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Crop Science 43:934-942 (2003)
© 2003 Crop Science Society of America

SEED PHYSIOLOGY, PRODUCTION & TECHNOLOGY

Quantitative Relationships between Pollen Shed Density and Grain Yield in Maize

Mark E. Westgate*,a, Jon Lizasob and William Batchelorb

a Department of Agronomy, Iowa State University, Ames, IA 50011
b Department of Agricultural and Biosystems Engineering, Iowa State University, Ames, IA 50011

* Corresponding author (westgate{at}iastate.edu)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
Pollen production generally is not considered a limiting factor in modern maize (Zea mays L.) production. In some modern hybrids, however, smaller tassel size, use of male sterile blends, and top cross production may limit pollen availability. This study was conducted to establish the lower limits for pollen production needed to ensure maximum kernel set, and to devise a method for predicting pollen production from simple measures of tassel development. Isolated blocks of male fertile plants were established in a field of male sterile plants. The level of male fertility was varied from 0 to 100% by detasselling (Pioneer 3978) or by using mixtures of male fertile and male sterile isolines (Pioneer 3925 and 3925S). Pollen shed was measured daily with passive pollen traps. A Population Index, derived from the percentage of plants shedding pollen and the average pollen production per plant, accurately predicted the seasonal pattern and total pollen shed for each male fertility treatment. Hybrids used in this study shed pollen for 10 to 12 d, with a peak intensity 2 to 3 d after anthesis (50% plants shedding pollen). Individual tassels produced 4.5 x 106 pollen grains on average, and shed pollen for 5 or 6 d. Variation in grain yield across male fertility treatments was closely correlated to kernels per plant (r2 = 0.998). Seasonal pollen production limited kernels per plant at pollen densities less than 3000 pollen grains silk-1. This lower limit for effective kernel set occurred at male fertility levels less than 50% for both hybrids. Grain yield, however, was maintained at male fertility levels as low as 20% because of compensation in grain size. These results demonstrate that a minimum pollen shed density per exposed silk is required to achieve maximum kernel set and grain yield. They also show that the seasonal pattern of pollen shed can be predicted from simple measures of staminate flower development. Together, these results provide a rational basis for achieving high kernel set under field conditions in which pollen production might be limiting.

Abbreviations: MF, male fertility • Pind, population index • PSD, daily pollen shed density


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
POLLEN PRODUCTION generally is not a limiting factor in modern maize production. Studies on the physiological basis for yield improvement over the past 50 yr show that greater yield of modern maize hybrids is associated with an increase in kernel number per unit area and a decrease in tassel size (Duvick, 1997). Yield gains have been due largely to a decrease in barren plants and the maintenance of a short anthesis-silking interval at higher plant population densities (Cárcova et al., 2000; Edmeades et al., 2000). Both factors reflect the importance of rapid ear and ovule growth during anthesis for high kernel set (Edmeades et al., 1993; Bassetti and Westgate, 1994; Zinselmeier et al., 1995). Although such results have led to the perception that maize plants continue to produce an overabundance of pollen (Garnier et al., 1993), use of small-tasseled inbreds in hybrid seed production, male sterile blends [50% male fertile (MF)], and top crosses (approximately 10% MF), coupled with environmental effects on pollen production and viability (Westgate and Bassetti, 1991) provide numerous opportunities for pollen production to limit kernel set under field conditions.

Published estimates of maize pollen production on a field scale are very limited, particularly in relation to kernel formation. The lack of quantitative information on pollen production reflects the laborious nature of the techniques used to quantify pollen shed, such as spinning rods (Flottum et al., 1984), tassel bags (Sadras et al., 1985a), and passive pollen traps (Bassetti and Westgate, 1994; Uribelarrea et al., 2002), and the need to collect samples daily to generate a seasonal integral of pollen production. These approaches for quantifying pollen production, however, have not taken full advantage of the predictable nature of tassel development and the process of pollen shed from the staminate flowers (Kiesselbach, 1999).

