Inferring the genetic basis of inbreeding depression in plants

Inferring the genetic basis of inbreedingdepression in plantsKermit RitlandAbstract: Recent progress in the genetic analysis of inbreeding depression in plants is reviewed. While thedebate over the importance of genes of dominance versus overdominance effect continues, the scope of inferenceshas widened and now includes such facets as the interactions between genes, the relative abundance of majorversus minor genes, life cycle stage expression, and mutation rates. The types of inferences are classified intothe genomic, where many genes are characterized as an average, and the genic, where individual genes arecharacterized. Genomic inferences can be based upon natural levels of inbreeding depression, purgingexperiments, the comparison of individuals of differing F (e.g., prior inbreeding), and various crossing designs.Genic inferences mainly involve mapping and characterizing loci with genetic markers, involving either a singlecross or, ideally, several crosses. Alternative statistical models for analyzing polymorphic loci causing inbreedingdepression should be a fruitful problem for geneticists to pursue.Key words: inbreeding depression, genetic load, self-fertilization, QTL mapping.RCsumC : Les rkcents progrks en matikre d'analyse gknetique de la dkpression consanguine chez les plantes sontpassks en revue. Bien que le dkbat se poursuive au sujet de I'importance relative de la dominance et de lasurdominance, la gamme des infkrences s'est klargie et inclut maintenant des aspects tels les interactions entregknes, l'abondance relative de gknes majeurs et de gknes mineurs, I'expression des gknes au cours du cycle vitalet les taux de mutation. Deux types d'infkrences sont distingukes : les infkrences gknomiques oh l'effet moyende plusieurs gknes est caractkrise et les infkrences gkniques oh des gknes individuels sont examinks. Lesinfkrences gknomiques peuvent s'appuyer sur des niveaux naturels de dkpression consanguine, sur desexpkriences de purgation, sur des comparaisons entre individus prksentant des niveaux diffkrents deconsanguinitk F et sur divers types de croisement. Les inferences gkniques impliquent surtout la cartographie etla caractkrisation de loci a l'aide de marqueurs dans le cadre de un ou, idkalement, plusieurs croisements. L'ktudede diffkrents modkles statistiques permettant d'analyser les loci polymorphes causant la dkpression consanguinedevrait s'avkrer une voie prometteuse pour les geneticiens.Mots cle's : dkpression consanguine, charge gknetique, autofkcondation, cartographie QTL.[Traduit par la Rkdaction]In many plant species, a major genetic factor responsible fordifferences in survival and reproduction between individualsis inbreeding depression. Inbreeding depression, first studiedby Charles Darwin in his 1876 book, The EfSects of Crossand Self Fertilization in the Vegetable Kingdom, is thereduced fitness shown by progeny of self-fertilization ormating between close relatives. It is a biological characterof no little importance, particularly in plants: inbreedingdepression has implications for the evolution of matingsystems (Barrett and Harder 1995), levels of genetic variation(Charlesworth and Charlesworth 1987), agriculturalproductivity (Gowen 1952), and species conservation(Simberloff 1988).ICorresponding Editor: R.S. Singh.Received July 27, 1995. Accepted September 6, 1995.K. Ritland. Department of Botany, University of Toronto,Toronto, ON M5S 3B2, Canada.IGenome, 39: 1-8 (1996). Printed in Canada / ImprimC au CanadaIn the past decade, research in plant population biologyand evolution has intensively focused on levels of inbreedingdepression. This is due in large part to the seminal butcontroversial work of Lande and Schemske (1985) andSchemske and Lande ( 1985). They postulated a direct linkbetween levels of inbreeding depression and the evolutionof self-fertilization, providing a rationale for measuringlevels of inbreeding depression in plants. To the plantdemographer, inbreeding depression has many ideal attributesas a character of study. It can be precisely defined as6 = 1 - w,IwI, where w, is the fitness of self-fertilizedprogeny and w, the fitness of outcrossed progeny. It canbe easily manipulated through artificial matings. Its effectsupon fitness are clear and easily measured owing to thesedentary nature of plants. In addition, with genetic markers,one can infer natural levels of selfing and inbreedingdepression (Ritland 1983, 1990).However, if one is to predict the longer-term evolutionaryimplications of inbreeding depression, we need information

