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Schultz, Stewart T.
Doctor of Philosophy - PhD
University of British Columbia
Numerical models are shown to allow the spread of males into equilibrium nucleo-cytoplasmic populations, resulting in the evolution of subdioecy or dioecy. Conditions for the evolution of subdioecy from two classes of nucleo-cytoplasmic gynodioecy are found to be similar to, and in some cases less stringent than, those required for evolution of sub dioecy from nuclear gynodioecy. Conditions for the evolution to dioecy from nucleo-cytoplasmic gynodioecy are likewise similar to those from nuclear gynodioecy, except that for someparameter sets, dioecy is not possible from nucleo-cytoplasmic gynodioecy due to the persistence of acytoplasmic polymorphism that allows continued production of hermaphrodites. Sex ratios in gynodioecious, endemic, Kauaian Bidens sandvicensis and B. cervicata are strongly correlated with elevation, aspect, and out crossing rate as estimated from analysis of electrophoretic genotypes at the phosphglucoisomerase and shikimate dehydrogenase loci. Female frequencies at four population centers averaged 0.33, 0.27, 0.14,and 0.18 from 1989 to 1992, and 1989 measured out crossing rates at these centers were0.50, 0.55, 0.75 and 0.71. In Bidens sandvicensis, significant inbreeding depression occurs in seed set (0.2 to0.5), germination (0.40), first-year survivorship in the field on Kauai (0.42), probability of first-year flowering (0.58) and number of heads produced per flowering plant (0.68). Total inbreeding depression thus exceeds 0.9. Performance of hermaphrodites relative to females was lower than one in seed set per head (0.7), and in quality of open-pollinated progeny: germination (0.73), first-year survivorship in the field (0.78), probability of flowering (0.95), and number of heads produced per flowering plant (0.80), although only the first three components were significantly different. Inbreeding depression in hermaphrodites thus appears sufficient to maintain females in populations of Bidens sandvicensis,and is responsible for at least 75% of the over threefold fitness of females relative to hermaphrodites. These results indicate that inbreeding depression can profoundly influence the evolution of floral structure and mating system on isolated oceanic islands.
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EVOLUTION OF GYNODIOECY AND DIOECY:THEORETICAL ISSUES AND THE CASE OFBIDENS SAND VICENSIS AND B. CERVICATAByStewart T. SchultzB. A. Reed CollegeA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESBOTANYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1993© Stewart T. Schultz, 1993In presenting this thesis in partial fulfillment of the requirements for an advanced degreeat the University of British Columbia, I agree that the Library shall make it freelyavailable for reference and study. I further agree that permission for extensive copyingof this thesis for scholarly purposes may be granted by the head of my department or byhis or her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Department of BotanyThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1Z1Date:9 q2AbstractNumerical models are shown to allow the spread of males into equilibrium nucleo-cytoplasmicpopulations, resulting in the evolution of subdioecy or dioecy. Conditions for the evo-lution of subdioecy from two classes of nucleo-cytoplasmic gynodioecy are found to besimilar to, and in some cases less stringent than, those required for evolution of sub dioecyfrom nuclear gynodioecy. Conditions for the evolution to dioecy from nucleo-cytoplasmicgynodioecy are likewise similar to those from nuclear gynodioecy, except that for someparameter sets, dioecy is not possible from nucleo-cytoplasmic gynodioecy due to thepersistence of acytoplasmic polymorphism that allows continued production of herma-phrodites.Sex ratios in gynodioecious, endemic, Kauaian Bidens sandvicensis and B. cervicataare strongly correlated with elevation, aspect, and outcrossing rate as estimated fromanalysis of electrophoretic genotypes at the phosphglucoisomerase and shikimate dehy-drogenase loci. Female frequencies at four population centers averaged 0.33, 0.27, 0.14,and 0.18 from 1989 to 1992, and 1989 measured outcrossing rates at these centers were0.50, 0.55, 0.75 and 0.71.In Bidens sandvicensis, significant inbreeding depression occurs in seed set (0.2 to0.5), germination (0.40), first-year survivorship in the field on Kauai (0.42), probabilityof first-year flowering (0.58) and number of heads produced per flowering plant (0.68).Total inbreeding depression thus exceeds 0.9. Performance of hermaphrodites relative tofemales was lower than one in seed set per head (0.7), and in quality of open-pollinatedprogeny: germination (0.73), first-year survivorship in the field (0.78), probability of flow-ering (0.95), and number of heads produced per flowering plant (0.80), although only thefirst three components were significantly different. Inbreeding depression in hermaphro-dites thus appears sufficient to maintain females in populations of Bidens sandvicensis,and is responsible for at least 75% of the over threefold fitness of females relative to her-maphrodites. These results indicate that inbreeding depression can profoundly influencethe evolution of floral structure and mating system on isolated oceanic islands.Table of ContentsAbstract^ iiList of Tables^ viiList of Figures^ xAcknowledgements^ xiii1 Introduction 11.1 Nuclear Gynodioecy ^ 21.1.1^Requirements for Maintenance of Females ^ 21.1.2^Sources of Female Advantage ^ 31.1.3^Pollen limitation ^ 141.2 Nucleo-Cytoplasmic Gynodioecy 151.3 All Gynodioecy: Empirical Results ^ 171.4 Dioecy and Subdioecy ^ 201.4.1^Theory of Male Invasion ^ 201.4.2^Sources of Male Advantage 231.5 Conclusions from Theory ^ 251.6 Objectives ^ 272 Theoretical Dynamics of Female Sterility 302.1 The Models ^ 302.2 Results 35iv2.32.2.1^Cytoplasmic Runaway and Rates of Evolution ^2.2.2^Conditions for Male Invasion ^Discussion 3543592.3.1^Rates of Evolution ^ 592.3.2^"Stable" Breeding Systems 603 Correlates of Female Frequency 703.1 Methods ^ 703.2 Results 803.2.1^Outcrossing Rates, Aspect, Elevation, and Taxon ^ 803.2.2^Pollen Flow and Sexual Dimorphism ^ 903.3 Discussion 1034 Inbreeding Depression and Maternal Parentage 1134.1 Methods ^ 1134.2 Results 1194.2.1^Seed set ^ 1194.2.2^Germination 1224.2.3^Survivorship ^ 1254.2.4^Flowering and fecundity ^ 1394.2.5^Morphology ^ 1534.2.6^Grazing 1624.2.7^Total Fitness Deficits ^ 1704.3 Discussion 1715 Conclusions and Directions for Research 1835.1^Theory ^ 1835.2 Hawaiian Bidens ^ 1875.2.1^Sex Ratio Correlates . . . . . ................ .^1875.2.2 Inbreeding Depression and Maternal Sex ^ 1905.2.3 Implications for Mating System Evolution 192Literature Cited^ 196viList of Tables2.1 Description of the Models ^312.2 Fitness Values of Genotypes in the S-S Model ^ 322.3 Fitness Values of Genotypes in the F-S Model 332.4 Generations to Dioecy under Nuclear and Nucleo-Cytoplasmic Gynodioecy 382.5 Threshold Male Fertility for Invasion or Conversion to Dioecy, S-S Model. 502.6 Threshold Male Fertility for Invasion or Conversion to Dioecy, F-S Model 533.7 Attributes of Sampled Populations ^ 743.8 Electrode and Gel Buffers for Starch Gel Electrophoresis ^763.9 Loglinear Analysis: Effect of Environmental Factors on Female Frequency,Year Controlled ^ 833.10 Loglinear Analysis: Effect of Environmental Factors on Female Frequencyby Year 853.11 Combined Probability Values for Environmental Effects on Female Frequency 863.12 Analysis of Covariance: Effect of Sex and Subpopulation on Seed Set . . 913.13 Analysis of Covariance: Effect of Sex, Size, and Subpopulation on Seed Set 913.14 Analysis of Covariance: Effect of Size, Sex, and Female Frequency on SeedSet ^ 923.15 Analysis of Covariance: Effect of Sex on Insect Visitation ^943.16 Analysis of Covariance: Effect of Sex, Subpopulation, and Capitula Num-ber on Capitula Visits ^ 953.17 Regression Analysis: Effect of Insect Visits on Female Frequency ^ 95vii3.18 Analysis of variance: Effect of Sex and Population on Capitula Number .^963.19 Analysis of Variance: Effect of Sex and Population on Height ^ 973.20 Analysis of Variance: Effect of Sex on Branch Length ^ 973.21 Nonparametric Analysis of Variance: Effect of Sex and Subpopulation onMorphology ^ 983.22 Mean Sexual Dimorphism ^ 1023.23 Regression of Sexual Dimorphism on Female Frequency ^ 1024.24 Analysis of Variance: Effect of Cross on Seed Set 1204.25 Analysis of Variance: Effect of Maternal Sex on Performance in GrowthChamber .........^. .....^1244.26 Loglinear Analysis: Effect of Maternal Sex on Survivorship ^ 1264.27 Loglinear Analysis: Effect of Maternal Sex on Regeneration ^ 1274.28 Loglinear Analysis: Effect of Maternal Sex and Season on Regeneration ^ 1284.29 Loglinear Analysis: Effect of Cross on Survivorship ^ 1344.30 Loglinear Analysis: Effect of Cross on Regeneration 1364.31 Loglinear Analysis: Effect of Sex on Adult Survivorship ^ 1374.32 Morphological Means by Parentage and Grazed Status 1434.33 Analysis of Variance: Effect of Maternal Sex on Morphology ^ 1444.34 Analysis of Covariance: Effect of Maternal Sex on Morphology ^ 1464.35 Analysis of Covariance: Effect of Cross on Morphology ^ 1514.36 Analysis of Variance: Effect of Sex on Morphology 1524.37 Analysis of Variance: Effect of Maternal Sex on Height Growth ^ 1544.38 Analysis of Covariance: Effect of Maternal Sex on Height Growth^1564.39 Analysis of Covariance: Effect of Cross on Height Growth ^ 1624.40 Analysis of Covariance: Effect of Grazing on Morphology 167viii4.41 Loglinear Analysis: Effect of Grazing on Survivorship ^ 168ixList of Figures2.1 Trajectories to Dioecy, Dominant Restorer, Deterministic ^362.2 Loss of Males Introduced out of Phase, S-S Model ^ 402.3 Antagonism and Rate of Evolution to Dioecy, S-S Model ^ 422.4 Invasion of D Cytoplasm into Dioecious Population 452.5 Cytoplasm-Restorer Fitness Pleiotropy and Stable Subdioecy, F-S Model^472.6 Cytoplasm-Restorer Fitness Pleiotropy, Overdominance, and Stable Sub-dioecy ^ 482.7 Dioecy and Cytoplasmic Polymorphism, S-S Model, Stochastic ^ 562.8 Sporadic Invasion of Hermaphrodites into Dioecious Population, S-S Model,Stochastic ^572.9 Oscillating Runaway and Gynodioecy, S-S Model ^ 583.10 Generic Box Plot ^ 723.11 Map of Kauai, Elevation Contours ^ 733.12 Map of Kauai, Rainfall Contours 753.13 Banding Patterns of PGI ^ 783.14 Banding Patterns of SKDH 793.15 Female Frequency by Year and Subpopulation ^ 813.16 Female Frequency by Aspect ^ 873.17 Female Frequency by Taxon 883.18 Female Frequency by Elevation ^ 893.19 Seed Set versus Density of Nearby Pollen Donors ^ 90x3.20 Box Plots of Seed Set per Capitula by Sex and Subpopulation ^ 933.21 Box Plots of Capitula Visits by Sex and Subpopulation ^ 963.22 Box Plots of Capitula Number by Sex and Supopulation 993.23 Box Plots of Height by Sex and Subpopulation ^ 1003.24 Box Plots of Branch Length by Sex and Subpopulation ^ 1013.25 Female Frequency versus Outcrossing Rate at Four Population Centers byYear ^ 1063.26 Female Frequency versus Population Center Outcrossing Rate, and Theo-retical Curves for Varying 1., ^ 1073.27 Female Frequency versus Population Center Outcrossing Rate, and Theo-retical Curves for Varying k, sf 0 ^ 1083.28 Female Frequency versus Population Center Outcrossing Rate, and Theo-retical Curves for Varying k, sf = 0.2 ^ 1093.29 Female Frequency versus Outcrossing Rate of Nine Subpopulations . ^ 1104.30 Inbreeding Depression in 14 Families ^ 1214.31 Source Female Frequency versus Germination Rate ^ 1234.32 Interval Survivorship by Parentage ^ 1294.33 Cumulative Survivorship by Parentage 1304.34 Relative versus Absolute Survivorship ^ 1314.35 Source Female Frequency versus Survivorship ^ 1324.36 Natural Adult Survivorship by Sex ^ 1384.37 Box Plots of Morphology by Maternal Sex 1474.38 Source Female Frequency versus Capitula Number^ 1484.39 Box Plots of Height Growth by Maternal Sex 1574.40 