The detection of plasticity genes in heterogeneous environments.
New insights into the genetic basis of plastic response have been gained (Schlichting and Pigliucci 1995; Via et al. 1995; Pigliucci 1996) since the extensive discussions by Schlichting (1986), Scheiner (1993), and Via (1993). Two possible hypotheses have been proposed to explore the genetic underpinnings for a set of phenotypic values produced in response to the environment, that is, the norm of reaction (Via et al. 1995). The allelic sensitivity hypothesis suggests that some alleles may be active in several environments with varying effects on the phenotype or that different alleles may be expressed in different environments (Via and Lande 1985, 1987; Van Tienderen 1991; Gomuliewicz and Kirkpatrick 1992). The gene regulation hypothesis assumes that regulatory loci may exert environmentally dependent phenotypes by turning on or off other (structural) genes in particular environments (Bradshaw 1965; Lynch and Gabriel 1987; Schlichting 1986, 1989; Jinks and Pooni 1988; Scheiner and Lyman 1991; Scheiner et al. 1991). Because both types of genetic mechanisms can cause plastic changes in the phenotype, either a locus showing allelic sensitivity or a regulatory locus with environment-specific action could be regarded as a plasticity gene (Via et al. 1995). However, major disputes have arisen about which kind of plasticity gene is more important in determining the norms of reaction, and whether the epistatic gene action of regulatory genes can cause the evolution of plastic responses (Scheiner 1993; Schlichting and Pigliucci 1993; Via 1993).
The genetic control of phenotypic plasticity at the individual-locus level can now be examined by using DNA-based marker mapping method (see Jansen et al. 1995). The number of quantitative trait loci (QTLs) affecting plastic response to the environment, the magnitudes of their gene effect, and their locations can be mapped throughout the genome. All these genetic parameters provide unique information to test the hypotheses proposed for the norm of reaction. Although in recent years considerable effort has been expended to identify QTLs for quantitative traits in multiple environments, especially in tomato, maize, and rice (Paterson et al. 1991; Stuber et al. 1992; Beavis and Keim 1996), none of these studies has explored the relative contributions of plasticity genes of each sort to plastic change in the phenotype.
Forest trees occupy a broad range of habitats and, thus, their distributions display high spatial environmental heterogeneities. Also, the longevity of forest trees means that temporal variation is likely to be experienced by these organisms. Although, on one hand, the genetic dissection of phenotypic plasticity is important for understanding the ecology and evolution of forest trees, their biological complexity, on the other hand, unavoidably frustrates such an effort. The questions related to the reaction norm evolution of forest trees can be addressed by using Populus as a model system (reviewed in Wu 1995). Populus trichocarpa (black cottonwood), native to the Pacific Northwest, has striking differences in morphology, anatomy, and physiology from P. deltoides (eastern cottonwood), which is naturally distributed in the eastern United States (Wu 1995). These two species were crossed to produce [F.sub.1] hybrids from which 375 [F.sub.2] progenies were further generated. Currently, a Populus genomic map based on part of these [F.sub.2] progenies has been constructed using over 300 DNA-based markers (Bradshaw et al. 1994) and QTLs for growth, morphology, and canopy structure mapped from a clonally replicated plantation (Bradshaw and Stettler 1995; Wu et al. 1997). The objectives of this study are to identify QTLs that affect phenotypic plasticity across two contrasting environments in the three-generation poplar hybrid pedigree and further compare these QTLs with those for the trait values within each environment.
MATERIALS AND METHODS
The Plant Pedigree and Linkage Map
A female P. trichocarpa clone, 93-968, from western Washington was crossed to a male P. deltoides clone, ILL-129, from central Illinois. In 1988 and 1990, two siblings of the [F.sub.1] family, 53-242 and 53-246, were crossed to generate an [F.sub.2] family with a total of 375 members. The seedlings of the [F.sub.2] progenies were cultured in a nursery at Farm 5 of the Washington State University Research and Extension Center near Puyallup, Washington.
A genetic linkage map consisting of 343 RFLP, STS, and RAPD markers was constructed based on a subset (90) of the [F.sub.2] progenies of P. trichocarpa x P. deltoides (Bradshaw et al. 1994; Bradshaw and Stettler 1995). The 19 largest linkage groups chosen are roughly equivalent to the 19 pairs of chromosomes in Populus.
