* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Marker-based inferences about fecundity genes contributing
Dominance (genetics) wikipedia , lookup
Epigenetics of depression wikipedia , lookup
Pathogenomics wikipedia , lookup
Gene desert wikipedia , lookup
Genetically modified crops wikipedia , lookup
Ridge (biology) wikipedia , lookup
Nutriepigenomics wikipedia , lookup
Epigenetics of human development wikipedia , lookup
Behavioural genetics wikipedia , lookup
Genetic engineering wikipedia , lookup
Biology and consumer behaviour wikipedia , lookup
Genomic imprinting wikipedia , lookup
Minimal genome wikipedia , lookup
Site-specific recombinase technology wikipedia , lookup
Artificial gene synthesis wikipedia , lookup
Gene expression programming wikipedia , lookup
Human genetic variation wikipedia , lookup
Public health genomics wikipedia , lookup
Population genetics wikipedia , lookup
Heritability of IQ wikipedia , lookup
Gene expression profiling wikipedia , lookup
Genome evolution wikipedia , lookup
History of genetic engineering wikipedia , lookup
Genome (book) wikipedia , lookup
Microevolution wikipedia , lookup
Designer baby wikipedia , lookup
Marker-based inferences about fecundity genes contributing to inbreeding depression in Mimulus guttatus YONC-BIFU' A N D KERMIT RITLAND Department of Botany, University of Toronto, Toronto, ON M5S 3B2, Canada Corresponding Editor: R.S. Singh Received January 1 1, 1994 Accepted July 28, 1994 K. 1994. Marker-based inferences about fecundity genes contributing to inbreeding Fu, Y.-B., and RITLAND, depression in Mimulus guttatus. Genome, 37: 1005- 10 10. Eight unlinked isozyme loci were used as genetic markers to characterize fecundity genes contributing to inbreeding depression in two selfed progeny arrays of Mimulus guttatus. Five fecundity traits were measured. Six of eight marked chromosomal segments were significantly associated with the expression of these traits. The number of genes detected for five traits in two progeny arrays varied, with an average of 2.8 genes per trait. Individual segments explained 1.44-9.29%, and together accounted for 3.85-1 1.32%, of phenotypic variation. Of 20 significant associations, 10 could be interpreted as exhibiting partial dominance, 7 overdominance, 3 partial recessivity, and 0 underdominance. Significant pairwise epistasis was rare. The results of this study suggest that inbreeding depression is caused by many deleterious genes of relatively small, partially dominant effects. Key words: linkage, isozymes, QTLs, inbreeding depression, Mimulus guttatus. Fu, Y.-B., et R I T L A N DK., 1994. Marker-based inferences about fecundity genes contributing to inbreeding depression in Mimulus guttatus. Genome, 37 : 1005- 10 10. Huit loci isoenzymatiques non lies ont kt6 employes comme marqueurs ginktiques afin de caractiriser les gknes de fkconditi qui contribuent B la perte de vigueur observke chez deux populations autoficondies de Mimulus gutratus. Cinq traits de fkconditi ont kt6 mesuris. Six des huit segments chromosomiques marquis montraient une association significative avec l'expression de ces traits. Bien que variable, le nombre de gknes ditectis pour les cinq traits chez les deux populations itait en moyenne de 2,8 gknes par trait. Pris individuellement, ces segments contribuaient de 1,44 B 9,29% de la variation phknotypique et, pris globalement, de 3,85 B 11,32% de la variation. Des 20 associations significatives, dix demontraient une dominance partielle, sept une surdominance, trois ktaient partiellement ricessives et aucune ne montrait de sousdominance. Lorsque comparis deux a deux, ces segments ont rarement montrk de l'kpistasie. Les resultats de cette etude suggkrent que la perte de vigueur associke a la consanguiniti est le produit de plusieurs gknes dilitkres aux effets partiellement dominants et de faible envergure. Mots cle's : linkage, isoenzymes, QTLs, consanguiniti, Mimulus guttatus. [Traduit par la redaction] Introduction Inbreeding depression, the reduced fitness of progeny produced by inbreeding, has been extensively studied because of its importance in many areas of biology (Darwin 1876; Charlesworth and Charlesworth 1987). Many attempts have also been made to explain this phenomenon and its inverse, heterosis ( e . g . , see Sprague 1983; Charlesworth and Charlesworth 1987; Srivastava 1991 ; Crow 1993). Among the explanations proposed for inbreeding depression, the dominance and overdominance hypotheses