Hybrid seed production requires close synchrony between receptive silks on the female parent and pollen shed by the male parent. Abundant pollen is critical for high seed set and genetic purity (Wych, 1988). Establishing the most productive combination of male to female rows and their densities for maximum yield per female, however, often is based on practical experience rather than quantitative information on the flowering biology of the crop (Culy et al., 1991). Seed yield could be managed in a more rational and cost-effective manner if simple measures of tassel development indicated the timing and intensity of pollen shed. Genetic purity also could be managed more effectively if lower limits of pollen production for maximum kernel set were defined on a field scale.

Therefore, this study was conducted to achieve two objectives: (i) to devise a method for predicting pollen production from simple measures of staminate flower development within a plant population; and (ii) to establish the lower limits for pollen production needed to ensure maximum kernel set on a field scale. The results of this study provide, for the first time, a quantitative basis for managing maize fields for maximum kernel set, and the minimum data set on flowering dynamics required to achieve it.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 REFERENCES
 
Plant Culture
Pollen shed density treatments were established within a 40- by 60-m field block at Morris, MN, on a Sioux sandy loam soil (sandy-skeletal, mixed Udorthentic Haproboroll). Each year 100 kg ha-1 of 13-33-33 NPK fertilizer was applied at planting, and a side-dress of 100 kg ha-1 N as urea was applied 5 wk later. The field received pre-emergence herbicide at planting and was irrigated with an overhead sprinkler system to maintain soil moisture tension above –0.3 MPa.

Two methods were used to create the required variation in pollen production needed to test when pollen shed density limited kernel set under field conditions. In 1986, the field was planted on 19 May to Pioneer 3978 (P3978; Pioneer Hi-Bred Intl., Johnston, IA) at approximately 7.2 plants m-2. All plants, except those in four 36-m2 plots, were detasselled after tassel emergence but before pollen shed. Tassels were removed by hand at the peduncle, and no leaves were removed to minimize disturbance to the crop canopy. Pollen shed density within the four MF plots was established by detasselling the appropriate number of plants to achieve 100, 50, 20%, or 0% male fertile plants (Fig. 1). In 1987, male sterile and male fertile isolines of Pioneer 3925 (P3925 and P3925S) were used to establish the pollen density treatments. This approach provided greater control of pollen density within each plot, and eliminated the labor requirement for detasselling. The field was planted on 11 May to the male sterile isoline at 5.7 plants m-2. Male fertility levels of 75, 50, 20%, and 0% were obtained within the four pollen density plots by planting the male fertile isoline of Pioneer 3925 in offset rows, and thinning to the appropriate ratio of male fertile and male sterile plants two weeks after emergence. In both cases (detasselling and male fertile/male sterile ratios), male fertile plants were spaced as evenly as possible within each treatment plot to provide a uniform pattern of pollen shed for the entire plot area.



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  		Fig. 1. Field arrangement for isolating pollen shed density treatments. MF indicates the percentage of plants in each treatment block that were allowed to shed pollen. The level of male fertility was controlled by detasselling P3978 in 1986 or by a mixture of male sterile and male fertile isolines of P3925 in 1987. Distances are in meters.

 
Flowering Dynamics
The progress of the flowering process was monitored daily throughout the pollen shed period. In each treatment plot, four groups of 20 to 40 consecutive plants, depending on the population, were examined for the progress of pollen shed and silk emergence each day at 0800 to 1000 h. The percentage of these plants at three development stages was recorded. These stages included plants that had begun to shed pollen (BegShed—anthers exserted on the main tassel branch only), were at or past maximum pollen shed (MaxShed- anthers exserted on main and side tassel branches), and had completed pollen shed (EndShed—no new anthers exserted, typically at base of tassel branches). In addition, the percentage of plants with silks emerged on the apical ear (Silking) was recorded. Plants reaching these stages are depicted in Fig. 2. Measurements continued until all plants in each treatment population had completed pollen shed and had emerged silks. The total number of silks per apical ear was estimated by counting emerged silks on 10 primary ears of each hybrid, nine days after first silk emergence (Bassetti and Westgate, 1993). These ears were covered with glassine bags before silk emergence to prevent pollination. Therefore, this measurement represents the potential number of florets available for fertilization.