In spring 1993, two experimental plantations, each including the original parents, the [F.sub.1] parents, and the 375 [F.sub.2] genotypes, were established in two contrasting environments, one east of the Cascades in Boardman, Oregon (continental), and the other west of the Cascades in the lower Columbia River Valley near Clatskanie, Oregon (maritime), using unrooted cuttings. Both plantations were laid out in the randomized complete block design with three (Clatskanie) or four replicates (Boardman) and two-tree plots (grown side by side) within each replicate at a spacing of 1.5 m x 3.0 m. The environmental conditions differ markedly between these two experimental sites. Boardman has higher temperature, higher solar radiation intensity, and lower precipitation during a growing season than Clatskanie. Also, the soil has a higher organic matter content (and therefore higher general fertility) and a low pH value near the surface at Clatskanie than Boardman. The plantation at Boardman was irrigated and fertilized during each growing season (from April to October). However, to assess the effect of watering on growth, trees in the fourth replicate received only half the amount of water relative to those in the other three replicates after year 2.
Quantitative traits used to study phenotypic plasticity included stem height, basal area, volume index, and stem allometry at two years of age. Basal diameter (and therefore area) was measured at the midpoint of the first year height increment (HTI1). Volume index was calculated using height x (basal diameter)(2) and stem allometry was expressed as the height:diameter ratio.
Measuring Phenotypic Plasticity
When discussing the sources of environmental variability, quantitative geneticists typically distinguish between predictable macroenvironment and unpredictable microenvironment (Allard and Bradshaw 1964; Jinks and Pooni 1988). An organism's internal "accidents" or "errors" of development and conditions immediately external to the organism represent examples of microenvironment. However, differences between sites as well as between natural habitats, are examples of macroenvironments. There has been much evidence to show differences in the nature of genetic control over macro- and microenvironmental sensitivities (Jinks and Mather 1955; Bucio Alanis et al. 1969; Jinks and Perkins 1970; Jinks et al. 1973; Perkins and Jinks 1973; Pooni et al. 1978). Studying phenotypic plasticity to both macro- and microenvironments is facilitated greatly by the use of clones (Sultan and Bazzaz 1993; Thomas and Bazzaz 1993; Waitt and Levin 1993). Clones permit a given genotype to be exactly repeated in multiple environments, which offers an excellent opportunity to understand variation in reaction norms at the genotype level. In this study, phenotypic response across the two contrasting plantation environments was defined as "macroenvironmental plasticity," whereas absolute difference between the two trees of the same genotype grown side by side in a small plot as "microenvironmental plasticity" (because it is due to unknown random environmental errors, which may be internal, external, or both; see above).
Determining the Genetic Mechanisms of Phenotypic Plasticity
Assuming that the value of a quantitative trait be x and y in two different environments, respectively, the phenotypic plasticity of the trait across the two environments is x - y, denoted z. Through a simple mathematical derivation, the genetic variance of z can be expressed by:
[Mathematical Expression Omitted], (1)
where [[Sigma].sub.[g.sub.x]] and [[Sigma].sub.[g.sub.y]] are the square roots of genetic variance of the trait expressed in two different environments, respectively, and [r.sub.g] is the genetic correlation of the trait values across the two environments. It can be seen that the genetic variation of phenotypic plasticity is affected by two components: the first, denoted V([[Sigma].sub.g]), is attributable to heterogeneity of genetic variance between the two environments, whereas the second, denoted L([r.sub.g]), is attributable to the lack of genetic correlations across environments. The genetic mechanisms of plastic variation can be further understood from individual structural loci affecting trait performance within each environment. The loci contributing to V([[Sigma].sub.g]) display environment-dependent genetic differentiation that is potentially mediated by regulatory genes (Schlichting and Pigliucci 1995). The loci contributing to L([r.sub.g]) cause an inconsistent change in genetic architecture by modifying their expression in varying environments. Thus, the role of regulatory loci in shaping phenotypic plasticity can be indirectly determined by testing the across-environment difference in genetic variance explained by the loci contributing to V([[Sigma].sub.g]). Those loci that are active only in a particular environment (unique locus) give a good example of gene regulation. Because the loci modifying plastic changes through allelic sensitivity lead to unparalleled performance, the genetic correlations across environments associated with these loci can be used as the criteria to test their effect on phenotypic plasticity. If [r.sub.g] resulting from a locus is significantly less than [absolute value of 1], then the allelic sensitivity of this locus is important to the genetic variation of phenotypic plasticity, although the net contribution also depends on the value of genetic variance within each environment. If [r.sub.g] resulting from the locus is significantly greater than zero, then the association between the states of a trait in two different environments results (common locus). When a common locus produces the same genetic variance between environments, no phenotypic plasticity is expected. It should be noted that regulatory loci and sensitivity loci are not totally exclusive because a locus may play a regulatory role and simultaneously display allelic sensitivity.
