Effect of partial root-zone drying irrigation (PRDI) on alfalfa available soil P

ABSTRACT This study focused on alfalfa (Medicago sativa) to investigate the effect of partial root-zone drying irrigation (PRDI) on N-fixing crops available soil P. A three-year field experiment was designed with two irrigation methods and four irrigation volumes. Two irrigation methods consisted of PRDI and conventional furrow irrigation (CFI), and four irrigation volumes were set as 70% ETc (alfalfa water requirement), 85% ETc, 100% ETc and 115% ETc. This study showed that the PRDI had no effect on alfalfa seasonal forage yield but increased alfalfa P uptake. The PRDI decreased the soil available P content and stock but had no effect on the total P content and stock, which demonstrates that effect of PRDI on crop available soil P was different when different P forms were used to estimate crop available soil P. This study also showed that the variation in the coefficient was below 3% between soil P (available or total P) contents and soil P stocks, indicating that soil P contents and stocks were similar when estimating alfalfa available soil P under PRDI conditions. The findings of this study present a pattern of estimating the N-fixing crops available soil P in relation to PRDI.


Introduction
Phosphorus (P) is a vital limiting nutrient for crop production  since P is an irreplaceable constituent of the plasma membrane and is necessary for nucleic acid synthesis (Alewell et al. 2020) and adenosine triphosphate formation (Song et al. 2019). The requirement of P in crop production is often derived from soil P supplies (Cordell et al. 2009). Generally, soil P is present in forms that are unavailable for plants ; therefore, some soils are considered P deficient for crop production. At present, 5.7 billion ha of cropland soils are P deficient worldwide (Dhillon et al. 2017), and 47 Tg (10 12 g) P fertilizers are applied to soil to overcome this soil P deficiency every year (Elrys et al. 2021) to improve crop production. However, over-P fertilization can lead to environmental problems, such as eutrophication (Cordell et al. 2009).
Therefore, there is a pressing need to quantify crop available soil P, which can provide information for properly managing P to improve crop production and to avert future environmental problems. Crop available soil P is often estimated by soil P contents (Alrajhi et al. 2017;Fan et al. 2020), soil P stocks (Margenot et al. 2017;Glaesner et al. 2019), or both (Bell et al. 2012;Cherubin et al. 2016). A number of studies have shown that soil P contents and stocks are affected by fertilizers (Gu et al. 2018;McLaren et al. 2019), tillage (Zhang, Dalal et al. 2021), rotation (Wu et al. 2020), and irrigation Mayakaduwage et al. 2021).
Partial root-zone drying irrigation (PRDI), a water-saving irrigation technique with low input and easy extension (Wang et al. 2017), can result in higher water productivity without a yield decline and improve the quality of many crops (Alrajhi et al. 2017;. Previous studies have shown that PRDI often triggers the 'Birch effect' (Birch 1958;Wang et al. 2017) by inducing the soil to experience repeated drying and wetting cycles (Kang et al. 1998), further influencing crop available soil P (Li et al. 2011;Wang et al. 2015;Alrajhi et al. 2017).
Some studies have documented that the PRDI increases (Wang et al. 2015), decreases Demir and Sahin 2019), or has no effect on crop available soil P (Sun et al. 2015;Alrajhi et al. 2017). This inconsistency is attributed to soil P types since some studies use soil available P contents to estimate crop available soil P (Li et al. 2011;Wang et al. 2015), and other studies use the soil total P contents to estimate crop available soil P (Alrajhi et al. 2017). In addition, all published literature has focused on the PRDI in relation to non-N-fixing crops available soil P. In agricultural practice, there are many N-fixing crops, and these N-fixing crops have greater external requirements for P than non-N-fixing crops (Ribet and Drevon 2010) because N-transforming bacteria and rhizobial nodules in the N-fixing process need or consume more P (Gu et al. 2018;Lu et al. 2020). Although soil P stocks are a better proxy to estimate crop available soil P (Abebayehu and Eyasu 2011;Bell et al. 2012), the PRDI in relation to soil P stocks has received very limited attention. Thus, it is necessary to simultaneously examine the effect of the PRDI on N-fixing crops available soil P by using soil available and total P contents and stocks.
Alfalfa (Medicago sativa), a perennially N-fixing crop, is widely grown in America (Bell et al. 2012), Europe (Strullu et al. 2020), and Asia  because it can sustain animal production and improve the soil quality (Gu et al. 2018). Previous studies have verified that the PRDI can increase the economic benefits ) and water productivity of alfalfa with the maintenance of the aboveground biomass . Although many studies have examined alfalfa production in relation to alfalfa available soil P (Gu et al. 2018;Sandral et al. 2019;Lu et al. 2020), the question of whether the PRDI influences alfalfa available soil P is not well documented. Therefore, more studies are needed to investigate the effect of the PRDI on alfalfa available soil P, which will present a possible and complete pattern of how the PRDI influences N-fixing crops available soil P.
Here, this study employed a three-year field experiment to investigate the PRDI in relation to the variation in N-fixing crop available soil P. Specifically, this study hypothesizes that (1) the PRDI increases the soil available P content and stock because the PRDI can encourage the soil to release available P (Wang et al. 2017) and (2) the PRDI has no effect on the soil total P content and stock since the alteration of soil drying and wetting has little effect on the soil total P on a small scale (Alrajhi et al. 2017). These results can provide useful information for efficiently managing P fertilizer use in alfalfa production under PRDI conditions.

