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Maternal inheritance and its effect on adaptive evolution: a quantitative genetic analysis of maternal effects in a natural plant population.

Resemblance between mothers and offspring due to Mendelian inheritance can be altered by phenotypic effects of a mother on her young, termed maternal inheritance (Kirkpatrick and Lande 1989, 1992; Lande and Kirkpatrick 1990). These non-Mendelian transgenerational effects have the potential to impact a population's evolutionary trajectory, but their evolutionary importance in natural populations has rarely been carefully examined. In a classic study of maternal effects in mice, Falconer (1955, 1965) found that large mothers had many small young. At maturity the females from these large litters had only a few large young. The lack of resemblance between mothers and their daughters in litter size and offspring size was mediated by the phenotypic effect of maternal size and its relation to maternal provisioning ability. This maternal effect had unusual, short-term evolutionary consequences. Artificial selection on litter size showed a reversed response to selection in a single generation (Falconer 1965). In the collared flycatcher, Schluter and Gustafsson (1993) experimentally determined how maternal condition and clutch size influenced the resemblance between mothers and daughters in clutch size. They documented that a daughter's condition was negatively affected by large maternal clutch size and positively affected by maternal condition. The balance between negative and positive maternal effects led Schluter and Gustafsson (1993) to predict a positive response to selection on clutch size in the first generation.

These two examples illustrate how maternal inheritance can impact the evolutionary process. A number of pathways can contribute to the evolutionary response when a trait is maternally inherited. Although the maternal environment can modify the expression of the maternal phenotype altering its subsequent impact on a trait in the offspring, the evolutionary response hinges on the genetic basis of maternal effects. The genetic basis of maternal effects can be divided into two categories: (1) heritability of maternal traits such as maternal size, condition, or provisioning ability; and (2) genetic correlations between these maternal traits and traits expressed in the juvenile stages such as birth weight or offspring size. The sign and magnitude of these genetic and environmental pathways define the structure of maternal inheritance and determine its consequence for adaptive evolution.

The best model to date for exploring the underlying structure of maternal inheritance was developed by Dickerson (1947). In this paper I utilize Dickerson's model to estimate the specific causal genetic and environmental components of variance relevant to maternal inheritance in a wild population of the winter annual plant Collinsia verna Nutt. (Scrophulariaceae). My goal is to describe how maternal inheritance affects the magnitude and direction of predicted response to selection for a number of traits expressed at different stages in the life cycle.


Maternal Inheritance Model

Dickerson's (1947) model considers two traits, the individual trait of interest and the maternal trait affecting its expression. The covariance (i.e., resemblance) between mothers and their offspring in the trait of interest is partitioned into explicit Mendelian and maternal components (Table 1; Dickerson 1947; Wilham 1963, 1972; Eisen 1967; Cheverud 1984; Lynch 1987; for current reviews, see Cheverud and Moore 1994; Lynch and Walsh 1998). The nine possible causal genetic and environmental components from Dickerson's model (Table 1) are obtained by the statistical partitioning of phenotypic covariances for the individual trait of interest among different types of relatives generated in a complex breeding design. The maternal trait is an unobserved, composite trait termed "maternal performance." The relationship between these causal components is depicted in the path diagrams of maternal inheritance described below. While Dickerson's path analytic approach assumes a causal model of maternal inheritance, the estimates of causal components are correlational in nature because they are derived from covariances.

With simple Mendelian inheritance [ILLUSTRATION FOR FIGURE 1A OMITTED], the phenotypic value of a trait ([P.sub.o]) is determined by additive genetic ([A.sub.o]) and environmental ([E.sub.o]) components where the subscript o refers to the individual trait of interest. In this two-generation path diagram, an offspring in the second generation (x) receives half of its genes from its mother in the previous generation (w). The square root of direct (i.e., Mendelian) heritability ([h.sub.o]), path coefficient 1, represents the square root of the fraction of the total phenotypic variance in the trait of interest [Mathematical Expression Omitted] that is determined by the direct additive genetic variance [Mathematical Expression Omitted], whereas the path coefficient 2 represents the proportion accounted for by random environmental variance ([Mathematical Expression Omitted]).

In contrast, in Dickerson's (1947) model of maternal inheritance [ILLUSTRATION FOR FIGURE 1B OMITTED], the phenotypic value of the trait of interest ([P.sub.ox]) is influenced not only by Mendelian inheritance (described above), but also by other, unmeasured aspects of the maternal phenotype ([]), where subscripts m and w refer to the maternal performance trait and the maternal generation, respectively. The phenotypic value ([]) for maternal performance is determined both by additive genetic ([A.sub.m]) and environmental ([E.sub.m]) values. Direct and maternal additive effects can be genetically correlated ([r.sub.A][o.sub.Am]). In this model the resemblance between a mother and her offspring [ILLUSTRATION FOR FIGURE 1B OMITTED] can be influenced by four additional pathways: (1) the square root of maternal heritability ([h.sub.m]), path coefficient 3, representing the square root of the proportion of the total phenotypic variance [Mathematical Expression Omitted] determined by the maternal additive genetic variance [Mathematical Expression Omitted]; (2) the maternal environmental variance [Mathematical Expression Omitted] as a fraction of the total phenotypic variance [Mathematical Expression Omitted], path coefficient 4; (3) direct-maternal additive genetic covariance ([[Sigma].sub.[A.sub.o][A.sub.m]]) standardized by the additive genetic variances of both the individual and maternal traits as a genetic correlation ([r.sub.[A.sub.o][A.sub.m]]), path coefficient 5; and (4) the proportion of the phenotypic variance in maternal performance phenotype [Mathematical Expression Omitted] that accounts for the variation in [Mathematical Expression Omitted], the maternal effect coefficient (m), path coefficient 6. Because the maternal phenotype ([]) is unobserved, the maternal heritability ([h.sub.m]) is calculated as a fraction of phenotypic variance in the offspring trait of interest [Mathematical Expression Omitted] rather than in the maternal trait [Mathematical Expression Omitted]. In this framework of maternal inheritance the direct-maternal genetic correlation (path coefficient 5) is distinguished from other genetic correlations by its association with transgenerational maternal effects. In a second version of Dickerson's model [ILLUSTRATION FOR FIGURE 1C OMITTED], a fifth component, the environmental covariance between the trait of interest and the maternal trait across generations [[Sigma].sub.[E.sub.o][E.sub.m]]) standardized as a direct-maternal environmental correlation ([r.sub.[E.sub.o][E.sub.m]]), path coefficient 7, can also contribute to the resemblance between a mother and her offspring. In this complete model of maternal inheritance, six additive and environmental causal components of variance contribute to seven paths influencing the resemblance between mothers and their offspring, with five of these paths (3-7) related specifically to maternal inheritance. Thus, relative to standard quantitative genetic models of Mendelian inheritance [ILLUSTRATION FOR FIGURE 1A OMITTED], the decomposition of the phenotypic variance for trait o ([P.sub.ox]) into genetic and environmental components is complicated by the additional paths of maternal inheritance.