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  		Fig. 2. A: Beginning pollen shed. Anthers on the main tassel branch are shedding pollen. B: Maximum shed. Pollen is being shed from the main tassel branch and side branches. C: End shed. Anthers at the base of the side branches and main branch have completed shedding pollen. D: Silk emergence. The first day silks emerge from the surrounding husks. Silks are typically 1 to 2 cm in length.

 
The field data for BegShed, MaxShed, EndShed, and Silking of each treatment population were fit to standard logistic curves of the form:

[1]
where Y = percentage of the population at the indicated stage (e.g., 20% at MaxShed), X = day of the year, a = treatment level of male fertility for the plot (e.g., 50% MF), b = rate factor controlling the change in Y per day at a/2, and c = day of year at a/2. For a population of 100% MF plants, for example, parameter c for BegShed is the day of anthesis for the population. Parameter a was defined for each treatment (Table 1), and parameters b and c were derived from the curve. This form of logistic curve was chosen because it provides a simple yet elegant description of population dynamics (Kingsland, 1982), requires a minimum of input parameters, and routinely provided r2 >= 0.95 for curves fit to the tassel stage parameters used in this study. The curves fit to BegShed, MaxShed, and EndShed data were used to generate a Population Index for estimating the daily rate of pollen shed for each treatment population (see below).


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  		Table 1. Pollen production in plots having a reduced number of male fertile tassels. Tassel numbers were varied in P3978 by detasselling, and in P3925 by using mixtures of male sterile and male fertile plants. Data are the mean ± SE for four (pollen deposition) or eight (population) samples.

 
Pollen Shed
The progress and intensity of pollen shed was monitored daily according to Bassetti and Westgate (1994). Briefly, pollen was collected passively on traps made of clear adhesive paper (Engineered Coated Products, Northbrook, IL) attached to a methyl methacrylate support (6 by 12 cm) mounted horizontally within the canopy at ear level (approximately 1 m above the ground). Four traps were placed at random in each plot and replaced daily between 1600 and 1700 h. On peak pollen shed days, traps were replaced at 1100h and 1700 h, and the values summed for the day. No attempt was made to prevent pollen desiccation during pollen collection or trap storage, as desiccation did not affect the quality of the image used to count the pollen grains. Pollen grains in four 0.5-cm2 areas were counted on a photographic image taken through a binocular microscope (Bausch & Lomb, Stereo Zoom 7) at 10x magnification. A high contrast image was created using a dark background and horizontal light source. The four images per trap were averaged to give grains per square centimeter per day for each daily sample. This method of pollen collection quantifies pollen density reaching the level of the exposed silks. Sadras et al. (1985a) reported that 70 to 80% of the pollen released at the top of the canopy ultimately reached this plane in the canopy.

Population Index for Pollen Shed
The dynamics of staminate flowering captured in the logistic curves for BegShed, MaxShed, and EndShed were used to create a Population Index (Pind) of the percentage of plants shedding pollen each day. Logically, the duration of pollen shed for a given treatment population brackets in days the first plants to begin shedding pollen and the last plants to complete shedding. And the maximum intensity of pollen shed should occur when the largest percentage of plants are shedding pollen. Preliminary analysis indicated that calculating the Pind value as the difference between the BegShed and EndShed curves overestimated pollen shed before the date of maximum shed measured in the field. Similarly, calculating the Pind as the difference between the MaxShed and EndShed curves underestimated pollen shed during this time (data not shown). Averaging daily BegShed and MaxShed values, however, provided a seasonal pattern of Pind values that closely corresponded to the seasonal pattern of pollen shed in duration and intensity for both hybrids. Therefore, the daily Pind value for each pollen density treatment was calculated as:

[2]
where Pind n is the Population Index (%) for pollen shed on the nth day of the year, and BegShed, MaxShed, and EndShed are the percentages of the population at these three stages on day n derived from logistic curves specific to each pollen density treatment.