Total Height Growth versus Height at Transplant ^ 158xi4.41 Relative versus Absolute Height Growth ^ 1594.42 Box Plots of Morphology by Cross 1634.43 Box Plots of Height Growth by Cross ^ 1644.44 Survivorship in Grazed and Ungrazed Individuals ^ 1694.45 Fitness Means by Parentage ^ 170xi iAcknowledgementsI would like to thank Dr. Fred Ganders for intellectual guidance and generous financialsupport of all phases of this thesis, Dr. Malcolm Greig for assistance with statisticalprocedures, Dr. Thomas Wells for instruction in electrophoretic technique, Mary Ellardfor laboratory assistance, and Patty Cotton for nursery care. I am also grateful to theNational Tropical Botanical Garden in conjunction with the Hawaiian Center for PlantConservation for nursery space, transportation, and accommodations; and to the NatureConservancy of Hawaii for financial support of the field portion of this thesis.Chapter 1IntroductionSystematic comparisons have shown that unisexuality is generally a derived condition inangiosperms, and evolves as hermaphrodites reduce or eliminate one or both sexual func-tions. The maintenance of male-sterility alleles in a hermaphrodite population, producinga stable coexistence of female and hermaphrodite individuals, yields the sexual polymor-phism "gynodioecy." The maintenance of female-sterility alleles, producing males andhermaphrodites, is "androdioecy." The maintenance of both classes of sterility alleles,such that male, female, and hermaphrodite individuals co-occur, is "subdioecy." Thiswill occur if recombination is possible between the male and female sterility loci, or if norecombination is possible and pollen fertility of males is below the dioecy threshold. Themaintenance of both male and female-sterility alleles in a reciprocally linked state, suchthat only male and female individuals are genetically possible, is "dioecy."The genetic requirements for evolution from cosexuality to unisexuality are straight-forward (Charlesworth, 1991). Strict dioecy requires linkage between the male-sterilitylocus and the female-sterility locus, and reciprocal dominance: if the male-sterility alleleis recessive (dominant) then the female sterility allele must be dominant (recessive). Thephenotype produced by the dominant sterility/fertility supergene (usually the male) isthe heterogametic gender. The leading hypothesis for the predominance of male het-erogamety is simply that females are generally required before female sterility alleles canestablish, and loss of function alleles are usually recessive (Charlesworth, 1991).Over the last 20 years a large number of theoretical arguments have been advanced1Chapter 1. Introduction^ 2to explicate the selective requirements for the evolution of gynodioecy, androdioecy, sub-dioecy, and dioecy from hermaphroditism (Lloyd, 1974; Lloyd, 1975; Charlesworth andCharlesworth, 1978; Ross, 1978; Lloyd, 1982; Gouyon and Couvet, 1985; Gouyon andCouvet, 1987). Following are the basic conclusions regarding conditions for the evolutionof gynodioecy, subdioecy, and dioecy.1.1 Nuclear GynodioecyThe selective forces for the evolution of unisexuality from cosexuality are those factorsfavoring (1) females relative to hermaphrodites, and (2) males relative to hermaphrodites.Several authors make a distinction between "genetic" and "ecological" forces (althoughin a broad sense these are by no means exclusive categories), which is essentially adistinction between inbreeding depression and everything else. In some cases, the term"sexual selection" (nonstandard usage) (Willson, 1979; Thomson and Barrett, 1981), or"ecological constraints" (Givnish, 1982) are used broadly to designate all phenomena notattributable to inbreeding depression. Such ambiguous terms are avoided in the followingdiscussion, which concentrates on specific fitness components.1.1.1 Requirements for Maintenance of FemalesFor nuclear male sterility with complete dominance and Hardy-Weinberg assumptions,equilibrium with females occurs when the genetic fitness of females equals that of her-maphrodites (Charlesworth and Charlesworth, 1978). Genetic fitness of an individual isthe number of successful gametes it passes on in its lifetime. A successful gamete is onethat undergoes fertilization to produce an individual that survives to reproduction.Genetic fitness of a female is then simply the number of successful ovules produced,Ff ="- Of.Chapter 1. Introduction^ 3Because hermaphrodite pollen fertilizes all successful ovules of both females and herma-phrodites, genetic fitness of hermaphrodites can be expressed solely in terms of successfulovules of females (of) and hermaphrodites (oh):Fh = female ovules per hermaphrodite(2)(hermaphrodite ovules per hermaphrodite)off 1f2oh,— (1.2)where f is the frequency of females. These equations show that whereas female geneticfitness is independent of female frequency, hermaphrodite fitness increases with femalefrequency: female ovules constitute an extra avenue of hermaphrodite pollen fitness.Hence females with a higher genetic fitness than hermaphrodites will increase in frequencyuntil hermaphrodite fitness rises to the same level. The equilibrium frequency f is foundsimply by setting Fh = Ff:_f = ^of2 _ 2o h •OfThe threshold value of of/oh necessary for female invasion, found by setting Equation1.3 to zero, is 2. The maximum f is 0.5, when hermaphrodites must have zero successfulovules, because at 50%, hermaphrodites already equalize fitness by matching each femaleovule with the pollen grain that fertilizes it.1.1.2 Sources of Female AdvantageThese arguments imply that the source of the female advantage must be any factorthat doubles the successful ovules of females relative to hermaphrodites. Prezygoticfactors that would increase of/oh, ceteris paribus, include greater ovule production offemales (directly or as a result of greater female survivorship) and lower rates of fertil-ization of hermaphrodite ovules. Postzygotic factors include greater dispersion of female(1.3)Chapter I. Introduction^ 