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Simulating potential kernel production in maize hybrid seed fields.

KENNEL NUMBER per plant is the yield component primarily responsible for variation in maize grain yield. For simulation purposes, the developmental events that determine kernel number per plant can be divided in three consecutive processes (Lizaso et al., 2003). In the first stage, male (tassels) and female (ears) reproductive structures are initiated and differentiated. The second stage involves functional maturation of flowers and pollination. Synchrony in floral development is critical to ensure that pollen shed coincides closely with silk exsertion and that tassels produce enough pollen to ensure pollination of exposed silks. During the third stage, pollination is followed by fertilization and kernel formation. Current models for simulating maize yield, such as CERES-Maize (Jones and Kiniry, 1986), focus exclusively on the third stage. They implicitly assume that neither flower initiation, differentiation, nor pollination limit kernel set. These assumptions might apply to typical commercial corn production in some cases, but the number of fertilized ovules can limit kernel yield in a wide array of circumstances.

When maize is stressed at flowering by water deficits (Westgate and Boyer, 1986), low light levels (Andrade et al., 1993), or nutrient deficiency (Lafitte and Edmeades, 1994a, 1994b), ear growth slows in relation to tassel growth and the anthesis-silking interval (ASI) increases. This increase is well documented and negatively related to kernel set (Bolafios and Edmeades, 1993). Lack of pollen, reduction in pollen viability, and silk receptivity are proposed as the main causes for the reduction in kernel production under these conditions.

Selection for improved hybrid performance under stressful conditions such as high population density has resulted in a decrease in tassel size among modern maize hybrids (Galinat, 1992; Duvick, 1997). This smaller tassel size is correlated with diminished capacity for pollen production (Fonseca ct al., 2003). Low levels of pollen production also occur intentionally in hybrid seed production, with 50% male-sterile hybrid blends, and in top-cross schemes used to produce high-oil corn (Fell et al., 2003). Although the maize plant has traditionally been considered an overabundant producer of pollen relative to the number of ovaries available for pollination, such genetic, management, and environmental influences on pollen production and viability provide numerous opportunities for the timing and density of pollen shed to limit kernel production under field conditions (Westgate et al., 2003).

This seems particularly clear for hybrid seed production since pollination could be less than desired for several reasons. First, pollen shed density is much less than in a grain field since inbreds typically produce less pollen than do their hybrid counterparts (Fonseca et al., 2003). Second, only a fraction of the field population is permitted to shed pollen, i.e., male inbred. A major goal in hybrid seed production, in fact, is to reduce the area dedicated to male rows as much as possible without decreasing the number of kernels harvested per area (Wych, 1988). Third, the level of pollen viability could be less than required for optimum pollination of receptive silks (Schneider, unpublished 2003). Finally, pollen shed and silk exsertion on physically separated plants increases the probability that floral asynchrony can lead to poor kernel set. Together these biological and physical factors create conditions in which kernel numbers could be limited primarily by the number of pollinated flowers. This potential for pollination, of course, depends directly on the dynamics of male and female flowering within the seed field.

Westgate et al. (2003) recently developed quantitative descriptions for the daily progress of pollen shed and silk emergence under field conditions on the basis of simple measures of male and female flowering. When coupled mathematically to the pollination efficiency curve generated by Bassetti and Westgate (1994), these estimates of male and female flowering can be translated into daily values for kernel set. Lizaso et al. (2003) showed that this mathematical approach was highly accurate at simulating kernel production for two maize hybrids across a wide range of pollen shed densities.

Our objectives were (i) to determine whether the mechanistic model of Lizaso et al. (2003) could be used to simulate kernel production in commercial hybrid seed fields, and (ii) to demonstrate the potential of this approach for optimizing kernel production for current inbred pairs or for defining the optimum management strategy for new combinations of inbreds.


Procedure for Simulating Potential Kernel Set

The procedure for simulating kernel production begins with developing a temporal profile of pollen shed for the male population and a profile of silk exsertion for the female population. These floral dynamics are translated into daily values of kernel production by the female inbred using the procedures described by Lizaso et al. (2003), which rely on the quantitative relationship between daily pollen shed density (grains per [cm.sup.2]) and percent kernel set published by Bassetti and Westgatc (1994). Table 1 lists the crop inputs required to generate the curves for male and female flowering dynamics. Details for collecting these data are outlined briefly below.

Amount and Temporal Distribution of Pollen Shed

The seasonal distribution of pollen shed is simulated from field observations of male flowering characteristics at the population level. This calculation assumes that pollen density is distributed homogeneously among the female population. One hundred consecutive male plants at each sampling site are examined for the progress of tassel development each morning. Beginning Shed (Beg Shed) is recorded as the proportion of plants that have anthers exserted on the main tassel branch. Plants that have exserted anthers on main and side tassel branches are at Maximum Shed (Max Shed). And those with no new anthers on any tassel branch are recorded as having completed pollen shed (End Shed) (Westgate et al., 2003). The progress of each population through Beg Shed, Max Shed and End Shed are readily described by a common set of sigmoid logistic functions separated in time by 1 to 5 d. The area between these curves provides a daily index of pollen shed for the population. Typically, the same group of plants is used to record the proportion of plants at Beg Shed, Max Shed, and End Shed to generate the population index curve. The actual rate of pollen shed (grains [cm.sup.-2] [d.sup.-1]) is calculated by multiplying this index value by the average pollen production per plant and the male population density.