Daily Pind values were scaled to predicted rates of daily pollen shed density as:

[3]
where PSDn is the daily pollen shed density (grains cm-2 d-1), Pind n is the daily Population Index, and grains per plant is the average pollen production per plant estimated from the total seasonal pollen shed in the 100% MF plot of P3978 and the 75% MF plot of P3925 (Table 1). Sheddays is the number of days the average plant in the population sheds pollen. This value cannot be measured directly, but it can be estimated for each treatment using parameter c in the logistic curves for BegShed, MaxShed, or EndShed. Parameter c indicates the day 50% of the population has reached the indicated stage. As such, plants entering the stage on this day most likely represent the average for the treatment. Sheddays (days) for each pollen density treatment was calculated with Eq. [4]:

[4]
where cEndShed, cBegShed, and cMaxShed values (day of the year) were derived from Eq. [1]. The calculation is analogous to that used for the Population Index in that the effective date when 50% of the population began to shed pollen is taken as the average of the 50% BegShed and 50% MaxShed dates. The calculation of Sheddays assumes all plants in the population shed a similar number of pollen grains and that pollen shed per plant is uniform for all shedding days. These assumptions are not biologically accurate, but neither is likely to have a practical consequence for estimating daily pollen shed under field conditions. On any given day, the population includes a mixture of plants at BegShed, MaxShed, or EndShed. And variation in pollen production among plants is obscured by aerial dispersal of the pollen after it is released from the anthers.

Grain Yield
Grain yield and yield components were determined on hand-harvested ears from four 4.6-m2 areas within each treatment plot. Ears were dried at 65°C to constant weight, shelled and pooled. Three sub-samples were taken to estimate average kernels per plant and average kernel weight. Plant population and ears plant-1 also were recorded for each harvest area. Grain yield and kernel weight are presented on a 155 g kg-1 moisture basis.

Data Analysis
Variables b and c in Eq. [1] for BegShed, MaxShed, EndShed, and Silking were derived from curves fit to field data by the least squares procedure in TableCurve 2D V5.0 (SPSS Inc., Chicago, IL). Means and standard errors were calculated for daily pollen shed and repeated yield measures to provide an estimate of variability within male fertility treatments. Where appropriate, pollen shed data were normalized on a population basis to facilitate comparisons across years and hybrids.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
REFERENCES
 
Flowering Dynamics
A primary objective of this work was to establish seasonal profile of pollen shed duration and intensity from simple measures of the flowering process. To this end, daily observations were taken on the population of tassels within each MF treatment to document their involvement in the process of pollen shedding. We assumed that each tassel underwent a similar pattern of pollen shedding that could be characterized in terms of the day pollen shed began, the day pollen shed entered its maximum phase, and the day pollen shed ended (Fig. 2).

Both hybrids exhibited the same general pattern of staminate flowering dynamics, and recruited new tassels into the pollen shedding population over a period of 6 to 8 d (Fig. 3). The percentage of tassels reaching the three phases of pollen shedding increased in a sigmoid fashion up to the maximum percentage of MF plants in each treatment. Taking 50% of the population shedding pollen as the typical benchmark for anthesis, these curves revealed that maximum shed followed anthesis by 2 to 3 d, and pollen shed ended 3 or 4 d later, depending on the genotype. Thus, the average tassel shed pollen for 5 (P3978) or 6 (P3925) d. If so, the earliest tassels to begin shedding pollen in each population must have completed pollen shed before the latest tassels had begun to do so.