are predominant because they are experimentally testable. The dominance hypothesis proposes that inbreeding depression is due to expression of recessive or nearly recessive deleterious genes in homozygotes, whereas the overdominance hypothesis states that inbreeding depression is caused by the loss of heterozygosity upon inbreeding because of heterozygote superiority at specific loci (Crow 1952). The empirical evidence collected over a century seems to favor the dominance hypothesis, although overdominance is not fully rejected (Wright 1977; Simmons and Crow 1977; Charlesworth and Charlesworth 1987; Barrett and Charlesworth 199 1 ; Stuber et al. 1992; Crow 1993; Mitton 1993). However, most empirical data come from quantitative genetics studies, which 'present address: Biotechnology Laboratory, University of British Columbia, #237-6174 University Blvd., Vancouver, BC V6T 123, Canada. Pr~ntedIn Canada 1 l m p r ~ m eau Canada usually characterize only the average effects of genes in the entire genome, but not those of individual genes (Wright 1977; Mather and Jinks 1982). Thus the molecular genetic basis of inbreeding depression is still not well understood. Inbreeding depression is a complex quantitative character, presumably controlled by many deleterious genes of different magnitudes of effect (Lande and Schemske 1985; Charlesworth et al. 1990). Recent marker-based studies have been successful in characterizing individual genes (or specific marker-linked chromosome regions) affecting quantitative characters (QTLs) in cultivated plants (e.g., Paterson et al. 1988; Stuber et al. 1992). Studies using codominant markers in F, populations have further revealed a wide range of marker-associated gene actions, from additivity to overdominance (e.g., Edwards et al. 1987). These marker-based methods raise the prospect that the genetic basis of inbreeding depression in plants can be studied at a resolution not attainable by classical quantitative genetics methods. However, inbreeding depression is difficult to measure directly (Lewontin 1974) and is usually expressed at different stages of the life cycle (Schoen 1983). Different analytic methods are required to characterize genes affecting various fitness-related components such as viability and fecundity. To study viability genes, we recently developed a markerbased, graphical method for inferring the relative importance of different modes of viability gene expression (Fu and Ritland 1994). Applying this method to data of 2577 selfed 1006 GENOME, VOL. 37, 1994 500 plants in population & Parent 1 & 8 t Maximization of 15 isozyme loci for homozygotes Parent 2 & t for homozygotes & t for heterozygotes again to select the most heterozygous plants. One F, plant in each cross, heterozygous for most of marker loci, was selfed to produce the F, progeny. For clarity in reporting, these two selfed progeny arrays are denoted as F,, and F,,, respectively. A total of 1080 F, seeds (540 per cross) were sown in 15 trays in a 50:50 mixture of ProMix and Pearlite. In each 72-cell tray, 36 F, seeds from each cross were randomly chosen and each sown at random (one seed per cell with ca. 1 in.3). The trays were randomly placed in a growth room (2.5 X 3 m2) and watered once a week. All F, plants were grown at 18"C/16 h light and 10°C/8 h dark with relative humidity of 80% for 2 months from sowing on April 21, 199 1. The germination rates and seedling mortality rates were 82.4 and 5.4% for F,, and 80.2 and 4.4% for F2b. (selfed) (Phenotyping F2 for five tramits) (Genotyping F2 for eight loci) FIG. 1. Diagram of experimental procedures for constructing single crosses in M. guttatus. progeny of 31 plants of Mimulus guttatus, we found that, in the chromosomal segments identified by isozyme markers, partial dominance played a predominant role in inbreeding depression (Fu and Ritland 1994). Less attention has been paid to fecundity genes in wild plants. Fecundity genes should play an important role in expression of inbreeding depression since strong inbreeding depression usually occurs in later stages of the life cycle in many plants (e.g., see Schoen 1983 and Charlesworth and Charlesworth 1987). In this paper, we report results of a marker-based study of fecundity genes contributing to inbreeding depression in t w o selfed p r o g e n y a r r a y s o f Mimulus g u t t a t u s D C (Scrophulariaceae), the common yellow monkeyflower. This plant (2n = 28) occurs throughout western North America