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SOYBEAN

Path Analyses of Population Density Effects on Short-Season Soybean Yield

^a Dep. of Plant Sciences, 51 Campus Drive, Univ. of Saskatchewan, Saskatoon, SK S7N 5A8, Canada
^b Agric. Statistics Lab., Agriculture Annex 101, Univ. of Arkansas, Fayetteville, AR 72704
^c Dep. of Biological and Agric. Eng., Univ. of Arkansas, Fayetteville, AR 72704 and Northeast Res. and Ext. Center, P.O. Box 48, Keiser, AR 72351
^d Dep. of Crop, Soil, and Environ. Sciences, Univ. of Arkansas, Fayetteville, AR 72704 and Northeast Res. and Ext. Center, P.O. Box 48, Keiser, AR 72351
^e Dep. of Crop, Soil, and Environ. Sciences, 1366 W. Altheimer Dr., Univ. of Arkansas, Fayetteville, AR 72704

Corresponding author (lpurcell{at}uark.edu)

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion REFERENCES

 
Yield component analysis provides a framework for identifying potentially useful traits for yield improvement. Consideration of how population density affects other yield components has not been addressed specifically for short-season soybean [Glycine max (L.) Merr.] production. We assessed the direct and indirect contributions of population density for short-season soybean yield and its components over a wide range of population densities (6–134 plants m^-2) using path-coefficient analysis. Data were from field tests conducted in 1997, 1998, and 1999 at Keiser, AR. Although population density had a large inverse association with pods plant^-1, the large direct effect of population density on yield was greater than its negative indirect effect via pods plant^-1. The direct effects of pod number plant^-1 and seeds pod^-1 on yield were positive, whereas mass seed^-1 had a negligible effect. Pods fertile-node^-1 differed between cultivars, and it was reduced by increasing population density. For early sowing, the contribution of population density to yield was less because pods m^-2 could be achieved at low population densities by a large number of fertile-nodes plant^-1 and pods fertile-node^-1. In contrast, at late sowing, the decreased potential for fertile-nodes plant^-1 was compensated by increasing plant population density. In short seasons, maximizing nodes m^-2 and pods m^-2 can be achieved by high population densities and early canopy closure, rather than the conventional system of larger plants with greater numbers of pods plant^-1 and pods fertile-node^-1.

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion REFERENCES

 
TRADITIONALLY, plant breeders have optimized yield largely by empirical selection with little regard for the physiological processes involved in yield formation. More recently, strategies to optimize yield in soybean [Glycine max (L) Merr.] have focused on specific production systems (Carter and Boerma, 1979), and the physiology and mechanisms involved in yield formation. Such physiological processes include setting seed number (Egli and Yu, 1991; Board and Tan, 1995) and filling these potential fruiting sites (Egli et al., 1984). However, selection of high yielding cultivars via specific traits requires knowledge not only of final yield but also of the many compensation mechanisms among yield components resulting from changing genotypic, environmental and management factors (Salado-Navarro et al., 1985; Akhter and Sneller, 1996).

Soybean yield may be broken down into yield components and expressed mathematically in a multiplicative form by Eq. [1]:

(1)

Pods plant^-1 can be further divided into two components, fertile-nodes plant^-1 and pods fertile-node^-1. The full soybean yield equation in multiplicative form is, therefore,

(2)

Path analysis is used to partition the relative contribution of yield components via standardized partial-regression coefficients. The correlation coefficients can be separated into the direct and indirect influences that one variable has on another (Dewey and Lu, 1959; Fig. 1) . Path analyses have been used to identify important yield components in various crops including rice (Oryza sativa L.; Gravois and McNew, 1993), wheat (Triticum aestivum L.; Costa and Kronstad, 1994), and soybean (Pandey and Torrie, 1973; Akhter and Sneller, 1996; Board et al., 1997, 1999a; Shukla et al., 1999).

