Published in Crop Sci. 44:1450-1455 (2004).
© 2004 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
PLANT GENETIC RESOURCES
Inflorescence Sampling Improves Effective Population Size of Grasses
R. C. Johnson*,
V. L. Bradley and
M. A. Evans
Dep. of Statistics, Washington State Univ., Pullman, WA 99164-6402
* Corresponding author (rcjohnson{at}wsu.edu).
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ABSTRACT
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Variation in seed production per plant leads to reductions in effective population size (Ne), which is a major factor promoting genetic drift of heterogenetic populations during seed collection and regeneration. The objectives of this study were (i) to compare Ne to the census population size (Nc) among different seed harvest methods; (ii) use inflorescence sampling to determine Ne/Nc for numerous heterogenetic grass species, and (iii) to predict the optimum number of inflorescences per plant to most efficiently increase Ne. Estimates of Ne/Nc from rubbing whole plants, cutting whole plants, and from sampling a constant two inflorescences per plant were made on Festuca pratensis Huds., Lolium perenne L., and Pseudoroegneria spicata (Pursh) Á. Löve accessions. Inflorescence sampling was also completed on four accessions of Bromus inermis Leyss., Dactylis glomerata L., F. arundinacea Schreb., L. perenne, Pseudoroegneria spicata, and Phalaris aquatica L. The mean Ne/Nc for the inflorescence method was 0.78, significantly higher then the 0.64 average for the cut or rub methods. For all species and entries, the slope of the curves describing Ne/Nc to inflorescence number was initially steep from 1 to 3 inflorescences and then leveled off asymptotically. Thus, most of the benefit occurs after sampling only a few inflorescences. The results show that sampling a constant number of inflorescences per plant promotes Ne and reduces the potential for genetic drift associated with collection and regeneration of heterogenetic grass populations.
Abbreviations: Nc, census population size • Ne, effective population size
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INTRODUCTION
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THE WESTERN Regional Plant Introduction Station (WRPIS) maintains more than 17000 forage and turf grass accessions. The majority of these are self-incompatible, wind-pollinated species with high levels of heterogeneity. Initial and periodic seed regeneration is needed to maintain this collection (Johnson et al., 2002). The potential for random genetic drift is a major concern in the relatively small populations associated with regeneration. The Ne rather than the Nc is the key parameter in genetic drift, and is defined as the size of an ideal population that would have the same amount of random genetic drift as the actual census population (Wright, 1931; Crow and Kimura, 1970). A major cause of reduced Ne is variation in fecundity or seed production per plant (Heywood, 1986). In some cases, mating can be controlled so that every individual in a population contributes two gametes to the next generation; Ne is then essentially doubled compared with Nc (Crow and Kimura, 1970). Other regeneration schemes to maximize Ne include various types of controlled polycrosses (Breese, 1989). When male and female gametes are uncontrolled and seeds are bulk harvested, variation in fecundity can substantially reduce Ne compared with Nc.
Johnson et al. (2002) found that variation in seeds per whole plant in grass populations caused a sharp decline in Ne. They also found that by sampling a constant two inflorescences per plant that Ne was increased almost 60% compared with whole-plant sampling. In that study, comparisons of Ne/Nc for different whole-plant sampling methods with inflorescence sampling were not made. Also lacking were Ne/Nc values derived from inflorescence sampling of numerous grass species, and information relating the number of inflorescences sampled to Ne/Nc. The objectives of this study are (i) to compare Ne/Nc among different harvest methods, (ii) to test inflorescence sampling among numerous grass species at the WRPIS, and (iii) to predict the optimum number of inflorescences to sample to most efficiently increase Ne.
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MATERIALS AND METHODS
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Calculation of Ne/Nc
The method for calculation of Ne/Nc used herein was developed by Heywood (1986) as outlined in Johnson et al. (2002). A similar approach by Robertson (1961) was discussed by Crow and Kimura (1970). Briefly, Heywood (1986) related variation in seed production per plant with the number of gametes individuals contribute to the population gamete pool. Variation in fecundity resulting from uneven contributions of gametes is a major factor reducing Ne and enhancing genetic drift. With Heywood's (1986) equation:
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where F is the fixation index (inbreeding coefficient), and 
and µ are the standard deviations among plants and the mean family size, respectively. We have further partitioned 2/µ2 into the between-plant (2b) and within-plant (2w) variance components in relation to m, the number of inflorescences per plant. When each parent contributes equally to the gamete pool, 2 is zero and Ne = Nc. It can also be seen that as m increases, the within-plant variance component will decrease and lead to a decrease in 2/µ2. An estimate of 2/µ2 is given by s2/z2 – 1/z, where s2 is the sample variance in seed number among plants and z is the sample mean seed number per plant in a given population. Often, seed production is high enough that the correction term, 1/z, has little effect.