in moist areas such as wet meadows, streambanks, or roadsides, and has many bee-pollinated, self-compatible flowers (Vickery 1978). This species exhibits a wide range of selfing rates in populations (with an average of 30-40%) and significant inbreeding depression in selfed progeny, with an average of 40-60% (Ritland and Ganders 1987; Ritland 1990; Dole and Ritland 1993; Willis 1993; Latta and Ritland 1994). This study was conducted using isozyme markers to infer (i) the minimum number of genes affecting five fecundity traits, (ii) the magnitude of the gene effects, (iii) the mode of the gene action, and (iv) pairwise epistasis of genes. Materials and methods Plant materials and trait measurements Experimental procedures for constructing single crosses in M. guttatus are given in Fig. 1. Seeds and corollas were collected in May 1989 from each of 500 plants along a linear transect through a population near Hough Springs, Lake Co., California. In this population, the selfing rate and inbreeding depression were inferred to be 0.29 and 0.06, respectively (Table 1 in Ritland 1990). On the basis of an isozyme survey of adult plants, 95 plants were selected. Their seeds were sown and several progeny (5-10) from each plant genotyped. Alternative homozygous plants were then selected for controlled crosses. Two crosses were made in Fall 1990 and their F, progeny were genotyped Fecundity traits used in this study were (i) relative growth rate, RT; (ii) number of nodes in main stem, NN; (iii) total number of flowers, NF; (iv) height, HT; and (v) aboveground dry weight, WT. During the experiment, the dates of both opening the first leaf and the first flower were recorded for each F, plant. When the experiment was terminated, NN, NF, and HT were scored and all F, plants were cut at the soil level for later measurement of WT. RT was determined by dividing 60 (days) by days from opening of the first leaf to the first flower. These traits showed significant levels of inbreeding depression in this experiment, ranging from 8% for NN to 25% for NF (data not shown). Electrophoresis While 15 isozyme loci could clearly be scored in this study, only eight loci were heterozygous in the F,s. These loci were aconitase 2 (Aco), diaphorase (Dia), esterase (Est), glutamicoxaloacetate transaminase (Got2), malic enzyme (Me), 6-phosphoglucose dehydrogenase 1 and 2 (6Pgdl and 6Pgd2), and triosephosphate isomerase (Tpi). Seven loci (Dia, Est, Got2, Me, 6Pgd1, 6Pgd2, and Tpi) were polymorphic in F,, and five loci (Dia, Est, 6Pgd2, Aco, and Tpi) in F,,. Fresh corollas were collected for electrophoresis using procedures described in Ritland and Ganders (1987). Linkage analyses of these isozyme data demonstrated that these eight loci are unlinked (data not shown) and thus individually represent specific chromosomal segments. Statistical analysis An analysis of variance with the fitness data was conducted using the SAS GLM procedure (SAS Institute 1988). Differences among trays were significant and were removed for subsequent analyses. For each trait, a test for normality was conducted using the Shapiro-Wilk's statistic (Royston 1982). For the traits with highly significant skewness, logarithm transformations were made to ensure the normality. Associations of marked chromosomal segments with QTLs were examined using the SAS GLM procedure. A one-way ANOVA (one trait on one locus with three genotypic classes in F, progeny) was computed for each segment. A significant F-test indicated segregation of genotypes of at least one QTL linked to the segment, and its R' value gave the proportion of total phenotypic variance explained by this segment, i.e., the magnitude of gene effect. The cumulative gene effect associated with all the significant segments for a trait was determined using the SAS GLM procedure with main-effects models. The resulting multiple R2 value gave the proportion of phenotypic variance by these significant segments. Following Edwards et al. (1987), the additive (a) and dominant (d) effects were calculated for each QTL as follows: a = 12[f,2%2 -fIl~I111 d = 2[fl,xI, - (f22X22 + fllX11)I where f is the observed frequency of each marker genotype and x is the observed phenotypic mean of a trait, conditioned on marker genotype. The ratio of these effects (d/a) was used to estimate the degree of dominance for the segment. For the 1007 FU A N D RITLAND TABLE1. Significant associations between chromosomal segments and loci affecting five