crops to maintain crop yield potential is a key point in the cropping system. In addition, it is very important to have knowledge about how different cultural practices, including cover crops among others, can influence the critical period for weed removal (CPWC) and weed biomass production. Estimation of critical period of weed control (CPWC) indicated that use of residual herbicides for weed control is required (Korres and Norsworthy, 2015). The use of effective POST herbicides could effectively control the problematic weed species, especially when the critical weed-free period is short Van Acker et al. (1993). A better understanding of the CPWC in different systems, including a high residue cover crop in corn, should help farmers to maintain yield and schedule appropriate weed control timing.