Field Experiments Comparing Harvest Methods for Ne/Nc
Estimates of Ne/Nc were made based on seed number per plant from three accessions, one each from three perennial grass species maintained at the WRPIS. The three entries were F. pratensis (W6 17784), L. perenne L. (W6 9344), and Pseudoroegneria spicata (PI 236681). The same accessions were also used in estimates of Ne/Nc by Johnson et al. (2002). These species are outcrossing, wind pollinated, and self-incompatible, so a value of F = 0 was assumed for the calculations of Ne/Nc (Brown, 1979; Johnson, 1998; Johnson et al., 2002).
Plants of each entry were established at Central Ferry (46°40'13'' N and 117°45'8'' W) and Pullman (46°43'55'' N and 117°9'25'' W), WA, locations. The soil at Central Ferry is a fine-silty, mixed, mesic Natrixeroll and at Pullman a fine-silty, mixed, mesic, Pachic Ultic Haploxeroll. Central Ferry is located approximately 50 km west of Pullman in the Snake River Canyon at about 200 m in elevation, about 500 m lower than Pullman. Plants at Central Ferry were grown under irrigation as described previously (Johnson and Li, 1999). Associated with its lower elevation and more westerly location toward the Columbia Basin desert, temperatures at Central Ferry average about 3.5°C higher and precipitation about 200 mm lower per year than at Pullman.
Plants of each accession were established in a greenhouse and transplanted to the field in the second week of April 2000 at Central Ferry and the second week of May 2000 at Pullman as described by Johnson et al. (2002). Field plot cultivation and fertilization were as described by Johnson et al. (2002).
Four blocks at each location were split into plots of 30 plants representing each accession. The 30 plants per plot were spaced 0.5 m within rows and 1.8 m between rows. Accessions (entries) were isolated from other accessions of the same species by at least 50 m. As expected, there was minimal seed production during the establishment year. Plants were maintained during the spring and summer of 2000 and mowed to about a 20-cm height in the fall.
In the spring of 2001, the 30 plants in each plot were randomly spilt into three subplots of 10 plants representing three harvest methods. Thus, the design was a randomized complete block in a split-plot arrangement with four replications at two locations. The harvest methods were designated as cut, rub, and inflorescence sampling. For the cut method, each of the 10 plants in a given subplot was cut with a sickle and placed in a bag. This was done when the maximum number of seeds was judged to have reached physiological maturity. For the rub method, seed from each plant was rubbed into a pan and placed in a bag. Rubbing of plants was repeated to obtain seeds from inflorescences maturing at different times. The inflorescence method consisted of sampling two inflorescences from each plant judged to be physiologically mature. The inflorescences were kept separate for estimates of variation in seeds per inflorescence. All cut, rub, and inflorescence samples were harvested during the spring and summer of 2001.
For the cut and rub methods, harvested material from each plant was cleaned and seeds weighed to obtain yield per plant. Seed mass was determined by counting and weighing 100 seeds per plant. The number of seeds per inflorescence was calculated by the equation
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For the inflorescence method, the two inflorescences sampled were cleaned, and the seeds were counted and weighed. The seeds from the two inflorescences represented the total seeds per plant sampled for the inflorescence method. For each method, the variance and mean seeds per plant were used to estimate Ne/Nc as described in Eq. [1]. Data were analyzed across locations with SAS GLM release 6.12 (SAS Institute, 1985), assuming fixed effects for location, entry, and method and random effects for blocks. Thus, inferences were made only for the Central Ferry and Pullman locations. The error terms used for testing location was the block within location mean square. The error term for testing entries and the entry x species interaction was the block x species within location mean square. For tests involving method and its interactions, the residual error term was used. Treatment differences were declared at P < 0.05 (SAS Institute, 1985). For the analysis of inflorescence number per plant, the inflorescence sample with a constant two per plant was not included since it was invariant and would otherwise skew the analysis. Similarly, seed weight per plant (yield) was analyzed for only cut and rub methods. Partial coefficients of determination (R2) were calculated as the ratio of the sum of squares of a given treatment factor to the total sum of squares (Neter et al., 1996). This gave the proportion of variation explained by location, entry, method, and associated interactions. Pearson's correlation coefficient was also computed for development and seed production factors.
