Variation in seed characters in Nemophila menziesii: evidence of a genetic basis for maternal effect.
Selection response depends on the magnitudes of direct additive genetic variance ([V.sub.A]) and covariance of characters ([Cov.sub.A]), due to variation in nuclear genes expressed in the individuals undergoing selection (Falconer and Mackay 1996; here and throughout, "direct" refers to the effects of the individual's own genotype and of the environment unique to it [Eisen 1967] to distinguish these from parental genetic and environmental effects that influence phenotypes of progeny). Variance due to direct environmental effects ([V.sub.E]) and to gene interactions (e.g., direct dominance, [V.sub.D]) are also routinely considered as contributors to phenotypic variation ([V.sub.P]) that do not contribute to selection response.
Other possible sources of variation are diverse, however, as are their implications for the evolution of phenotypes undergoing selection (Kirkpatrick and Lande 1989, 1992). These additional influences include effects of maternal and paternal parents on progeny phenotypes, excluding the transmission of nuclear genes. Such extranuclear or parental effects on progeny phenotypes can be due to differences in the environments in which parents grow (e.g., maternal parents: Alexander and Wulff 1985; Mazer and Wolfe 1992; Platenkamp and Shaw 1993; paternal parents: Case et al. 1996) or to genetic differences (whether nuclear or cytoplasmic) expressed in maternal parents during maturation of their offspring (e.g., Reznick 1981; Garbutt and Witcombe 1986; Schmid and Dolt 1994). In particular, it is widely recognized (reviews in Roach and Wulff 1987; Riska 1991; Mousseau and Dingle 1991; Bernardo 1996a; Rossiter 1996) that traits of juveniles may be greatly affected by maternal attributes, apart from the direct expression of genes following their Mendelian transmission to progeny. Thus, juvenile traits seem particularly subject to a wide variety of influences. It is therefore an especially challenging empirical problem to infer the causes of variation in them. Variation in phenotypes of offspring due to effects of the maternal parent ([V.sub.M]) can be partitioned as follows: (1) into an additive, heritable component attributable to segregation of nuclear genes expressed in maternal individuals and influencing phenotypes of their progeny ([V.sub.Am]); (2) a component due to organelle genes, which are often maternally inherited; and (3) a nonheritable component, including effects due to maternal environment and to gene interactions expressed in the maternal parent (which we here subsume in [V.sub.Em]) in a manner analogous to the partitioning of direct effects. Paternal effects can similarly, in principle, be partitioned into components, [V.sub.Ap] and [V.sub.Ep].
One experimental approach to distinguishing some of these causes of variation employs the diallel crossing scheme and, related to it, the reciprocal factorial design. These designs permit the most detailed partitioning of the variation in progeny characters that is possible from an experiment encompassing a set of parents of unknown relationship and their progeny from controlled matings (Cockerham and Weir 1977). Several recent studies making use of this approach have focused on the determinants of seed mass (Antonovics and Schmitt 1986; Schwaegerle and Levin 1990; Waser et al. 1995), whereas others have partitioned phenotypic variation for this and other juvenile traits (Wolff 1990; Biere 1991; Montalvo and Shaw 1994). These studies have consistently demonstrated overwhelming influence of maternal parent on seed mass. In addition, Schwaegerle and Levin (1990), Biere (1991), and Montalvo and Shaw (1994) have reported an unanticipated result: that a component of variance ([V.sub.K]) due to interactions between parents, excluding dominance, makes significant contributions to variation in seed mass. From these studies, it has not been possible to determine the basis of these "reciprocal specific" effects (i.e., differences between reciprocal full-sib groups), but these could include, for example, quantitative expression during seed development of incompatibilities between maternal cytoplasmic and the paternal nuclear contributions to the embryo and endosperm (cf. numerous demonstrations of nuclear-cytoplasmic interactions affecting pollen fertility, reviewed in Frank  and Levy ).
We assessed the determinants of two seed characters in a population of Nemophila menziesii, using the reciprocal factorial design. Results of this study motivated a further partitioning to determine the heritability of the maternal effect on seed mass and to clarify the nature of a parental interaction effect identified in the first experiment. We employed a three-generation design patterned after one proposed by Shaw and Waser (1994, p. 631-632) for assessing the genetic and environmental components of variation when both intra- and intergenerational effects are likely to influence the traits of interest. In our design, half-sib relationships are available for both maternal and paternal parents. This experiment extends results of a previous study that employed full-sib groups of maternal parents grown in a greenhouse to examine broad sense heritability of maternal effect and the influence of maternal competitive environment on juvenile traits in this species (Platenkamp and Shaw 1993). Throughout, we regard seed mass and germination time as traits of the progeny and analyze individual values, an approach that is justified by findings of individual selection on seed characters (see above).
MATERIALS AND METHODS
The Study System
Nemophila menziesii H. and A. (Hydrophyllaceae, "baby blue eyes") is an annual species native to California and Oregon, where it commonly occurs in coastal sage scrub and grassland communities below 800 m elevation (Munz 1959). The species is self-compatible, but protandrous. In southern California, its lifecycle is cued to the winter rains. Seeds germinate early in January. The plant grows initially as a rosette, then bolts and produces flowers in a cyme. Senescence of the plants coincides with onset of summer drought in early- to mid-April. In our previous study of juvenile traits, we demonstrated a large reduction in seed mass due to crowding of the maternal parent by the grass, Bromus diandrus. We also demonstrated significant direct additive genetic variation ([V.sub.A]) for germination time (Platenkamp and Shaw 1993).