However, seed production managers typically collect data only on the progress of Beg Shed for their male inbreds. This was the case in the six Syngenta seed production fields, which required us to assume the dynamics of pollen shed followed published patterns (Lizaso et al., 2003; Westgate et al., 2003). Lizaso et al. (2003) showed that the seasonal pattern of pollen shed followed a Gauss curve according to Eq. [1]:


where PR is the daily rate of pollen shed (grains [cm.sup.-2] [d.sup.-1]), P is the total seasonal amount of pollen produced by the male population (grains [cm.sup.-2]), W is the width of the pollen shed curve measured at half the maximum pollen shed rate (d), and t and [t.sub.x] are the current day and the day of maximum pollen shed. The total seasonal amount of pollen, P, was defined by the average pollen production per plant and the plant population density. The day of maximum pollen shed, [t.sub.x], typically occurs 2 or 3 d after anthesis (50% Beg Shed) (Bassetti and Westgate, 1994; Fonseca et al., 2003). The width of the pollen shed curve, W, was determined empirically for each field by forcing the Gauss curve to start pollen shed at Beg Shed = 0% and end pollen shed at Beg Shed = 100% + 5 d. The addition of 5 d was based on prior studies (Westgate et al., 2003; Lizaso et al., 2003) indicating that the interval between Beg Shed and End Shed for an individual tassel was typically 5 d. The daily value for pollen shed density was used in Eq. [2] and [3] to calculate daily percent kernel set.

Amount and Temporal Distribution of Exserted Silks

The temporal distribution of silks exposed for pollination is calculated from the progress of female flower development at the population level and at the plant level. At the population level, 100 consecutive plants are examined for silking each morning. The percentage of population with exposed silks progresses in a sigmoid fashion similar to the population curves generated for tassel development. At the plant level, silks emerge from the surrounding ear leaf sheaths (husks) over a period of days in a curvilinear fashion. The process is described by a monomolecular equation, using rate of silk exsertion and maximum silk number per ear as genotype-specific variables (Lizaso ct al., 2003). When 30% of the population has started silking, ears on five plants about to exsert silks are covered with glassine bags to prevent pollination. Silks are sampled 1, 3, 5, 7, and 9 d after first silks appear. Two-centimeter segments of exposed silk tissue are cut at husk level, transferred to plastic bags containing 500 g [kg.sup.-1] ethanol, and stored at 4[degrees]C until counted manually.

The daily and cumulative number of silks exserted per unit land area were calculated by combining the daily dynamics of silking for the population, the daily rate of silk exsertion for each plant, and the female plant population density (plants per female ha).

Relationship between Kernel Set and Daily Pollen Shed Density

Exposed silks were pollinated at a rate determined by two consecutive linear functions on the basis of the pollination efficiency curve of Bassetti and Westgate (1994). Their pollination efficiency curve was generated by means of receptive florets in the middle of the rachis for which no abortion occurred. Therefore, this efficiency curve provides the expected percentage of kernel set when receptive silks are exposed to a known density of pollen shed for 1 d. The limits of pollen shed density for each equation are:

[2] ks = 0.96 x pr 0 < pr [less than or equal to] 100


[3] ks = 96 pr > 100

where ks is the percentage kernel set (%), and pr is the daily rate of pollen shed (grains [cm.sup.-2] [d.sup.-1]). These equations indicate that percent kernel set is linearly related to daily pollen shed density up to 100 grains [cm.sup.-2] [d.sup.-1] with an efficiency of 96% (i.e., at 50 grains [cm.sup.-2] [d.sup.-1], 48% of exposed silks will be pollinated). At pollen shed densities greater than 100 grains [cm.sup.-2] [d.sup.-1], 96% of the exposed silks are pollinated. The remaining unpollinated silks are added to the next day's pool available for pollination. Exposed unpollinated silks were considered to remain receptive to pollen for five additional days. Silks that were not pollinated by the sixth day were assumed to lose receptivity and no longer contribute to kernel set (Bassetti and Westgate, 1993b).

Effect of Asynchronous Pollination within the Ear on Kernel Set

Prior fertilization has been shown to decrease the percentage of kernels set by later pollinated flowers on the same ear (Freier et al., 1984; Cfircova et al., 2000). This effect of asynchronous pollination was incorporated into the calculation of kernel production for each ear by multiplying the daily value for kernel production by an efficiency factor, which varied with the cumulative number of florets pollinated on each ear (Lizaso et al., 2003). On the basis of the published data of Carcova et al. (2000), this efficiency factor decreased from 100% of potential set for initial pollinations at the base of the ear to near zero set at the ear tip depending on population density.