The genetic variance of phenotypic plasticity can also be directly partitioned into its underlying loci based on the left side of equation (1) without the consideration of the trait state in each environment. If the loci for trait states within environments are epistatically interacted with genetic background, the loci identified from the left side of equation (1) may be different from those identified from the right side. Significant effects on phenotypic plasticity but no corresponding effects on the mean in each environment exhibit direct evidence for gene regulation. The regulatory genes affect the genetic variance of phenotypic plasticity, but they do not make any direct contribution to the genetic variance of the trait in a single environment. They can be identified by excluding the loci for the trait in both environments from those for phenotypic plasticity across the two environments.
Quantitative Trait Locus Analysis
In this QTL mapping experiment, only a subset (90) of the [F.sub.2] genotypes were used to construct the Populus genomic map. Therefore, the accuracy and power for detecting a QTL may be limited due to the small number of progeny used. However, this can be largely overcome by use of clonal replicates for two reasons. First, as derived by Knapp and Bridges (1990), an additional clonal replicate of a progeny can increase statistical power, which is analogous to adding another progeny genotype if all the additive genetic variance is explained by markers (this condition may be partially met because the significant markers I identified accounted for large percentages of the genetic variance; see Results). Second, clonal replicates provide a means for excluding the contamination of the replicate and QTL x replicate interaction effects from the QTL effect, thereby increasing the accuracy of QTL identification. Because interval mapping based on maximum likelihood has not incorporated clonal replicates in the current program package, the two-way analysis of variance (ANOVA) method was used to detect the effects of QTL, replicate, and QTL x replicate interaction in the [F.sub.2] poplar progeny within each environment. At Boardman, such QTL analyses only included the first three replicates that each received a similar watering regime. The significance level of P [less than] 0.001 was chosen to declare the existence of a putative QTL associated with a marker. Assuming that the QTL effect is random, the component of quantitative genetic variance explained by the significant QTL ([Mathematical Expression Omitted]) was estimated by equating the mean squares with the expected mean squares derived from Type III sums of squares, PROC GLM (SAS Institute 1988). The percentage of the total phenotypic variance accounted for by the QTL, that is, broad-sense heritability at the single genetic locus level ([Mathematical Expression Omitted]), and its standard deviation were estimated following the procedures for estimating broad-sense heritability on the clonal mean basis (Wu and Stettler 1997). By treating different states (x and y) of the same trait expressed in two sites as separate traits, the across-environment genetic correlation contributed by a significant QTL ([r.sub.[g.sub.Q]]) was estimated using the equation:
[r.sub.[g.sub.Q]] = [[Sigma].sub.[g.sub.Qxy]]/[[Sigma].sub.[g.sub.Qx]][[Sigma].sub.[g.sub.Qy]], (2)
where [[Sigma].sub.[g.sub.Qxy]] is the genetic covariance between x and y explained by the QTL, which was estimated by equating the mean cross-products with the expected mean cross-products (SAS Institute 1988), and [[Sigma].sub.[g.sub.Qx]] and [[Sigma].sub.[g.sub.Qy]] are the genetic variance of x and y explained by the QTL, respectively.