Study site
The study site is situated in Wuwei city in Gansu Province, northwest China (37°42′N, 102°48′E, elevation 1710 m) (Figure S1), and this region is characterized by a typical continental temperate climate with hot and dry summers and cold winters. The mean annual air temperature from 1951 to 2014 in this region was 9°C, and the mean maximum and minimum temperatures were approximately 36.06°C in July and −19.14°C in January, respectively. The mean annual rainfall was 175 mm, with 70% falling from June to September, and the average annual pan evaporation was approximately 2000 mm. The groundwater level is approximately 30 m below the soil surface. Therefore, irrigation is a necessary agricultural measurement for crop production.
The daily precipitation and maximum and minimum air temperatures during the study period (2017-2019) are shown in Figure 1. The soil type is classified as irragric Anthrosoils according to the Chinese Soil Classification System (Gong 2001) and IUSS working group WRB (World Reference Base for soil resources), 2015. The soil is characterized by a soil bulk density of 1.49 g cm −3 , a mean field capacity of 22.01% (g/g), and a wilting point of 8.05% (g/g) for the 0-2 m soil layer, and the detailed value for field capacity, wilting point and soil clay at each soil depth are shown in Table S1. Prior to the beginning of the experiment, the 0-40 cm soil layer had a pH of 8.20 and contained 12.90 g organic carbon kg −1 , 0.86 g total N kg −1 , 1.34 g total P kg −1 , 11.92 g total K kg −1 , 33.50 mg hydrolyzable N kg −1 , 28.39 mg Olsen-P kg −1 , and 253.18 mg exchangeable K kg −1 soil.