traits in two selfed progeny arrays of M . guttatus F2 progeny F2, Marked chromosomal segment Frequency of marker genotypes AIAl AlA2 Observed means for marker genotypes A2A2 Trait AIAl A,A2 A2A2 F-test Dia Got2 Me Tpi Dia 6Pgd2 Aco Tpi TABLE2. Estimates of gene effects and d/a ratios of QTLs affecting five traits in two selfed progeny arrays of M . guttatus F2 progeny Trait Marked chromosomal segment Gene effect" Single Multiple Gene action d/a ode^ Dia Tpi Me 6Pgd2 Tpi 6Pgd2 Tpi Me 6Pgd2 Tpi Got2 Me 6Pgd2 Tpi Dia Tpi Aco 6Pgd2 6Pgd2 6Pgd2 "The magnitude of gene effect is determined by the proportion of the total phenotypic variance explained by single and all the significant chromosomal segments, respectively. he mode interpreted is based on the observed d/a ratio. The observed d/a ratios for four modes are as follows: d/a > 1 , OD (overdominance); 1 2 d/a > 0, PD (partial dominance); 0 2 d/a > - 1 , PR (partial recessivity); and d/u I - I , UD (underdominance). interpretation of gene action, these estimates were classified into four types: d/a > 1 for overdominance (OD), 1 2 d/a > 0 for partial dominance (PD), 0 2 d/a > - 1 for partial recessivity (PR), and d/a I - 1 for underdominance (UD). Pairwise epistasis (i.e., interactions between two marked chromosomal segments in their associated effects on each trait) was tested using a two-way ANOVA on each trait in both F2s, with the two marker loci as main effects. GENOME, VOL. 37. 1994 T A B L E3. Significant pairwise epistasis between chromosomal segments for five traits in two selfed progeny arrays of M. guttatus Nonsignificant association F2 progeny Trait Pair of segments R' X 100" F2n RT NF WT NF WT Got2 X TpiT* MeX6Pgd2?* Dia X 6 P g d l * DiaX6Pgd2?** DiaXEst* Dia X 6 P g d 2 t ** 2.47 2.67 3.90 4.4 1 4.32 3.84 F,, NOTE: *, significant interaction at the 0.05 level; t. significant main effect at the 0.05 level; **, significant interaction at the 0.01 level. "R' represents the proportion of the phenotypic variation explained only by the interaction term. , , O ! I I I 1 Dominant/additive ratio FIG. 2. Frequency distribution of 60 observed d/a ratios. Results and discussion Number of QTLs detected All the traits studied showed continuous variation, typical of quantitative traits, and most of them exhibited approximately normal distributions (data not shown). Significant associations of six chromosomal segments with traits examined in two F,s are given in Table 1. Of the 6 0 possible marker-trait combinations in two F2s, 20 (33%) showed significant associations, of which 11 were significant at the 1.0% level or lower (note that three of these significant associations, 5% of 60, may be due to chance alone). Among the six segments, three (Dia, Got2, and Aco) were significantly associated with only one trait and three (Me, 6Pgd2, and Tpi) with more than one trait in the two F,s. Table 1 also shows the significant associations with the traits in each of the F,s: 14 for F,, with the seven loci employed (i.e., 4 0 % of the associations tested) and six for F,, with the five loci (i.e., 24% of the associations tested). The number of QTLs detected for RT, NN, NF, HT, and W T were 2, 3, 2, 3, and 4, respectively, with an average of 2.8 QTLs per trait in the two F,s (Table 2). However, the number of QTLs detected for each trait (except for RT) varied between the two F2s (Table 2). For WT, for example, four QTLs were detected in F,, and one in F,,. These results imply that, as expected, a large number of fecundity genes are involved in the expression of inbreeding depression. However, the number of QTLs found for each trait here should be considered a minimum estimate. We examined only a small portion of the whole genome (1 1.2% based on calculations following Bishop et al. 1983) so that genes in the other regions of the genome were not included. Also, even in these marked regions, it is quite possible that genes of small effect and (or) multiple genes were undetected. Phenotypic variation explained by QTLs T h e phenotypic variation of a trait explained by single chromosomal segments was small, ranging from 1.44 for HT to 9.29 for RT in R2 X 100 in the two F2s, and differing between the two F,s (Table 2). For example, the value of R2 X 100 owing to Tpi for RT was 9.29 in F2a and 2.06 in F,, (Table 2). For the segments (Me, 6Pgd2, and Tpi) that were significantly associated with the expression of more than one trait, the proportions of phenotypic variation that