To assess the determinants of seed traits in this species, we conducted two series of crosses. One, completed in 1988, consisted of two sets of reciprocal factorial crosses. We have previously reported on the genetic determination of competitive performance in this species, based on a study of a subset of the progeny from these crosses (Shaw and Platenkamp 1993). The second, conducted in 1994, involved three-generation pedigrees related to the plants studied in Shaw et al. (1995).
Reciprocal Factorial Cross. - From a natural population within 1.5 km of the campus of University of California, Riverside (UCR), we sampled seedlings of N. menziesii, restricting our sampling to plants that were at least 2 m from each other. These seedlings were grown to maturity in the greenhouse and divided into crossing groups with eight plants assigned to each of two groups. Within each group, we conducted a reciprocal factorial cross (i.e., plants 1-4 were mated as sires to plants 5-8 used as dams, and, reciprocally, plants 5-8 were mated as sires to plants 1-4 used as dams (see e.g., fig. 1 in Shaw and Platenkamp 1993). In contrast to simpler designs, this crossing scheme permits estimation of components of variance of parental effects due to extranuclear genetic or environmental causes and the nuclear genetic components of variance (additive and dominance) unbiased by parental components (Cockerham and Weir 1977). A disadvantage of this design relative to simpler (e.g., nested) designs is that the increase in the number of crosses per parent inevitably restricts the number of individuals that can be sampled from the reference population.
Flowers were emasculated in bud, and about three days later, when stigmas were receptive, they were pollinated. At least ten flowers were pollinated for each of the 64 combinations of mates (hereafter, "matings"). When they became completely brown, capsules were collected and grouped together by mating. Progeny were assayed for seed mass and time to germination. Up to 45 seeds per mating were chosen at random. Seeds were individually weighed to [10.sup.-6] g. They were then positioned at random on germinator pads (Nasco West, Modesto, California) in petri dishes, moistened with deionized water, and kept at 9 [degrees] C in a dark incubator. The dishes were left three days without disturbance. Thereafter, seeds were checked, removed if germinated and watered daily for 50 days.
Three Generation Design. - An additional experiment was conducted to provide a further partitioning of the components of variation in seed mass estimated in the reciprocal factorial study. In particular, we wished to determine the basis of the parental interaction effect on seed mass (see Results of Reciprocal Factorial Experiment). The plants were handled as described above, except as noted. Seedlings were sampled on a 2-m grid from an unmanaged area within the UCR Botanic Gardens. These were crossed in a paternal half-sib design, with 52 plants designated as sires (grandsires of the seeds eventually measured) and a distinct, randomly chosen set of three plants designated as dams mated to each ([ILLUSTRATION FOR FIGURE 1 OMITTED]; generation 0). The contamination rate from these crosses was very small (0.16% on the basis of seed set from emasculated flowers that had not been pollinated; Shaw et al. 1995).
Forty of these 52 paternal half-sib groups were chosen at random to provide individuals to serve as parents in a further series of crosses; a distinct set of eight paternal half-sib groups was chosen at random for each of five crossing blocks. Within each block [ILLUSTRATION FOR FIGURE 1 OMITTED], half-sib progeny groups from five sires in generation 0 (i.e., progeny of sires designated A through E in [ILLUSTRATION FOR FIGURE 1 OMITTED]) were designated at random to provide individuals to be used as sires (e.g., A-1, A-2, A-3) in further matings, while the remaining three half-sib progeny groups (i.e., progeny of sires I, II, III) provided individuals to be used as dams (e.g., I-17, I-18, I-19) in further matings. Thus, for all plants in generation 1, paternal half-sib relationships were available. In generation 1, sires were drawn from more lineages than were dams, to increase the statistical power for testing paternal effects, which were expected to be subtle, relative to maternal effects. This experiment complements that of Platenkamp and Shaw (1993) in which sires were unrelated to one another and in which full-sib, rather than half-sib, relationships between maternal parents were used.
Ten seeds representing each full-sib group in generation 1 were weighed individually and germinated in Eppendorfer tubes. From each full-sib group, one individual was chosen to serve in the crosses ([ILLUSTRATION FOR FIGURE 1 OMITTED]; generation 1).The plants were positioned at random (without regard to crossing block) in a greenhouse at the University of Minnesota, St. Paul, and grown to maturity. They were then crossed factorially within crossing blocks ([ILLUSTRATION FOR FIGURE 1 OMITTED] bottom). In order to avoid confounding age or condition of parental plants with the effects of sires, all sires available on a given day were used in crosses on a given maternal parent. Thus, the replicates of a given mating were distributed throughout the period of crossing. Fruits were collected and stored individually, prior to the weighing of five seeds individually from each of four fruits per mating ([ILLUSTRATION FOR FIGURE 1 OMITTED]; generation 2). The contamination rate in the crosses among plants in generation 1 was estimated to be less than 1.6%.