Experimental design
The field experiment was performed from April 2017 to September 2019, and it was organized in a split plot design with main factors and subfactors to facilitate irrigation practices. The main factors were irrigation methods, which consisted of PRDI and conventional furrow irrigation (CFI). The subfactors were the four irrigation volumes. The irrigation volumes were set up based on fractions of crop evapotranspiration (ETc) and were designated I 1 (70% ETc), I 2 (85% ETc), I 3 (100% ETc) and I 4 (115% ETc). ETc was calculated based on the recommended FAO56 formula (Allan et al. 1998): ETc = ET 0 × K c , where ET 0 (mm/d) was the reference evapotranspiration and was computed using 20 years of climatic data from the local meteorological station, and the results showed that ET 0 was 1072 mm. Kc was the crop coefficient, and its average value for alfalfa during the entire growth period was 0.88, which was obtained in previous study in this region (Xiao et al. 2015). The calculation results showed that the alfalfa ETc was 943 mm, and the alfalfa ETc per season from initial, to mid and end stage are presented in Table S2.
In the PRDI, irrigation was practiced by alternate furrow irrigation, meaning that the neighboring two furrows were alternately irrigated during consecutive watering. In CFI, every furrow was evenly irrigated at each irrigation event ( Figure S2). Thus, the experimental plan resulted in 8 treatments as follows: PRDI+I 1 , PRDI+I 2 , PRDI+I 3 , PRDI+I 4 , CFI+I 1 , CFI+I 2 , CFI+I 3 and CFI+I 4 , and each treatment was repeated three times. There were 24 subplots in total. Here, the PRDI subplots received half the irrigation amount applied to the CFI subplots. Based on the experimental plan, a 0.27 ha (45 m × 59 m) farmer's field was used to establish the experimental field, and it was divided into three equal blocks of 45 m × 19 m for 3 replications. Each block was further divided into eight 10 m × 8 m subplots, and each subplot consisted of 13 row ridges and 14 furrows. All subplots were 1.0 m from each other to alleviate the effect of lateral water movement. In addition, each subplot was surrounded by 30 cm wide and 30 cm tall ridges to avoid surface runoff.
The same irrigation amount (40 mm) was applied to each subplot on 25 March 2017. Based on the local farmer experiences, the same base fertilizers (75 kg ha −1 urea (N 46%) and 650 kg ha −1 calcium superphosphate (P 2 O 5 , 15.5%) were applied to each subplot on April 7, and then a ridge-and-furrow system was built by shaping, in which the soil surface was set into alternate ridges and furrows . The ridges (50 cm wide and 800 cm long) served as the plant zone, and the furrows (30 cm top width, 25 cm bottom width and 20 cm depth) served as the irrigation zone. The 50 cm distance between furrows could guarantee that the PRDI treatment occurred ). On April 8, alfalfa seeds ('8920-FM' from Canada as the commonly used cultivars in the experimental region) were sown in two rows with a density of 18 kg ha −1 by a hole-sowing machine, and the sowing depth and row spacing were 2 cm and 30 cm, respectively.

Irrigation treatments and crop management
Alfalfa is often harvested multiple times when it supplies forage, and the harvest times are determined by the times of the early flowering stages (10% bloom). In this study, the irrigation date was determined by the schedule of local alfalfa production and the critical water requirement stages of alfalfa , and the detailed irrigation dates and irrigation volumes from 2017 to 2019 are shown in Table S3 and Table S4.
This study used an irrigation control system to accurately control the irrigation volumes of each subplot. The irrigation equipment used are described in detail by . Identical field practices, including fertilizers (same calcium superphosphate (P 2 O 5 , 15.5%)), weeds, pests and disease control, were adopted to manage the alfalfa pasture for each subplot in this experiment.

Soil water content
The gravimetric soil water content was measured at 20 cm intervals in the 0-200 cm soil depth by a gravimetric method (Ojeda et al. 2018) with 10-15 day intervals. Two replicate soil samples were randomly taken in each subplot using a soil auger with a 4 cm diameter and a 20 cm height between the tenth day of the first irrigation date and the last harvesting date of each year. The holes caused by the soil auger were filled with soil from the experimental field to avoid the effect of the holes on water infiltration at each time. Fresh soil samples were taken and weighed immediately, and the soil samples were then dried to a constant weight in an oven at 105°C. Then, the gravimetric soil water content was calculated as the ratio of the weight difference between the fresh and dried samples to the fresh weight of the soil samples.