The response to selection on the maternally inherited individual trait (Pox) will be determined by the total heritability ([Mathematical Expression Omitted]; Dickerson 1947; Wilham 1963; van Vleck 1970):

[Mathematical Expression Omitted]. (1)

The total heritability is a function of the direct additive genetic variance [Mathematical Expression Omitted], the maternal additive genetic variance [Mathematical Expression Omitted], and the direct-maternal additive genetic covariance ([[Sigma].sub.[A.sub.o][A.sub.m]]) relative to the total phenotypic variance [Mathematical Expression Omitted]. When the direct-maternal genetic covariance ([[Sigma].sub.[A.sub.o][A.sub.m]]) is negative and greater than [Mathematical Expression Omitted], the response will be in the opposite direction to selection (Lynch and Walsh 1998). Similarly, positive maternal additive genetic variance [Mathematical Expression Omitted] and direct-maternal genetic covariance ([[Sigma].sub.[A.sub.o][A.sub.m]] can accelerate response to selection. Thus, the underlying structure of maternal inheritance influences the direction and rate of adaptive evolution. The time lag in the maternal inheritance can also affect the rate, direction, and duration of the selection response (Kirkpatrick and Lande 1989, 1992; Lande and Kirkpatrick 1990).

Empirical estimates of the causal variance components affecting evolutionary response in domesticated and experimental laboratory species for traits such as litter size, birth weight, and weaning weight show that maternal additive genetic effects can be substantial, can increase from birth to weaning, and generally display significant negative directmaternal additive genetic covariances (e.g., Young and Legates 1965; Bondari et al. 1978; van Sanford and Matzinger 1982; Cantet et al. 1988; Southwood and Kennedy 1990; Meyer 1992b and references therein; Shi et al. 1993; van Arendonk et al. 1996). Maternal effects on a single trait through ontogeny decline after weaning (Cheverud et al. 1983; Atchley 1984).

In contrast in natural populations, empirical estimates of the specific causal variance components determining maternal inheritance are generally lacking. Most studies use simpler methods to obtain less detailed estimates of the genetic and environmental components of maternal effects (reviewed by Bernardo 1996a,b; Rossiter 1996). In plants, the magnitude of maternal effects also shows a decline through ontogeny. In general, traits expressed early in the life cycle such as seed weight, emergence time, or seedling size are influenced more strongly by maternal genetic effects than direct (i.e., Mendelian) genetic effects (Biere 1991; Platenkamp and Shaw 1993; Montalvo and Shaw 1994; Schmid and Dolt 1994; Byers et al. 1997). The duration of maternal genetic effects beyond the seedling stage is rare (Schmid and Dolt 1994). Maternal genetic effects tend to persist longer in competitive environments (Schmid and Dolt 1994), a pattern analogous to the persistence of initial size differences in more competitive environments (Gross 1984; Stanton 1985; Waller 1985; Weiner 1985, 1990; Stratton 1989; Gross and Smith 1991). Although maternal environmental effects are well documented (e.g., Lacey 1996, Lacey et al. 1997; reviewed by Roach and Wulff 1987) and can persist for multiple generations (Lacey 1991; Miao et al. 1991; Case et al. 1996), studies examining the magnitude of maternal genetic and maternal environmental effects have found that maternal genetic effects predominate over maternal environmental effects for traits expressed early in the life cycle (Biere 1991; Schmid and Dolt 1994). In a recent multigeneration study, Byers et al. (1997) obtained estimates of specific causal components relevant to maternal inheritance for seed weight in Nemophila menziesii. They found substantial maternal additive genetic variance and a positive direct-maternal additive [TABULAR DATA FOR TABLE 2 OMITTED] genetic covariance resulting in predicted accelerated responses to selection as a result of maternal inheritance.

In this paper, I present a quantitative genetic analysis of maternal effects and estimate the causal variance components relevant to maternal inheritance for several traits throughout the life cycle in a natural plant population. Causal components are critical for predicting the dynamic role that maternal inheritance plays in adaptive, multivariate evolution. By examining a large number of traits expressed both early and late in the life cycle of the winter annual C. verna, I explore how maternal inheritance changes through ontogeny. In addition, I compare how genetic correlations among traits within a generation differ from the between-generation genetic correlations associated with maternal inheritance. The goal is to describe the underlying genetic architecture of maternal inheritance and its implication for evolution by natural selection.


Study Species

Collinsia verna (Scrophulariaceae), a winter annual plant, germinates in the fall in response to diurnal temperature fluctuations (Baskin and Baskin 1983), overwinters under the leaf litter and snow as a small rosette, and bolts and flowers in mid to late May in mesic floodplain forests throughout the Midwest. Seed and seedling traits vary significantly among maternal families (Thiede, unpubl. data), suggesting the likelihood of maternal inheritance early in the life cycle. Seed and seedling traits also strongly influence individual survival and fecundity (Kalisz 1986; Thiede 1996). Thus, maternal inheritance is also likely to affect adaptive evolution. In this study, I consider traits expressed at four stages in the life cycle: seed, seedling, overwintering fall rosette, and preflowering spring rosette (Table 2). By considering the same trait at multiple stages, I evaluate the magnitude of maternal inheritance through ontogeny.

In Dickerson's (1947) model, estimates of causal components of variance and covariance are obtained by partitioning the phenotypic covariances among relatives (Table 1) for traits hypothesized to be influenced by maternal effects. In this approach a single trait is measured in various relatives, whereas the maternal trait exerting the effect is not quantified. The magnitude of the maternal components is estimated solely by partitioning the covariance of the trait of interest into causal components, assuming different models of inheritance. In essence, this design treats the maternal effect as a composite of all maternal traits that influence a particular trait in the offspring (Cheverud 1984; Cheverud and Moore 1994).

Three-Generation Breeding Design

I obtained the seven types of relatives in Table 1 from a three generation breeding design [ILLUSTRATION FOR FIGURE 2 OMITTED]. In the first generation (G1), 100 wild grandmaternal individuals bearing naturally pollinated seeds were collected every 2 m along a 200-m transect from a natural population of C. verna in Kalamazoo County, Michigan, in May 1991. Twelve seeds from each grandmaternal plant founded the second generation (G2), which was grown to maturity in the greenhouse. The G2 individuals contributed to the estimates in one of two ways: (1) a subset of individuals served as parents in the nested breeding design to generate the third generation (see below); and (2) the remaining individuals were classified as parental relatives [ILLUSTRATION FOR FIGURE 2 OMITTED]. To determine the coefficients of causal components for parental relatives (Table 1), I assumed that G2 individuals within a G1 grandmaternal family were full-sibs produced by natural outcrossing. This assumption is justified because the outcrossing rate in this population was consistently greater than 0.85 for three years (including 1991). Furthermore, estimates of correlated mating from Ritland's (1994) multilocus mating system program based on the same electophoretic alleles suggest that these outcrossed individuals share the same father (Thiede, unpubl. data; for a statistical description of correlated mating estimates, see Ritland 1989).