Reciprocal Factorial Design. - We employed the "bio" model of Cockerham and Weir (1977) and considered six components of the phenotypic variance ([V.sub.P]). These include two explicitly genetic components of variance, direct additive variance ([V.sub.A]) and direct dominance variance ([V.sub.D]). In considering variation due to progeny genotype, we cannot, with the reciprocal factorial design, distinguish effects of genes expressed in the diploid embryo from those expressed in the triploid endosperm (Shaw and Waser 1994). Two further components, namely maternal and paternal components of variance, quantify the variation due to parental effects. Because this design does not permit partitioning of parental effects into their underlying causes (e.g., [V.sub.Am], [V.sub.Ap]), the variance components obtained from this experiment are designated generally as [V.sub.M] and [V.sub.Pat]. An additional component, [V.sub.K], quantifies the contribution to the overall variance that is attributable to parental interactions, including interaction between the nontransmitted effects of the two parents, as well as interaction between the nuclear (transmitted) contribution of one parent and the parental effect of the other. Finally, microenvironmental variance ([V.sub.E]) quantifies the unaccounted for variation among individuals that is attributable to the effects of variation among the environments experienced by individual seeds during maturation. The analyses were conducted jointly for the two traits, seed mass and germination time, and thus yielded estimates of the corresponding covariance components. For this and all other analyses, the phenotypic variance of a trait ([V.sub.P]) was obtained as the sum of all the variance components for that trait. Shaw and Platenkamp (1993) provide further information relating these causal components to the components defined by Cockerham and Weir (1977). The effects of blocks were also included in the model. Thus, the initial overall model directly partitioned phenotypic variance and covariance among additive, dominance, maternal, paternal, parental interaction, and environmental components of variation, while accounting for fixed effects due to blocks.
For all analyses, both seed mass and germination time were log transformed, which greatly improved the fit of residuals to the assumed normal distribution. The analysis was done by restricted maximum likelihood (REML), a general approach to estimation and hypothesis testing. It avoids the limitation of Cockerham and Weir's (1977) computational method which requires a balanced set of data (Kendall and Stuart 1973; Meyer 1991; Shaw 1987). We used the computer program, nf6.p, in the program set, Quercus (Shaw and Shaw 1994).The cutting plane algorithm (Shaw and Geyer 1997) was used to constrain estimates to feasible values (i.e., variance components [greater than] = zero, component correlations between -1 and 1).
Three Generation Design. - The phenotypic variance of seed mass was initially partitioned using analysis of variance employing SAS GLM (SAS 1985).The model included all the factors in the crossing design and their interactions, i.e., maternal grandsire, paternal grandsire, dam nested within maternal grandsire, sire nested within paternal grandsire, their interactions, and fruit within mating, all considered random. REML analysis of this full model is possible, in principle, but would be extremely cumbersome computationally.
Components of variance attributable to these factors in the design were interpreted according to their genetic and environmental causes, as follows. The direct additive genetic variance ([V.sub.A]) can be estimated from the component of variance due to paternal grandsire (PGS) as 16 [[[Sigma].sub.PGS].sup.2], or from the component of variance due to Sire(PGS) as 4 [[[Sigma].sub.(PGS)].sup.2]. The first of these interpretations depends on an assumption that the nuclear genotype of sires has a negligible influence on offspring phenotype, apart from Mendelian transmission, i.e., that variance due to additive genetic paternal effect ([V.sub.Ap]) is negligible. The second interpretation assumes that environmentally induced paternal effects on offspring phenotype are slight. We offer evidence for both of these assumptions below. The variance of additive genetic maternal effects ([V.sub.Am]) can be estimated from the component of variance due to maternal grandsire (MGS) as 4([[[Sigma].sub.MGS].sup.2] - [[[Sigma].sub.pGS].sup.2]; see Eisen 1967). Confounded in this estimate of [V.sub.Am] is the covariance between direct additive and additive maternal effects (Coy[A, [A.sub.m]], but see below). (Note that in Platenkamp and Shaw , p. 544, the coefficient for [V.sub.Am] is given in error as 1/8. There, the correct value is 1/2. This change has negligible effect on the interpretation of the results of that study). Included in the variance due to individual dams, Dam(MGS), is variance due to maternal effects that are environmentally induced or attributable to genetic interactions ([V.sub.Em]), as well as a fraction (3/4) of [V.sub.Am]. The direct dominance variance ([V.sub.D]) can be inferred from the interaction between MGS and PGS as 16 [[[Sigma].sub.MGS x PGS].sup.2].
This design yields tests of three distinct interactions whose variance components would contribute to the overall parental interaction variance, [V.sub.K], inferred from the reciprocal factorial experiment: MGS x sire(PGS), PGS x dam(MGS), and dam(MGS) x sire(PGS), relating respectively to interactions of the maternally transmitted nuclear effect with the paternal effect, to interactions of paternally transmitted nuclear effect with maternal effect, and to interactions of extranuclear contributions of both parents. Each would, however, have a distinct set of possible mechanisms. For example, selective provisioning by particular dams of seeds from particular sires, according to their genetic contribution to the seeds (see e.g., Marshall and Folsom 1991, p. 51), would be expected to appear as an interaction between PGS and dam(MGS). In contrast, differences among sires that are environmentally induced and that vary in their effect on seed mass depending on the maternal sporophyte would be evidenced as an interaction between dam(MGS) and sire(PGS).