View larger version (15K): [in this window] [in a new window]   Fig. 1 Path diagram showing causal relationships between the response variable, yield (x5), and the four component variables, population density (x1), pods plant-1 (x2), seeds pod-1 (x3), and mass seed-1 (x4). Path coefficients are represented by P15, P25, P35, and P45, which correspond to direct effects on yield from population density, pods plant-1, seeds pod-1, and mass seed-1, respectively. For any two component variables (e.g., x1 and x2), their correlation (r12) multiplied by the path coefficient of the second component variable (e.g., P25) gives the indirect effect of one component (x1) on x5 through the effect of another component (x2). The residual is the remaining portion of yield not accounted for by the four yield components

Path analyses for both conventional and late-sown soybean systems in Louisiana (Board et al., 1997, 1999a) indicated that seed m^-2, reproductive nodes m^-2, and pods reproductive-node^-1 served as the best selection criteria. Although these data included three row-spacing by population density treatment combinations, the range of plant population density was limited. It is possible that compensation among yield components in response to population density may negate the importance of particular components of yield. The contribution of population density to yield components has not been directly addressed.

Board et al. (1999b) more recently proposed pod number reproductive-node^-1 as a selection criterion for high yield. The cumulation of pod number reproductive-node^-1 for the number of fruiting nodes on a plant is the equivalent of pod number plant^-1. High values of pod number plant^-1 are typically associated with low density stands (Boquet, 1990), whereas yields for short-season soybean crops are increased by high population densities (Ball et al., 2000a). Selection of yield via pod number reproductive-node^-1 will, therefore, be greatly influenced by plant population. In addition, plant architecture and node number are affected by population density (Boquet, 1990) and sowing date (Parvez et al., 1989). Determinate cultivars bred for the southern USA may also be more branched compared with indeterminate cultivars at late sowing (Board and Settimi, 1986; Akhter and Sneller, 1996).

We propose that the importance of individual yield components, as presented in Eq. [2], varies with length of growing season, weather, and irrigation. For production systems with periods of long vegetative development, yield appears to be closely associated with plant size factors, i.e., components affecting the number of pods plant^-1, fertile-nodes plant^-1, and pods fertile-node^-1 (Board et al., 1997, 1999a). In contrast, short growing seasons may limit vegetative development and plant size, thereby increasing the importance of population density (Parvez et al., 1989) as a direct component of yield. The objective of this research was to determine the contribution of individual yield components to yield for short-season production systems, in which yield was responsive to relatively high population densities (Ball et al., 2000a).

	Materials and methods

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion REFERENCES

 
1997 and 1998 Population Density Study
Details of this study were reported in Ball et al. (2000a), and only a brief description is given below. Field tests were sown on 8 July 1997 and 26 June 1998 at the Northeast Research and Extension Center, Keiser, AR (35°67'N, 90°83'W), on a Sharkey silty clay (Vertic Haplaquepts; USDA taxonomy). Two cultivars of maturity group IV soybean were evaluated: `Asgrow 4922' (A4922), an indeterminate, and `Manokin', a determinate. There were two levels of irrigation treatment (irrigated and nonirrigated). Irrigated treatments received water from an overhead irrigator when the estimated soil-moisture deficit reached 50 mm (Cahoon et al., 1990).

The experiment had three row spacings (0.19, 0.57, and 0.95 m), each with five levels of population density. The experiments were sown with a commercial grain drill (Model 750, Deere and Co., Moline, IL), and different row spacings were achieved by blocking selected seed tubes in the hopper. For each cultivar and target population density, the drill was calibrated to deliver selected seeding rates. Population density was determined approximately 14 d after emergence by counting plants in 1.5-m lengths of row at four random sites within each plot. Stand counts within a target seeding rate did not differ statistically among cultivar or irrigation treatments. In 1997, observed population density ranges were 12 to 135 plants m^-2 for 0.19-m rows, 7 to 66 plants m^-2 for 0.57-m rows, and 9 to 49 plants m^-2 for 0.95-m rows. In 1998, observed population density ranges were 12 to 91 plants m^-2 for 0.19-m rows, 7 to 54 plants m^-2 for 0.57-m rows, and 6 to 34 plants m^-2 for 0.95-m rows.