To produce the third generation, a single individual (G2) from each grandmaternal family was randomly assigned to serve as a parent (either a sire or dam) in a nested breeding design in May 1992. Twenty-four sires were crossed to three dams per sire in a standard nested design to generate 24 paternal half-sib and 72 maternal full-sib families [ILLUSTRATION FOR FIGURE 2 OMITTED]. Flowers were emasculated in bud and pollinated within five days postemasculation. Pollinations were performed on all floral whorls to control for position effects. Fruits were harvested as they matured. An accident in the laboratory eliminated 10 maternal full-sib families, resulting in a total of 62 maternal full-sib families.

The third generation (G3) was planted in a randomized block design in two locations: greenhouse (n = 871 offspring from 24 sires and 58 dams) and field (n = 1212 offspring from 24 sires and 62 dams). Seeds were planted to a depth of 1 cm in Sunshine seedling mix (Premier Horticulture, Inc.) either in 96 well trays (greenhouse) or in 2-cm long plastic tubes that were 16 mm in diameter (field). In both locations one individual from each maternal full-sib family was planted into each of 20 blocks. In the greenhouse each block consisted of a 96 well tray, all 20 on a single bench in the greenhouse. In the field each block of G3 individuals was divided into three sets of 24, and each set was then randomly assigned to one of three 0.5-[m.sup.2] quadrats at one of 20 locations. The addition of 24 seeds and/or seedlings per 0.5 [m.sup.2] did not elevate densities beyond the natural range of densities at any life stage. The 20 blocks spanned the natural habitat and included forest edge and interior sites.

Traits Measured through Ontogeny

To estimate maternal inheritance, I measured the same trait in the G2 and G3 generations: 10 traits at four stages in the life cycle in the greenhouse or four traits at three stages in the field (Table 2). Prior to planting, seeds were weighed to the nearest 0.1 [[micro]gram]. After seedling emergence, seed coats were carefully excavated from the soil, air dried, and weighed (G2 and G3 in greenhouse only). Embryo weight was calculated as the difference between seed weight and seed coat weight. Embryo weight more accurately reflects the diploid component of the seed compared with total seed weight, which contains both the embryo, a small amount of residual endosperm, and the maternal seed coat.

Seedling emergence date was scored weekly in the field (G3) and every three to four days in the greenhouse (G2 and G3) from September to the beginning of December. Emergence date was defined as the first day when cotyledons were expanded. At emergence, I quantified seedling size by measuring cotyledon diameter. In the G2 generation, cotyledon diameter at emergence was the average of cotyledon length and width. In the G3 generation, maximum cotyledon diameter was measured using a template of circles of increasing diameter in increments of 0.5 mm.

At two subsequent stages, in late fall prior to overwintering and in early spring prior to flowering, I quantified individual size by measuring three traits: cotyledon diameter, length of the most basal leaf (mm), and number of leaves. Fall rosettes were measured in November (G2) or early December (G3). Cotyledon diameter was measured as cotyledon length (G2) or maximum cotyledon diameter using circular templates (G3). In December, greenhouse-grown plants (G2 and G3) were transferred to a sheltered area outdoors and covered with a thick layer of leaf litter to mimic natural field conditions. Overwintering survival was greater than 90%. In April I returned plants to the greenhouse and transplanted a random subset of two to three individuals per maternal grand-dam (G2) or all seedlings (G3) into 15-[cm.sup.2] pots filled with a 2:1:1 mix of Sunshine seedling mix (Premier Horticulture, Inc.), perlite (Silbrico Corporation), and turface (Applied Industrial Materials Corp.). Size traits were measured on preflowering spring rosettes (G2 and G3) after transplanting.

Estimation of Genetic and Environmental Causal Components

Estimation Models. - I estimated six of the nine causal components relevant to maternal inheritance (Table 1), additive ([Mathematical Expression Omitted], [Mathematical Expression Omitted], [[Sigma].sub.[A.sub.0][A.sub.m]]) and environmental components ([Mathematical Expression Omitted], [Mathematical Expression Omitted], [[Sigma].sub.[E.sub.0][E.sub.m]]) by considering three sequential models of inheritance in a hierarchical approach [ILLUSTRATION FOR FIGURE 1 OMITTED]. The simplest model of inheritance was a purely additive Mendelian model ([ILLUSTRATION FOR FIGURE 1A OMITTED], hereafter model 1) in which [Mathematical Expression Omitted] and [Mathematical Expression Omitted] were estimated. In model 2, maternal inheritance was incorporated by estimating three additional components, [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted], [ILLUSTRATION FOR FIGURE 1B OMITTED]. In model 3, all six additive and environmental covariances were considered by including [[Sigma].sub.[E.sub.o][E.sub.m]] [ILLUSTRATION FOR FIGURE 1C OMITTED]. The hierarchical approach allowed me to ask: (1) Did the more complex estimation model for maternal inheritance better describe the data? (2) Which causal components were significant in each estimation model?

In addition to standard quantitative genetic assumptions of random mating, linkage equilibrium, and the absence of epistasis and of genotype-by-environment interactions (Wilham 1963; Eisen 1967; Thompson 1976), the three hierarchical models described above, required the assumption that direct and maternal dominance variances and their covariance ([Mathematical Expression Omitted], [Mathematical Expression Omitted], [[Sigma].sub.[D.sub.o][D.sub.m]]) were zero. It is common to estimate only the additive and environmental components of maternal inheritance (e.g., Bondari et al. 1978; Meyer 1992b; Shi et al. 1993) because it is very difficult to obtain all the kinds of relatives needed to estimate all nine components including dominance (Table 1; for an example of the design required for the full model, see Cantet et. al. 1988). To test the assumption of zero dominance variances and covariance, I included them in some preliminary analyses and found no evidence for direct or maternal dominance variances.