Because computational limitations precluded analysis of all the progeny data with the full model, two partial analyses were conducted: (1) an analysis that included all terms of the model above for each block separately and (2) a joint analysis of all five blocks using a reduced model with maternal grandsire, paternal grandsire, dam nested within maternal grandsire, sire nested within paternal grandsire, and the interactions of MGS x sire(PGS) and PGS x dam(MGS), all considered random. Omitting the two factors, fruit within mating and dam(MGS) x sire(PGS), confounds their effects with variation within fruits and therefore leads to an erroneous denominator mean square for tests of the two-way interactions. This latter model does, however, provide appropriate tests of the main effects for the full dataset, as well as estimates for the corresponding variance components.
These analyses suggested a simpler model amenable to analysis by REML. In it, the total variance in seed mass was partitioned directly into the following components: [V.sub.A], [V.sub.Am], the covariance between direct additive effects and maternal additive effects, Cov(A, [A.sub.m]), variance due to environment common to maternal sibs [V.sub.Em], and variance due to environmental effects unique to individuals, [V.sub.E]. A regression of offspring phenotype on maternal phenotype was also included in the model to account for environmentally induced covariance between offspring and mother. This analysis, developed by Meyer (unpubl.), thus joins estimation of variance components with the regression approach for inferring maternal effect (Falconer 1965).The generality of REML permitted inclusion of the observations on the parents in a joint analysis accounting for both parent-offspring and sib resemblances.
Reciprocal Factorial Experiment. - A total of 1963 seeds were weighed. Of these, 1601 germinated. For the remaining seeds, germination time was treated as missing. In univariate analyses of seed mass and germination time, [V.sub.Pat], accounted for less than 1% of the variance in either trait. The bivariate analysis of the full six-component model did not converge, suggesting that the information was insufficient for estimation of all 18 parameters. We therefore eliminated the paternal components to obtain the estimates presented in Table 1.
Variation in seed mass was primarily attributable to two sources of variation among crosses. [V.sub.M] accounted for 15% of the variation in mass of individual seeds and was highly significant. In this design, [V.sub.M] is attributable to all possible sources of maternal effect, including differences in nuclear or organelle genotype and in environments of maternal plants. [V.sub.K], while accounting for a small fraction of the variation (5%), was nevertheless also highly significant, suggesting that there were specific interactions between parents. The contribution of [V.sub.D] was comparable in magnitude with [V.sub.M] but was not statistically significant. Seed mass was highly variable within matings, such that [V.sub.E], reflecting variation in effects on individual seeds, made up 65% of the total variance.
Variation in germination time contained significant [V.sub.A], corresponding to a narrow-sense heritability of 11%. In addition, it contained a small, but significant, [V.sub.K], accounting for 3% of the total variation. Estimates of [V.sub.D] and [V.sub.M] were similar to [V.sub.K] in magnitude, but did not approach significance. Estimates of the component correlations were positive, with the exception of the dominance correlation. None of these was statistically significant, but they suggest that factors (apart from dominance) causing seeds to be larger tend also to make them germinate later. As with seed mass, germination time was highly variable within matings. Nearly 80% of the total variance was attributable to [V.sub.E].
Three-Generation Design. - For the analysis of seed mass in the third generation, 11,016 observations were available altogether. Substantial maternal effects on seed mass were found consistently in all blocks and were highly significant (Table 2, Dam(MGS) effect), accounting for as much as 20% of [V.sub.P] in seed mass and as much as 75% of the variation among matings (Block A; values not shown). Variance due to maternal grandsire accounted for 10% of the overall variance in three of the five blocks. This factor did not approach statistical significance in analyses of the blocks singly, but this is not surprising given that the very limited number of maternal grandsires per block (3) is expected to afford extremely low power. The joint analysis of all five blocks permitted a more powerful test of this factor, but required a simpler model, omitting the factors, Dam(MGS) x Sire(PGS) and Fruit(Dam(MGS) x Sire(PGS)). In this larger analysis, the variance due to maternal grandsire was marginally significant, accounting for 5.3% of [V.sub.P] (Table 3). This implies that [V.sub.Am] is 0.033, accounting for 20.4% of the [V.sub.P]. Taking this estimate for [V.sub.Am], the variance due to Dam(MGS), estimated as 14.1% of the total variance, is quite closely accounted for by the expected variance due to genetic segregation within half sib groups ([3/4] [V.sub.Am]), suggesting that maternal effect due to variation in environment or cytoplasmic genes is negligible in this study.
TABLE 1. REML estimates of quantitative genetic components of variance and covariance for seed mass (sm, in mg) and germination time (gt, in d to germination) in the reciprocal factorial study of Nemophila menziessi. Both traits were transformed to natural logarithms. The model partitioned the phenotypic (co)variance into additive, dominance, maternal, parental interaction and environmental components. The means, backtransformed to the original scale, are 1.60 mg for seed mass and 5.05 d for termination time. Variance components are given as x 1000. In parentheses are percentage values of the total variance and in square brackets are component correlations. Seed mass Germination time [V.sub.A] sm 0.58 4.83 (0.5%) [1.0] gt 40.51(*) (11%) [V.sub.D] sm 18.2 -9.58 (15%) [-0.60] gt 13.87 (4%) [V.sub.M] sm 18.59(**) 2.71 (15%) [0.21] gt 8.85 (2%) [V.sub.K] sm 5.96(***) 4.44 (5%) [0.52] gt 11.96(**) (3%) [V.sub.E] sm 79.14 27.32 (65%) [0.18] gt 289.69 (79%) * P [less than] 0.05; ** P [less than] 0.025; *** P [less than] 0.001.