The potential QTLs were identified for growth traits within each site and their macro- or microenvironmental plasticity, that is, the difference of trait value across the corresponding environmental type (see above). To determine the types of plasticity genes, the genetic variance of a trait is statistically compared between the two sites and the genetic correlation of the trait states across the environments tested (see above). If the genetic variance explained by a QTL in an environment is significantly different from the genetic variance explained by the same QTL in the other environment, this QTL is viewed as regulatory locus. If the across-environment genetic correlation contributed by a QTL is significantly different than one, this QTL is viewed the locus showing allelic sensitivity. The common loci that result in the across-environment genetic correlation not significantly different than one and that display the nature of regulatory genes are excluded because they do not result in genetic variance in phenotypic plasticity (see eq. 1).
The QTL analysis of microenvironmental plasticity within a site was based on absolute differences of the two trees of the same genotypes in a plot using the additive-multiplicative model (Appendix). This model can detect the QTL, replicate, and QTL X replicate interaction effects, despite the fact that only a single cell is used. However, replicates cannot be specified for macroenvironmental plasticity because it is expressed as the difference of trait value between environments. In fact, the "replicate" effect for macroenvironmental plasticity can still be determined by pairing a replicate in Boardman with the other in Clatskanie. Such pairings based on plot means have six possibilities between the two sites. A potential pairing was made for each trait using the bootstrap resampling statistical technique (Efron 1982). A hundred boostrap replicates were used to determine the probability level for the statistical test. The additive-multiplicative model was employed to estimate the variance component due to QTL differences by removing the confounding "replicate" and QTL X "replicate" interaction effects (see Appendix). Theoretically, estimates of allelic effects from the analysis of variance can be biased downward because the QTLs identified are not necessarily located at markers. However, this may not be a serious problem given an intermediately high marker density of the Populus genome map (Bradshaw and Stettler 1997).
Additive and dominant effects were calculated from the mean trait values for the [F.sub.2] trees having homozygous P. trichocarpa, homozygous P. deltoides, and heterozygous genotype at each of the significant QTLs. The mode of gene action is based on the ratio of dominance to additivity (Wu et al. 1995). For dominant RAPD markers, however, the ANOVA cannot determine the mode of QTL action because the heterozygote and a homozygote are not distinguishable. The contribution to the total phenotypic variance by multiple QTLs was estimated with the multifactor ANOVA model (SAS Institute 1988).
Heterozygosity was calculated based on codominant RFLP markers collected for each [F.sub.2] genotype at a minimum of 25 loci (Bradshaw and Stettler 1995). The relationship between the proportions of heterozygous loci and measures of phenotypic plasticity was estimated (SAS Institute 1988).
Pronounced variation was observed in phenotypic response among the mapped [F.sub.2] genotypes of P. trichocarpa x P. deltoides [ILLUSTRATION FOR FIGURE 1 OMITTED]. Below, I used the QTL mapping approach to determine the genetic basis for such significant variation in plasticity.
QTL analysis was performed within each site, with more QTLs detected for all stem traits at Boardman than Clatskanie, each explaining a larger proportion of the total phenotypic variance (Table 1). A total of four QTLs, each from a different linkage group (E, M, O, and X), significantly affected height: they were all activated at Boardman, but only one (carried by M) at Clatskanie. Thus, the three QTLs unique to Boardman may be mediated by regulatory loci. The QTL expressed in both Boardman and Clatskanie was also under the regulatory control, as evidenced by a significant environmental difference in genetic variance associated with the QTL. Yet, this QTL was sensitive in allelic effect because its resulting across-environment genetic correlation was significantly less than one. At most loci and in both environments, the P. deltoides parent contributed favorable alleles to increased height growth and displayed an overdominance effect over the P. trichocarpa allele. Of the three QTLs affecting basal area in Boardman, a QTL on linkage group J also affected the same trait in Clatskanie, with no difference in its resulting genetic variance between the two environments. However, the QTL exhibited different dominant directions between the two sites, with [r.sub.[g.sub.Q]] not significantly greater than zero. Therefore, this QTL appears to affect the phenotypic plasticity of basal area only through the environmental modification of its allelic effect. For volume index, no QTLs were detected to be shared between Boardman and Clatskanie. There were three QTLs responsible for stem allometry in Boardman, but none were detected for this trait in Clatskanie. For all traits studied, the multiple regression model combining all the significant QTLs explained approximately]0.40 of the total phenotypic variance at Boardman, whereas the corresponding value at Clatskanie was 0.07-0.17. Thus, gene regulation seems to play an important role in determining the phenotypic plasticity of stem growth. However, low across-environment genetic correlations contributed by these QTLs for basal area and volume index indicate that allelic sensitivity from structural loci may also be important for plastic response in these two traits.