4fruit, higher female seed quality, and greater expression of genetic load in hermaphroditeprogeny due to self fertilization.Relaxing the complete dominance assumption permits an additional genetic source ofthe advantage to male-sterility alleles. Overdominance at the nuclear male-sterility locuscan maintain the sterility allele even in the absence of any female advantage (Ross andWeir, 1976; Ross, 1978), and even if hermaphrodites on average have greater fitness (aswhen the allele is recessive). This phenomenon, however, has little empirical support.Prezygotic FactorsResources that would have been committed to male organs might be metabolically trans-ferred to female or vegetative organs, resulting in developmental changes in females thatincrease survivorship, total production of flowers and fruit, or total production of ovulesper flower if such development is indeterminate. Such superiority may be habitat-specific,as the two sexual morphs evolve some degree of specialization/polarization in resource ac-quisition rates, which may then produce a significant environment x sex ratio interaction(e.g., Delph, 1990a).However, resource transfer may be unlikely to double the ovule production of femalesfor three reasons. First, male:female resource allocation is likely to be less than 1:1 ina partially selfing species. Second, even for 1:1 allocation, resource transfer is likelyto be less than 100% efficient. Third, even for efficient transfer the limiting resourcefor ovule production may be different from the limiting resource for pollen production.Nevertheless, some increase in ovule or flower production (less than twofold) seems likelyin most species. Alternatively, formerly male resources might be used to increase femaleattractiveness to pollinators by increasing nectar content or corolla size. This, however,will not increase the rate of fertilization of female ovules relative to hermaphrodites inspecies for which pollen limitation (for moderate female frequencies) is minimal or nil,Chapter I. Introduction^ 5and fruit set is limited more by resources than by fertilization rates.Transfer of formerly male resource to female vegetative structures is unlikely to doublefemale survivorship unless survivorship is a step-function of resource, and the transferfortuitously traverses a wide threshold, or unless the function is unusually steep. A stepfunction can be created by animal behavior if, e.g., herbivores or parasites avoid femalesbecause of a slight or moderate resistance.Transfer of resource to reproductive structures, and resulting increase in flower or fruitnumber, is likely to increase the total ovule success of females not only through greaterproduction, but perhaps also through greater fruit- and seed dispersion to safe sites. Inspecies with fleshy fruits dispersed by frugivores, a steep learning curve in the dispersingspecies may result in an attraction to females more than linear with the increase in fruitquantity, and depending on ecological conditions, the resulting greater seed dispersionmay more than double the ovule success of females for perhaps an only slight increase infruit production. This component of female advantage will be greater in long-lived speciesin closed communities where seedlings establish in or under vegetation gaps, which maybe rare and distant from the maternal parent. In this scenario, hermaphrodite fruit maybe largely ignored (depending on fruiting phenology), and the resulting female advantagesubstantial as hermaphrodite progeny fail to establish in intensely competitive conditionsnear or under the parent.Postzygotic Factors: DevelopmentalTransfer of resources devoted to male structures to nutritive tissue of seeds will have a po-tentially greater effect on survivorship than transfer to vegetative functions of the parent,because seedlings are likely to suffer far greater mortality, and a small advantage earlyon may under intense seedling competition accrue to a large adult advantage. Of course,herbivore or parasite interaction can accelerate or multiply any advantage. Conceivably,Chapter 1. Introduction^ 6females could increase fruit attractiveness to frugivores not only through quantity, butalso through increases in fruit quality (e.g., greater sugar, protein, or pulp content), asappears to be the case in papaya, but this phenomenon has been rarely documented. Inaddition to a quality effect, a quantity effect could result postzygotically from lower ratesof fruit abortion in species whose fruit set is resource limited.Postzygotic Factors: Inbreeding DepressionIf hermaphrodites have no other means of preventing self-fertilization (or if mutation ratesto low-selfing features are low) then loss of functional pollen might be a stable means ofavoiding expression of genetic load. Inbreeding depression is defined as the difference infitness between a selfed and outcrossed individual, relative to the outcrossed. On average,one-half of the homologous alleles in a selfed individual are identical by descent from itsparent. Inbreeding depression results from a negative correlation between fitness andhomozygosity, which in turn may be caused by overdominance at one locus or several, orby deleterious recessive alleles built up to a mutation/selection equilibrium.With 100% selfing, the proportion i' of loci next generation that are autozygous, oridentical by descent is(1.4)where i is the proportion autozygous this generation. After n generations the proportionautozygous i, is then1^1in , 1^2n_1 + y; (1 + io), (1.5)where i, is the initial autozygosity. Clearly, for complete selfing autozygosity rapidlyapproaches 100%.However, for fixed selfing rates less than 100%, the autozygosity settles rapidly intoan intermediate equilibrium. In this case the proportion i' autozygous next generationChapter 1. Introduction^ 7is expressed as= [(autozygosity of selfs) x (number of sells)+ (autozygosity of outcrosses) x (number of outcrosses))divided by total number of individuals.Because autozygosity of outcrosses is defined to be zero, this reduces to= (autozygosity of selfs) x (proportion sells in population).