The nature of maternal inheritance dictates that direct and maternal components of variance are correlated in maternal lineages (Table 1). This biological reality results in a statistical limitation in estimation because causal components are correlated even when numerous types of relatives are considered (Eisen 1967; Thompson 1976; Foulley and Lefort 1978; Wilham 1980; Meyer 1992a). A correlation analysis of the coefficients of the variance components from the linear equations in Table 1 demonstrates that for the types of relatives obtained from the breeding design in this study many of the variance components are correlated. Because [Mathematical Expression Omitted] and [Mathematical Expression Omitted] were perfectly correlated, only [Mathematical Expression Omitted], [Mathematical Expression Omitted], or their sum was estimable. The maternal component, [Mathematical Expression Omitted], was positively correlated with [[Sigma].sub.[A.sub.o][A.sub.m]], and [Mathematical Expression Omitted] (r = 0.85, 0.80, 0.80, respectively, P [less than] 0.05 for all) and direct components, [Mathematical Expression Omitted] and [Mathematical Expression Omitted], were also positively correlated (r = 0.94, P [less than] 0.001). However, even in more complicated designs involving 10-13 types of relatives, Eisen (1967) found similar correlations among causal components. Thus, the inclusion of more types of relatives did not necessarily decrease correlations among causal components. Experimentally decoupling direct and maternal transmission (e.g., Riska et al. 1985; Cowley 1991; Sinervo 1991) or using second cousins in which direct and maternal effects are less confounded (Wilham 1980) are possible alternatives to this approach. The inability to estimate all nine causal components and the high sampling correlation between components are statistical limitations of this approach. Nevertheless, predicting response to selection of a maternally inherited trait hinges on this detailed partitioning of the variance.

Restricted Maximum Likelihood Analysis. - To estimate the causal components of variance and covariance, I employed a modified version of a six-component restricted maximum-likelihood (REML) program (Shaw 1987; Shaw and Shaw 1992). REML is not sensitive to lack of balance in the data, is flexible in handling nonstandard designs, and assumes multivariate normality (Shaw 1987; Meyer 1992a; Thompson and Shaw 1992).

Each normally distributed trait was analyzed separately to estimate the causal components related to maternal inheritance. A fixed effect for generation was included in each model because trait means differed between G2 and G3 generations (Table 2) and including a fixed generation effect in the model resulted in higher likelihoods. The convergence criterion determining the termination of iterations was set at 0.001. Non-negativity constraints on causal component estimates were not imposed because of their adverse effect on significance tests (Shaw 1987).

The log-likelihood ratio test was utilized to evaluate significance in two contexts. First, I evaluated the significance of the models by calculating twice the difference in log-likelihoods for sequential models (1-3). This statistic has a chi-squared distribution with degrees of freedom determined by the difference in the number of components estimated in the two models (Shaw 1987; Shaw and Shaw 1992). Second, I utilized this test to evaluate the significance of all components (except [E.sub.o]) within a given model. To test the significance of each component, I constrained the component of interest to be zero, obtained the log-likelihood of the constrained model, and compared twice the difference in log-likelihoods between the constrained and full models to a chi-squared distribution with one degree of freedom.

The estimates of variance components were used to calculate direct and maternal heritabilities and direct-maternal genetic correlations. Resampling methods required to determine the standard errors around these heritabilities and genetic correlations would require inordinate computing time. Here I indicate the significance of heritabilities and genetic correlations based on the significance of the variance components in the numerator of each respective ratio. A conservative interpretation of significance in this case reflects the potential for evolutionary response, but not the rate of evolutionary response (Shaw and Platenkamp 1993). The calculation of total heritability has several components in the numerator (eq. 1) and, therefore, no significance is indicated.

An important assumption of this REML analysis is the independence of residual effects, that is, that the contribution of random environmental effects contributing to each individual's phenotype is uncorrelated among individuals and therefore does not affect their phenotypic covariance. This study was specifically designed to estimate maternal effects which if not included in an analysis can lead to the violation of this assumption. The presence of [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [[Sigma].sub.[D.sub.o][D.sub.m]], or other factors such as uniparental or cytoplasmic inheritance could have inflated some phenotypic covariances and thus violate the assumption of independent and random error terms (for models incorporating cytoplasmic inheritance, see Lynch and Walsh 1998). A second bias resulted from not estimating m, the maternal effect coefficient, a scaling factor for maternal phenotypic effects that affected the dam-offspring covariance. A bias in some estimates would necessarily result in errors in the estimation of all components because they are estimated simultaneously.

Within-Generation Genetic Correlations. - Genetic correlations among traits are referred to as within-generation genetic correlations to distinguish them from the between-generation genetic correlations associated with maternal inheritance. To estimate within-generation genetic correlations among traits, I considered each pairwise combination of traits in two hierarchical models, Mendelian inheritance in model 4 [ILLUSTRATION FOR FIGURE 3A OMITTED] and maternal inheritance in model 5 [ILLUSTRATION FOR FIGURE 3B OMITTED]. In model 4, I included only the direct additive ([Mathematical Expression Omitted]) and environmental components ([Mathematical Expression Omitted]) for each trait as well as their respective covariances ([[Sigma].sub.[A.sub.o1][A.sub.o2]], [[Sigma].sub.[E.sub.o1][E.sub.o2]]) to estimate direct genetic correlations ([r.sub.[A.sub.o1][A.sub.o2]]), path coefficient 1[ILLUSTRATION FOR FIGURE 3A OMITTED]. In model 5, I incorporated the components relevant to maternal inheritance to estimate two types of within-generation genetic correlations: direct ([r.sub.[A.sub.o1][A.sub.o2]]) and maternal ([r.sub.[A.sub.m1][A.sub.m2]]; [ILLUSTRATION FOR FIGURE 3B OMITTED]). However, the structure of the bivariate model depended on the results of the separate analysis of each trait. For example, in Figure 3B I show all possible components that would be estimated if both traits were best described separately by model 3 [ILLUSTRATION FOR FIGURE 1C OMITTED]. If both traits were described separately by model 2 [ILLUSTRATION FOR FIGURE 1B OMITTED]), then the direct-maternal environmental covariances ([[Sigma].sub.[E.sub.o][E.sub.m]]) would not be estimated. Thus, the structure of model 5 varied depending on the traits included. I estimated direct and maternal genetic correlations when both traits displayed maternal inheritance or only direct genetic correlations when only one trait displayed maternal inheritance. All covariances were unconstrained (i.e., ([[Sigma].sub.[A.sub.o1][A.sub.o2]], [[Sigma].sub.[E.sub.o1][E.sub.o2]], [[Sigma].sub.[A.sub.m1][A.sub.m2]], [[Sigma].sub.[E.sub.m1][E.sub.m2]]) except the covariances between traits for direct-maternal additive covariance ([[Sigma].sub.[A.sub.o][A.sub.m1][A.sub.o][A.sub.m2]]) and direct-maternal environmental covariance ([[Sigma].sub.[E.sub.o][E.sub.m1][E.sub.o][E.sub.m2]]) components that were constrained to zero.