The commonality of QTLs for different traits also exhibited different patterns across the two sites (Table 1). At Boardman, linkage group E was found to carry two different QTLs each for height and basal area, whereas there was no common linkage group for these two traits at Clatskanie. Two QTLs on linkage groups C and E each displayed observable pleiotropic effects on basal area and volume index in Boardman, but only a QTL on linkage group J pleiotropically affected these two traits in Clatskanie. At Boardman, the association between height and volume growth might be due to a pleiotropic QTL on linkage group O and two linked QTLs on linkage group E, whereas no shared genetic basis was found for these two traits at Clatskanie. Perhaps through linkage effects, two QTLs on linkage groups M affected the association between height and stem allometry and another two QTLs on linkage group C affected the association between basal area and stem allometry.
At Boardman, QTLs were further mapped for growth traits on trees from the fourth replicate, which was watered with half of the amount received by the other three replicates in year 2. Fewer, and in many cases different, QTLs were observed for stem growth in replicate 4 (data not shown) relative to the other replicates (Table 1).
Three or four loci had been mapped for across-environment differences of growth traits, each explaining a high proportion (0.10-0.25) of the total phenotypic variance in macroenvironmental plasticity (Table 2). Given the broad-sense heritabilities of 0.40-0.72 estimated by the additive-multiplicative model (Appendix), these QTLs explained a considerable portion of the genetic variance. It was found that some of these identified loci displayed the regulatory control over phenotypic plasticity. For example, from the four QTLs identified for the across-environment difference of height, three QTLs on linkage groups A, B, and R specifically responded to the environmental alteration from Boardman to Clatskanie or Clatskanie to Boardman, although the other QTL on linkage group M was also involved in trait variation within environments (Table 1). For both basal area and volume index, a regulatory locus identified by the across-environment difference was mapped to linkage group G. Obviously, this locus pleiotropically affects the macroenvironmental plasticity of these two traits.
The actions for the three regulatory QTLs identified from height plasticity were overdominant, that is, the plasticity of the heterozygotes transcended the range of the two homozygotes (see Wu 1997). At each QTL, the P. deltoides allele was associated with increased plasticity of height, despite no difference in plasticity between the original parents. The multiple regression model incorporating these three regulatory QTLs and a partially sensitive QTL on linkage group M accounted for 32.4% of the total phenotypic variance or 51.5% of the genetic variance. At the regulatory locus identified for basal area and volume index plasticity, the P. trichocarpa parent contributed alleles to increase plasticity for these two traits in an overdominance fashion. The regulatory QTL on linkage group G and two other QTLs on different linkage groups jointly explained about 46% of the phenotypic variance and 63-70% of the genetic variance for the macroenvironmental plasticity of basal area and volume index.
A QTL on linkage group X was detected to play a regulatory role in plasticity to soil moisture in all growth traits at Boardman (Table 3). This QTL had partial dominance to overdominance of gene action and accounted for 14-24% of the total phenotypic variance. The P. deltoides alleles at this QTL always showed an increased effect on the sensitivity of [F.sub.2] trees to watering regimes, consistent with earlier comparative observations that P. deltoides was more sensitive to water loss than P. trichocarpa (Braatne et al. 1992).
Regulatory QTLs causing microenvionmental plasticity for [TABULAR DATA FOR TABLE 1 OMITTED] growth traits were different from those for macroenvironmental plasticity and also differed between macroenvironments and traits (Table 4). In most cases, they displayed overdominant effects on plastic response to the microenvironment. At Clatskanie, a putative regulatory QTL on linkage group I was identified to affect the microenvironmental plasticity of stem height at the marginally significant level (P = 0.05) at which the P. trichocarpa alleles showed increased microenvironmental plasticity for height growth. At Boardman, no regulatory QTL was observed for height plasticity to fluctuating environments.