^(1.6)In the absence of inbreeding depression, the proportion sells in a population is simplythe effective proportion s^1 — t of ovules self fertilized, and Equation 1.4 implies that= (-3 )(1 + i).2This gives an equilibrium autozygosity 21 — tzt 'independent of the starting autozygosity, reached in a few generations.In the presence of inbreeding depression, the proportion sells in a population becomess(1 — d)/[s(1 — d) (1 — s)], where d is the inbreeding depression in survivorship to theage/size class at which autozygosity is measured. Substituting this expression for s inEquation 1.7 givess(1 — d)(1 + i)=z 2(1 — sd)^•Equilibrium autozygosity is thenSolving for inbreeding depression,(1 — d)(1 — t)z(1 + d)t + 1 — d• (1.10)(1.7)(1.8)(1.9)d^(1 + ^i)t^— 1(1 — i)t +i — 1.Chapter I. Introduction^ 8If autozygosity is in equilibrium with the selfing rate, then Equation 1.11 can be usedto estimate inbreeding depression from the stage at which selfing is estimated to adult.If the equilibrium assumption is violated due to varying selfing rate, then inbreedingdepression may be estimated from a comparison of autozygosities at two or three lifestages (for details see Ritland, 1990).If reduced fitness in homozygous genotypes is caused by overdominance, selection canmaintain genetic load as a balanced polymorphism in the absence of mutation. In thepresence of even moderate selfing, however, all alleles but the fittest will be eliminatedrapidly unless overdominance is perfectly symmetrical (Charlesworth and Charlesworth,1990). If the lower fitness of homozygotes is caused by dominance and sheltering ofdeleterious recessive alleles, then the frequency of these alleles will always decrease inthe absence of mutation and drift. Because the rate of loss of any allele increases withintensity of selection against it, a large inbreeding depression can be short-lived. How-ever, if inbreeding depression is caused by a large number of deleterious recessive alleles,each with small effect, then inbreeding depression can persist at a high stable muta-tion/selection equilibrium. The weaker the selection against any allele, the lower themutation rate needed to prevent its loss. The cumulative effect of a large number of suchweakly maintained alleles is a large inbreeding depression that is simultaneously a strongselective force against self-fertilization, and an ironically weak selective force against anyparticular deleterious recessive allele. The more numerous the unlinked deleterious re-cessive alleles, the greater the likelihood that two highly autozygous individuals will befixed for a different suite of alleles. Even with high total selfing rate and autozygosity,the progeny of these two individuals will contain most of the deleterious recessives in asheltered state. If an adult is heterozygous at an average of n loci for recessive lethalalleles, and if no two adults are heterozygous for a lethal at the same locus, then themean inbreeding depression due to those lethals will be 1 — (3/4)n.Chapter 1. Introduction^ 9Inbreeding depression is of course environmentally variable, and generally decreasesas the overall environmental stress or lethality decreases (Dudash, 1990; Schmitt andEhrhardt, 1990).If outcrossing advantage is the only female advantage, thenoh^wos(1 —^wo(1 — s)w — =Of1 — sd, (1.12)where s is the hermaphrodite selfing rate (and the female selfing rate is assumed to bezero), wo is the fitness of outcrosses, and d is the inbreeding depression (d =1 — wslwo,where ws is the fitness of selfs). Females will invade only if w < 0.5 or sd > 0.5.Substitution of Equation 1.12 into Equation 1.3 gives equilibrium female frequency1 — 2(1 — sd)^2sd —1(1.13)2 — 2(1 — sd)^2sdwith 50% females reached when both inbreeding depression and selfing rate are unity(see Lloyd, 1975).The criterion sd > 0.5 is stringent, and will not be met over the long term if geneticvariation can appear that reduces hermaphrodite selfing rate, if the conditions changeto favor pollinators more efficient in outcrossing, or if genetic load can be reduced fastenough to compensate for mutation to new deleterious alleles.However, nonzero sd < 0.5, combined with an intrinsic female advantage k < 1 maybe jointly sufficient for the establishment of gynodioecy. Relative ovule fitness is thenoh^w0s(1 — d)+ w0(1 — s)w0(1 + k)1 — sd1+k'^(1.14)and equilibrium female frequency is then (see Charlesworth and Charlesworth, 1978)1^2 [ 11-+skd2^2 [1--sd]1+kwoW = =Off =Chapter 1. Introduction^ 102sd — 1 + k(1.15)2sd + 2kThe above equations assume zero effective selfing in females, the presence of whichreduces the equilibrium female frequency (assuming selfing in hermaphrodites and non-complete inbreeding depression); see Equations 3.30 and 3.33.Sex allocation theory predicts that a large intrinsic advantage of females should beaccompanied by a large inbreeding depression, but that the converse is not necessarilytrue. Large female advantage due to transfer of formerly male resources can occur onlyif investment to male function is high in hermaphrodites. But high investment to malefunction will not persist in the long term if inbreeding depression is low (below 0.5 insimple models). This is because, in the absence of pollen discounting and inbreedingdepression, alleles causing self fertilization have a 50% advantage over alleles causingnonself fertilization (Fisher, 1941; Wells, 1979). Spread of these alleles will increasethe selfing rate, and because outcrossing is not necessary, alleles that reduce the pollenproduction to a level sufficient for self fertilization will be favored. Hence a large intrinsicfemale advantage will generally occur only in species in which a high inbreeding depressionfavors a large pollen production as a means of maintaining a high outcrossing rate. Casesin which a large female advantage occurs with low inbreeding depression (e.g., Shykoff,1988; Eckhart, 1992; perhaps Delph, 