Plant and soil sampling
Since sampling alfalfa roots in the first year can affect the root samples in the next year, this study designed a method to accurately sample forage yield and root biomass over 3 continuous years. First, three permanent 1 m 2 quadrats were randomly selected and positioned at each subplot, and they were used to measure the forage yield. Second, a protected area for each permanent quadrat was established by setting a 1.2 m diameter circle, whose center coincided with the permanent quadrat center, to ensure accurate measurement of the forage yield. Third, the outside of the protection areas were equally divided into six parts, which were designed as roots and soil sampling areas. Fourth, a 25 cm × 25 cm quadrat was set in each part to collect the root and soil samples, which were paired and sampled in the diagonal scheme for each year. This design can sample the roots and soil over three years.
Shoot biomass (forage yield) was manually harvested in the permanent quadrats at 10% flowering for each subplot by cutting the alfalfa plants at 5 cm aboveground. There were three harvests in 2017 and four harvests in 2018 and 2019 (Table S3), and the seasonal forage yield was the sum of each harvest yield for each year. Root and soil samples were collected when the last shoot biomass was harvested for each year. In each subplot, root and soil samples were collected in the quadrat at five soil depths (0-20, 20-40, 40-60, 60-80, and 80-100 cm) with 6 replicates by digging the soil column, and then each soil column at each soil depth was divided into root and soil samples through a 2 mm sieve. Then, the root samples of each subplot were combined depthwise to make composite root samples, which were washed free of soil with tap water, and the soil samples from the same layer of each subplot were thoroughly mixed into a representative sample of that layer. In addition, the soil profiles produced by collecting the soil columns were used to collect the soil for determining the soil bulk density (BD) at 20 cm depth increments to a 100 cm depth as described by Pang et al. (2020).

Plant and soil samples analysis
Fresh shoot, root and soil samples were immediately transferred to the laboratory. The enzymes in the shoots were inactivated at 105°C for 1 h, and then the inactivated shoots and fresh roots were dried at 65°C to a constant weight for dry weight determination. The oven-dried shoots and roots were crushed into powder with a grinder and used to determine the total P contents. The soil samples were air-dried until they could pass through a 1 mm sieve for Olsen P analysis and a 0.25 mm sieve for total P analysis. Afterward, plant and soil total P content were colorimetrically determined (UV-2102C, UNICO, Shanghai, China) at 660 nm after the digestion of the plant and air-dried soil in an HNO 3 , HClO 4 and H 2 SO 4 mixture (Medorio-García et al. 2020). Soil available P was extracted with 0.5 M NaHCO 3 (pH 8.5) and was determined by using a spectrophotometer (by the ammonium molybdate-antimony potassium tartrate-ascorbic acid method) (Olsen 1954).

Alfalfa available soil P
Generally, crops available soil P is estimated with the residual soil available P and total P contents (Darch et al. 2018;Gu et al. 2018), stocks (Margenot et al. 2017;Glaesner et al. 2019) or both (Bell et al. 2012) in cropland ecosystems. It is an interesting issue that the soil P contents or soil P stocks are better for estimating alfalfa available soil P. Therefore, this study used soil available and total P contents and stocks to estimate alfalfa available soil P.
Plants P uptake can reduce the soil P and further affect the soil residual P contents and stocks (Lemming et al. 2019). Thus, estimating alfalfa P uptake is beneficial to explain alfalfa available soil P.
Alfalfa plant P uptake (kg ha −1 ) was the sum of shoot P uptake (kg ha −1 ) and root P uptake (kg ha −1 ).

Alfalfa P uptake from soil
where P contentj is the P content in the shoots at harvesting time j; shoot biomassj is the shoot biomass at harvesting time j; and j represents the harvesting times during each year. P content is the P content in the roots.
Soil available P stock in every 20 cm layer was derived from the measured available P contents and bulk density as follows: Soil available P stock = soil available P content × BD × 20 ( 2) where BD is the bulk density (g cm −3 ), and 20 is the soil depth in centimeters.
Soil total P stocks in every 20 cm layer were derived from the measured total P contents and bulk density as follows: Total P stock = total P content × BD × 20 (3) where BD is the bulk density (g cm −3 ), and 20 is the soil depth in centimeters. The coefficient of variation, defined as the ratio of the standard deviation to the mean, is considered a proxy to reflect the data variability when the data dimension is inconsistent (Wies and Maddonni 2020). In addition, the size of coefficient of variation reflects the data sensitivity ). Therefore, this study employed the coefficient of variation to estimate whether the P content or P stock is better for estimating the alfalfa available soil P.