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  		Fig. 3. Percentage of the plant population in each treatment block that has begun to shed pollen (Beg Shed), is at maximum pollen shed (Max Shed), has completed pollen shed (End Shed), or has silks visible (Silking). MF indicates percentage of plants allowed to shed pollen. The level of male fertility was controlled by detasselling (P3978), or by using a male sterile isoline (P3925). Data are the mean ± SE of 4 reps of 20 to 40 plants each.

 
The percentage of silking plants also increased in a sigmoid fashion and generally mirrored the onset of pollen shedding (Fig. 3). The close correspondence between the dynamics of plants beginning to shed pollen and plants silking often is taken as a measure of the floral synchrony required for a high level of kernel set (Bolaños and Edmeades, 1993; Cárcova et al., 2000). Yet, these population dynamics provide no direct quantitative information about the intensity of pollen shed, or the actual dynamics of silk exsertion for the population. Such quantitative relationships between pollen shedding, silk emergence, and kernel set on an area basis require basic information on the pattern of silk exsertion on each ear and the efficiency of pollination at various pollen shed densities. These quantitative relationships and their consequences for predicting yield formation are considered in the companion paper (Lizaso et al., 2003, this issue).

The MF treatments provided a wide range of pollen shed densities, without altering the timing of pollen shed relative to silk emergence. Fig. 4 shows that pollen shed occurred over a period of 10 (P3925) to 12 d (P3978) and peaked 2 to 3 d after anthesis (Day 200 for P3978, Day 198 for P3925, see Fig. 3). These general patterns of pollen shed are similar to those reported earlier (Bassetti and Westgate, 1994). Altering the percentage of fertile plants decreased the daily values as expected, but had no discernible effect on the general pattern of pollen shed in agreement with the population flowering data (Fig. 3).



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  		Fig. 4. Seasonal pattern of pollen shed for the various male sterility treatments used to decrease pollen shed density. Pollen was collected on passive pollen traps placed at ear height within each treatment block. MF indicates percentage of plants allowed to shed pollen. The level of male fertility was controlled by detasselling (P3978), or by a male sterile isoline (P3925). Each point is the mean ± SE of 3 traps.

 
Seasonal pollen deposition, estimated by summing daily values for the entire pollen shed period, varied from 316 x 109 pollen grains ha-1 in the 100% MF P3978 plot to just over 3 x 109 grains ha-1 in the 0%MF P3925 plot area (Table 1). Seasonal deposition values for the 50, 20, and 0% MF treatments for P3978 were greater than expected given the level of detasselling imposed. The 0% MF plot, for example, received the equivalent of 32 x 109 pollen grains ha-1, or just over 10% of the 100% MF rate. It is unlikely that this extra pollen originated from tassels within the plot area since plants were detasselled well in advance of pollen shed and the appearance of new tassels was monitored daily thereafter. The pollen probably came from missed tassels outside the plot area or from fertile tassels in the other three MF treatments, given their relative proximity to the 0% MF plot (Fig. 1). Use of a mixture of male sterile (P3925S) and male fertile (P3925) isolines proved to be a more effective method of attaining very low levels of pollen shed density. Nonetheless, the values presented in Fig. 4 and Table 1 provide a realistic estimate of daily pollen densities reaching the plane of exposed silks, which are the relevant values for assessing the relationships between pollen density and kernel set.

Effective pollen production per plant (i.e., pollen reaching the plane of exposed silks), calculated from seasonal deposition values and the effective portion of seasonal pollen shed, ranged from 4.3 to 5.2 x 106 grains plant-1 (Table 1). These values are considerably less than early estimates for maize hybrids (Hall et al., 1982; Sadras et al., 1985b), but are similar to those reported recently on the basis of similar collection techniques (Fonseca et al., 2002). The lesser values probably reflect the trend toward decreasing tassel size in maize (Fischer et al., 1987; Duvick, 1997). The values of pollen per plant reported here likely underestimate pollen production per tassel to some extent because some pollen remains trapped in leaves above the ear (Sadras et al., 1985a), and the seasonal pollen deposition does not account for pollen dispersion out of the field (Westgate et al., 2000).