Review / Syn'thesethan in diploids of the same species, supporting therecessive model (B. Husband and D. Schemske, personalcommunication).Charlesworth et al. (1990) showed that data on inbreedingdepression in highly self-fertilizing species can, infact, be used to estimate the rate of mutation to mildlydeleterious alleles. They showed that in a highly selfingpopulation, the genomic mutation rate can be estimatedas U = -2 ln(1 - 6)1(1 - 2h), where h is the dominancecoefficient (h = 0 corresponds to recessive, h = 112 correspondsto additive, h > 112 corresponds to overdominant).This formula applies regardless of the intensity of selection(thus mutations of mild as well as strong effects enter thisestimate) but requires independent estimates of the degreeof dominance h.Johnston and Schoen (1995) used this method to estimatemutation rates in two species of the California annualAmsinckia. They first determined the dominance level as theslope of the regression of outcrossed-progeny fitness on thesum of the selfed-progeny fitnesses of the two parents constitutingthe outcrossing mating (Fig. I). They found levelsof dominance near zero in one species but moderate levels(0.25-0.35) in another. This gave estimates of minimal mutationrates of U of 0.25-0.87 per diploid genome per generation.These mutation rates are high and, together with the estimatesof dominance, suggested that partial recessive mutations,rather than overdominance, are responsible for inbreedingdepression in Amsinkia. Charlesworth et al. (1994) alsoinferred U based upon inbreeding depression of two inbreedingLeavenworthia species but had to assume values of h toinfer U. For reasonable values of h, they inferred the genomicmutation rate to be 0.7-0.9 for L. uniflora and 1.3- 1.7 forL. crassa. These values are higher than those inferred forseveral inbreeding species by Charlesworth et al. (1990),who regarded U = 1 and h = 0.2 as a rough estimate forplants, a value that gives the theoretical reduction of fitnessof selfed progeny as a reasonable 6 = 0.26.Drosophila studies have also indicated high mutationrates. The classic studies of Mukai (1964) found a mutationrate for the second chromosome of 0.15 per generation.Overall, the total deleterious mutation rate in Drosophila isat least U = 1 .O per zygote (Crow 1993). Interestingly,this is an order of magnitude higher than was originallythought back when overdominance was thought to be predominant(Crow 1948; p. 479, U = 0.1). However, oneshould note that estimates of U critically depend on h.Sved and Wilton (1989) inferred that, in Drosophila, hcould be as low as 11128 or as high as 118, interestingly,values that are somewhat lower than for plants.The importance of mutation in evolution has onlyrecently been realized. As James Crow (1993) writes, "Theproblem of how a population tolerates a larger number ofoverdominant loci has been replaced by the problem ofhow the population tolerates a high mutation rate." Inplants, one relevant issue is whether mutation rates evolvein response to changes in inbreeding: for example, dospecies that practice greater selfing show lower mutationrates than their outcrossing relatives. Interest has alsorecently focused on the role of mutations of large effectin causing measurable genetic variation among families forinbreeding depression (J.H. Willis, personal communication).Fig. 1. The crossing design of Johnston and Schoen usedto estimate mutation rates in Amsinckia. (A) Selfed andoutcrossed progeny are generated and their fitness wmeasured. (B) Across several pairs of parents, the slopeof the regression of outcrossed fitness on. the sum of theselfed fitness gives h (adapted from Johnston and Schoen1995).Inferences about gene action from purgingIf the rate of inbreeding is increased above that normallyexperienced by a population, the amount of inbreedingdepression should be reduced owing to increased purgingof deleterious genes. In the extreme, one can employenforced selfing to cause strong purging. The effectivenessof enforced inbreeding increases with the degree of recessivityof genes causing inbreeding depression (Charlesworthand Charlesworth 1990), so that the degree of recessivitycan be indirectly inferred by the change of inbreedingdepression under enforced inbreeding.As an example of this inference, Barrett and Charlesworth(1991) selfed water hyacinth plants (Eichornia paniculata)for five successive generations. Two populations were studied,one a predominant outcrosser from Brazil, the other aselfer from Jamaica. As expected, in the outcrosser, fivegenerations of selfing substantially reduced inbreedingdepression, while in the selfer, no reduction occurred. Theycompared these results with those generated by theoreticalmodels and found that, in the outcrosser, the model of mutationto mildly detrimental partially recessive alleles mostclosely fit the observed purging in the outcrosser (Fig. 2).Another approach is to compare levels of inbreedingdepression among species differing for natural levels of selfing.If mutation rates do not evolve, then under recessiveinheritance, purging would reduce inbreeding depression inspecies with higher selfing rates. When making such comparisons,closely related species should be used to eliminate

Genome, Vol. 39, 1996Fig. 2. (A) Changes in the fitness of a habitual outcrossingpopulation of Eichornia paniculata over five generationsof selfing (shaded bars), following by outcrossing (hatchedbar). The initial outbred population is given by the blackbar. (B) Theoretical expectations under the best fittingmodel of deleterious recessives (adapted from Barrett andCharlesworth 199 1).Successive generationsconfounding adaptive changes of life-history characters(which are closely tied to fitness). For this, the Mimulusguttatus (monkeyflower) species complex is ideal, as it hasseveral closely related inbreeders and outbreeders (Ritland andRitland 1989). Latta and Ritland ( 1994) compared 15 populationsamong four of these taxa. They found associationsbetween inbreeding depression and prior inbreeding (measuredby Wright's F) to be weakly consistent with a recessivemodel of inbreeding depression. However, the complexityof the relationship also suggested genotype-by-environmentinteractions and complex modes of inheritance.Inferences about gene interaction using individuals ofdiffering FIn the 1950s and 1960s, the "genetic load" due to deleteriousmutations was characterized in a number of organisms, primarilyhumans and Drosophila. This load was often describedin terms of lethal equivalents, which according to Mortonet al. (1956; p. 857) are "a group of genes of such numberthat, if dispersed in different individuals and made homozygous,would cause an average of one death." On a per zygotebasis, this number equals 2 ln(R)I(F, - F,), where R is theratio of the fitnesses of individuals with inbreeding coefficientF, to those of individuals inbred to degree F, (the inbreedingcoefficient F is the probability that the two alleles at a diploidlocus are identical by descent or are copies of the same allelefrom a recent ancestor). Normally, outcrossed individualsare used for the latter case (F, = 0).Estimates of lethal equivalents for plants did not appearuntil Sorenson's (1969) classic study with Douglas-fir.Comparing the seed set of selfed cones (F, = 0.5) withthat of outcrossed cones (F, = 0), he found a median of10 lethal equivalents with a range of 3-27 per tree. Levinand Klekowski have also applied this method to Phlox(Levin 1989) and ferns (Klekowski 1988). However, thisapproach cannot distinguish between deaths attributableto few loci of large effect and those due to deleteriousalleles at many loci with a net lethal effect. Althoughlethals or semilethals may be responsible for most of thegenetic load in the outbreeding Drosophila (Crow andSimmons 1983), they do not explain heterosis in highlyselfing species, where one expects major deleterious allelesto be eliminated owing to strong purging. In addition,polyembryony in conifers may confound estimates of lethalequivalents (T. Mitchell-Olds, personal communication).With two levels of F, one must assume no fitness interactionsbetween loci. If more than two levels of F arecompared, one can infer the presence of interactions or"synergism" between fitness loci. The usual expectationis that if mutations at different loci interact synergistically,then fitness declines at a rate greater than expected undermultiplicative effects. However, it