Application to Commercial Seed Production Fields

We tested the procedure for simulating the number of kernels per hectare from flowering dynamics with measured values for kernel yield in six seed production fields in 2002 in Washington County, IA, managed by Syngenta Seeds Inc. (Washington, IA). The fields were chosen to provide a range of male and female flowering characteristics (Table 2). Descriptive terms commonly used in the seed industry such as "good," "fair," and "poor" for a male inbred and "regular" or "small" for female ear size are provided for the benefit of the reader and do not imply a quantitative basis for comparison between inbreds.

Female inbreds were planted between 4 and 10 May 2002. In most cases, male inbreds were planted within 1 or 2 d of the female. Exceptions were Field A in which the male was planted 7 d before the female and Field D in which the male was planted 6 d after the female inbred. The planting pattern was 4 female: 2 male rows in all cases. To extend the period of pollen shed, plant development was delayed in one of the two male rows by burning away exposed leaf area at the V4 to V5 stage. This management practice, commonly referred to as "flaming," effectively delayed pollen shed up to 3.5 d in the treated row.

Flowering dynamics for the male inbred populations and female inbred were assessed at one location in each field. The location was selected 2 wk before flowering to be representative of typical inbred development across the field. The sampling area was approximately 125 [m.sup.2] and at least 25 m from the field border.

Average pollen production per plant was documented by covering 10 representative tassels with clear bags (Pantek, Montesson, France) designed to exclude moisture but allow gas exchange around the tassel. Pollen was harvested from the bags and quantified with a Coulter Multisizer II (Coulter Electronics Limited, Luton, Beds, England) according to Fonseca et al. (2003). We used average pollen production per plant and approximate population densities (based on data collected by field managers) to calculate total pollen production for each male population.

The interval between Male 1 and Male 2 curves was taken as the difference in days between 50% Beg Shed for the two populations. Separate but identical pollen shed curves were generated for each male population. These curves then were combined to produce a total pollen shed curve for the field. The resulting pollen amount per unit area was adjusted for the female-male planting ratio for each field. The calculated rates of total pollen shed matched measured rates using passive traps according to Fonseca et al. (2002).

Approximately 1.3 ha of the female inbred were harvested from each field to estimate kernel number per female hectare. The yield was calculated in kilograms per hectare and adjusted to 155 g [kg.sup.-1] moisture. Average kernel weight was calculated from the number of kernels in a 454-g subsample, and adjusted to 155 g [kg.sup.-1] moisture. Harvested kernel number per female ha was calculated as grain yield (kg [ha.sup.-1])/average kernel weight (kg [kernel.sup.-1]). Information regarding prolificacy was not available and assumed to be one ear per plant.

The intent of this analysis was to test the robust nature of the model for simulating kernel set across a wide range of seed production fields and practices. Therefore, regression analysis was used to evaluate the relationship between observed and simulated kernel set across seed fields. Assessing the impact of within-field variation on simulated kernel set was beyond the scope of this study.

Simulating Possible Seed Production Scenarios

We used the kernel set model to examine how altering management variables or flowering kinetics might affect potential kernel set. Various scenarios were tested by altering the value of one input variable at a time, such as pollen production per tassel or rate of silk exsertion. A series of simulations generated a kernel set response curve for each input variable tested. Because these response curves were specific to the flowering characteristics of a given inbred pair, they provided a basis for comparing the potential impact of various management scenarios on kernel production for that pair.

Field F was chosen for this scenario analysis because simulated values for kernel production were within 1% of measured values, kernel yield was relatively high, but pollination efficiency was fairly low. The model indicated only 55% of florets set kernels. Amount of pollen per tassel, male-female synchrony, peak pollen shed interval, silking uniformity, and silk exsertion rate were adjusted relative to the initial conditions established for Field F. Variables that remained constant were approximate female plant density = 65 200 plants per female ha, approximate male density = 63 300 plants per male ha, maximum silks per ear = 505, and prolificacy = 1. For simplicity, only one variable was adjusted at a time, although multiple factors can be adjusted simultaneously to assess interactions between management and genetic factors.

Tassels in Field F produced about 1.5 million grains per tassel, on average. Kernel production response to altered pollen amount (maleness) was tested from 0 to 3.5 million pollen grains per tassel. Kernel production dynamics for a good male (about 2.0 million grains per tassel) and a poor male (about 0.5 million grains per tassel) are provided for comparison.

The anthesis-silking interval for Field F was -0.55 d. Since male planting was split in Field F, the anthesis-silking interval is measured relative to the first male planting (AISI). We examined the impact of altering male female synchrony over a wide range of ASIs, from -8 to +14 d. For this example, the silk exsertion dynamic for the population was held constant and the timing of pollen shed was varied. An alternative approach would have been to alter ASI by changing both the timing of silk exsertion and pollen shed. Kernel production dynamics for male anthesis 2 d ahead and 2 d after 50% silking are provided for comparison.

Flaming one of the paired male rows in Field F resulted in an interval of I d between peak pollen shed for the two pollen sources. We tested the response of kernel production to increasing this interval up to 11 d. Kernel set response to delaying peak pollen shed of the second male by 3 and 5 d is provided for comparison.