The experiment was a split-split-split plot arrangement of treatments in a randomized complete block design with four replications. The factors applied to the hierarchy of plots, beginning with the main plot, were irrigation, row spacing, cultivar, and population density. Plot length for all row spacing treatments was 46 m, and there were 16 rows for the 0.19-m row spacing, six rows for the 0.57-m row spacing, and four rows for the 0.95-m row spacing.

Pods were counted on a subsample of six plants (1997) or 12 plants (1998) per plot the day before harvest. Grain was harvested from a plot length of 12.2 m, avoiding borders, with a plot combine. The center eight rows, three rows, and two rows were harvested from the 0.19-, 0.57-, and 0.95-m row spacing treatments, respectively. Yield was expressed at 130 g kg^-1 moisture. Mass of a 100-seed subsample was used to calculate the mass of an individual seed. Seed m^-2 was calculated from the quotient of yield and individual seed mass, and seeds pod^-1 was the quotient of seed m^-2 and pods m^-2. Pods m^-2 was calculated as the product of pods plant^-1 and a mean value of population density (averaged over irrigation regime, cultivar, and replication).

1998 Nodal Data Set
In 1998, detailed measurements were made at the nodal level (Keisling and Counce, 1997) from a subsample of plants from selected plots at R8, harvest maturity (Fehr and Caviness, 1977). Treatment factors were irrigated and nonirrigated regimes, A4922 and Manokin cultivars, 0.19-m row width, and population densities of 16, 20, 34, 42, 54, and 91 plants m^-2. Pod-bearing nodes, pods, and seeds were counted on 12 adjacent plants in each plot. Pods fertile-node^-1 was the quotient of total pods and total nodes, and seeds fertile-node^-1 was the quotient of total seeds and total nodes.

1999 Sowing Date and Population Density Study
In 1999, a study similar to that described for 1997 and 1998 was conducted at the same location. `Hartz 4994' (H4994), a determinate cultivar, and A4992 were sown in 0.19-m rows for early (26 May) and late (25 June) sowing dates. The experiment was a multiple split-plot arrangement of treatments in a randomized complete block design with four replications. The hierarchy of treatments from the main plot treatment to that in the final split was sowing date, irrigation, cultivar, and population density. Stand counts within a target seeding rate did not differ among cultivar or irrigation treatments, and mean population densities were 12, 24, 45, 80, and 101 plants m^-2 for the early sowing date, and 7, 14, 27, 45, and 66 plants m^-2 for the late-sowing date. The number of fertile nodes (nodes with pods present) and the number of pods were counted from a subsample of 6 (lowest population density) to 54 (highest population density) plants from a plot 1 wk before harvest. This wide range of plants for subsampling was designed to give approximately equivalent pod numbers per subsample over the population density range. These pods were then threshed to obtain yield as g seed plant^-1. Data on a plant basis were averaged over the subsample of plants per plot. Grain was harvested using a plot combine as in 1997 and 1998. Mass seed^-1 was from the mass of a 100-seed subsample taken from the harvested grain, and seeds plant^-1 was calculated as the quotient of g seed plant^-1 and mass seed^-1. Seeds pod^-1 was then calculated as the quotient of seeds plant^-1 and pods plant^-1.

Statistical Analyses
Path analyses for the multiplicative yield models (1997 and 1998 population density data; 1999 population density and sowing date data) used the actual population densities from the stand counts for each individual plot. Before path analysis, five observations were removed from the data set (total no. of observations = 480). These observations were outliers based on one pass through the transformed data using Cooks D and Student's residual statistics as described by Ball et al. (2000b). In 1999, we removed one outlying yield value (total no. of observations = 160), which was from a low population density treatment (14 plants m^-2). Path analysis was conducted on each combination of year x irrigation regime x cultivar for 1997 and 1998, and sowing date x irrigation x cultivar for 1999. Data within each group included treatment factors of plant population density, row spacing, and replication.