they explained varied for different traits, even in the F, progeny of one cross (Table 2). For the segment marked by Tpi in F,,, for instance, the values of R' X 100 were 9.29 for RT and 2.83 for NN (Table 2). Phenotypic variation explained by several significant segments was relatively large, ranging from 3.85 for RT to 11.32 f o r N F (in R' X 100) in both F2s. It a l s o varied between the two F2s (Table 2). For RT, the values of total R2 X 100 owing to both Dia and Tpi were 11.22 in Fla and 3.85 in F,, (Table 2). Gene effects of the detected QTLs influencing the five fecundity traits are relatively small, because individual significant chromosomal segments explained a small proportion of total phenotypic variation. This seems to suggest that fecundity genes contributing to inbreeding depression have small effects. However, the proportion of phenotypic variation explained by all significant segments can be large ( u p to 11.32%). Considering that about 11.2% of the M. guttatus g e n o m e was marked by the seven markers in F,,, these results suggest that a saturated marker m a p may explain 100% of the phenotypic variance, or that these traits have 100% heritabilities. This could be due to fortuitous sampling of QTLs o r to nonadditive genetic and (or) genotype-byenvironmental variances (Edwards et a]. 1987). Gene action of QTLs The estimates of d/a for the significant associations are given in Table 2. These estimates ranged from -0.41 to 7.27 for the five traits in both F,s. Of 2 0 significant associations, 10 could be interpreted as showing partial dominance, 7 overdominance, 3 partial recessivity, and 0 underdominance (Table 2). To examine the distribution of d/a ratios, all the observed d/a ratios including nonsignificant associations in the two F,s are plotted in Fig. 2. It becomes clear that the d/a ratios f o r the significant associations showed a bimodal distribution, consisting of either partial dominance and partial recessivity, or overdominance. Examination of the m o d e s of g e n e action within a n d between t h e F,s s e e m s to indicate s o m e heterogeneity (Table 2). For example, while partial dominance was observed for almost all the associations with the segment by Tpi, the modes for the associations with the segment by 6Pgd2 were different between the F,s. Overdominance was observed for all the associations with the segments by Dia, Me, Got2, FU A N D RITLAND and Aco, but only the associations with the segment by Dia were consistently found in both F,s. The distribution of d a values in Fig. 2 suggests that partial dominance is relatively predominant over the other modes in the expression of the traits in the selfed progeny. This is particularly true because these overdominant loci may include those of pseudooverdominance, i.e., the complementary action of linked recessive or nearly recessive loci in repulsion (Crow 1952; Charlesworth 1991). One possible way to determine true overdominance is to examine these loci in the F, progeny of many crosses. If the overdominant effects were due to true overdominant loci segregating in the populations studied, one could find these loci in most crosses, or at least more often than partially dominant loci. Unfortunately, this pattern cannot be determined from only two crosses, but at least, less agreement for the cases of overdominance than those of partial dominance was observed between these two crosses (Table 2). Thus while the number of overdominant loci should be fewer than estimated, the number of partially dominant loci is at least as many as observed. However, the finding of the predominance of partially dominant loci, such as those found for viability genes (Fu and Ritland 1994), is not consistent with either the dominance or overdominance hypotheses proposed to account for inbreeding depression. The dominance hypothesis described above strictly refers to only the genes of complete or partial recessivity and does not include those of complete or partial dominance (Crow 1993), because neither complete nor partial dominance contributes to reduction in fitness of selfed progeny (i.e., the mean of the homozygote fitnesses exceeds that of the heterozygote). The reason for this unexpected finding remains unknown. Further study is certainly needed for correctly interpreting these partially dominant loci. The advantage of such an inference about gene actions over the quantitative genetics methods lies mainly in the ability to estimate d/a