should be noted thatsuch nonlinearity arises only from dominance by dominanceinteractions and not from other forms of epistasis involvingadditive effects (Crow and Kimura 1970; page 80).To test for synergism in this way, Willis (1 993) generatedlines of monkeyflowers with expected inbreeding coefficientsof 0, 0.25, 0.5, and 0.75 (corresponding to progenyof outcrosses, full-sib matings, selfs, and second generationselfs, respectively). Although most fitness traits declinedsubstantially with inbreeding, little evidence of synergismwas found. Willis makes the point that fitness traits shouldbe logarithmically transformed and, when doing so withseveral published datasets, he finds strong evidence forsynergism, particularly in forest trees. The usual trend wasthat mildly inbred progeny (F I 0.25) showed little inbreedingdepression, while strongly inbred progeny (F 2 0.5)showed rapid deterioration of fitness.However, one significant problem with any experimentthat uses lines derived from inbreeding is that the very objectof study, inbreeding depression, can be purged during thecreation of these lines. In particular, negative synergism maybe masked by the extinction of lines possessing those allelesthat in combination are lethal. For example, regressions of fitnesson F may be linear when extinct lines are ignored butcurvilinear downwards when extinct lines are included.Diallele crosses and other classical approachesIn the 1950s, quantitative geneticists devised several experimentaldesigns for characterizing the dominance of genesfor a quantitative trait. Comstock and Robertson (1952)summarized three experimental procedures (North Carolinadesigns I, 11, and 111), involving intermating (designs I and11) or backcrossing (design 111) F,s. All were aimed at inferringaverage degree of dominance. Hayman (1960) revieweddiallele cross methods, which involve crossing inbred strainsin all possible combinations (including selfs). These methodsare generally concerned with inferring general combiningability or the dominance variance due to heterosis. Henoted the distinction between measuring the properties of theinbred lines themselves, as opposed to the properties ofthe population from which the lines are sampled.This raises a related issue: the method should distinguishbetween measuring properties of genes expressed in inbred

Review I Syntheseindividuals, as opposed to the properties of genes in outbredindividuals. Most designs measure the latter, in that theycharacterize genes underlying heterosis. Although inbreedingdepression may be termed the "converse" of heterosis, itdoes not follow that gene effects are the same for both.The quantitative basis for this expectation lies in the workof Jacquard, whose formulae allow for differences betweendominance deviations of alleles in the outbred referencepopulation versus dominance deviations of alleles in thederived homozygous population. Jacquard (1 974;pp. 13 1-1 35) and Cockerham and Weir (1984) discuss therelationship between these two components of dominance.It seems the proper quantitative genetic characterizationof inbreeding depression would involve these quantities.Genic inferencesWe now focus on approaches that identify specific locicausing inbreeding depression. This approach may ultimatelyresolve the so-called "genetic architecture" ofinbreeding depression, which includes all facets of itsgenetic control, such as the type of action (dominance vs.overdominance), the numbers of genes (few vs. many),the strength of action (lethal, sublethal, mild), and theinteractions and linkages of genes.In principle, such inferences could be made by extensionsof classical quantitative genetic approaches. For example,the crossing of inbred lines can reveal segregation of individualloci and, over all lines and crosses, one should beable to recover information about gene number, gene frequency,and the distribution of gene effects. With the adventof cheap computing, it should be possible to invent experimentaldesigns with complex genetic inferences, solvedby numerical methods such as the Markov-Chain Monte-Carlo algorithm (Thompson 1994).A different route would be to employ the "reverse" geneticsapproach, where one first identifies individual genes,then infers their mode of action and interaction by measuringfitness of known genotypes. While it is a common andpowerful mode of