Statistical analyses
Data from 2017 to 2019 were separately analyzed for consideration of the treatment's effects by using the following procedure. All data variables (alfalfa seasonal forage yield, alfalfa P uptake, available P and total P contents and stocks) from 2017 to 2019 were assessed for normality and homoscedasticity by the Shapiro-Wilk and Levene tests, respectively. Data were transformed when needed to fulfill the normality and homoscedasticity for the analysis of variance (ANOVA).
A two-way ANOVA was performed using general linear models in univariate analysis to examine the main and interactive effects of the irrigation methods and irrigation volumes on alfalfa seasonal forage yield, alfalfa P uptake, available P and the total P contents and stocks, in which the irrigation methods and irrigation volume were considered fixed factors and the abovementioned variables were considered separate dependent variables. Significant differences among the treatments were assessed using Tukey's multiple comparison post hoc method when the effect or interaction was significant, and the probability level for significance determination was 0.05. All statistical analyses were conducted with the SPSS 17.0 software package from SPSS Inc., Chicago, IL. USA.
If the two-way ANOVA of the abovementioned variables was similar among 2017, 2018 and 2019, data from all three years were used to proceed with correlation analysis and structural equation modeling (SEM) analysis; if the two-way ANOVA of the abovementioned variables was different among 2017, 2018 and 2019, data from each year were used to proceed with correlation analysis and SEM analysis separately. The correlations between soil available P and total P contents and stocks and alfalfa seasonal forage yield were calculated to determine whether the available P and total P should be considered simultaneously, and a selected soil depth layer with a significant effect was applied to SEM. The correlation analysis was performed using the software package R 4.0.3, R Development Core Team, 2020. Finally, SEM was applied to identify how irrigation methods and irrigation volumes affect the soil available and total phosphorus, directly and indirectly, affecting the alfalfa seasonal forage yield. This method was used to determine whether the proposed causal relationships from a priori knowledge matched the empirical results of this experiment. Correlation analysis was used to select the major predictor of variance for the alfalfa seasonal forage yield to further refine the model. The fit of the models was evaluated using p-values, χ 2 values, the goodnessof-fit index (GFI), and the root mean square error of approximation (RMSEA), according to Hooper et al. (2008). SEM was carried out by using Amos 17.0 (SPSS Inc., Chicago, IL, USA).

Soil water content
The soil water distribution was similar throughout the period of 2017-2019 (Figure 2). The soil water content in each soil layer increased as the irrigation volume increased. The soil water content under the PRDI condition decreased as the soil depths increased. With an increasing soil depth, the soil water content under the CFI condition decreased when the irrigation volumes were below 85% ETc, and it first decreased, increased, and then decreased when the irrigation volumes were over 85%ETc. These results demonstrated that the PRDI facilitated the soil water to distribute into the topsoil depths (0-60 cm), whereas the CFI facilitated the soil water to distribute at deep soil depths (> 60 cm), especially with irrigation volumes exceeding 85% ETc (Figure 2).

Seasonal forage yield and alfalfa P uptake
The responses of the alfalfa seasonal forage yield and the P uptake to the irrigation methods and irrigation volumes were similar from 2017 to 2019. The irrigation methods significantly impacted the alfalfa plant P uptake (P < 0.05) (Figure 3), whereas it had no effect on alfalfa seasonal forage yield; irrigation volumes significantly impacted the alfalfa seasonal forage yield and alfalfa P uptake (P < 0.05), and the interaction between the irrigation methods and irrigation volumes only significantly impacted alfalfa P uptake (P < 0.05).
Alfalfa seasonal forage yield first increased and then decreased as irrigation volumes increased and peaked under I 3 irrigation conditions. The PRDI increased the alfalfa P uptake, especially under I 3 irrigation conditions. As the irrigation volume increased, alfalfa P uptake under the PRDI conditions first increased and then decreased, whereas alfalfa P uptake under CFI conditions first increased and then remained stable (Figure 3).