Maternal Inheritance

The hierarchical analysis demonstrated that the inclusion of causal components related to maternal inheritance (models 2 and 3 in [ILLUSTRATION FOR FIGURE 1 OMITTED]) significantly improved the likelihood for a number of traits expressed throughout the life cycle (Table 3). In the greenhouse, six of 10 traits are best described by maternal inheritance (Table 3, [ILLUSTRATION FOR FIGURE 4A OMITTED]), however the causal components contributing to maternal inheritance change over the course of development. Early in the life cycle, maternal inheritance for seed weight and embryo weight is best described by the most complete maternal inheritance model, model 3. Traits expressed beyond the seed stage exhibit both Mendelian and maternal inheritance, with maternally inherited traits best described by model 2, the simpler maternal inheritance model.

Four components contribute to phenotypic variation in seed and embryo weight: [Mathematical Expression Omitted], [Mathematical Expression Omitted], [[Sigma].sub.[A.sub.o][A.sub.m]], and [[Sigma].sub.[E.sub.o][E.sub.m]] (Table 3, [ILLUSTRATION FOR FIGURE 4A OMITTED]). Maternal additive genetic variances ([Mathematical Expression Omitted]) are two to three times as large as direct additive genetic variances ([Mathematical Expression Omitted]). Direct-maternal additive genetic covariances are negative. Maternal environmental variances ([Mathematical Expression Omitted]) are small, presumably as a result of relatively uniform environmental conditions in the greenhouse. The positive covariance in environmental effects ([[Sigma].sub.[E.sub.o][E.sub.m]]) results from the temporal overlap of environmental conditions in the mother and her young at this stage. For all traits expressed beyond the seed stage, the covariance in environmental effects does not appear to contribute to the resemblance between mothers and offspring, most likely because both parents and offspring were randomized across environmental conditions. The magnitude of these four components in model 3 is similar for seed weight in the field [ILLUSTRATION FOR FIGURE 4B OMITTED], however, the trait is best described by model 2 in which only the maternal environmental component is significant (Table 3).

In the seedling stage, three variance components contribute to the phenotypic value for cotyledon diameter at emergence in the greenhouse: [Mathematical Expression Omitted], [Mathematical Expression Omitted], and negative [[Sigma].sub.[A.sub.o][A.sub.m]] (Table 3, [ILLUSTRATION FOR FIGURE 4A OMITTED]). Direct and maternal additive effects are more similar in magnitude when compared to seed traits. In the field, cotyledon diameter is best described by the strictly Mendelian model (Table 3, [ILLUSTRATION FOR FIGURE 4B OMITTED]). Emergence time is best described by Mendelian inheritance both in the field and greenhouse. The pattern of maternal inheritance for cotyledon diameter in the greenhouse remains the same throughout subsequent stages in the life cycle (Table 3, [ILLUSTRATION FOR FIGURE 4A OMITTED]) with three additive genetic components contributing to an individual's phenotypic value. Because variance components were not constrained to be positive, [Mathematical Expression Omitted] was negative for a number of traits and, therefore, outside the range of feasible values. Non-significance of [Mathematical Expression Omitted] indicates that this component is not different from zero, while a significantly negative [Mathematical Expression Omitted] suggests some other variance component is inflated.

Size-related traits at later stages in the life cycle show both Mendelian and maternal inheritance. The number of leaves and leaf length show no additive genetic variation when traits are expressed in fall rosettes in the greenhouse (Table 3, [ILLUSTRATION FOR FIGURE 4A OMITTED]). However, prior to flowering in the spring, leaf length displays the same pattern of maternal inheritance as cotyledon diameter at all three stages (Table 3). In contrast, the number of leaves displays Mendelian inheritance in the spring (Table 3).

The structure of maternal inheritance appears to differ between the field and greenhouse environments. Seed weight is maternally inherited in both environments, but the best model differs between environments. Emergence week is best described by Mendelian inheritance in both environments, although incorporating maternal inheritance (model 2) marginally improved the log-likelihood in the field. Expressed in the field, cotyledon diameter at emergence does not display maternal inheritance, however, it does at all three stages in the greenhouse.

These results indicate that the resemblance between mothers and offspring, maternal relatives and offspring, and full-sibs will be influenced by maternal inheritance for a number of traits (Table 1, [ILLUSTRATION FOR FIGURE 1 OMITTED]). For example, mothers and their offspring resemble each other in embryo weight (Table 3, [ILLUSTRATION FOR FIGURE 1C OMITTED]) because (1) offspring inherit genes for embryo weight from their mother, ([Mathematical Expression Omitted] incorporated in path coefficient 1); (2) mothers possess heritable maternal traits (i.e., provisioning) that influence embryo weight in their offspring ([Mathematical Expression Omitted] incorporated in path coefficient 3); and (3) the environment that offspring experience is similar to the environment that influences maternal performance ([[Sigma].sub.[E.sub.o][E.sub.m]] incorporated in path coefficient 7). This mother-offspring resemblance is decreased because mothers and their offspring possess genes that differ in their effect on embryo weight ([[Sigma].sub.[A.sub.o][A.sub.m]] incorporated in path coefficient 5). Mothers that produce heavier embryos as a result of their maternal attributes ([]) also possess genes for-lighter embryos ([A.sub.ow]) and transmit these genes to their offspring ([A.sub.ox]), whereas mothers with poor provisioning possess genes for heavy embryos. This negative genetic correlation decreases the resemblance not only between mothers and their offspring, but also between four other classes of relatives including sire-offspring (Table 1).

Direct, Maternal, and Total Heritabilities

Direct, maternal, and total heritabilities reflect the extent to which [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [[Sigma].sub.[A.sub.o][A.sub.m]] contribute to the total phenotypic variance and influence response to selection. For models best describing the inheritance of each trait, maternal heritabilities were greater than direct heritabilities early in the life cycle for maternally inherited traits, seed weight and embryo weight (Table 4, [ILLUSTRATION FOR FIGURE 5 OMITTED]. Subsequently, maternally inherited traits had significant direct and maternal heritabilities that were similar in magnitude (Table 4, [ILLUSTRATION FOR FIGURE 5 OMITTED]).

For maternally inherited traits, total response to selection is a function of [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [[Sigma].sub.[A.sub.o][A.sub.m]] (eq. 1). Despite substantial and significant [Mathematical Expression Omitted] and [Mathematical Expression Omitted] for a number of traits, total heritabilities were near zero or negative (Table 4, [ILLUSTRATION FOR FIGURE 5 OMITTED]) because [[Sigma].sub.[A.sub.o][A.sub.m]] tended to be negative (Table 3). Negative covariances resulted in negative genetic correlations for most traits (Table 4) indicating that only alleles that differed in their effects on individual phenotype and maternal performance were maintained. The prediction from the total heritabilities is that phenotypic selection on a single trait would produce reversed response to selection for seed weight and embryo weight and minimal responses for maternally inherited traits from the seedling stage onward.