An analysis of variance on each combination of irrigation regime, and cultivar for the 1998 nodal data set was performed using a general linear model (SAS Inst., 1998) on the variables listed in Table 6, to be consistent with the grouping of data for path analyses. This data set was used because it was from samples independent of the main path analysis, and it also included an additional level of data on number of nodes and pods node^-1.

(3)

The correlations among transformed variables of yield and yield components were assessed from the Pearson product-moment correlation statistic from PROC CORR in SAS (SAS Inst., Version 7, 1998). The path coefficients, which are the standardized regression coefficients (Dewey and Lu, 1959), were obtained from PROC REG. For the 1999 sowing date study, data were analyzed separately for each combination of sowing date, cultivar and irrigation regime. A path diagram is shown in Fig. 1, where P₁₅, P₂₅, P₃₅, and P₄₅ represent path coefficients to yield from population density, pods plant^-1, seeds pod^-1, and mass seed^-1, respectively. The direct effect of each yield component on yield is the path coefficient from that component to yield. The indirect effect of one component through a second component is the product of the path coefficient from the second component and the correlation between the two components (e.g., Dewey and Lu, 1959). Yield data for the 1999 path analysis were fitted with five variables using the logarithm transformation of Eq. [2], where P₁₆, P₂₆, P₃₆, P₄₆, and P₅₆ represent path coefficients of population density, fertile-nodes plant^-1, pods fertile-node^-1, seeds pod^-1, and mass seed^-1, respectively.

	Results

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion REFERENCES

 
Responses of Yield and Pods to Population Density
Grain yield response to population density, expressed as g seed m^-2, was reported in Ball et al. (2000a)(2000b). Generally, yield responded to population density similar to that of pods m^-2, due to relatively minor changes in individual mass seed^-1 (g seed^-1) in response to population density and irrigation regime (Ball et al., 2000b). Response of seeds pod^-1 changed with population density, pods plant^-1, and cultivar, but not in an easily explainable fashion (Ball et al., 2000b). As population density increased, pods m^-2 increased in an asymptotic manner for irrigated treatments of A4922 (Fig. 2A) and Manokin. Nonirrigated treatments generally showed fewer pods m^-2 compared with irrigated treatments at similar population densities (Fig. 2A).

View larger version (21K): [in this window] [in a new window]   Fig. 2 (A) Pods m-2 and (B) pods plant-1 in response to varying plant population density for late-sown irrigated and nonirrigated treatments of Asgrow 4922 in 1997

The indirect effect of population density on yield via seeds pod^-1 was small but positive for A4922 (0.17 for irrigated; 0.14 for nonirrigated), and negative for Manokin (-0.42 for irrigated; -0.07 for nonirrigated). Certainly with population density, the order of importance was the direct effect of plant population density, followed by the indirect negative effect of population density on yield via pods plant^-1. A small indirect effect of population density on yield via seeds pod^-1 and a negligible via mass seed^-1 were seen.

For pods plant^-1 (Table 3), the indirect effect of pods plant^-1 on yield via population density was the largest effect for any of the four irrigation regime and cultivar combinations (e.g., -1.45 for irrigated A4922), which was larger than the direct effect of pods plant^-1 (1.05 for irrigated A4922). Smaller and negative indirect effects were seen for pods plant^-1 on yield via seeds pod^-1 and mass seed^-1 (-0.33 and -0.05, respectively, for irrigated A4922). Certainly for the late-sown, short growing season of 1997, the indirect effect of pods plant^-1 on yield through population density was large and negative, and was also negative through seeds pod^-1. At low population densities, plants had large numbers of pods, but few seeds pod^-1. The indirect effect of pods plant^-1 on yield via mass seed^-1 was negligible, again reflecting the ability of the soybean plant to maintain seed size within an irrigation regime for each cultivar.