Soil available P content and stock
The responses of the soil available P content and stock at each soil layer to irrigation methods, irrigation volumes, and the interaction between the irrigation methods and irrigation volumes were consistent among the three years. Irrigation methods had a significant impact on the soil available P content and stock at the 0-80 cm soil depth (P < 0.05) ( Figure 4A, Figure 4B), and irrigation volumes also had a significant impact on the soil available P content and stock at the 0-40 cm soil depth (P < 0.05), whereas the interaction between irrigation methods and irrigation volumes had no impact on the soil available P content and stock.
The PRDI decreased the soil available P content and stock at the 0-80 cm soil depth. With increasing irrigation volumes, the soil available P content and stock first increased from the I 1 irrigation condition to the I 3 irrigation condition and then decreased from the I 3 irrigation condition to the I 4 irrigation condition. The coefficient of variation of the soil available P content was approximately similar to the coefficient of variation of the soil available P stock at each soil depth layer from 2017 to 2019 (Table S5).

Soil total P content and stock
The responses of the soil total P content ( Figure 5A) and stock ( Figure 5B) at each soil depth layer to the irrigation methods and irrigation volumes were in accordance among the three years. Irrigation methods, irrigation volumes and their interaction had no significant impact on the soil total P content and stocks at each soil depth layer. The soil total P content exhibited a similar coefficient of variation of the soil total P stock at each soil depth from 2017 to 2019 (Table S6).

The relationship between seasonal forage yield and alfalfa available soil P
The coefficient of variation of soil available P and total P showed that soil P contents and stocks were similar to the estimated alfalfa available soil P. This study only used the soil P content to proceed with SEM analysis. The SEM analysis with three years of data showed that irrigation methods and irrigation volumes explained 26%, 28% and 88% of the variations in the soil available P content, total P content, and alfalfa seasonal forage yield ( Figure 6). The SEM results revealed that irrigation methods exerted only indirect effects on the alfalfa seasonal forage yield by negatively affecting the soil available phosphorus, consequently maintaining the alfalfa seasonal forage yield. Irrigation volumes not only had direct positive effects on alfalfa seasonal forage yield but also had indirect effects on the alfalfa seasonal forage yield by negatively affecting the soil available phosphorus. Taken together, the irrigation volume was the most important direct factor maintaining the alfalfa seasonal forage yield, and soil available P content was the most important indirect factor that can contribute to the stable alfalfa seasonal forage yield.  -20, 20-40, 40-60, 60-80, and 80-100 cm soil depths among 2017-2019. PRDI and CFI represent partial root-zone drying irrigation and conventional furrow irrigation, respectively; I 1 , I 2 , I 3 , and I 4 represent four irrigation volumes, and *, ** means significant at the P < 0.05 and P < 0.01 levels, respectively.