In agreement with the reciprocal factorial results (Table 1) and also with our prior work (Platenkamp and Shaw 1993), this analysis indicated that direct effects of progeny nuclear genotype on seed mass are very small. The heritability of seed mass, inferred from either the variance component for Paternal Grandsire or Sire(PGS) was estimated as 3.2% and 4.8%, respectively (Table 3). Direct dominance variance, inferred from the variance component for MGS x PGS was not detectable (Table 3). These results also imply that additive genetic paternal variance ([V.sub.Ap]) contributes little to variation in seed mass. Because [V.sub.Ap] is here confounded with the direct additive genetic contribution ([V.sub.A]) to seed mass, we have assumed above that it is negligible in order to estimate [V.sub.A]. Alternatively, an upper bound for [V.sub.Ap] of 1.08 (= 0.8%) is obtained by assuming [V.sub.A] is zero.
Evidence for environmentally induced paternal effect on seed mass (Sires (PGS)) was weak and inconsistent. In Block B only was this effect found to be significant (P [less than] 0.05), yet even in that case, the variance component was less than 3% of the total (values for individual blocks not shown). In every other case, the variance component was at least an order of magnitude less than that obtained for maternal grandsire, and in the joint analysis of all five blocks, was less than 1% of the total (F = 1.2, df 20, 30.8, ns).
We confirmed our inferences of the relative magnitudes of [V.sub.A], [V.sub.Am], and [V.sub.Ap] by two further analyses. We regressed the mean of the fullsib groups jointly on the seed mass of the maternal and paternal parents. The estimates of the regression slope on maternal value ([b.sub.M] = 0.130, SE 0.042) and on paternal value (be = 0.006, SE = 0.038) agreed well with the values expected from Table 3, under a model in which paternal effects (apart from Mendelian transmission) are negligible (i.e., [b.sub.M] = ([V.sub.A] + [V.sub.Am])/2[V.sub.P] estimated as (8 [[[Sigma].sub.PGS].sup.2] + 2 ([[[Sigma].sub.MGS].sup.2])/[V.sub.P] = 0.124 and [b.sup.P] = [V.sub.A]/2[V.sub.P], estimated as 8 [[[Sigma].sub.PGS].sup.2]/[V.sub.P] = 0.018).
The finding that paternal effects were slight justified analysis of a simpler model omitting paternal effects. This was carried about by REML in order to permit inclusion of the observations on parents to gain statistical power and reduce sampling covariances between the parameters. This analysis supported the results obtained by ANOVA, indicating that [V.sub.Am] was highly statistically significant, exceeding [V.sub.A] by a factor of four. It also yielded a highly significant regression of offspring phenotype on maternal phenotype and indicated that there was negligible contribution to variance as a result of further shared environmental effects ([V.sub.Em]). In addition, the REML analysis provided an estimate of Cov(A,[A.sub.m]) as positive and significant, yielding a correlation of 0.67.
To summarize our several analyses of main genetic and parental effects, maternal effects were largely attributable to substantial additive genetic maternal variance ([V.sub.Am]). Direct additive genetic variance ([V.sub.A]) was small, but the covariance between direct additive and maternal additive effects (Cov[A, [A.sub.m]]) was appreciable. Evidence for variance due to extranuclear paternal effects [[[Sigma].sup.PGS].sup.2] was limited to a single block.
This experiment was designed to reveal the source(s) of [V.sup.K], the parental interaction detected as highly significant in the reciprocal factorial study. In the three generation experiment, these would be evidenced as PGS x Dam(MGS) or, possibly, MGS x Sire(PGS). A further source of [V.sub.K] is interaction between extranuclear effects of both parents. Various mechanisms could be responsible, including interaction between environmentally induced conditions of the two parents. In this case, the interaction, Sire(PGS) x Dam(MGS), is expected. However, we found that none of these interactions approached significance in four of the blocks (Table 1). In those blocks, F-ratios [less than] = 1 were obtained in 10 of the [TABULAR DATA FOR TABLE 2 OMITTED] 12 cases, indicating that the best estimate of the associated variance component is zero. In Block A alone, the standard F-ratios yielded significant tests of the two nuclear x parental interactions (P [less than] 0.05), with variance component estimates about 20% of that for maternal dam. This finding raises the possibility that there are real, but sporadic interactions between the haploid pollen contribution and the maternal plant and also between the haploid ovule contribution and the pollen parent, but detailed consideration of these tests casts doubt on their statistical and biological significance.