Seeds pod^-1 had a positive direct effect on yield (e.g., 0.64 for irrigated A4922, 1997), which was greater than the negative indirect effect of seeds pod^-1 on yield via pods plant^-1 (e.g., -0.55 for irrigated A4922). It was also greater than the respective indirect effect of seeds pod^-1 on yield via population density within a treatment combination of year, irrigation, and cultivar, with the exception of nonirrigated A4922 in 1998 (Tables 3 and 4). Effects of seeds pod^-1 on yield through the component mass seed^-1 were negligible. Finally, mass seed^-1 affected yield indirectly through population density (e.g., 0.41 for irrigated A4922) and pods plant^-1 (-0.30 for irrigated A4922), with a small indirect effect of mass seed^-1 on yield via seeds pod^-1 (0.06 for irrigated A4822).

Data for 1998 path analyses (Table 4) were similar to patterns found in 1997. The direct effect of population density on yield was greater than the indirect effects of population density on yield through its action on pods plant^-1 or seeds pod^-1. Pods plant^-1 had a large negative indirect effect on yield via population density, a positive direct effect on yield, and a smaller but negative indirect effect on yield through its action on seeds pod^-1. Plant population density had the greatest effect overall on yield for a late-sown crop via the direct population density effect, and a corresponding inverse indirect effect on yield through pods plant^-1.

Sowing Date Study, 1999
Models for the five-component multiplicative model (Eq. [2]) poorly explained the variation in yield (adjusted R² 0.69; Table 5) compared with the four-component models of 1997 and 1998, which used late-sown soybean crops. Sample size for each combination of sowing date, irrigation regime and cultivar also reduced the model fit in comparison to the 1997 and 1998 data . Water-deficit stress experienced by the crop in 1999 was so severe that nonirrigated treatments showed little yield response, and data were not comparable with other years. Therefore, results from 1999 will be limited to responses from irrigated treatments.

In summary, the early-sown soybean showed that most yield variation was via direct and indirect effects from the components population density, fertile-nodes plant^-1, and pods fertile-node^-1. The direct effect of population density was stronger for the determinate cultivar (H4994), whereas the indirect effect of population density via pods fertile-node^-1 was stronger for the indeterminate cultivar (A4922). However, the magnitude of the effects by population density and pods plant^-1 was less than those from the 1997 and 1998 data.

For the late-sown, irrigated treatment in 1999, yield increased more gradually than for the early-sown treatment. Yield reached an asymptote of approximately 412 (A4922) and 410 (H4994) g m^-2 at population densities >40 (A4922) and 30 (H4994) plants m^-2 (Ball, Purcell, and Vories, unpublished data, 1999). Models for late-sown soybean generally explained more of the yield variation (higher values of R²) compared with early-sown soybean (Table 5). Higher correlations between population density and yield were seen in late-sown A4922 and H4994 . Late-sown A4922 and H4994 showed large negative correlations between fertile-nodes plant^-1 and yield (-0.79 and -0.62 for A4922 and H4994, respectively). Late-sown H4994 also showed a negative association between pods fertile-node^-1 and yield . Late-sown A4922 accounted for much of the variation in yield by the direct effect of population density (0.81). Important indirect effects were: fertile-nodes plant^-1 on yield via population density (-0.67), pods fertile-node^-1 on yield via population density (-0.49), and seeds pod^-1 on yield via population density (-0.21; Table 5). The large correlation of yield with population density for late-sown H4994 was due to a large indirect effect of population density on yield via fertile-nodes plant^-1 (0.50), the direct effect of fertile-nodes plant^-1 on yield (-0.58), and the indirect effect of pods fertile-node^-1 on yield via fertile-nodes plant^-1 (-0.42).

With earlier sowing, pods fertile-node^-1 also had large direct effects of 1.17 for irrigated A4922, and 0.31 for irrigated H4994, respectively. The direct effect of pods fertile-node^-1 for late-sown soybean was less than the early-sown counterpart (0.15 for irrigated A4922 and 0 for irrigated H4994). In 1999, and especially the late-sown treatment, population density had a lower range than 1997 and 1998. The lower population densities may have lessened the magnitude of responses of yield components.

Nodal Data from 1998
Cultivars A4922 and Manokin increased yield with increasing population density (Ball et al., 2000a), which was associated with increased pods m^-2 and fertile-nodes m^-2 as population density increased (Table 6). Nonirrigated treatments showed a similar response to irrigated treatments except that yield, nodes m^-2 and pods m^-2 were of lesser magnitude.