Survey of Species Ne/Nc by Inflorescence Sampling
In addition to the above experiment, a survey of Ne/Nc using the inflorescence sampling method was completed with species in WRPIS regeneration nurseries during 2001. Inflorescence samples from a total of six species represented by four accessions each were sampled at Central Ferry and Pullman. The species analyzed were B. inermis, D. glomerata, F. arundinacea, L. perenne, Pseudoroegneria spicata, and Phalaris aquatica. The species are all wind-pollinated and highly outcrossing (Fryxell, 1957), so F in Eq. [1] was assumed to be zero. For each accession, two inflorescences were sampled separately from each of 15 plants, cleaned, and total seeds counted. The standard deviation and mean seed number was determined, and Eq. [1] was used to estimate Ne/Nc.
Within each species at each location, four accessions were randomly selected. Thus, the accessions are random effects and represent the units of replication for this design. The experiment was a completely randomized design with a two-way treatment structure (location and species). The accession within species x locations term was the residual error and used for comparing differences among species. Estimates of Ne/Nc were made as described above for each plot. Data were analyzed across locations with SAS GLM release 6.12 (SAS Institute, 1985), assuming fixed effects for location and species with inferences confined to the Central Ferry and Pullman locations. Treatment differences were declared at P < 0.05 (SAS Institute, 1985). The R2 values for location, species, and the location by species interaction were calculated as described above (Neter et al., 1996).
Modeling the Ne/Nc Response to Inflorescence Number
Estimates of the relationship between inflorescence number sampled per plant and Ne/Nc were made based on the estimated sample mean (z) and variance (s2) when inflorescence number was m = 2, the number sampled in the studies described above. For the inflorescence sampling, a random sample of n plants was selected with a random sample of two inflorescences selected from each plant, resulting in a completely randomized design with m = 2. The ANOVA model for this design partitions the variance into between-plant variation and within-plant components.
Let Yij represent the number of seeds on the jth inflorescence (j = 1, 2, ···, m) of the ith plant (i = 1, 2, ···, n). The estimator of the mean number of seeds per inflorescence for the ith plant is
and the mean number of seeds per inflorescence across all plants is
On the basis of these two quantities, the formula for the mean square between plants is
and the mean square within plants is
Under the completely randomized design, the expected value of the mean squares are E
= m2b + 2w and E
= 2w, where 2b represents the between-plant variance component and 2w represents the within-plant variance component. An estimator of 2w is the MSwithin and an estimator of 2b is (MSbetween – MSwithin)/m.
For the estimation of Ne/Nc, with sampling based on a completely randomized design, the variable of interest is the number of seeds sampled per plant, or
The expected value of Yi. is µ and the variance is 2 = m22b + m2w. Thus, an estimator of µ is
and an estimator of 2 is
Substituting these values into Eq. [1] provides an estimate of Ne/Nc.
Estimates of how Ne/Nc varies as m* = 1, 2, ···, M, the desired inflorescence number, can be obtained. The mean number of seeds sampled per plant can be estimated by z(m*) = m* x z/m and the variance in the number of seeds sampled per plant can be estimated by
Here, z, MSbetween and MSwithin were computed from the original data with m = 2. Substituting the values of z(m*) and s2(m*) into Eq. [1] provides an estimate of Ne/Nc for m* = 1, 2, ···, M. Estimates of s2(m*) and z2(m*) were made with inflorescence samples collected in the harvest methods study and the species survey study as outlined above.
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RESULTS AND DISCUSSION
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Comparing Harvest Methods for Ne/Nc
For seeds per plant, all treatment factors and interactions were significant, with the method effect showing the highest fraction of variation (Table 1). This was expected, given that the inflorescence sample, with a constant two, had much fewer seeds per plant then the cut and rub samples, which represented all inflorescences per plant. The entry effect had the most variation for seeds per inflorescence, but all interactions were significant (Table 1). For inflorescences per plant, with data from only the cut and rub methods, the only significant treatment factor was entry, accounting for nearly 83% of the variation. Much of this was because the L. perenne had 544 inflorescences per plant compared with only 133 for the F. pratensis entry and 135 for the Pseudoroegneria spicata entry. Nearly 95% of the variation for seed mass was associated with entry effects (Table 1). All entries differed in seed mass: F. pratensis averaged 1.97 mg, L. perenne 1.51 mg, and Pseudoroegneria spicata 4.60 mg. Since each entry represented a different species, it was expected that large entry effects would be observed for different yield components, and they were.
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Table 1. Summary of the mean, CV, R2 values (percentage variation explained), and statistical significance resulting from ANOVAs for attributes associated with seed production and the ratio of effective to census population size (Ne/Nc). The locations were Pullman and Central Ferry, WA, in 2001. Entries were Festuca pratensis (W6 17784), Lolium perenne (W6 9344), and Pseudoroegneria spicata (PI 236681). Harvest methods were hand-cutting all plants, rubbing all plants, or sampling two inflorescences per plant.