TABLE 3. Estimates of variance components (x 1000) from the joint analysis of variance of seed mass for all five blocks of the three generation experiment. Masses were transformed to natural logarithms. The mean, backtransformed to the measurement scale, is 1.89 mg. A reduced model was used (see Methods). Thus, the "Residual" here comprises the last three effects given in Table 2, i.e., the last interaction, and the variation both within and among fruits. Maternal Grandsire [MGS] 8.6+ (5.3%) Dam(MGS) 24.2(***) (14.1%) Paternal Grandsire [PGS] 0.27 (0.2%) Sire(PGS) 1.5 (0.9%) MGS x PGS -1.5 (0%) Dam(MGS) x PGS 5.6 (3.3%) MGS x Sire(PGS) 5.7 (3.3%) Residual 124.4 (73.3%) + P [less than] 0.08; *** P [less than] 0.0001.
We illustrate this point by detailed consideration of the test of MGS x Sire(PGS) in Block A. A priori, the denominator for this test is the mean square quantifying the variation among matings, i.e., the interaction Dam(MGS) x Sire(PGS), as given in Table 2. The test for this latter interaction yields an F-ratio substantially less than 1, the value expected under the null hypothesis that there is no variation among matings. This result indicates that the variation among matings was less than expected, given the variation among fruits. In general, this could occur if, in this block, fruits developing on the maternal plant were relatively clumped according to paternal parent. Under the assumptions that sampling variance accounts for the aberrantly low F-ratio (cf. corresponding tests in the remaining blocks) and that the variance component for Dam(MGS) x Sire(PGS) is zero, a practice advocated by many statisticians is to reduce the model, testing the MGS x Sire(PGS) interaction with the following denominator:
([SS.sub.fruit] + [SS.sub.Dam(MGS)xSire(PGS)])/([df.sub.fruit] + [df.sub.Dam(MGS)xSire(PGS)])
(Sokal and Rohlf 1969, pp. 266-267). According to this procedure, the test of this factor yields an F-ratio of 1.21 (df 16, 332, P [greater than] 0.1). This approach likewise modifies the test of the PGS x Dam(MGS) interaction, eliminating evidence of this interaction (F = 1.34, df 20, 332, P [greater than] 0.1). Thus, these data do not support our previous inference of interactions between parents in their effects on seed mass. We also reexamined the single case of a significant component of variance for Sire(PGS) in Block B (see above), using this approach. In this case, support for the alternative hypothesis that individual sires differed in their effects on seed mass was weakened, but remained significant at P [less than] 0.05 (F = 2.1, df 10, 80).
In contrast to the small components of variance due to nuclear x parental interaction, this experiment revealed that variation among fruits within matings was consistently large and highly significant (Table 2), accounting for 50-70% of the total variation in seed mass. To investigate the degree to which this reflects a decline in resources for provisioning later fruits, as well as genetic variation in the change of provisioning with fruit order, we conducted a supplementary analysis which included fruit order as a covariate and an interaction between maternal grandsire and fruit order. In each block, there was a highly significant decline in seed mass with fruit order, with slopes ranging from -0.06 to -0.1, implying a 6-10% decrease in mean seed mass for each succeeding fruit, presumably due to the increasing demand on resources available within maternal plants. This analysis provided no compelling evidence for genetic variation in the change of seed provisioning (MGS x Fruit order, P [greater than] 0.1). Variation among seeds within fruits accounted for about 20% of the variation in seed mass.
We have confirmed our finding (Platenkamp and Shaw 1993) of substantial additive genetic variation for germination time in Nemophila menziesii, demonstrating the potential for appreciable response to natural selection favoring earlier germination as we have observed in a recent field experiment (Shaw and Platenkamp, unpubl.). We have also documented substantial variation due to maternal effects on seed mass. This finding differs from the effect, demonstrated in our earlier study (Platenkamp and Shaw 1993), of experimentally varying maternal competitive environment. Further, we have determined that the additive genetic variance of maternal effects ([V.sub.Am]) is large, under the conditions of our study. In contrast, we found that paternal effects on seed mass were slight, as were the effects of interactions between parents.
Accumulating evidence that maternal effects dominate in producing variation in seed mass among crosses of wild plant species (recently summarized in Waser et al. 1995; see also Winn 1988) and also in juvenile traits of diverse animals (Mousseau and Dingle 1991; Bernardo 1996a,b; Rossiter 1996) has left unresolved the extent to which these maternal effects have a genetic basis and would therefore support evolutionary response to natural selection. Similarly, the reciprocal factorial experiment presented here confirmed a large maternal contribution to seed mass in Nemophila menziesii, but could not, in principle, reveal its basis.
Our three-generation experiment provides direct estimates of [V.sub.Am], which exceeded 20% of the total variance in the three generation experiment as a whole. [V.sub.Am] contributes directly to selection response (R) as does the covariance between direct additive and maternal additive effects (Cov(A, [A.sub.n]). Given a selection differential, S, the response to selection is predicted as
R = ([V.sub.A] + 3Cov([A, [A.sub.m])/2 + [V.sub.Am]/2) S/[V.sub.P] (1)
(Willham 1963). Thus, this finding indicates that substantial genetic variation is available to support response to selection on seed mass, through both the maternal genetic contribution to this trait and the positive covariance between the additive maternal effect and the additive direct effect on seed mass. It is noteworthy that an analysis using a model that failed to account for environmentally induced resemblance between mother and offspring yielded an estimate of this covariance that was substantial and negative. Such a discrepancy has recently been documented as an artifact accounting for frequent reports of negative values for Cov(A,[A.sub.m]) in animal breeding studies (Meyer 1997). Our inference of substantial potential for response to selection on seed mass contrasts with the body of studies failing to find appreciable (direct) additive genetic variance ([V.sub.A]) in seed mass (reviewed in Platenkamp and Shaw 1993), which has suggested that response to observed phenotypic selection on this trait in nature is likely to be negligible. Our substantial estimates of [V.sub.Am] and positive Cov(A,[A.sub.m]) for seed mass indicates that this inference should be reconsidered.