ratios at specific loci or at least specific chromosomal segments. With these estimates, one could distinguish between the modes of selection operating at specific loci, allowing more precise distinction between the dominance and overdominance hypotheses of inbreeding depression. However, these estimates of d/a could be biased either downward by loose linkage or upward by linkage of multiple QTLs. Linked markers are required to resolve this bias. Pairwise epistasis between chromosomal segments Epistatic interaction was tested between pairs of marked chromosomal segments for each trait. Of 155 pairs for the five traits in the two F,s, only six (3.9%) were significant, less than would be expected by chance (Table 3). Of 31 pairs for each trait, one significant interaction was found for RT, two for NF, and three for WT; no significant interactions were observed for the traits NN and HT. Also, all these interactions explained small proportions of phenotypic variation, ranging from 2.47 to 4.32% (Table 3). These results provide little evidence that pairwise epistasis is an important factor in the expression of inbreeding depression, because few significant interactions were detected and little variation was explained by these interactions. However, these results do not rule out the importance of multiple gene interactions in the expression of inbreeding depression. We have performed analyses of multiple gene interactions for these data and found that multiple gene interactions in deleterious homozygotes are largely multiplicative in nature, 1009 although some synergistic interactions could not be fully ruled out (Y.-B. Fu and K. Ritland, in preparation). Marker-based churucterization of genes influencing inbreeding depression This study represents the first use of genetic markers to infer the nature of gene action at specific chromosome regions affecting fecundity in a wild plant. The results of this study clearly demonstrate that fecundity genes contributing to inbreeding depression can be characterized in terms of gene effects, gene actions, and gene interactions in M. guttatus. Thus this approach seems to be suited for characterizing fecundity genes contributing to inbreeding depression in wild plants. One obstacle to the more widespread use of this approach to investigate the genetic basis of inbreeding depression is the limited number of genetic markers available for most wild plants. However, recent development of molecular technology has provided researchers with numerous molecular genetic markers such RFLPs, RAPDs, and microsatellites (Botstein et al. 1980; Williams et al. 1990; Herne et al. 1992). These new types of markers supersede in many ways the limitations of isozymes and thus make this approach feasible for studying wild plants. As more easily assayed markers are used, more families are analyzed in different environments, and specific experimental designs are combined, some trends may become apparent in selfed progeny. These include areas of the genome that consistently have an effect on a particular trait, types of gene action generally exhibited for fecundity traits, and patterns of gene interaction. Studies of this nature will allow better understanding of the genetic basis of inbreeding depression in later stages of the life cycle in wild plants. Acknowledgments We thank Lloyd Smith for technical assistance and Spencer Barrett, Scott Reinhart, Bob Latta, and Neal Straus for their comments on this project. We also thank Jeffery Dole and Sean Graham for their critical reading on the early version of this manuscript and Deborah Charlesworth for her helpful comments that added greatly to the final version. This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada to K.R. and a University of Toronto Open Doctoral Fellowship and a Mary H. Beatly Fellowship to Y.B.F. Barrett, S.C.H., and Charlesworth, D. 1991. Effects of a change in the level of inbreeding on the genetic load. Nature (London), 352: 522-524. Bishop, D.T., Cannings, C., Skolnick, M., and Williamson, J.A. 1983. The number of polymorphic DNA clones required to map the human genome. I n Statistical analysis of DNA sequence data. Edited by B.S. Weir. Marcel Dekker, Inc., New York. pp. 18 1-1 98. Botstein, D., White, R.L., Skolnick, M., and Davis, R.W. 1980. Construction of a genetic linkage map in man using restriction fragment length polymorphisms. Am. J. Hum. Genet. 