1990a), may be transient in evolutionary time, asmale allocation in hermaphrodites and resulting female advantage are gradually reducedby natural selection, and male-sterility alleles eventually lost.On the other hand, high inbreeding depression will not always necessitate a highinvestment in male function. In cases, for example, of complete inbreeding depressionand competing selfing and out crossing, each self fertilization is a waste of a pollen grain. Ifthe selfing rate of pollen grains decreases with total pollen production, then pollen fitnesswill tend to be a sigmoid function of pollen production, with very low fitness gains forChapter 1. Introduction^ 11production increases when absolute production is low (and pollen selfing is high). Whenselfed ovules become saturated, then fitness will increase more rapidly with increasingpollen production. Eventually, however, a plateau is reached, at a point determined bythe outcrossing efficiency of the pollinating vector. If outcrossing efficiency is low, thenthe plateau may be reached for relatively low pollen production, and for low investmentto male function relative to female function. Hence in species whose female advantageis predominately an outcrossing advantage (e.g. Kohn, 1989; Sakai, et al., 1989), lowallocation to male function (and low intrinsic female advantage) may be evolutionarilystable due to outcrossing inefficiency.Fitness deficits of selfed progeny of hermaphrodites may occur at any stage of de-velopment, but will mimic the effects of an intrinsic hermaphrodite inferiority in seedprovisioning, and undoubtedly other sources of female advantages in seed quality, suchas a statistical genetic effect of restorer alleles on progeny of hermaphrodites (see below).The outcrossing advantage of open-pollinated progeny of females can be distinguishedfrom other sources of advantage by comparing the fitness of experimentally outcrossedprogeny of females to those of hermaphrodites sired by the same pollen donors: anysuperiority of the former progeny class is likely to be independent of, and in additionto, an outcrossing advantage. Alternatively, the non-outcrossing advantages of progenyof females may be estimated more simply by comparing the fitness of open-pollinatedprogeny of females to experimentally outcrossed progeny of hermaphrodites, providingcertain assumptions are met, as follows.For a fitness wof of effectively outcrossed progeny of females (i.e., from ovules fertilizedby unrelated hermaphrodites), an inbreeding depression d, and effective selfing rate S f offemales, the total fitness of open-pollinated progeny of females can be written as:W f = Wo f ( 1 — 8 jd) .^ (1.16)Chapter 1. Introduction^ 12If effectively outcrossed progeny of females are superior to effectively outcrossed progenyof hermaphrodites (with fitness woh ), so that Ivo = woh(1 k) where k is the measureof female advantage, then the fitness of open-pollinated progeny of females relative toeffectively outcrossed progeny of hermaphrodites isand k is thenWI^= (1 — s f d)(1 k),woh(1.17)k = ^f1.^ (1.18)woh(1 — sfd)This implies that the advantage to progeny of females, independently of any outcross-ing advantage, can be calculated from knowledge of fitness of open-pollinated progenyof females, experimentally outcrossed progeny of hermaphrodites, effective selfing rate offemales, and inbreeding depression. This, however, makes two assumptions. The first isthat inbreeding depression is identical in females and hermaphrodites, which may not betrue if the two sexual morphs tend to differ in their inbreeding coefficient. If females aremore often the result of outcross events and hence have a lower mean inbreeding coeffi-cient, then they may have a lower mean inbreeding depression (see page 174), dependingon the nature of associations that develop between the load loci and the male-sterilitylocus as purging occurs in selfed lines of hermaphrodites. The second assumption is thatthe inbreeding coefficient of experimentally outcrossed progeny of hermaphrodites is zero.However, the degree of relatedness between the parents of such outcrosses is generally un-known, especially in studies (such as the present) that attempt to measure the differencebetween selfs and outcrosses produced under normal natural conditions, through within-population outcrosses. Hence, the fitness of the experimental "outcrossed" progeny willnot equal woh, and in such studies will generally be less than woh. As a result, Equation1.18 is useful primarily as a means of estimating the maximum possible k, when substi-tuting woh for the fitness of experimental outcrosses, and the hermaphrodite inbreedingChapter 1. Introduction^ 13depression.If, however, experimentally outcrossed progeny of hermaphrodites (with fitness w,)have the same inbreeding coefficient as open-pollinated progeny of females, then thefitness of the latter relative to the former iswf^ = 1 + k,Woe(1.19)and estimation of k requires no knowledge of either inbreeding depression or the effectiveselfing rate of females.In any case, these calculations make no distinction between different sources of non-outcrossing advantages to progeny of females. Quantifying the genetic inferiority inprogeny of restored hermaphrodites would require detailed studies of among family vari-ation in fitness of progeny of hermaphrodites and of females, for several pollen donors,and perhaps knowledge of the genetics of male sterility as well. However, a maximumestimate of the non-outcrossing advantage of progeny of females, k, can be made byoverestimating d and .s, and underestimating woh, in the above equations.Any superiority of adult females in survivorship and fecundity, though easily measur-able in natural populations, nevertheless may not indicate any non-outcrossing femaleadvantage. This is because, if females tend to predominate in the progeny of outcrossevents (as would often be the case if male sterility is cytoplasmic, or if nuclear and domi-nant), then females on average will have a lower inbreeding