Model Comparison

The absolute magnitude of the causal components [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [[Sigma].sub.[A.sub.o][A.sub.m]] differs among the three models of inheritance [ILLUSTRATION FOR FIGURE 4 OMITTED] and consequently affects the relative magnitude of direct, maternal, and total heritabilities among models [ILLUSTRATION FOR FIGURE 5 OMITTED]. The inclusion of additional causal components in estimation will necessarily change the estimates of the components common to both models. However, this comparison of models does allow us to evaluate how the assumption of Mendelian inheritance may bias our view of response to selection. When maternal effects biased the estimation (model 1), most traits displayed substantial to moderate heritabilities from early to late in the life cycle, indicating that most traits would be capable of responding to selection [ILLUSTRATION FOR FIGURE 5 OMITTED]. However, incorporating maternal inheritance (model 2 or 3) decreases the direct heritabilities early in the life cycle relative to model 1 and increases them later in life for traits displaying maternal inheritance. In addition, the estimate of the total heritability obtained by incorporating maternal inheritance shows that in all models including maternal inheritance decreases the predicted rate of response to selection relative to model 1. The comparison of the models is particularly interesting for seed weight. In the greenhouse, the rate of response under Mendelian inheritance (model 1) and maternal inheritance (models 2 and 3) would be 56%, 12%, and - 19% (i.e., in the opposite direction to selection), respectively. In model 2, the total heritability is greater than direct heritability because the direct-maternal additive genetic correlation is positive. Therefore, maternal inheritance accelerates the predicted response in model 2. In contrast, the negative direct-maternal genetic correlation in model 3 generates a negative total heritability. Thus, the incorporation of maternal inheritance dramatically alters predicted responses to selection from standard Mendelian models and shows that maternal inheritance can both accelerate and reverse responses to selection.

Maternal Effects at Different Stages in Ontogeny

For the three size traits measured in the greenhouse at multiple stages in the life cycle, maternal heritabilities did not decrease through ontogeny [ILLUSTRATION FOR FIGURE 6 OMITTED]. For cotyledon diameter, best described at all stages by model 2, significant maternal and direct heritabilities were similar in magnitude from emergence to spring. Leaf length displayed no heritable variation in the fall (model 1) and significant direct and maternal heritabilities in the spring (model 2), demonstrating an increase in maternal inheritance through ontogeny. Number of leaves displayed no heritable variation in fall or spring (model 1). For cotyledon diameter at all stages and spring leaf length, the total heritabilities remained at low values because of the negative [[Sigma].sub.[A.sub.o][A.sub.m]].

Within-Generation Genetic Correlations

In contrast to between-generation genetic correlations (Table 4), within-generation genetic correlations calculated from a strictly Mendelian model [ILLUSTRATION FOR FIGURE 3A OMITTED] were positive among a number of size-related traits (Table 5). Seed weight and embryo weight were both positively correlated with cotyledon diameter at all three stages in the greenhouse, and seed weight and cotyledon diameter at emergence were also positively correlated in the field. Other traits in the greenhouse showed the following pattern. Cotyledon diameter at emergence was positively correlated with cotyledon diameter at the two subsequent stages with a value close to one. Embryo weight and cotyledon diameter at emergence were also positively correlated with spring leaf length. Emergence date was positively correlated with seed weight, embryo weight, and spring [TABULAR DATA FOR TABLE 3 OMITTED] cotyledon diameter, and negatively correlated with fall number of leaves, the only significant, negative correlation.

When maternal effects were included in the estimation of genetic correlations [ILLUSTRATION FOR FIGURE 3B OMITTED], 31 of 34 estimation models that converged showed improvement in log-likelihood. Direct genetic correlations were smaller in magnitude and differed [TABULAR DATA FOR TABLE 4 OMITTED] in significance from those estimated in a strictly Mendelian model (Table 5). Seed weight was positively correlated with cotyledon diameter at emergence in the field and with fall and spring cotyledon diameter in the greenhouse. Emergence date was also positively correlated with spring cotyledon diameter in the greenhouse. Fall number of leaves and spring cotyledon diameter were negatively correlated in the greenhouse. Three trait pairs that showed genetic correlations close to a value of one in the simpler Mendelian model did not converge under maternal inheritance (Table 5). Maternal genetic correlations were not significant for any estimation model in which they were included. Only one trait pair, spring leaf length and fall cotyledon diameter, displayed a large positive value ([r.sub.[A.sub.m1][A.sub.m2]] = 0.73), however, significance tests for this component did not converge. Therefore, this study did not provide compelling evidence of maternal genetic correlations.


The most significant result in this study is the effect of maternal inheritance on predicted response to selection. Negative genetic correlations between the direct additive and maternal additive effects ([r.sub.[A.sub.o][A.sub.m]]) result in total heritabilities near zero for traits expressed at all stages in the life cycle. These negative correlations are so large early in life that seed and embryo weight exhibit negative total heritabilities, resulting in predicted selection response in the opposite direction to selection. The structure of maternal inheritance in C. verna is such that transgenerational effects of a mother on her offspring dramatically constrain the evolutionary response of traits expressed both early and late in the life cycle. It is also interesting that maternal inheritance persists throughout the life cycle in this annual plant. Below I summarize the pattern of maternal inheritance and its consequence for adaptive evolution.

Maternal Inheritance

This hierarchical analysis clearly shows that the magnitude and structure of maternal inheritance changes throughout the life cycle. Seed traits are influenced more by genes expressed in the mother than by genes expressed in the individual embryo with strong, negative genetic correlations between direct and maternal components (Table 3; [ILLUSTRATION FOR FIGURES 4, 5 OMITTED]). Furthermore, the temporal overlap of maternal and offspring environments early in life likely generates the positive covariance between maternal and offspring environments. Subsequently, traits in the seedling and rosette stages show both Mendelian and maternal inheritance. In all cases, the simpler, five-component model best describes maternally inherited traits because randomization eliminated all potential for covariance between offspring and maternal environments. Genes expressed in the mother and genes expressed in the offspring contribute more equally to phenotypic expression and strong, negative genetic correlations between maternal and direct components persist for maternally inherited traits. Maternal environmental effects appear minimal for most traits, not a surprising result because mothers were raised in uniform conditions in the greenhouse.