Population Index for Pollen Shed
The flowering data collected from each plot revealed a uniform and predictable pattern of tassel development within each hybrid population. As such, a single sigmoid equation was sufficient to model the progress through each development stage (Fig. 5). Because these curves were mathematical descriptors of the population of tassels at BegShed, MaxShed, and EndShed, they could be used to calculate a daily index of the percentage of plants shedding pollen in each MF treatment. Figure 5 shows the curves for the 100% MF treatment of P3978 and the 75% MF treatment of P3925. The Population Index for Pollen Shed (Pind), calculated as the average of BegShed and MaxShed curves minus the EndShed curve for each day (Eq. [2]), increased from the first day a shedding tassel was detected to a peak of pollen shedding activity, then decreased to zero on the day the final tassels in the plot completed pollen shed. There obviously was a close correspondence between the measured patterns of pollen shed and the dynamics of the Pind curves, because the Pind values peaked on the same day measured values for pollen shed peaked for both hybrids (Day 202 for P3978, Day 200 for P3925; Fig. 4). To determine if the Pind curves could be used to predict the actual rate of pollen shed, we converted daily Pind values to grains per square centimeter per day using average pollen production per plant, the number of plants per hectare (Table 1), and number of days the average tassel shed pollen (Eq. 3 and 4). Predicted pollen shed curves generated from these converted Pind values corresponded closely to the measured pollen shed curve in both duration and intensity (Fig. 5).



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  		Fig. 5. Population Index (Pind) for pollen shed, and the predicted pattern of seasonal pollen shed calculated from three stages of tassel development. The Pind is a daily measure of the percentage of plants shedding pollen. Plant population and average pollen production per plant (Table 1) are used to scale the Pind curve to daily pollen shed on an area basis.

 
To determine whether this approach of estimating pollen shed density was robust for a wide range of pollen production levels, Pind curves were generated for the four MF treatments imposed on the two hybrids. In this case, the effective percentage of plants shedding pollen (Table 1) was used to convert the Pind curves to pollen shed densities, because these values reflected the actual rate of pollen shed reaching the level of the silks within each MF plot. Fig. 6 shows that the Pind -based pollen shed curves for the MF treatments matched the actual pattern of pollen shed fairly well. This analysis assumes that pollen shed per tassel was similar among MF treatments for each hybrid, which is reasonable since plant populations were fairly uniform (Uribelarrea et al., 2002).



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  		Fig. 6. Predicted seasonal patterns of pollen shed density at four levels of male fertility for P3978 and P3925. Curves were generated from the Population Index (Fig. 4) and the average pollen production per plant in each treatment (Table 1). Symbols are the daily values for pollen shed density from Fig. 2.

 
Predicted values for seasonal pollen production, calculated from the Pind -based pollen shed curves in Fig. 6, were essentially identical to the measured values for all eight MF treatments (Fig. 7A). The same Pind -based curves accounted for 87% of the variation in daily pollen shed density across all treatments (Fig. 7B). This mathematical analysis confirms that relatively simple measures of tassel development and average pollen production per tassel can be used to estimate both the daily intensity of pollen shed and seasonal pollen production reaching the level of exposed silks. Earlier studies (Sadras et al., 1985a,b) recognized this possibility, but this study is the first to provide a quantitative analysis of these relationships and document their utility across a wide range of pollen shed densities.



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  		Fig. 7. Comparison of measured and predicted rates for seasonal (A) and daily (B) pollen production at four levels of male fertility (MF) for P3978 and P3925. Measured values are field data presented in Table 1 and Fig. 6. Predicted values are taken from the Pind -generated curves in Fig. 6. Predicted seasonal pollen production is the sum of daily Pind -curve values for the entire pollen shed period. Predicted daily pollen production is the Pind -curve value corresponding to the daily measured value for each MF treatment.