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For Ne/Nc, the location effect, the method effect, and the location x entry interaction were significant (Table 1). The Pullman location had a higher overall Ne/Nc at 0.75 than the Central Ferry location at 0.63. The interaction with entry resulted because Ne/Nc did not increase in Pullman for Pseudoroegneria spicata, averaging 0.65, as it did for L. perenne, which increased from 0.59 at Central Ferry to 0.84 at Pullman.
For F. pratensis and L. perenne, the Pullman environment was more favorable for seed production then the Central Ferry environment, as seen by the sharp increase in seeds per plant in the cut and rub treatments (Table 2). This was associated with increased seeds per inflorescence at Pullman. For Pseudoroegneria spicata, however, there was no difference detected between locations (Table 2). Inflorescences per plant were generally unaffected by location except for a lower value for L. perenne observed in the rub method at Pullman than at Central Ferry (Table 2). The general trend toward increased seed mass at Pullman compared with Central Ferry was most pronounced for F. pratensis (Table 2).
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Table 2. Means for seeds per plant sample, seeds per inflorescence, inflorescences per plant, and seed mass for different locations, entries, and methods of seed harvest. The entries were Festuca pratensis (W6 17784), Lolium perenne (W6 9344), and Pseudoroegneria spicata (PI 236681), and data were collected in 2001. Harvest methods were hand-cutting all plants, rubbing all plants, or sampling two inflorescences per plant.
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Johnson et al. (2002), working with the same entries as in this study, found that rubbed F. pratensis, L. perenne, and Pseudoroegneria spicata had Ne/Nc values of 0.56, 0.39, and 0.59, respectively, compared with 0.74, 0.65, and 0.60 in the current data. So, environment played an important role in the Ne/Nc value for different accessions, as might be expected given that Ne/Nc is based on seed production factors that often vary with environmental conditions.
For Ne/Nc, none of the interactions with method were significant, showing that method means were consistent across location and entry. The significant method effect for Ne/Nc showed inflorescence sampling improved Ne and confirmed the overall advantage of harvesting a constant number of inflorescences per plant suggested by previous work (Johnson et al., 2002). The mean Ne/Nc for the cut and rub methods were not significantly different (0.63 and 0.66, respectively). The inflorescence sample, however, with an Ne/Nc of 0.78, was higher than either the cut or rub harvest methods. In other words, if seeds from 100 plants were harvested and bulked, variation in seed production per plant would lower Ne to about 65 plants. If two inflorescences per plant were harvested and bulked, Ne would be lowered to just 78 plants. For this study, that was a 20% increase. In the Johnson et al. (2002) study with the same entries, Ne/Nc values averaged 0.81 for the inflorescence samples and only 0.51 for the whole-plant samples. This represents a 59% average increase in Ne/Nc attributed to inflorescence sampling. The larger effect of increased Ne/Nc for Johnson et al. (2002) then in the current study was mostly attributed to a lower Ne/Nc for whole plant than in the current study rather then substantial differences in Ne/Nc for inflorescence samples. Thus, seeds per whole plants appeared to vary with environment more that for inflorescence sampling.
The increase in Ne/Nc with inflorescence sampling can be attributed to two factors. First, by taking a constant number of inflorescences per plant, the variation associated with inflorescences per plant is completely eliminated as a factor contributing to the variation in seeds per plant. This is an important reason why variability in whole-plant seed production would be expected to be greater than for inflorescence sampling. Second, as more and more inflorescences are sampled per plant, the variation in seed number within plants is reduced, and this in turn reduces the total between-plant variance as shown in Eq. [1]. Thus, sampling a constant number of inflorescences per plant should maintain a higher Ne and reduce the potential for genetic drift compared with whole-plant sampling.
Survey of Species Ne/Nc by Inflorescence Sampling
The survey of six species at Central Ferry and Pullman by inflorescence sampling showed significant location, species, and location x species effects for seeds per plant, but no difference for Ne/Nc (Table 3). Results in Table 1 showed that location and entry may interact for Ne/Nc; that is, entry Ne/Nc may vary depending on environment. The results in Table 3 show, however, that variation of entries within species for Ne/Nc was large enough that differences among species were not observed. If they had been observed, it would mean that the optimal number of inflorescences sampled may vary with species, suggesting a different inflorescence number per plant would be needed for a given species to maintain a given Ne/Nc. Since this was not the case, a single inflorescence sampling protocol for constant inflorescence number appeared most practical and efficient.