inference in human genetics wheresequences of disease genes are routinely assayed, we are along way from such modes of inference with wild plant populations.One compromise is to find simply inherited fitnesstraits and then to elucidate their genetic basis by crossingand testing for Mendelian segregation ratios. Such traits arerare, but an excellent example in plants is chlorophyll deficiency.Willis ( 1992) found synergistic epistatis between twoloci controlling chlorophyll deficiency in Mimulus guttatus,in the form of duplicate gene expression (recessives at bothloci needed for the lethal condition of no chlorophyll).Quantitative trait locus mapping with single crosses:heterosisTo study individual loci and the "genetic architecture" ofinbreeding depression, one can employ genetic markers tomap individual "quantitative trait loci" (QTLs) by followingthe cosegregation of fitness with genetic markers undercontrolled selfs or crosses. Although genetic markers havebeen used to study quantitative traits for over 70 years,the advent of molecular markers has made such detaileddissections of architecture possible. One disadvantage ofmarker methods is that the experimental effort needed forfine scale resolution may be prohibitive because of thesample sizes needed to detect rare recombination events.One major advantage is that purging can be minimized byusing experimental designs based upon one generation ofsegregation.In an exemplary study only possible with a model organism,Stuber et al. (1992) utilized 76 markers to map QTLsaffecting seven agricultural traits in a cross between twowidely used maize inbred lines. Nine regions affectingyield were mapped and eight of these showed significantoverdominance. This could reflect apparent overdominance(linked recessives in repulsion), although they did try tominimize this effect by using F,s to increase recombinationbetween QTLs. They also compared two QTL mappingmethods, the "single marker method" (Soller and Brody1976) and the interval mapping method (Lander andBotstein 1989), and found that the two methods yieldedalmost identical results. However, they point out that intervalmapping is still preferable, particularly when markersare closely linked and the map location of the QTL isdesired, and when there is a substantial portion of missingdata. In addition, in conflict with these marker-derivedconclusions, the experiences of corn breeders indicate thatoverdominance is usually not responsible for heterosis incorn. High yielding maize inbreds have been developedthat are not as good as the best hybrids, but are better thanwould be expected if there were large contributions byoverdominant loci (Crow 1993).In a rigorous statistical examination of the evidence fordominance versus overdominance of QTLs, Mitchell-Olds(1995) mapped viability loci contributing to heterosis inArabidopsis. He found a 50% reduction of viability ofhomozygotes relative to heterozygotes in a short interval ofchromosome 1 and found this apparent heterosis to bebetter explained by functional overdominance than bypseudo-overdominance (associative overdominance or overdominanceof a linked locus). He also noted that intervalmapping may give spurious "LOD humps" owing to violationsof the assumptions of the estimation procedure.One assumption possibly violated is the normal distributionof error residuals. Also, he states that an interval that doesnot contain an actual QTL may show a LOD maximumnear the center of the interval, since this position is farthestfrom any potentially conflicting data at the observed markers.Many statistical problems remain with complex analysesposed by such data.QTL mapping with single crosses: inbreeding depressionHeterosis occurs in hybrids between distinct strains, lines,or populations and the alleles causing such differenceshave relatively large effects and hence are easy to map. Bycontrast, the proper inferential procedure for inbreedingdepression would involve selfs and outcrosses using individualsfrom a single interbreeding population. However,the alleles segregating within populations are usually ofsmall effect, resulting in lower power for detection ofQTLs compared with hybrid mapping. This necessitatesmuch larger sample sizes, making the interval mappingapproach, with its requirements of a saturated marker linkagemap, difficult for studies of inbreeding depression.