Two traits, seed weight and cotyledon diameter, are best described by different inheritance models in field and greenhouse environments (Table 3). It is not unusual for causal components of variance to differ between environments (e.g., Mazer and Schick 1991; Montalvo and Shaw 1994). Growing offspring in two environments suggests that maternal effects depend on the offspring environment, a result consistent with other studies (Stratton 1989; Schmitt et al. 1992; Schmid and Dolt 1994). In this study, inheritance may differ between environments because the census interval differed; cotyledon diameter was measured weekly or twice per week in the field and greenhouse, respectively. As a result, I expected and observed larger variances associated with these two traits in the field (Table 2). Although others have focused on the magnitude of genotype-by-environment interactions, their impact on maternal effects, and their role in the evolution of traits across environments (Schmitt et al. 1992; Platenkamp and Shaw 1993; Schmid and Dolt 1994; Galloway 1995), the detailed partitioning of maternal effects into explicit, specific causal components related to maternal inheritance in this study shows that maternal inheritance may depend on the environment of the offspring and will constrain the evolution of traits within an environment due to large negative direct-maternal genetic covariances for most traits.

In natural plant populations, the magnitude of maternal effects have been investigated using diallel designs (e.g., Antonovics and Schmitt 1986; Mazer 1987; Biere 1991; Kelly 1993; Montalvo and Shaw 1994), nested breeding designs (Mitchell-Olds 1986; Mitchell-Olds and Bergelson 1990; Schwaegerle and Levin 1991), and clones (Biere 1991; Schmitt et al. 1992; Schmid and Dolt 1994; Galloway 1995). Unlike the multigeneration approach presented in this study (see also Platenkamp and Shaw 1993; Byers et al. 1997), these studies do not provide estimates of specific causal components related to maternal inheritance, but do allow one to compare the magnitude of maternal genetic versus environmental effects, as well as to measure specific genotype-by-environment interactions.

The general pattern of maternal effects documented in this study is consistent with previous studies. Seed weight exhibits low direct heritabilities and substantial maternal effects, whereas the influence of maternal effects on emergence date varies among studies (Biere 1991; Kelly 1993; Montalvo and Shaw 1994; Schmid and Dolt 1994; Byers et al. 1997). Subsequent size-related traits exhibit moderate direct heritabilities and maternal genetic effects in some studies (Biere 1991; Schmid and Dolt 1994), but not in others (Montalvo and Shaw 1994). Maternal genetic effects generally decline through the life cycle (Biere 1991; Montalvo and Shaw 1994; Schmid and Dolt 1994). Using a more explicit maternal inheritance model, I was able to show that maternal genetic effects continue to contribute significantly to phenotypic variation all the way through the life cycle for two of three traits ([ILLUSTRATION FOR FIGURE 6 OMITTED]; for another exception see Schmid and Dolt 1994). Maternal genetic effects contributed more to the phenotypic variance than maternal environmental effects in this study as well as in others (Biere 1991; Schmid and Dolt 1994). However, there is ample evidence that maternal genotype-by-environment interactions may eliminate the direct maternal genetic effect when maternal genotypes are replicated across contrasting environments (Schmitt et al. 1992; Platenkamp and Shaw 1993; Schmid and Dolt 1994). These genotype-by-environment interactions for maternal effects should not obscure maternal genetic effects in this study because all mothers were raised under relatively uniform greenhouse conditions. However, understanding the impact of maternal genotype-by-environment interactions on the evolution of maternally inherited traits hinges on the development of theoretical models that incorporate these higher-order interactions in the response to selection (for a possible model, see Rossiter 1996).

Evolutionary Consequences of Maternal Inheritance

The advantage of the multi-generation design in this study is that estimation of specific causal components related to maternal inheritance allows explicit predictions about evolutionary responses to selection. Previous studies of maternal effects have often suggested that response to selection on juvenile traits such as seed mass or emergence time will be slower (i.e., Antonovics and Schmitt 1986; Roach and Wulff 1987; Biere 1991) because maternal genetic effects mask the small amount of zygotic genetic variation. Several authors have suggested that selection may act solely on the maternal genetic variation for juvenile traits lacking direct additive genetic variation (Biere 1991; Platenkamp and Shaw 1993; Montalvo and Shaw 1994; Schmid and Dolt 1994). It is, of course, possible for selection to differentiate among offspring and also among mothers. The resulting response to multiple levels of selection will depend critically on the genetic variance for both offspring phenotype and maternal performance. The strength of the approach presented here is that it allows one to evaluate the response to selection, not only based on direct and maternal additive genetic variances, but also based on their covariance. This study clearly demonstrates that these direct-maternal genetic covariances will constrain selection response ([ILLUSTRATION FOR FIGURE 5 OMITTED], Table 4).

Intergenerational Covariances

Direct-maternal additive genetic covariances between maternal performance and the trait of interest in the offspring are consistently negative for six of seven traits displaying maternal inheritance (Table 3). Furthermore, the magnitude of this direct-maternal covariance is large enough to result in predicted reversed response to selection for two traits, seed weight and embryo weight. For all other traits, the negative direct-maternal covariance reduces the predicted response to selection to near zero [ILLUSTRATION FOR FIGURE 5 OMITTED]. Thus, despite substantial direct and maternal additive effects, the evolutionary potential of these traits is limited by the underlying direct-maternal additive genetic covariances.

Since Dickerson's (1947) seminal paper documenting the evolutionary consequences of maternal effects in domestic hogs, a number of animal breeders and evolutionary biologists have demonstrated negative direct-maternal additive genetic covariances (Young and Legates 1965; Bondari et al. 1978; van Sanford and Matzinger 1982; Cantet et al. 1988; Southwood and Kennedy 1990; Meyer 1992b; Shi et al. 1993). Others utilizing Falconer's (1965) simplified approach have demonstrated negative maternal effect coefficients (m). Negative m's have been found for litter size in mice (Falconer 1955, 1965), age to maturity in springtails (Janssen et al. 1988), and clutch size and condition in flycatchers (Schluter and Gustafsson 1993). In some cases, the magnitude of these direct-maternal covariances or maternal effects coefficients are large enough to produce reversed responses to selection in the short term. In theory, long-term responses to consistent selection should asymptotically approach the expected rate in the absence of maternal effects (Kirkpatrick and Lande 1989). In nature, however, spatial and temporal variation in selection (e.g., Kalisz 1986; Kelly 1992; Stratton 1992) in conjunction with maternal inheritance can be expected to produce complex evolutionary dynamics.