 
Given the predictable nature of the staminate flowering process, it should be possible to generate the population dynamic curves from a minimum set of inputs. On the basis of the results of this study, these inputs are (i) day of first pollen shed, (ii) day of 50% start shed, (iii) day of 50% end shed, (iv) day of end pollen shed, and (v) average pollen production per tassel. Of these required inputs, average pollen shed per tassel is the most challenging data to obtain. Bagging tassels, weighing tassels before and after pollen shed, and collecting pollen in aqueous media or on sticky traps all provide useful information, but each has its limitations in terms of accuracy and labor requirements. Passive pollen traps were chosen for this study because they are well suited for documenting the daily intensity of pollen shed reaching the plane of exposed silks and their integral over the pollen shed period could be related directly to pollen production per plant. It is evident from the close correspondence between the Pind -generated pollen shed curve and the actual pollen shed intensities (Fig. 6 and 7) that relatively few dates of pollen shed data are required to generate a seasonal pollen shed curve. Peak pollen shed consistently occurs 2 to 3 d after anthesis for the population. Therefore, the seasonal pollen shed curve would be very well defined by collecting pollen only on the days of (i) first pollen shed, (ii) 50% pollen shed, (iii) 2 to 3 d after 50% shed, (iv) 50% end shed, and (v) end of pollen shed. In fact, collecting pollen only during the peak days (2–3 d after anthesis) and documenting the beginning and end of shed for the population would likely provide a sufficiently accurate pollen shed curve for many uses, such as characterizing inbred male pollen production.

Minimum Pollen Shed Required for Maximum Kernel Set
Grain yield and yield components were measured in each MF treatment plot to determine when pollen amount limited yield formation. Fig. 8 shows that grain yield of both hybrids remained stable with decreasing pollen availability until less than 20% of the population shed pollen. This large reduction in pollen availability without yield penalty confirms the commonly held notion that pollen supply under normal conditions is well in excess of needs for maximum kernel set (Sadras et al., 1985a; Duvick, 1997; Kiesselbach, 1999). Analysis of yield components, however, revealed that kernels per ear decreased in the 20% MF treatment. Grain yield of the 20% MF plots was maintained through a compensating increase in kernel size.



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  		Fig. 8. Grain yield and yield components for P3978 and P3925 grown at four levels of male fertility. The level of male fertility was controlled by detasselling (P3978), or by a mixture of male sterile and male fertile isolines (P3925). Fraction of plants shedding pollen is the target value for each treatment. Data from second ears are included in the analysis. Data are the mean ± SE of 4 replicate yield measurements of 40 to 80 plants each within each treatment block.

 
Relating grain yield to kernels per hectare confirmed that kernel number was the primary yield determinant for all MF treatments (Fig. 9). Therefore, it was of interest to compare the performance of the P3978 and P3925 canopies directly for their capacity to form kernels at different levels of pollen availability. The 20% MF treatment, which evidently limited kernels per ear in both hybrids (Fig. 8), differed more than two-fold in total seasonal pollen deposition (45 x 109 grains ha-1 for P3925 and 105 x 109 grains ha-1 for P3978) (Table 1). A number of factors likely contributed to this difference including genetic potential for kernel set, plant population density, pollen viability, and the number of silks exposed for pollination. We normalized for genetic differences by dividing total seasonal pollen shed by the number of kernels produced in each MF treatment. Figure 9 shows that both hybrids followed the same linear relationship between pollen density per kernel and kernels per hectare at low pollen densities. Kernels per ear increased with pollen grains per kernel up to a point of apparent pollen saturation. The amount of pollen required to saturate kernel production, however, was much greater for P3978. These results indicate there was no inherent difference between P3978 and P3925 in their capacity to form kernels at low levels of pollen production. They also imply pollen produced by P3978 and P3925 was similar in percent viability since their response to increasing pollen density was identical. If so, P3925 shed sufficient pollen in the 75% and 50% MF treatments to produce kernels per hectare at a much higher level than observed. Evidently, there were too few pistillate flowers per hectare in the P3925 treatment plots to take advantage of the extra pollen. Increasing plant population density would be an effective means to increase the number of silks per hectare available for pollination. The trend in modern corn production in fact has been to increase population density to ensure that the number of pollinated silks per hectare is at or past the genetic potential for kernel set (Duvick, 1997).