Silking of the female population (i.e., from 5 to 95% of plants) occurred over a period of 11 d in Field F. The uniformity of the female population for silking was varied from 6 to 21 d to test the impact on potential kernel set. Two scenarios, represcnfing more uniform and more variable populations relative to Field F, are shown for comparison.

The average ear for the female inbred in Field F required about 6 d to exsert 95% of its silks. The effect of more rapid or slower rates of silk exsertion on kernel production was tested assuming the final number of silks exserted remained fixed at 505 silks per ear. Results for a faster silk exsertion (4 d to 95% of silks exserted) and a slower silk exsertion (9 d to 95% of silks exserted) are provided for comparison to initial conditions for Field F.


Simulating Potential Kernel Production in Seed Production Fields

The model developed by Lizaso et al. (2003) relies on quantitative measures of male and female flowering dynamics to calculate the potential number of kernels set on an area basis. Their approach was validated using hybrids under field conditions in which pollen shed density was varied by detasseling or by mixing male-fertile and male-sterile isolines (Lizaso et al., 2003; Wcstgate et al., 2003). In the current study, we examined whether the quantitative relationships developed for maize hybrids could be applied to inbred pairs used in hybrid seed production. In this case, pollen production often is limiting and floral synchrony between inbred pairs is critical. Therefore, the capacity to simulate kernel set for an assortment of inbred pairs that vary in pollen production, silking dynamics, and seed yield should provide a rigorous test of the underlying theory and the model's general utility.

The first component needed to simulate kernel production on a field scale was the temporal distribution of pollen shed. This parameter was estimated according to Westgate et al. (2003) from the flowering characteristics, plant density, and average pollen production per tassel for the male inbred population in each field (Fig. 1). Westgate et al. (2003) and Lizaso et al. (2003) showed that pollen shed dynamics calculated in this way closely reflect the seasonal pattern of pollen shed. Because the practice of flaming one of the male rows typically delayed pollen shed in the flamed row, pollen shed was quantified separately for each male population and then summed to generate a total pollen shed curve for the field.


The temporal distribution of silk exsertion per hectare provided the maximum number of florets that could be pollinated each day. This parameter was calculated from the daily dynamic of silk exsertion per ear, the silking dynamic for the female population, and the plant population density measured for each female inbred (Fig. 2). Silk exsertion per hectare occurred over a period of 6 to 12 d for the female inbreds examined in this study (Fig. 3).


We tested our approach for simulating kernel production in six commercial seed production fields (designated A-F), which included various combinations of male and female flowering characteristics (Table 2). Male inbred in Field A was considered a poor pollen source. The inbreds in Fields B and C were fair pollen sources. And those in Fields D, E and F were designated as good pollen sources according to their measured field performance. Female inbreds in Fields B and C typically produced small ears; females that produced regular sized ears were used in Fields A, D, E, and F, according to their measured exserted silks per ear (Table 2).

Field A combined a poor male inbred with a regular-eared female inbred (Fig. 3A). The average male tassel shed approximately 520 000 pollen grains, which provided only low daily pollen densities for about 5 d. The dense stand of female plants combined with an average silk exsertion of 577 per ear (Table 2) resulted in a cumulative number of about 33.5 million receptive silks per female hectare. On the basis of the temporal dynamics of pollen shed and silk exsertion, the model indicated that this combination of inbreds and field management would produce about 22.3 million kernels per female ha, or about 66.4% of the exposed silks. This simulated value assumes each pollinated silk results in ovary fertilization (Westgate and Boyer, 1986). Therefore, despite close synchrony between pollen shed and silk emergence, not all florets with exposed silks were fertilized during rapid pollen shed. The kernel set simulation also considers the effect of asynchronous pollination within the car by decreasing the number of late-pollinated florets that produce kernels (Carcova et al., 2000). However, this latter effect is small relative to the lack of pollination (Lizaso et al., 2003). These results confirm that pollen availability limited potential kernel production in Field A.

Field B combined a fair male inbred with a female inbred producing a small sized ear (Fig. 3B). Although pollen production per tassel was slightly greater than in Field A, the low population density for the male inbred resulted in a very low pollen density that peaked at about 40 pollen grains [cm.sup.-2] [d.sup.-1]. Initial silk exsertion preceded pollen shed by 3 d, but 12 d were required to reach maximum silk exsertion for the population (about 16 million silks per female ha). The model simulated only about 64% of these receptive silks would be pollinated and set kernels. As in Field A, the lack of complete pollination of exposed silks during pollen shed indicated pollen amount limited kernel set.

Field C combined a fair male inbred with a female inbred expected to produce a small ear (Fig. 3C). Both inbred populations were significantly higher than in Fields A and B. And pollen shed by Male 1 and Male 2 were nearly synchronous. About 23.0 million silks per female ha were exposed for pollination, but less than 70% of these were expected to set kernels. As in Fields A and B, the male inbred failed to pollinate a large fraction of newly exposed silks each day even during peak pollen shed.

In Field D, a good male producing nearly 1.5 million pollen grains per tassel was matched with a normal-eared female inbred (Fig. 3D). In this case, flaming of Male 2 effectively separated pollen shed for the two male populations. The expanded period of pollen shed coupled with close synchrony between pollen shed and silk exsertion minimized the number of silks left unpollinated during peak pollen shed. The model indicated nearly 77% of the 28.4 million exserted silks per female ha were pollinated. Only those florets with late emerging silks failed to set kernels.