32: 3 14-33 1. Charlesworth, D. 199 1. The apparent selection on neutral marker loci i n partially inbreeding populations. Genet. Res. 57: 159- 175. Charlesworth, D., and Charlesworth, B. 1987. Inbreeding depression and its evolutionary consequences. Annu. Rev. Ecol. Syst. 18: 237-268. Charlesworth, D., Morgan, M.T., and Charlesworth, B. 1990. Inbreeding depression, genetic load, and the evolution of 1010 GENOME, VOL. 37, 1994 outcrossing rates in a multilocus system with no linkage. Evolution (Lawrence, Kans.), 44(6): 1469-1489. Crow, J.F. 1952. Dominance and overdominance. In Heterosis. Edited b y J.W. Gowen. Iowa State College Press, Iowa. pp. 282-297. Crow, J.F. 1993. Mutation, mean fitness, and genetic load. Oxf. Surv. Evol. Biol. 9: 3-42. Darwin, C.R. 1876. The effects of cross and self-fertilization in the vegetable kingdom. John Murray, London. Dole, J.A., and Ritland, K. 1993. Inbreeding depression in two Mimulus taxa measured by multigenerational changes in the inbreeding coefficient. Evolution (Lawrence, Kans.), 47: 361-373. Edwards, M.D., Stuber, C.W., and Wendel, J.F. 1987. Molecularmarker-facilitated investigation of quantitative-trait loci in maize. I. Numbers, genomic distribution and types of gene action. Genetics, 116: 113-125. Fu, Y.B., and Ritland, K. 1994. Evidence for the partial dominance of viability genes contributing to inbreeding depression in Mimulus guttatus. Genetics, 136: 32 1-33 1. Herne, C.M., Gosh, S., and Todd, J.A. 1992. Microsatellites for linkage analysis of genetic traits. Trends Genet. 8: 288-294. Lande, R., and Schemske, D.W. 1985. The evolution of selffertilization and inbreeding depression in plants. I. Genetic models. Evolution (Lawrence, Kans.), 39: 24-40. Latta, R.G., and Ritland, K. 1994. The relationship between inbreeding depression and prior inbreeding among populations of four Mimulus taxa. Evolution (Lawrence, Kans.). In press. Lewontin, R.C. 1974. The genetic basis of evolutionary change. Columbia University Press, New York. Mather, K., and Jinks, J.I. 1982. Biometrical genetics. Chapman & Hall, London. Mitton, J.B. 1993. Theory and data pertinent to the relationship between heterozygosity and fitness. In The natural history of inbreeding and outbreeding. Edited b y N.D. Thornhill. The University of Chicago Press, Chicago. pp. 1-41. Paterson, A.H., Lander, E.S., Hewitt, J.D., Paterson, S., Lincoln, S.E., and Tanksley, S.D. 1988. Resolution of quantitative traits into Mendelian factors by using a complete linkage map of restriction fragment length polymorphisms. Nature (London), 335: 72 1-726. Ritland, K. 1990. Inferences about inbreeding depression based on changes of the inbreeding coefficient. Evolution (Lawrence, Kans.), 44(5): 1230- 124 1. Ritland, K., and Ganders, F.R. 1987. Crossability of Mimulus guttatus in relation to components of gene fixation. Evolution (Lawrence, Kans.), 41: 772-786. Royston, J.P. 1982. An extension of Shapiro and Wilk's W test for normality to large samples. Appl. Stat. 31(2): 115-124. SAS Institute Inc. 19$8. SAS users guide: statistics. SAS Institute, Cary, N.C. Schoen, D.J. 1983. Relative fitnesses of selfed and outcrossed progeny in Cilia achilleifolia (Polemoniaceae). Evolution (Lawrence, Kans.), 37: 292-301. Simmons, M.J., and Crow, J.W. 1977. Mutations affecting fitness in Drosophila populations. Annu. Rev. Genet. 11: 49-78. Sprague, G.F. 1983. Heterosis in maize: theory and practice. In Heterosis: reappraisal of theory and practice. Edited b y R. Frankel. Springer-Verlag, Berlin. pp. 47-70. Srivastava, H.K. 1991. Theories of heterosis: classical and modern. In Advances in plant breeding. Vol. 1. Edited b y A.K. Mandal, P.K. Ganguli, and S.P. Banerjee. CBS Publishers & Distributors, Shahdara, India. pp. 261-275. Stuber, C.W., Lincoln, S.E., Wolff, D.W., Helentijaris, T., and Lander, E.S. 1992. ldentification of genetic factors contributing to heterosis in a hybrid from two elite maize inbred lines using molecular markers. Genetics, 132: 823-839. Vickery, R.K., Jr. 1978. Case studies in the evolution of species complexes in Mimulus. Evol. Biol. 11: 405-507. Williams, J.G.K., Kubelik, A.R., Livak, J., Rafalski, A., and Tingey, S.V. 1990. DNA polymorphisms amplified by arbitrary primers are useful as genetic markers. Nucleic Acids Res. 18: 653 1-6535. Willis, J.H. 1993. Partial self-fertilization and inbreeding depression in two populations of Mimulus guttatus. Heredity, 71: 145-154. Wright, S. 1977. Evolution and the genetics of populations. Vol. 3. University of Chicago Press, Chicago.