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  		Fig. 9. Relationships between grain yield, kernel number, and pollen availability per kernel. Pollen grains per kernel were calculated from the seasonal pollen deposition (Table 1) and total kernels per hectare. The curve for grain yield vs. kernel number is Y = 0.4205X - 0035X2, r2 = 0.998.

 
These results imply that the number of ears per hectare and exposed silks per ear established the minimum level of pollen production required to saturate kernel set. If true, a common threshold for kernel production should emerge when differences in plant population and ear size (flower number) are taken into account. To examine this possibility, we compared the response of kernels per plant and yield per plant to an increasing number of pollen grains per exposed silk for the two hybrids. Fig. 10 shows that yield per plant and kernels per plant increased with increasing pollen density per silk up to a threshold of approximately 3000 pollen grains per silk. The response of grain yield per plant to increasing pollen density per silk was identical for both hybrids despite large differences in plant population (Table 1). The greater number of kernels per plant formed by P3978 at this pollen per silk threshold reflects the greater number of florets per ear and more rapid emergence of silks during pollen shed, compared with P3925 (Lizaso et al., 2003). This threshold is an empirical value emerging from a host of plant and environmental factors that can affect pollen-silk interactions. Data collected in this study to do not allow us to distinguish between possible plant factors such as pollen viability, pollen dispersal, silk display, or silk receptivity. But the methodology presented provides an ideal framework to test their relative contributions to kernel set under field conditions.



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  		Fig. 10. Dependence of grain yield and kernels per plant on pollen availability per silk. Differences in total pollen production per ha across treatments were normalized to the total number of emerged silks per hectare. This calculation assumes each plant produces the average number of silks for the hybrid, and second ears (when present) produced an equal number of silks. Average silks per ear for P3978 = 670, and for P3925 = 607. Note that yield and kernel number decrease at pollen densities less than 3000 pollen grains per silk.

 
Because this threshold is based on the amount of pollen reaching the plane of exposed silks and is normalized for the amount of pollen shed per silk, it must reflect a limitation imposed by the physical nature of the pollination process itself. Exposed silks represent only a small fraction of the surface area through which pollen grains pass as they fall from the tassel to the ground (Sadras et al., 1985a; Kiesselbach, 1999). Therefore, the likelihood of pollen passing through the area occupied by exposed silks is small, and a large number of pollen grains relative to receptive stigmas (silks) are required to ensure successful pollination (Sadras et al., 1985a; Bassetti and Westgate, 1994; Cárcova et al., 2000). While it is tempting to calculate the probability of a pollination event on the basis of this relative silk area, the accuracy of such calculations is complicated by uncertainties in silk display and actual pollen settling patterns.

The value of a threshold for pollen production to achieve maximize kernel formation on an area basis is readily apparent. It provides, for the first time, a quantifiable target for pollen shed needed in a hybrid seed production field to achieve the highest possible level of genetic purity. Using this seasonal threshold of pollen production as a guide, seed field managers can adjust male plant density in a rational manner to account for variation in pollen production among inbred males. Similar applications to ensure maximum seed set from the intended male parent also are possible for top-cross production schemes and organic production systems. Developing simple and accurate estimates of pollen production per tassel and applying these estimates to predict grain yield under various production schemes are subjects of current investigations.

Received for publication May 15, 2002.


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