Few studies of seed mass in wild species have been designed to reveal the magnitude of [V.sub.Am]. In a garden experiment with wild radish, in which maternal parents related as full sibs and paternal halfsibs were grown in two densities, Mazer and Wolfe (1992) detected no effects of maternal grandsire on mean seed mass (termed a "paternal" effect by these authors, p. 1187; see also Mazer 1987). In contrast, Thiede (1996) detected significant [V.sub.Am] for seed mass and other traits in Collinsia verna. Moreover, studies of crop and turf species provide abundant evidence of substantial heritable variation in seed mass (refs. in Harper et al. 1970; more recently, e.g., Sidwell et al. 1976; Hussey and Holt 1986; Tinius et al. 1991). Detection of genetic variation in seed mass assayed, as in these studies, as a mean value for each maternal parent, corresponds to finding genetic variation in maternal effect on individual seed mass, as we have done. Differences in definition of the trait, seed mass (i.e., as individual values vs. as a mean for a maternal individual or for a mating), complicate quantitative comparison of our estimates with ones from the agricultural literature, as do other differences in approach. For example, heritabilities of seed mass have been inferred from response to selection where the base population is established from a cross of divergent cultivars (e.g., Sidwell et al. 1976; Tinius et al. 1991). Because pedigree information is not generally available in such studies, contributions of direct and maternal genetic effects to observed genetic variation cannot be distinguished, as is possible in our study. Nevertheless, these studies are consistent with a generalization that additive genetic variation in seed mass, whether through direct or maternal effects, is at least as great in many agricultural populations as we have found within our study population of N. menziesii.
Quantitative prediction of response to natural selection would require further studies in which the magnitude of [V.sub.Am], as well as estimates of selection, could be inferred in nature. The available studies of selection on seed mass in nature have provided evidence only of selection favoring larger seeds (Stanton 1984a; Wulff 1986; Mazer 1987), but it is difficult to know whether this represents a nearly universal tendency or reflects the challenge of conducting selection studies in conditions under which selection would favor the opposite extreme (e.g., under crowding in the site of origin, such that seeds dispersing farther tend to have higher fitness). Stanton (1984b) has suggested other circumstances in which selection favoring reduction in seed size is plausible.
One basis for conflicting selection on seed size is suggested by our reciprocal factorial experiment in which positive correlations between seed mass and germination time were found at both the level of additive genetic effects and of maternal effect. Though the additive genetic and maternal correlations were not statistically significant in this study of modest scale, they suggest that evolutionary increase in seed size may be accompanied by delay in germination time. Delay in germination can appreciably reduce eventual fitness, as we have observed in field experiments (Shaw and Platenkamp, unpubl.; see also Howell 1981; Kalisz 1986). Thus, directional selection tending to increase seed mass of progeny individuals may conflict with selection on germination time. Moreover, selection on both these juvenile traits may vary with environmental conditions.
Selection response may also be modified by selection on traits expressed in maternal plants (e.g., seed number, as discussed, for example, by Stanton 1984a; Lloyd 1987; Winn 1991). Numerous studies in diverse organisms have demonstrated negative phenotypic correlations between the size and number of offspring produced by a given female (e.g., in plants: Stanton 1984a; Cipollini and Stiles 1991; Richardson and Stephenson 1991; Winn 1991; Mehlman 1993; copepods: Pouilin 1995; lizards: Sinervo 1990; fish: Reznick and Yang 1993; Reznick et al. 1996; and mammals: Sikes 1995. See reviews in Reznick 1985; McGinley et al. 1987; Bernardo 1996b. Michaels et al.  provides an exception). In many of these studies, both of these traits vary among maternal individuals such that mothers produce larger offspring at the expense of reduced numbers of young, apparently as a result of resource limitation (Stanton 1984a; Sinervo 1990; Richardson and Stephenson 1991; Reznick et al. 1996). If these negative phenotypic correlations between size and number of offspring reflect a genetic trade-off, response to selection on these traits is expected to be constrained (Reznick 1985; Rausher 1992). We examined this potential evolutionary constraint using counts of seeds obtained from each fruit in our three generation experiment. We found that although there was a negative phenotypic correlation between seed mass and seed number per fruit (-0.21, Shaw and Byers 1997), there was no evidence for additive genetic variance in seed number. It remains possible that a genetic trade-off between seed size and seed number at the level of whole plants constrains response to selection on these two traits. The opposition of selection processes could maintain genetic variation in seed mass, but this depends on the quantitative relationships between selection at different stages of the lifecycle (Hartl and Clark 1989, pp. 208-209) and on details of the genetic distributions of the traits (Turelli and Barton 1994; Curtsinger et al. 1994).