Field E also combined a good male inbred with a normal-eared female inbred (Fig. 3E). Although the male inbred was planted at a relatively high density, the average male tassel produced more than 1.9 million pollen grains. As such, pollen production in Field E was the greatest among the fields examined. Silk exsertion began 4 or 5 d in advance of pollen shedding and was nearly completed when pollen shed ceased. The model simulated that this combination of protogynous silk exsertion and high pollen shed density would produce more than 25.6 million kernels per female ha, or about 84% of exposed silks. These values were the greatest kernel yield and pollination efficiency observed for the six production fields examined in this study.

In Field F, a good male inbred and a regular-eared female inbred were planted at high population densities (Fig. 3F). Unlike the other production fields, silk exsertion in Field F was delayed relative to pollen shed. As such, the model simulated that all early-emerging silks would be pollinated on the day they were exserted from the husks. But a large fraction of late-emerging silks failed to be pollinated. Ultimately, only about 55% of the 32.4 million silks potentially available for pollination were expected to produce a kernel. In this case, pollen shed duration apparently posed a greater limitation on kernel production than did pollen amount.

Simulated vs. Measured Kernel Set

Harvested kernel number varied from about 8.4 to 23.1 million kernels per female ha among the six seed production fields (Table 2). Values provided by our kernel set model were closely correlated ([r.sup.2] = 0.98) with these measured values (Fig. 4). This result clearly indicates that variation in kernel production can be assessed directly from the flowering dynamics of the inbreds used to produce hybrid seed.

Model simulations, however, overestimated kernel production by 11%, on average. Evidently, one or more plant or canopy factors that might have limited kernel were not taken into account. Barrenness, pollen viability, pollen capture by leaves, and slow silk growth on apical florets were not considered as variables in the initial analysis. Also, the process of mechanical detasseling itself can reduce the yield potential of the female inbred, a factor not considered by the model. Prolificacy was not documented and assumed to be 1 ear per plant for all female inbreds. This assumption is not likely to be valid, since there is usually a small percentage of barren plants at the female plant densities used in this study. Overestimating ears per plant will result in direct overestimation of potential kernel set, since it defines the number of cars per unit surface. Pollen viability also was not quantified for each male inbred. Viability was assumed equal to that reported by Bassetti and Westgate gate (1994) in their relationship between percent kernel set and daily pollen shed density for a maize hybrid. This relationship has proven to be very robust for estimating kernel production of hybrids across a wide range of pollen shed densities (Lizaso et al., 2003). Nonetheless, variation in pollen viability among male inbreds has been observed (Fonseca, unpublished 2003) and needs to be considered as a model refinement in the future. Finally, the amount of pollen available for pollination, as estimated from bagged tassels, likely overestimates the quantity of pollen reaching the plane of exposed silks. Leaves above the ear intercept some of the pollen released from the anthers. Values for pollen capture by the upper canopy are lacking, but they could be estimated if leaf numbers and leaf angles were known (Aylor et al., 2003).

Recent evidence indicates prior pollination of older florets can decrease kernel set by younger florets on the same ear either by inhibiting their silk growth (Carcova et al., 2003) or by preventing kernel development (Carcova et al., 2000). Silk exsertion rates used in this study are calculated from data collected on unpollinated silks, which likely overestimates the actual number of florets that become pollinated on an ear. However, on the basis of the work of Carcova et al. (2000, 2003), the model does consider the impact of prior pollination on kernel set by younger (apical) florets by decreasing kernel set efficiency as kernel number per ear increases. Mechanical detasselling removes leaf area. The amount removed depends on the depth of the cutting and detasseling operations. Loss of sufficient leaf area will decrease light interception and photosynthate production per plant, which has been shown to limit kernel production at high plant densities (Andrade et al., 1993; Lizaso et al., 2001). We are currently expanding the model to simulate kernel production under both pollen-limited and assimilate-limited conditions (Lizaso et al., 2002).

Nonetheless, the model in its current form simulated kernel production with consistent accuracy across a wide range of seed yields (Fig. 4). This result indicates that simulating kernel set based on inbred flowering dynamics is an entirely suitable approach for assessing potential kernel production for inbred pairs and for testing management options to optimize their productivity.


Optimizing Seed Production

Once the flowering dynamics for a given inbred pair are known, the model can be used to test alternative management scenarios to optimize their kernel production per hectare. Various genetic characteristics that might affect flowering dynamics can be tested as well. As examples, we examined the effect of altering pollen production per tassel (maleness effect), varying the timing between pollen shed and silk exsertion (ASI), modifying the anthesis-interval between pollen sources, varying silking uniformity within the female inbred population (homogeneous vs. non-homogeneous populations), and altering silk exsertion rates (fast vs. slow females).