Boardman and Clatskanie each had a QTL that regulatorily influenced the microenvironmental plasticity of basal area. The two QTLs were located on linkage groups J and P, respectively. In Boardman, the P. trichocarpa alleles increased the microenvironmental plasticity, whereas the inverse direction was detected in Clatskanie. Two QTLs on linkage groups E and F were associated with the microenvironmental [TABULAR DATA FOR TABLE 2 OMITTED] plasticity of volume index at Boardman, whereas only a QTL on linkage group P was found at Clatskanie. On linkage groups F and P, the P. deltiodes alleles increased the microenvironmental plasticity for volume growth and were dominant to the P. trichocarpa alleles. The microenvironmental plasticity of stem allometry appeared to be affected by a QTL on linkage group B and H in Boardman and Clatskanie, respectively.
Phenotypic plasticity has been classified into two main developmental types: proportional responses and discrete or switched responses (Schlichting and Pigliucci 1995). They are called "dependent development" and "autoregulatory morphogenesis" by Schmalhausen (1949) or "phenotypic modulation" and "developmental conversion" by Smith-Gill (1983). Genetic loci that result in plastic responses to the environment are also suggested to consist of two types: regulatory loci determining response/no response and structural loci determining the amount of response. Schlichting and Pigliucci (1995) suggested that discrete responses (developmental conversion) might stem from the gene regulation of the first set, whereas proportional responses (e.g., phenotypic modulation) arise from the allelic sensitivity of the second set. However, such a correspondence relationship has been criticized by Via et al. (1995), who predicted that observed reaction norms were likely the result of interactive [TABULAR DATA FOR TABLE 3 OMITTED] influences from both types of genetic mechanisms. Although the allelic sensitivity of structural genes is potentially mediated by regulatory loci that affect the amount of gene product, the major action of a switch gene can also be modified by accompanying allelic sensitivity at structural loci. Although there is some controversy regarding the evolutionary significance of gene regulation (Scheiner 1993; Schlichting and Pigliucci 1993; Via 1993), regulatory loci, through whose action variation in structural genes is allowed, have been observed in all five biological kingdoms (Goransson et al. 1989; Dixon and Harrison 1990; Scandalios 1990; Liu and Ambros 1991; Song et al. 1991). In teosinte, for example, a "mutant" allele, tb1-teosinte, was suggested to regulate the plastic response to environments (Doebley et al. 1995); through turning this allele on or off (determined by environments), the plants produce short or long lateral branches, respectively.
In this paper, I used a combined quantitative and molecular genetic approach to detect the influence of regulatory genes and loci showing allelic sensitivity on phenotypic plasticity. Two different methods direct and indirect, were proposed to examine the effect of regulatory genes. The direct method identifies the regulatory genes by excluding the QTLs that affect trait values within environments from those for across environment differences. Through a statistical test for the significance of the difference in genetic variance explained by a QTL across environments, the indirect method can evaluate [TABULAR DATA FOR TABLE 4 OMITTED] the effect of regulatory genes on the expression of structural genes. I found that there was significant genetic variation in the response to two contrasting environments [ILLUSTRATION FOR FIGURE 1 OMITTED] and that gene regulation might play a prevailing role in determining this variation. By using the Populus genome map, many more QTLs were identified in the optimal condition of Boardman than in the suboptimal condition of Clatskanie. Such indirect evidence for gene regulation by which the expression of structural loci is mediated in a particular environment does not appear to be due to more environmental noise at Clatskanie, because the replicate and error effects were smaller at Clatskanie than Boardman, as shown by a quantitative genetic analysis (Wu and Stettler 1997). Allelic sensitivity seems to also have the effect on phenotypic plasticity, but some difference exists between stem height and basal area in the relative contribution to reaction norms by these two mechanisms. For stem height, four linkage groups carry QTLs that are likely mediated by gene regulation; a comparative QTL analysis indicates that two regulatory loci on linkage groups A and X may further add to the macroenvironmental plasticity of this trait. The relative effect on the reaction norms by gene regulation seems to be lower for basal area, because, of the three basal area QTLs, two display a regulatory influence and one is purely sensitive. In addition, only one regulatory locus was detected to affect the plasticity of basal area to the environment. For volume index and stem allometry both derived from stem height and diameter, the former was more similar to the basal area pattern and the latter was more similar to the height pattern.