Discussion
This study shows that the coefficient of variation of P (available or total P) contents and stocks at each soil depth layer are similar to both the PRDI conditions and CFI conditions during the experimental period of 2017-2019, demonstrating that soil P content or soil P stock can both be used to estimate the alfalfa available soil P, and this can also be verified by the correlation coefficients between the soil P content, stock and alfalfa seasonal forage yield ( Figure S3).
This study also showed that the PRDI decreases the soil available P content and stock, and this does not support the first hypothesis. The response of soil available P content and stock to the PRDI is similar to that of N-needing plants  but different from that of nitrophilic plants (Li et al. 2011), indicating that the effect of the PRDI on soil available P content and stock with different nitrogen dependencies is inconsistent. This finding suggests that farmers or farms wishing to apply the PRDI to the culture of crops with different nitrogen dependencies should adopt different  -20, 20-40, 40-60, 60-80, and 80-100 cm soil depths under different treatments in the three years. PRDI and CFI represent partial root-zone drying irrigation and conventional furrow irrigation, respectively; I 1 , I 2 , I 3 , and I 4 represent four irrigation volumes. strategies of P fertilizer management. The lower soil available P for alfalfa caused by the PRDI can be explained by three mechanisms: first, the PRDI can encourage alfalfa roots to develop more nodules , which often consumes more soil available P to proceed with the biological N fixation (Sandral et al. 2019); second, the PRDI induces the soil to experience a dry period, which can encourage phosphate in the soil rapidly to react with Ca (Shirgure and Srivastava 2013) and further forms Ca-associated P, which can transfer some available P into unavailable P ; third, the PRDI can induce a higher root length density and increase the root surface area  to enlarge the contact area between the soil and roots, which can encourage the alfalfa to uptake more soil available P (Figure 2), resulting in a decrease in soil available P content.
This study also found that the PRDI has no effect on soil total P content and stock, in agreement with the second hypothesis, which has also been reported in the N-needing plants (Li et al. 2011;Alrajhi et al. 2017). This indicates that the PRDI in relation to the soil total P may be consistent between N-fixing crops and N-needing crops. PRDI has been verified to increase the soil organic P by accelerating the turnover of microorganism and root (Wang et al. 2017), and an increase in organic P can compensate for the loss of soil available P, which is the main mechanism of PRDI having no effect on soil total P availability. These results suggest that organic amendments, which can transfer unavailable P into available P, worked quite well on alfalfa pasture with PRDI application to maintain sufficient available P.
Similar to the previous studies , this study also found that PRDI had no effect on alfalfa seasonal forage yield. The correlation analysis shows that alfalfa seasonal forage yield is related to the soil available P and soil total P content and stock ( Figure S3), implying that soil P plays an important role in maintaining the alfalfa seasonal forage yield when the PRDI is applied. In addition, the SEM analyses further verified that the relatively stable alfalfa seasonal forage yield under PRDI conditions can be ascribed to the indirect effect of irrigation methods on soil available P content and the direct effect of irrigation volumes on alfalfa seasonal forage yield, which is in accordance with the ANOVA results. In addition, the SEM analysis further shows that irrigation methods have no indirect impact on soil total P, whereas the decrease in soil available P can affect the soil total P, which demonstrates that soil total P can impact the alfalfa seasonal forage yield. The numbers adjacent to the arrows are standardized path coefficients, and the width of the arrows indicates the strength of the standardized path coefficient. The solid lines and dotted lines indicate positive path coefficients and negative path coefficients, respectively (* P< 5% ** P < 1% *** P < 0.1%). R 2 , appearing alongside each dependent variable in the model, represents the proportion of the variance explained for each endogenous variable. Soil AP and TP represent soil available phosphorus and soil total phosphorus, respectively.
This study suggests that the effect of PRDI on alfalfa available soil P was different when soil available P and total P were used to estimate the alfalfa available soil P, although both soil P contents and stocks can be used to estimate the alfalfa available soil P. Management of soil available P is important for alfalfa production when the PRDI is applied. Notably, the irrigation methods and irrigation volume have no effect on soil total P, whereas soil total P contains many fractions. Therefore, more attention should be focused on P fractions in relation to PRDI in alfalfa pastures.

Conclusions
This study employed alfalfa as an experimental crop to investigate the effect of the PRDI on N-fixing crops available soil P. This study finds that the soil P content or stock is similar to the estimated crops available soil P when the PRDI is applied. This study also shows that the PRDI has no effect on alfalfa seasonal forage yield and the soil total P content and stock, and increases alfalfa plant P uptake, while it decreases the soil available P content and stock. This study further finds that irrigation methods maintain alfalfa seasonal forage yield by indirectly affecting soil available P, and irrigation volumes directly influence alfalfa seasonal forage yield. The findings of this study suggest that soil available P management is important for alfalfa production when the PRDI is applied, which presents a pattern of the PRDI influencing N-fixing crops available soil P.