coefficient and hence greaterfitness in the presence of inbreeding depression. However, this confounding factor canbe easily ruled out comparing adult performance within parentage classes. If femalesare superior in some fitness component independent of the effects on that component oftheir inbreeding coefficient, then among outcrossed progeny of hermaphrodites, femaleindividuals should exhibit superior performance in that component.Chapter 1. Introduction^ 141.1.3 Pollen limitationUntil now I have assumed that the number of successful ovules of either females orhermaphrodites is independent of female frequency. However, because the presence offemales reduces the total pollen reservoir, pollinators on average might carry fewer pollengrains and fertilize fewer ovules per visit. For a sufficiently small reservoir this will resultin fewer successful ovules in both females and hermaphrodites.If a female plant is visited n independent times by pollinators, and each visit fertilizesa proportion €(1 — f) of unfertilized ovules, where E is a fertilization efficiency constant,then the total proportion q of ovules fertilized will beq=1 —[1 — c(1 — f)]n . (1.20)The total female successful ovules will then be of = bfqlf, where bf is the total ovulesproduced and if is the survivorship of fertilized female ovules, equal to w, without anyintrinsic female effect.For a fixed outcrossing rate of hermaphrodites, if their outcrossed ovules experiencethe same pollen limitation as female ovules, then the total successful ovules of herma-phrodites will beOh = w0bh[3(1 — d) q(1 — s)]. (1.21)The exponential function q of f then prevents explicit solution for equilibrium femalefrequency. Solution for d givesd =[1 — e(1 — n]n{1 - f — s(1 + f)] f — 1s(f — 1) 2f — 1(1.22)23(1 — f)bhChapter 1. Introduction^ 151.2 Nucleo-Cytoplasmic GynodioecyMale sterility in the majority of gynodioecious species appears to be caused by a mutationin a cytoplasmic genome that is negated by a restorer allele or alleles at a nuclear locusor loci. Nucleo-cytoplasmic gynodioecy can be extremely complex, depending on thenumber of sterile cytoplasms, the number of restorer loci, whether a restorer locus actson one or several sterile cytoplasms, and whether fertile cytoplasms coexist with thesterile.At present no general theory exists that provides conditions for female invasion in anyclass of nucleo-cytoplasmic gynodioecy. Nevertheless, numerical models have suggestedsome qualitative conclusions. In the F-S model, a single fertile cytoplasm and sterilecytoplasm are possible, and the sterile cytoplasm is restored by a single nuclear locus. Ifthe restorer allele and the sterile cytoplasm have no pleiotropic effect on female fertility,then the cytoplasmic polymorphism is lost (Charlesworth and Ganders, 1979). If theabove conditions for nuclear gynodioecy are met, the sterile cytoplasm is fixed, whereuponthe system becomes equivalent to nuclear gynodioecy; if the above conditions are unmet,the sterile cytoplasm is lost.If the restorer allele and the sterile cytoplasm (both or singly) have pleiotropic ef-fects on female fertility, and if those effects are multiplicative, then conditions for fe-male invasion can be relaxed, equilibrium female frequency can be higher than would beexpected under nuclear theory, and gynodioecy maintained under conditions in whichfemales would be lost in the absence of the cytoplasmic polymorphism (Charlesworth,1981; Delanney, et al., 1981; Ross and Gregorius, 1985).In the S-S model, no fertile cytoplasms exist, but two sterile cytoplasms are possible,and each must be restored by its own nuclear locus. This model has not been thoroughlyChapter 1. Introduction^ 16explored, but the current results indicate that conditions for female invasion and equi-librium female frequencies are the same for nuclear gynodioecy unless the two restorerloci are antagonistic (Gouyon, et al., 1991). If the restorer allele at one locus interfereswith the restorer allele at the other locus, such that neither completely restores malefertility in its respective cytoplasm, then undamped limit cycles in frequency of the twocytoplasms and in female frequency can develop, and their amplitude increases with thedegree of antagonism.Negative pleiotropy of the restorer allele in the F-S model constitutes an additionalgenetic form of a "female advantage" which, strictly speaking, is a disadvantage to somehermaphrodites (but not to those in the fertile cytoplasm that lack a restorer). Althoughthe antagonism between restorer alleles in the S-S model can result in the presence offemales in higher frequencies than would be predicted from nuclear equilibrium theory,such antagonism does not necessarily produce a mean female superiority. If antagonismis expressed as a depressed male fertility, then female invasion is facilitated only by aperiodic low frequency (or elimination) of one of the two restorer alleles, which allowsinvasion of females of the unrestored cytoplasm. Of course, females invade in this processonly if they have some mean superiority over hermaphrodites, but this advantage isentirely independent of the restorer antagonism. If antagonism affects the female functionof the restored hermaphrodite, then it will produce a mean inferiority in seed fitness ofhermaphrodites in addition to the periodic elimination of one or the other restorer allele.Any negative side effect of a restorer can be considered a genetic defect, which onecould reasonably expect to diminish over evolutionary time as selection favors modifieralleles that compensate for the defect, or alternative mutants that restore fertility withoutreduction of other components of fitness. Although negative pleiotropy of restorers hasyet to be demonstrated in natural populations, its existence has been defended on thebasis of an asserted similarity between cytoplasmic male-sterility with nuclear restorerChapter I. Introduction^ 17genes, and respectively plant pathogen-infection and nuclear resistance-genes, coupledwith