One prominent concern among animal breeders is that estimation of direct-maternal additive genetic covariances may show a systematic bias because this causal component is often estimated to be strongly negative (Baker 1980; Meyer 1992b; Robinson 1996; Lee and Pollack 1997). Robinson (1996) showed that a small negative maternal effect coefficient could bias both the direct-maternal additive genetic covariance as well as maternal environmental variance. He suggested either including the maternal phenotype as a covariate or eliminating the dam-offspring covariance from estimation equations as alternatives for avoiding this bias (for other alternatives, see also Baker 1980 and Cantet et al. 1988). Byers et al. (1997) found that including the maternal phenotype as a covariate in estimating maternal effects on seed weight changed the direct-maternal additive genetic covariance from negative to positive, suggesting a negative maternal effect coefficient. They conclude that maternal inheritance will not reduce the response to selection. However, interpreting how the response to selection is likely to be influenced by this bias is not straightforward because the maternal effect coefficient is not incorporated in the predicted response (eq. 1), [TABULAR DATA FOR TABLE 5 OMITTED] but in other approaches has been shown to influence response. to selection (e.g., Falconer 1965). Bias as a result of not estimating the maternal effect coefficient is one possible explanation for the large direct-maternal genetic correlations observed in this study (Table 4).

Trade-offs between life-history traits have been central in the theory of life-history evolution (e.g., Williams 1957; Lande 1982). In his review of life-history trade-offs, Stearns (1992) points out that most of the theoretical and empirical literature on life history have dealt with trade-offs within an individual such as allocation to current versus future reproduction or current reproduction versus subsequent survival. However, trade-offs between generations have received less attention. This analysis of maternal effects in C. verna suggests that there is a fundamental, genetically based, intergenerational trade-off between maternal performance and offspring phenotype for six of 14 traits examined (Table 4). Perhaps the simplest explanation for the existence of antagonistic pleiotropy is that directional selection on maternal performance and/or offspring phenotype has led to the maintenance of alleles that differ in their phenotypic effect at successive life stages (Falconer 1981; for a contradictory result from artificial selection on a maternally inherited trait, see Swartz and Famula 1994). The evolutionary mechanisms that influence the sign of genetic correlations have been explored in a series of models in which the functional genetic architecture influencing the trade-off is broken into components related to resource acquisition and allocation (Charlesworth 1990; Houle 1991; de Jong and van Noordwijk 1992). Furthermore, the nature of the pleiotropic effects can influence how a genetic correlation influences correlated response to selection (Gromko 1995). Therefore, how these negative direct-maternal genetic correlations impact multivariate, adaptive evolution will depend on the functional architecture of the constraint in the multivariate framework of the genetic variance-covariance matrix (Charlesworth 1990) as well as on the nature of pleiotropy (Gromko 1995). In the simple framework of direct selection on the trait of interest, however, the prediction from the negative direct-maternal genetic correlations is that the joint evolution of maternal performance and offspring phenotype will be constrained for a number of traits at different stages in the life cycle of C. verna.

Within-Generation Covariances

In contrast to intergenerational covariances described above, most of the significant additive genetic covariances between traits within a generation are positive. Under Mendelian inheritance in model 4 [ILLUSTRATION FOR FIGURE 3A OMITTED], these positive direct genetic correlations show substantial positive pleiotropic effects for traits related to size early in the life cycle. However, when maternal inheritance is included in the estimation of these genetic correlations [ILLUSTRATION FOR FIGURE 3B OMITTED], the magnitude and significance of direct genetic correlations changes substantially (Table 5). Most correlations remain positive, but many are no longer significant. The inclusion of maternal inheritance in the estimation model reveals decreased pleiotropy. Both negative and positive correlations have been observed among size-related traits expressed at different stages in the life cycle in plants (e.g., Roach 1986; Montalvo and Shaw 1994). In general, morphological traits tend to show positive genetic correlations (Roff 1996), however, many of these estimates may be inflated by maternal effects. Although morphological traits show some pleiotropy, there is no evidence for significant genetic correlations among the unobserved maternal performance traits.

Multivariate Evolution

Equations for predicting multivariate evolution require estimates of the additive genetic variance-covariance matrix (G) for all traits as well as estimates of the selection gradient (Lande 1982; Lande and Arnold 1983). However, it is not clear how univariate estimates of direct and maternal additive components and bivariate estimates of genetic correlations between traits such as those estimated in this study translate into a multivariate G. Currently, evolutionary biologists are technically constrained from obtaining these multivariate estimates with Dickerson's (1947) genetic model for estimating maternal effects. Evidence of these technical difficulties is apparent in estimating within generation genetic correlations (Table 5) where some of the most complex models failed to converge. An alternative approach for considering the evolutionary consequences of maternal effects in a multivariate framework describes the structure of maternal inheritance by a single term, the mother-daughter covariance (Kirkpatrick and Lande 1989, 1992; Lande and Kirkpatrick 1990; Riska 1991). This covariance approach may allow us to explore the multivariate evolutionary dynamics of maternal inheritance.


This quantitative genetic analysis demonstrates that maternal inheritance will influence the evolutionary dynamics for a number of traits in this natural plant population. Traits reflecting individual size at the seed, seedling, and adult stages in the life cycle were significantly influenced both by direct and maternal additive genetic variances and their covariance. Perhaps the most significant finding is that direct-maternal additive genetic covariances are often negative, potentially constraining adaptive evolution in a natural plant population. In conjunction with direct and maternal additive genetic variances, this direct-maternal additive covariance results in predicted reversed response to selection for two traits, seed weight and embryo weight, and minimal responses to selection in traits later in the life cycle. In contrast, within-generation genetic covariances among size traits are likely to enhance selection response such that direct selection for increased seed or seedling size will result in size increases in prior or subsequent traits. The incorporation of within- and between-generation covariances in a multivariate framework for predicting response to selection remains a challenge. Although most authors have suggested that maternal effects may slow the evolutionary response by masking the zygotic genotype, this study illustrates that maternal effects have the potential either to enhance or constrain the selection response, depending on the sign and magnitude of the direct-maternal additive genetic covariance. In the study population, the joint evolution of maternal performance and individual phenotype is constrained for all traits displaying significant maternal effects, suggesting an underlying fundamental trade-off between mothers and their offspring.


This work benefited from extensive discussion with S. Kalisz; I thank her for encouragement and guidance. L. Galloway, T. Getty, K. Gross, D. Hall, C. Kelly, R. Shaw, M. Stanton, A. Tessier, and S. Tonsor provided helpful comments on earlier versions of the manuscript. I thank R. Shaw and E Shaw for modifying their maximum-likelihood program to handle the pedigrees from this design and for their insightful discussions about the analysis; Balkema Sand and Gravel Company for access to this population; and T. Derr, S. Gibb, J. Tsao, K. Thompson, and P. Woodruff for excellent field assistance. Support for this research was provided by National Science Foundation grants DEB-9224046, DEB-9421781, DIR-9113598, and a Barnett Rosenberg Fellowship from Michigan State University. This is KBS contribution no. 837.


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Author:Thiede, Denise A.
Date:Aug 1, 1998
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