These scenarios were simulated relative to the initial conditions for Field F. Only 55% of the exserted silks were expected to set kernels in this field, which implies there is ample opportunity to improve pollination efficiency. Inbreds were planted in a 4:2 (female:male) pattern at relatively high population densities (Table 2). One male row was flamed, and peak shed differed by 1.2 d for the two populations. The average tassel produced about 1.5 million pollen grains. The anthesis-silking interval ([A.sub.1]SI) was 0.55 d, which means 50% of the male inbred population began to shed pollen within 1 d of 50% silking for the female inbred population. Each female plant was assumed to produce 1 ear bearing up to 505 kernels.

In each case, kernel production was calculated over a wide range of values for each response variable (e.g., pollen production per tassel). The daily dynamics of flowering and kernel production were plotted for two of these values to illustrate the basis for the change in kernel production relative to the initial conditions in Field F.

Pollen Production (Maleness)

Pollen production per tassel varies among inbreds and typically decreases with increasing population density (Fonseca et al., 2003). As such, optimum male inbred management depends on a quantitative evaluation of kernel set response to pollen shed density. Figure 5 shows the response of kernel production in Field F to variation in pollen production per tassel. Model simulations indicated that harvested kernels per female hectare increased asymptotically with pollen amount. Increasing pollen production per tassel from 1.5 million grains (Field F) to 2.0 million grains (Example 5A) increased harvest to about 19.0 million grains per female ha, or 59.3% of the exserted silks. Thus, a 37% increase in pollen production in Field F would have improved potential kernel production by only 8%. As in the original condition within Field F (Fig. 3F), a large fraction of late-emerging silks remained unpollinated. If pollen production were limited to 0.5 million grains per tassel, only 10.9 million (33.6%) of the silks would set kernels (Fig. 5B). Relative to the original situation, this 66% reduction in pollen availability resulted in a 39% reduction in potential kernel set.


Simulating the dynamics of potential kernel production for these scenarios (Fig. 5A and B) and comparing them to the original conditions (Fig. 3F) provides considerable insight into the yield limitations in Field F. It is clear that having a male inbred that produces 1.5 million pollen grains per tassel contributes to the efficient pollination of early-emerging silks. But the relative insensitivity of kernel set to large changes in pollen production per tassel indicates pollen shed density was not the most important factor limiting potential kernel production in Field F. Kernel production was limited to a greater extent by the large fraction of silks exposed after pollen shed density started to decline (Fig. 3F). Altering the synchrony between male and female flowering, rather than increasing pollen availability, would likely have a greater impact on improving pollination efficiency in this field.

Anthesis-Silking Interval

A short ASI typically is considered optimum for kernel set (Bolanos and Edmeades, 1993; Duvick, 1997; Edmeades et al., 2000). Limited pollen availability in seed production fields makes careful management of this kernel set factor especially important. In this case, anthesis is taken as the day 50% of the Male 1 population begins to shed pollen. Silking is taken as the day 50% of the female inbred plants have silks visible. Figure 6 shows the potential consequences of altering the ASI on kernel production in Field F. Of all the genetic and management variable tested, variation in the ASI had the greatest impact on harvested kernels per female ha. Delaying silking by 1.5 d relative to the original condition in Field F to an ASI = -2 would cause a 35% reduction in potential kernel production to about 11.5 million kernels per female ha (Fig. 6A). But if silking in field F were advanced to 2 d before anthesis (ASI = +2), pollination efficiency would increase to nearly 76%, and potential kernel production would increase by 38% to 24.6 million kernels per female ha (Fig. 6B). There are two likely reasons for such a significant enhancement in kernel production. First and foremost, a much larger fraction of late-emerging silks are pollinated when pollen shed is delayed relative to silking. Second, all the early emerging silks are pollinated as well because they remain receptive to pollen for several days after they appear (Bassetti and Westgate, 1993a, 1993b).


This example clearly demonstrates why floral synchrony between male and female inbreds is such an important management variable in hybrid seed production. A delay in silking relative to pollen shed of 1 or 2 d has a large impact on potential kernel production when pollen amount is limiting. It is important to note that perfect synchrony (i.e., ASI = 0, silking and anthesis on same day) did not correspond to optimum potential kernel production for Field F (Fig. 6). Maximum kernel yield was obtained by delaying anthesis for the male inbred population by about 4 d, relative to silking.

This evaluation does not take into account the risk of out-crossing from foreign sources of pollen. Delaying pollen shed to maximize kernel yield could expose the seed field to increased potential for out-crossing of the early-emerging silks. On the other hand, greater coverage of late-emerging silks by delaying pollen shed dramatically increases kernel yield and thereby decreases the potential for out-crossing for the later silkers in the female population. The best approaches to managing floral synchrony will depend on the specific risk of foreign pollen entry during silking. The model provides the framework to quantify such risks when coupled with an estimate of adventitious pollen entry.

Interval between Pollen Sources

It is common practice in seed production fields to flame the male inbred to delay pollen shed and expand pollen shed duration. In this study, one row in each pair of male rows was flamed for this purpose. This treatment resulted in anthesis intervals of 1 or 2 d between adjacent male rows (Fig. 3). In the initial condition for Field F, anthesis for the two male populations was separated by 1.2 d. We simulated the response of kernel harvest to an increase in the interval between anthesis for the two male populations up to 11 d (Fig. 7). For this set of simulations, the synchrony between anthesis for the first male population and silking for the female inbred population was not altered.