Genome, Vol. 39, 1996Fig. 3. The observed segregation ratios illustrating geneaction in Mimulus (the level of statistical significance isindicated). Adapted from Fu and Ritland (1994a).underdomlnantV00.5Homozygote marker frequency(less frequent homozygote)eutralAn alternative is to use only a handful of unlinked markersto obtain a "random sample" of linked QTLs in thegenome. Such a random sample of the genome is particularlyappropriate for the character of inbreeding depressionbecause its mutant alleles are probably infrequent at individualloci and widely distributed throughout the genome.The number of markers adequate for such a random sampleis quite low, about the number of isozyme markers typicallypolymorphic in an outbreeding species, thus allowing studiesof wild populations by workers with limited resources.In the first attempt to provide such a practicable approachfor mapping QTLs controlling inbreeding depression,Hedrick and Muona (1990) showed that, assuming a singlerecessive QTL linked to a marker locus, one can estimatethe recombination fraction and strength of selection at theQTL. In their approach, a plant heterozygous for the markeris selfed and the segregation ratio of progeny is analyzed.They found a near-lethal gene at a locus closely linked toan esterase marker in Scots pine.Because there are only two degrees of freedom in suchdata, one cannot infer the degree of dominance at theselected locus, as any dominance will bias estimates. Inan extension of the method of Hedrick and Muona, Fu andRitland (1 994a) presented a graphical method for analyzingthe "space" of single-locus segregation ratios, within whichall modes of gene action can at least be partially distinguished.Using this method, we found partial dominance tobe the primary mode of gene action in selfed progeniesof monkeyflowers assayed for 5-8 segregating isozymemarkers (Fig. 3). However, this method is of limited value,because some segregation ratios can be attributed to morethan one alternative mode of gene action (see Fig. 3) andit cannot disentangle the strength of gene effect from itslinkage. To increase the resolution of gene effect, one canuse linked markers or a combined self-testcross design.The method of assayed selfed progeny for markers canalso be extended to a multilocus analysis (Fu and Ritland1996) to make inferences about synergistic interactionsbetween QTLs. This method involves regressing the numberof apparently deleterious homozygous loci (ADH loci) inselfed progeny against the fitness of progeny. Other modesof selection can be incorporated by a bivariate regressioninvolving both homozygote and heterozygote markers inselfed progenies. Note that self-fertile organisms arerequired: related experimental designs could be used forinferences about genes causing inbreeding depression undermilder forms of inbreeding.QTL mapping with multiple crossesLike most human diseases, inbreeding depression undoubtedlyhas a complex genetic basis: most QTLs controllinginbreeding depression are homozygous in any single individualand different individuals are heterozygous for differentQTLs. Ideally, several crosses should be performed andall crosses jointly analyzed for parameters such as genefrequency of individual QTLs and the distribution of alleleeffects. To this end, Fu and Ritland (1 9946) presented astatistical model for the joint analysis of several selfedprogeny arrays. We found that under our model, there is anoptimal number of arrays (assuming a fixed total numberof progeny); the precise optimum depended on the linkagedistance between the marker and the QTL, as well as thegene frequencies and strength of selection acting on theQTL. Alternative statistical models for analyzing polymorphicQTLs should be a fruitful problem for statisticalgeneticists to pursue.ConclusionThe extension of marker-based inferences to the populationlevel completes the circle of methods and poses the question,where do we go from here? Significant advances willbe made by new experimental protocols, involving bothmolecular methods and statistical inferences, combinedwith a wise choice of species, particularly "model" speciessuch as Drosophila, Arabidopsis, or Mimulus. However,the question remains as to how well these model speciesrepresent the rest of the biological world. In particular, doannual plants represent long-lived perennials, such as trees,and do inbreeders represent what is found in outbreeders?Another question remains as to how well laboratorystudies, with their high resolution, represent what is actuallyoccurring in nature. A major problem in studying any fitnesscharacter is the evaluation of fitness under realisticconditions, the native environment of the species. Estimatesof fitness are often conducted in noncompetitive conditions,in gardens, greenhouses, or growth chambers. Under theseconditions, inbreeding depression is usually less than thatfound under natural conditions. In fact, the major focusof a recent book, The Natural History of Inbreeding andCrossbreeding, edited by Nancy Thornhill, is upon fieldstudies involving nonmodel species. However, this is whenthe genetic basis of characters is most difficult to determine.Unless significant methodological advances are made

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