From correlation analysis of irrigated treatments (Table 7), pods fertile-node^-1 was poorly and negatively correlated with yield ( for Manokin), but yield was highly correlated with fertile-nodes m^-2 ( for Manokin). For A4922, fertile-nodes m^-2 was strongly associated with population density , but pods fertile-node^-1 was negatively correlated with number of fertile-nodes m^-2 and population density . Manokin showed responses similar to those of A4922.

	Discussion

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion REFERENCES

 
For short-season soybean production, population density can be used to manage the number of nodes m^-2 and number of reproductive nodes m^-2. Although pods plant^-1 was inversely correlated with population density, it was a lesser effect compared with the contribution of plant population. Effects of population density on mass seed^-1 and seeds pod^-1 were small compared with those of population density and pods plant^-1 and for a particular combination of irrigation, cultivar and year, these components were approximately constant.

In contrast to reports using later-maturing cultivars and longer growing seasons (Board et al., 1997, 1999a, 1999b), pods fertile-node^-1 did not correlate strongly with yield for the late-sown treatments. Population density and fertile-nodes plant^-1 accounted for much of the yield variation at the later sowing date in 1999. Fertile-nodes plant^-1 and pods fertile-node^-1 appeared to be more closely associated with yield for the early sowing date compared with the late sowing date. For the early sowing date, the contribution of population density was less because pods m^-2 could be achieved at low population densities by a large number of fertile-nodes plant^-1 and high number of pods fertile-node^-1. In contrast, at late sowing, the decreased potential for fertile-nodes plant^-1 was compensated by increasing plant population. Pods fertile-node^-1 remained within a similar range across population density in 1999, but in 1998 this component was decreased at the highest population density (91 plants m^-2).

The components nodes m^-2 and pods m^-2 are those most closely associated with higher yields (Table 7; Board et al., 1997, 1999a, 1999b). Depending on the length of the growing season and availability of irrigation, we propose two ways to maximize number of nodes and pods m^-2. The first way fits a full-growing season (sowing in May or early June), where the target is growing fewer plants to a greater size, to produce many nodes plant^-1 and pods plant^-1. Vegetative growth correlates with plant height, number of nodes, number of reproductive nodes, and yield (Akhter and Sneller, 1996). Reduction in growth m^-2, even during vegetative growth, will result in lower node number and reduced yield capability. Lower density crops grown to maximize the full growing season necessitate optimum vegetative growing conditions for the development of adequate leaf area. Use of narrow rows or approximately equidistant sowing (Board et al., 1992) will also contribute to maximizing light use.

The second way of maximizing number of nodes and pods m^-2 is more suited to late-sown, double-crop, or short growing seasons, where light interception is dependent upon high population density (>60 plants m^-2; Ball et al., 2000a). The aim is to grow many plants of smaller individual size. A short growing season compromises the height and number of nodes for a soybean plant because the length of the vegetative period is usually reduced by sowing late, but the reproductive period is not affected greatly (Egli et al., 1978). Any reduction in growth resulting from water-deficit stress or the late sowing of a crop at conventional-system population densities (25–35 plants m^-2), may result in fewer nodes m^-2 and reduced yield capability. Yield is, therefore, strongly determined by the population density component, with less emphasis on contributions from pods plant^-1, nodes plant^-1, and pods fertile-node^-1.

As seasons become progressively shorter, the population density effect becomes more critical. For short-season soybean production systems, high plant population density ensures early canopy closure and maximum light interception, high rates of crop growth, increased node number m^-2, and greatest yield potential.

	ACKNOWLEDGMENTS

 
We thank Bob Glover and the staff at NEREC for help and expertise in preparation and measurement of field plots. Jeremy Wolf, April Kercheville, Jennifer Wolf, Faye Owens, and C.J. Gordon were responsible for processing the node count samples.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Discussion REFERENCES

 
This paper is published with the approval of the director of the Arkansas Agric. Exp. Stn. as Manuscript no. 00016.

Received for publication February 25, 2000.

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