The number of QTLs and the magnitude of their effects affecting a quantitative trait are a function of environment (see also Paterson et al. 1991; Beavis and Keim 1996). In a previous study, larger genetic differentiation was documented in the warm, high-radiation, and well-watered regime of the interior (Boardman) than in the cooler coastal conditions of Clatskanie (Wu and Stettler 1997). Further QTL analysis showed that this trend was likely to be due to more genes and their stronger expression in the more benign conditions of Boardman than in the stressful conditions of Clatskanie. Although height was highly associated with basal area in both environments (as reported in Wu and Stettler 1997), its genetic underpinning was observed only in Boardman where two QTLs on the same linkage group E seemed to be responsible for this association through linkage.
The genetic basis of phenotypic plasticity appeared to vary across different environmental gradients. By combining the third plantation located in Puyallup, Washington, that belongs to moderately maritime climate type, I found fewer regulatory loci underlying the norms of reaction between this plantation and either Boardman or Clatskanie (Wu 1995). Thus, it is tempting to suggest that the genetic complexity of plasticity is a function of how similar the two environments are. A more complicated genetic basis is necessary for reaction norm evolution across a pair of environments showing larger differences (e.g., continental Boardman vs. pronouncedly maritime Clatskanie) than for a pair of environments showing smaller differences (e.g., continental Boardman vs. moderately maritime Puyallup). Also, phenotypic plasticity to a single environmental factor, such as soil moisture, may display a simpler genetic basis than simultaneous responses to an interacting heterogeneity of conditions. I found that the norm of reaction across different watering regimes was affected only by a QTL on linkage group X. Thus, as suspected by Jasienski et al. (1997), potential evolutionary pressures resulting from variation in soil moisture may be qualitatively different than those caused by variation in other environmental factors. The discussion of complexity of plastic responses and environmental divergences is also discussed in Pigliucci et al. (1995).
The microenvironmental plasticity to random factors (internal or external to the organism) is under low genetic control (Wu 1997). Yet, in this study there were still some QTLs identified for the microenviromental norm of reaction sometimes at the marginal significance level (Table 4). These microenvironmental plasticity QTLs varied over macroenvironments and traits, and also differed from the QTLs for macroenvironmental plasticity and trait values within each macroenvironment. It seems possible that the genetic systems underlying microenvironmental plasticity, whose expression is contingent upon the organism, the macroenvironment, and their interaction, have been independent of the genetic systems for other developmental aspects in the long-term evolution of organisms.
I also examined the extent to which the genetic basis of phenotypic plasticity is met by Lerner's (1954) homeostasis theory (Soule 1979; Mitton and Grant 1984). I calculated the correlations between marker heterozygosity (based on RFLP markers) and macroenvironmental plasticity for all growth traits studied and found that they were nonsignificant (r = 0.05-0.11, P [greater than] 0.45). However, the effects of heterozygotes (D) at the QTLs identified are highly negative (Table 2) in most cases and, therefore, are less sensitive than homozygotes. These indicated that the homeostasis hypothesis was only held for macroenvironmental plasticity at functioning loci in the poplar pedigree. However, for microenvironmental plasticity, Lerner's theory seemed to be accepted at the whole-genome level, as evidenced by its significant relationships with marker heterozygosity (r = 0.30-0.54, P [less than] 0.05).
The understanding of the genetic basis underlying reaction norms helps to predict the evolution of phenotypic responses to the environment. If plastic responses are purely due to different expression of structural genes in different environments, current quantitative genetic models can adequately predict the (at least short-term) response of selection (Via and Lande 1985, 1987; Via 1987; Van Tienderen 1991; Gomulkiewicz and Kirkpatrick 1992). This is because most of the genetic variance expressed by structural genes is additive and because genes with epistatic effects influence the response to individual selection through their contribution to the additive genetic variance (Crow and Kimura 1970). However, if plastic responses are influenced by both structural and regulatory genes, as demonstrated in this study, it will be necessary to detect the epistatic gene action between these two sets of loci and its impact on reaction norm evolution (Schlichting and Pigliucci 1995). In this study, I uncovered strong evidence for a wide range of nonadditive effects within plasticity loci, from partial dominance to overdominance. However, epistatic effects may play an important but unrecognized role in the evolution of phenotypic plasticity, although I did not explore epistasis between plasticity loci due to a lack of a sufficiently powerful analytical method. In addition, different evolutionary dynamics for phenotypic plasticity can be expected when its genetic basis includes few major effect loci or many minor loci (Lande 1983; Schlichting and Pigliucci 1995). One of the most interesting results in this study is that a large proportion of genetic variation for phenotypic plasticity can be explained by a few QTLs with major effects; the remaining genetic variation may be due to many QTLs with small effects that cannot be detected without a more powerful experimental design. To predict the consequences of long-term selection on phenotypic plasticity, further empirical and theoretical work should be focused on the use of a combined quantitative and molecular genetic method to analyze evolutionary processes. Potentially, such work may lead to a better understanding of the mechanisms by which adaptive reaction norms evolve.