Our finding that [V.sub.Am] accounts for much of the maternal effect in this experiment indicates that differences among environments of maternal plants made negligible contributions to variation in seed mass. This finding does not conflict with a view that maternal environment can profoundly affect seed mass. Direct experimental manipulation of particular aspects of maternal environment in this species (Platenkamp and Shaw 1993) and in others (e.g., Alexander and Wulff 1985; Stamp 1990; Mazer and Wolfe 1992) clearly demonstrates that maternal environment can have substantial influence on seed mass. Similarly, in animal studies, maternal environment (e.g., availability of food, temperature, and length of photperiod) has been shown to influence juvenile traits (Mousseau and Dingle 1991; Reznick et al. 1996). In the present study, environmental variation among maternal plants was limited to inevitable variation in temperature and light among locations in the greenhouse, and this can reasonably be expected to be small relative to differences obtained by deliberate manipulation of environment. The relative magnitudes of additive genetic and environmentally induced maternal effect variances expressed under field conditions are unknown, but variance due to the latter source seems likely often to be larger than in our greenhouse study and this would tend to slow response to selection in nature.
By far the greatest variation in mass of individual seeds occurs within matings, with variance among fruits up to four times that observed within fruits, as revealed by our second experiment (Table 2; see also Thompson 1984; Michaels et al. 1988). This is partially accounted for by a trend for seed mass to decline with date of fruit set, as has been found in other species (e.g., Stamp 1990; Fenster 1991; Winn 1991), suggesting that the decline may be due in part to decrease in resources available to maturing fruits as maternal plants age or bear increasing numbers of fruits. This is, thus, an environmental maternal effect, attributable to variation within maternal plants in the environment of maturing seeds. There was no clear evidence of genetic variation among maternal plants in the decline of seed mass with date of fruit set. Resource limitation is evidenced in Campanula americana as reductions in probability of fruit set and number of seeds per fruit, though not in mean seed mass per fruit, with increased loads of previously set fruits (Richardson and Stephenson 1991).
Despite the previous lack of evidence of paternal influence on seed mass in this species (whether by nuclear contributions or nonnuclear effects), we designed the three-generation experiment to provide power particularly for detection of paternal effects. This decision was motivated both by the increasing interest in environmental induction of paternal effects on reproduction (Schlichting 1986; Young and Stanton 1990; Mazer and Gorchov 1996) and by our recognition that our earlier experiments (Platenkamp and Shaw 1993, the present reciprocal factorial) had relatively limited power for detecting such effects, if they are subtle. Given this larger design, sampling effects of 72 sires and 25 paternal grandsires, the small estimates of paternal effects (i.e., Sire[PGS]) support the conclusion that they are weak or nonexistent in single donor pollinations, given the environmental variability of the greenhouse. Similarly, no effect of pollen parent was found in single donor crosses of Chamaecrista fasciculata (Fenster 1991). We cannot rule out environmental or genetic paternal effects on fertilization success of sires in multiple donor pollinations (e.g., Schlichting 1986; Young and Stanton 1990), due, for example, to pollen competition or maternal discrimination, as has been documented in several species (reviewed in Charlesworth et al. 1987; Lyons et al. 1989; Marshall and Folsom 1991). Our result does, however, support the validity of inference of additive genetic components of (co)variance from resemblance of paternal half-sibs in experimental studies using the common practice of single-donor crosses.
One of the objectives of the three generation experiment was to identify the sources of [V.sub.K] inferred in the reciprocal factorial study, as also in studies by Schwaegerle and Levin (1990), Biere (1991) and Montalvo and Shaw (1994). For example, developmental incompatibilities between maternal sporophytic tissue and the genetic contribution of pollen, whether expressed in embryo or endosperm, would have appeared as an interaction between Dam(MGS) and PGS. Our original finding of significant [V.sub.K] appears, however, to be an artifact of the failure to account for variation among fruits within matings, given that the three generation study failed to provide compelling evidence for any of the three interactions subsumed in [V.sub.K]. The artifactual inference of [V.sub.K] is further demonstrated by the fact that tests of all three interactions would be deemed significant in all blocks, if the fruit effect were omitted from the model to mimic the analysis of the reciprocal factorial experiment in which information on association of seeds in fruits was lacking (analysis not shown). In contrast, the detection of [V.sub.K] by Montalvo and Shaw (1994) is not accounted for by variation among fruits (A. Montalvo, pers. comm.). Regardless of the causes of variation in seed mass among fruits, it is clear that interpretation of the importance of other contributions to variation depends critically on taking this variation into account, a methodological point made evident by comparison of the results of the two studies presented here.
We thank W. G. Hill, D. S. Falconer, M. Mackinnon, S. Mbaga, and E H. Shaw for helpful discussions, K. Meyer for generously performing the REML analysis of the three generation experiment, and A. Sakai and three anonymous reviewers for their thoughtful comments on the manuscript. Part of this work was supported by NSF award BSR-8817756. RGS gratefully acknowledges sabbatical support from the Underwood Fund of the BBSRC (U.K.) and the Bush Sabbatical Supplement Program of the University of Minnesota.
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