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Table 3. Summary of the mean, CV, R2 values (percentage variation explained), and statistical significance resulting from ANOVAs for seeds sampled per plant and the ratio of effective to census population size (Ne/Nc). Samples of two inflorescences per plant were obtained from six grass species and four accessions within each species. The locations were Central Ferry and Pullman, WA, in 2001.
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Modeling the Ne/Nc Response to Inflorescence Number
Increasing inflorescence number sampled per plant generally increased Ne/Nc as expected (Fig. 1)
. Although the effect varied in the amount of gain, the basic shape of the curve was the same for all entries at both locations. There was an initial steep response as inflorescence number increased from 1 to about 3, followed by an asymptotic leveling off (Fig. 1). It was also apparent that Ne/Nc varied depending on the location and entry. For example, the location x entry interaction for Ne/Nc (Table 1) was observed in the generally lower values for Pseudoroegneria spicata at Pullman compared with other entries at Pullman (Fig. 1). In addition, the initial slope of the curve to increasing inflorescence number was greater at Central Ferry than at Pullman. The reasons for differing initial slopes and maximal responses is related to how the variation between plants is partitioned. When the within-plant variance 2w is large compared with the between component 2b, then sampling additional inflorescences m will give a larger, more positive response to Ne/Nc. If the within-plant variation is initially low compared with the between-plant component, then the response to increased inflorescences per plant is more muted. For example, the values of Ne/Nc for Pseudoroegneria spicata at Pullman were about equal to those of F. pratensis at Central Ferry when inflorescence number was two to four (Fig. 1). Yet, the initial slope and the values at higher inflorescence numbers were lower for Pseudoroegneria spicata at Pullman than for F. pratensis at Central Ferry. This was because the between-plant variance component for Pseudoroegneria spicata at Pullman was more than five times larger than the within-variance estimate, but the between-plant variance estimate for F. pratensis at Central Ferry was actually less than the within-variance estimate. This higher relative within-variance component for F. pratensis at Central Ferry allowed the more pronounced increase in Ne/Nc with increasing inflorescence number m (Fig. 1). As seen in Eq. [1], increasing m works to reduce the contribution of the within-variance component, which reduces the overall variance in seeds per plant. This effect was also seen between the locations: a higher relative within-plant variance lead to the more pronounced increase in Ne/Nc with m at Central Ferry compared with Pullman (Fig. 1).
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Fig. 1. Relationship between the ratio of effective to census population size (Ne/Nc) and increasing inflorescences sampled per plant for Festuca pratensis, Lolium perenne, and Pseudoroegneria spicata grown at Central Ferry (CF) and Pullman (Pul), WA, in 2001.
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The relationship between Ne/Nc and inflorescence number for the survey of six species showed the same basic curve shape (Fig. 2)
observed for the entries in Fig. 1. The initial response was quite strong as Ne/Nc increased from 0.65 to 0.77 as inflorescence number increase from one to two. As before, the curve started to level off after about three inflorescences. The steep initial slope resulted from a favorable balance of the within and between variance components as was observed for Central Ferry entries in Fig. 1.
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Fig. 2. Relationship between the ratio of effective to census population size (Ne/Nc) and increasing inflorescences sampled per plant averaged for four accessions each of Bromus inermis, Dactylis glomerata, Festuca arundinacea, Lolium perenne, Pseudoroegneria spicata, and Phalaris aquatica grown at Central Ferry and Pullman, WA, in 2001.
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Regardless of the difference in gain associated with increasing the inflorescence number sampled per plant, most of the effect is seen before three to five inflorescences. Thus, most of the benefits are realized after only a few inflorescences are sampled. The details of slope and maximal effects for inflorescence sampling to improve Ne/Nc will vary with growing environment and with individual entries, but the basic dynamics and shape of the relationship between inflorescence number and Ne/Nc should remain the same regardless of accession, species, and environment. Therefore, constant inflorescence sampling should be considered in other species, during field collection of germplasm, and in selection programs to help maximize Ne and the diversity of heterogenetic populations. This study was undertaken to advance and clarify sampling procedures used for regeneration of grasses to maintain as high Ne as possible with minimal inputs. We considered the maternal effects of sampling seeds but not the paternal pollen effects. Certainly methods that control male and female gametes will result in equal or even greater Ne than Nc (Breese, 1989). However, the resources to do this are often limiting, especially for large germplasm collections with large regeneration programs (Johnson et al., 2002). In these cases, such as at the WRPIS, inflorescence sampling is recommended as a cost-effective way to improve Ne.
Received for publication August 22, 2003.
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