When anthesis for the second pollen source was delayed from the original 1.2 to 3 d relative to the first pollen source, the model indicated that nearly 68% of the silks would be pollinated and potential kernel yield would increase 23% to about 21.9 million kernels per female ha (Fig. 7A). If the interval between pollen sources were increased to 5 d, potential kernel yield would be increased about 38%, which represents an increase of about 6.8 million kernels over the initial conditions in Field F (Fig. 7B).

In this particular field, the optimum delay between pollen sources to maximize kernel yield was about 6 d. From our study of all six seed fields (Fig. 3), it was clear that there is great potential to improve potential kernel yield by carefully managing the anthesis interval between pollen sources to increase pollen shed duration. The number of sources, the timing between them, and the proportion of plants assigned to each source are management options that can be tested and optimized by the model.

Silking Uniformity

The time required for the entire female inbred population to begin silking obviously has an impact on potential kernel yield. Therefore, we tested the response of kernel yield to variation in silking uniformity from 6 to 21 d to progress from 5 to 95% of plants silking. To simplify this analysis, the interval between pollen shed and silking remained constant at ASI = -0.55. This approach effectively spread silking for the population across a greater number of days, but advanced silk emergence for a proportion of the population (Fig. 8A and B). An alternative approach would have been to hold the beginning of silking constant. But decreasing the uniformity of population in this latter case would effectively increase the ASI.


Kernel yield decreased linearly with decreasing uniformity of silking for the population (Fig. 8). The impact of silking uniformity on kernel yield, however, was much smaller than that of other variables tested. Two scenarios representing a more uniform population (8 d to 95% silking) and a much less uniform population (20 d to 95% silking) than Field F revealed that improving the population uniformity by 12 d would set only about 2.4 million additional kernels per female ha. As such, effort to improve the uniformity of silking in Field F from 11 to 8 d would likely have little impact on harvested kernels.

Duration of Silk Exsertion

Repeated sampling of silks on unpollinated ears indicated that the female inbred in Field F required about 7 d to exsert 95% of the silks on an average ear. A similar rate has been reported for maize hybrids with normal-sized ears (Bassetti and Westgate, 1993a; Lizaso et al., 2003). Since the availability of silks for pollination depends directly on the duration of silk exsertion, we tested whether altering silk exsertion on individual plants could improve harvested kernel yield. The amount of pollen, timing of pollen shed, and ASI were held constant.

As was the case with silking uniformity for the population, decreasing the uniformity of silking on individual ears had a direct negative impact on kernel yield (Fig. 9). Simulated kernel yield, however, was much more sensitive to the duration of silk exsertion. A female inbred capable of exserting 95% of the silks within 4 d would increase potential kernel production about 17% to 20.8 million kernels per female ha (Fig. 9A). A female requiring 9 d to exsert 95% of the silks would produce 15% fewer kernels, and leave more than 50% of the exposed silks unpollinated (Fig. 9B).


This analysis confirmed that both the population and individual plant components of silking affected kernel yield. The duration of silking per ear, however, had a greater impact on potential kernel set. By analogy to the capacity for pollen shed by males inbred, more detailed characterization of female inbreds for their silking uniformity (fast vs. slow female; small vs. big sized ear), as well as their response to changing environments (i.e., population density), would be of considerable value for making management decisions based on these model simulations.

Comparisons among Seed Fields

The dynamic characterization of male and female flowering allowed us to simulate differences in potential kernel production among fields and to expose the primary causes for low pollination efficiency. Fields A and F, for example, exserted a similar number of silks per female hectare. The male inbred in Field F produced nearly three times as much pollen, but Field A produced almost 17% more kernels per ha (Table 2). The kernel set model accurately simulated this outcome on the basis of the genotypic differences in flowering synchrony, pollen shed density, pollen shed duration, and silking duration. This comparison confirms that a poor male can be used to produce acceptable kernel yields if pollen shed is delayed relative to silk emergence and silking of the female population is uniform.

Fields A, B, and C produced markedly different kernel yields (10.2-22.2 million kernels) despite very similar pollination efficiencies (64 to 70%). The female inbreds in Fields B and C produced about two-thirds as many kernels per ear as in Field A. The male inbred in Field C produced nearly twice as much pollen per tassel as in Field A. And the greatest number of pollen grains available per exserted silk occurred in Field B. A common feature of all three fields, however, was that pollen shed was delayed relative to silking (Fig. 3). Therefore, pollination of early-emerging silks was highly effective in these fields, even at the low pollen densities observed in Field A. This delay in pollen shed and the uniform exsertion of a large number of silks combined to produce the high kernel yield in Field A.

In nearly all fields, a larger interval between pollen sources has the potential to improve kernel production significantly as well as to reduce the risk of out-crossing from an adventitious pollen source. The exception was Field D in which anthesis for Male 2 was delayed about 3 d relative to Male 1. Pollen shed covered almost completely the entire period of silk exsertion (Fig. 3D). Pollination efficiency of exposed silks was nearly 80%, with a male producing less than 1.5 million pollen grains per tassel (Table 2).