I thank R. F. Stettler, H. D. Bradshaw Jr., T. M. Hinckley, D. M. O'Mally, B.-L. Liu, Z.-B. Zeng, T. F. C. Mackay, and R. R. Sederoff for stimulating discussions regarding this work and two anonymous reviewers for critical comments on the earlier version of this manuscript. I am especially grateful to S. Via, C. Schlichting, D. Stratton, and C. Lively for thoughtful reviews that much improved the presentation of this paper. The Populus genome map was constructed by the College of Forest Resources Molecular Genetics Laboratory, University of Washington, which is directed by H. D. Bradshaw Jr. The plantations were maintained by the Washington State University Western Research and Extension Center, the Boise Cascade Corporation, and the James River Corporation.
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The traditional analysis of variance is less powerful for estimating the heritabilities of macro- and microenvironmental sensitivities as measured in this study, because the variance due to genotype x replicate interactions cannot be estimated based on plot means. Ignoring this variance component, however, would lead to an inflated estimate of the heritability of these two developmental aspects. In this study, a more robust additive-multiplicative model (Gimelfarb 1994) was applied to estimate genetic, replicate, and their interaction variance components. By assuming phenotypic plasticity as a trait, this model can be expressed by
p = g + r + [Xi]gr, (A1)
where p is the phenotypic value of macro- or microenvironmental plasticity; g and r are the genotypic and replicate contributions to p, respectively; and [Xi] is the parameter characterizing the strength of genotype X replicate interaction: there is no interaction if [Xi] = 0, whereas larger values of [Xi] indicate more multiplicative interaction. It is assumed that g and r are distributed independently of each other with the mean and variance of g denoted as [m.sub.g] and [Mathematical Expression Omitted], and with the mean and variance of r denoted as [m.sub.r] and [Mathematical Expression Omitted]. Thus, the phenotypic mean, M, and the phenotypic variance, V, are derived as:
M = [m.sub.g] + [m.sub.r] + [Xi] [m.sub.g][m.sub.r] (A2)
[Mathematical Expression Omitted], (A3)
which can be rewritten, by letting [m.sub.r] = 0, as:
M = [m.sub.g] (A4)
[Mathematical Expression Omitted]. (A5)
In this study, clone was used for each genotype. Because for a given genotype, k, the phenotypic mean is simply the genotypic contribution and the variance of the genotypic contributions equals zero, the phenotypic (or environmental) variance of this genotype was obtained as:
[Mathematical Expression Omitted]. (A6)
When a number of genotypes are included in the experimental design, [Mathematical Expression Omitted] and [Xi] can be estimated by the least squares fit of the above nonlinear equation to the dataset. Thus, by estimating [Mathematical Expression Omitted] from eq. (A5), the broad-sense heritability of phenotypic plasticity is calculated using the equation:
[Mathematical Expression Omitted]. (A7)
The model (A1) can be extended to include molecular information by partitioning g into two parts: QTL effect at a marker (q) and remaining genetic effect within QTL genotypes (w). The same procedure described above is used to estimate the remaining genetic variance within each of the three QTL genotypes. Thus, the genetic variance associated with the marker can be estimated by subtracting the sum of the three remaining genetic variances from the total genetic variance [Mathematical Expression Omitted]. The sampling variance of the marker-associated genetic variance is accordingly calculated based on its mathematical expression. The significance test for the marker-associated genetic marker is carried out by using an approximate F-statistic derived from one-way (marker) ANOVA. Generally, one should first test the significance of the marker-associated genetic variance and then estimate its value using the above additive-multiplicative model.
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