Field F was the only one in which pollen shed began before silk exsertion. Model analysis indicated that potential kernel production in this field could have been 44% greater if pollen shed were delayed by as few as 3 to 4 d relative to silking. Affecting this delay, based on an understanding of the flowering dynamics of the male and female inbreds in this field, would have set an additional 7.8 million kernels per female ha.


We have applied the kernel set model of Lizaso et al. (2003) to simulate kernel production in hybrid seed fields from the flowering dynamics of the inbreds. This model provides an easy and reliable approach to assess the impact of seed production practices on kernel production and to define management strategies to maximize seed production per female hectare. With a minimum of information on the flowering dynamics of male and female inbreds, the model can also be used to establish production requirements for new combination of inbreds.

For simplicity of demonstration, response to several genetic and management variables were examined one variable at a time. Of the variables tested, ASI and the anthesis interval between pollen sources had the greatest impact on kernel number. But the model is structured to allow several variables to be adjusted simultaneously so that their additive and synergistic effects can be assessed. The approach for simulating kernel production also provides the mathematical basis for testing the impact of adventitious pollen entry on the potential for out-crossing events in the hybrid seed field.

The combination of inbreds examined in this study did not permit an evaluation of the kernel set model as a predictive tool. Predicting kernel set across locations for a given inbred pair requires more detailed information about environmental effects on female silking dynamics, male pollen viability, and pollen shed dynamics. Seed companies interested in using the kernel set model for predictive purposes will need to collect this information as part of their inbred parent evaluation and development.
Table 1. Inputs required to simulate potential kernel production for
a given pair of male and female inbreds.

Characteristics                  Units               Data collection

  Population density    plants per male ha        documented at
  Average pollen
    per tassel          grains per tassel         collect pollen from
                                                    10 representative
                                                    tassels; quantify
                                                    with Coulter
  Pollen shedding
    phenology           cumulative % of plants    document dates at
                          at beginning, maximum     which 100 plants
                          and end of shedding       reach each stage
  Planting pattern      female/male rows ratio    defined at planting
  Population density    plants per female ha      documented at
  Silk exsertion
    dynamic             cumulative no. of         collect and count
                          exserted silks per        exposed silks 1, 3,
                          ear                       5, 7, and 9 d after
                                                    initial silk
                                                    emergence from 10
  Silking phenology     cumulative % of           document dates at
                          plants silking            which 100 plants
                                                    have exposed silks
  Prolificacy           no. ears per plant        document no. of ears
                                                    harvested from 100

Table 2. Comparison of simulated and measured kernel production for
six seed production fields having various combinations of male and
female inbred flowering characteristics.


                                        A         B         C

  Approximate plant                  53 400    49 900    59 800
    density (plants [ha.sup.-1])
  Measured pollen grains             521 945   800 887   912 976
    per tassel
  Calculated pollen shed             27.8      40.0      54.6
    (grains per ha x [10.sup.9])
  Approximate plant                  59 300    44 000    65 200
    density (plants [ha.sup.-1])
  Measured silks per ear             577       386       350
  Calculated silks                   34.2      17.0      22.8
    (silks per ha x [10.sup.6])
Simulated kernel number              22.3      10.2      15.9
    (kernels per ha x [10.sup.6])
Measured kernel number               20.5      8.4       14.0
    (kernels per ha x [10.sup.6])
Simulated/measured x 100             108%      121%      114%


                                         D           E           F

  Approximate plant                  57 300      66 200      63 300
    density (plants [ha.sup.-1])
  Measured pollen grains             1 476 774   1 915 279   1 456 094
    per tassel
  Calculated pollen shed             84.7        126.8       92.1
    (grains per ha x [10.sup.9])
  Approximate plant                  51 900      58 800      65 200
    density (plants [ha.sup.-1])
  Measured silks per ear             560         528         505
  Calculated silks                   29.1        31.1        32.9
    (silks per ha x [10.sup.6])
Simulated kernel number              21.8        25.6        17.8
    (kernels per ha x [10.sup.6])
Measured kernel number               19.5        23.1        17.6
    (kernels per ha x [10.sup.6])
Simulated/measured x 100             111%        111%        1011


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Agustin E. Fonseca, Jon I. Lizaso, Mark E. Westgate, * Lahcen Grass, and David L. Dornbos, Jr.

A.E. Fonseca and M.E. Westgate, Dep. of Agronomy, Iowa State Univ., Ames, IA 50011; J.I. Lizaso, Dep. of Agricultural and Biosystems Engineering, Iowa State Univ., Ames, IA 50011; L. Grass and D.L. Dornbos Jr., Syngenta Seeds, Washington, IA 52353. Received 18 Sept. 2003. * Corresponding author (
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Title Annotation:Seed Physiology, Production & Technology
Author:Fonseca, Agustin E.; Lizaso, Jon I.; Westgate, Mark E.; Grass, Lahcen; Dornbos, David L., Jr.
Publication:Crop Science
Date:Sep 1, 2004
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