the observation that resistance genes often have negative side effects (Gouyon, etal., 1991).In any case, in both the F-S and the S-S models, a wide range of female frequenciesare possible for any given selfing rate, inbreeding depression, and non-outcrossing femaleadvantage. Testing of sex ratio theory under these conditions is not possible without acomplete understanding of the genetics of male sterility, fitness information on a largenumber of genotypes, and in some cases long-term monitoring of populations.1.3 All Gynodioecy: Empirical ResultsResearch on the sources of the female advantage in gynodioecious angiosperms, regard-less of the inheritance of male sterility, have entirely put to rest any notion that suchadvantage is at all unitary. In some species inbreeding depression and selfing rate inhermaphrodites appear sufficiently high to maintain females at or near their observedfrequencies assuming nuclear inheritance (Kohn, 1988; Sakai, et al., 1989). In oth-ers inbreeding depression appears to play no appreciable role in maintaining females,and developmental advantage (termed "resource compensation" by Eckhart [1992]) ap-pear to be sufficient or nearly so (Shykoff, 1988; Ashman, 1992; Eckhart, 1992; Delph,1990a). In still others, both inbreeding depression and developmental advantages simul-taneously contribute significantly to the female advantage (Assouad, et al., 1978). Inself-incompatible species, stigmatic clogging of self pollen may block access, germination,or tube growth of nonself-pollen, and thereby reduce rates of fertilization in hermaphro-dites (Kikuzawa, 1989). Pollen-seeking florivorous insects may decimate the seed set ofhermaphrodites while leaving females untouched (Wagner and Miller, 1984).Because the degree of ovule success in part determines the sex ratio in a gynodioeciousChapter 1. Introduction^ 18population, the latter can provide information on the sources of the female advantage. Ifthe sex ratio varies among populations due to varying female ovule success, then correla-tions between sex ratio and other biotic and abiotic factors may be due to an advantageconferred by those factors on females (Sun and Ganders, 1986; Delph, 1990a). Suchcorrelations, however, constitute incomplete evidence for the sources of female advan-tage, because they can only indicate which component of female fitness varies amongpopulations; this component may not be the primary source of female advantage.The above empirical studies and theoretical research over the last 15 years suggest atleast five possible causes of spatiotemporal variation in sex ratio: founder effect, variationin sex allocation, cyclical frequency-dependent ovule success, variation in pollen flow, andvariation in inbreeding depression. To date the founder effect has been studied in detailonly for nucleo-cytoplasmic male sterility (Belhassen, et al., 1989; Boutin, et al., 1989;Frank, 1989). If several male-sterile cytoplasms exist, each restored by a different nuclearlocus, then colonization will often result in the presence of sterile cytoplasms in theabsence of their specific nuclear restorers, whose presence requires independent, possiblylow-frequency, dispersal events. In this case, female frequencies will be high initially,and will decrease over time as restorer alleles migrate into the population. The resultwill be a negative correlation between female frequency and age of the population, anda time trend within any population of decreasing female frequency until an equilibriumis reached.Cyclical frequency-dependent ovule success occurs in both the F-S and S-S modelsof nucleo-cytoplasmic male sterility (Charlesworth, 1981; Gouyon, et al., 1991). In theF-S model, negative pleiotropy of the restorer often produces slow, damped oscillationsin female and cytoplasm frequency, and undamped oscillations in some regions of theparameter space (Schultz, unpublished). In the S-S model, a high frequency of one sterilecytoplasm can select against the restorer of a different sterile cytoplasm, reducing theChapter I. Introduction^ 19frequency of that restorer. This allows the other sterile cytoplasm to invade as females,and the temporary low frequency of its restorer allows transient high female frequencies,with the amplitude of the oscillation higher for more severe antagonism.Variation in sex allocation may operate in phenotypically plastic species in whichthe plasticity is qualitatively different in females and hermaphrodites (Delph, 1990b; seealso Charnov, 1982; Charlesworth, 1989; Kohn, 1989; Atlan, et al., 1992; Delph andLively, 1992). Under low resource conditions, any individual may allocate less materialand energy to growth, reproduction, or both; if females preferentially reduce allocationto growth, and hermaphrodites to seeds and fruits, then relative ovule fitness of herma-phrodites can be reduced at poor sites, and both female frequency and hermaphroditeallocation patterns will be correlated with site quality.In the presence of inbreeding depression in self-compatible species, spatiotemporalvariation in pollinator population density, in species composition, and in foraging be-havior can result in variation in the efficiency of outcrossing, and this in turn will causevariation in expression of inbreeding depression in hermaphrodites, and relative herma-phrodite ovule success. If outcrossing rates vary among populations consistently withtime, then female frequency will be negatively correlated with outcrossing rate in a givenflowering season. Because the dependence of sex ratio on outcrossing is influenced byinbreeding depression, variation in the latter will also contribute to female frequency. Inthe absence of among-population variation in outcrossing rate, sex ratio variation maybe explained by variation in inbreeding depression alone. Some workers have suggestedthat the presence of gynodioecy in some populations of a taxon and not others may beexplained by recent bottlenecks of the non-gynodioecious species, which resulted in lossof genetic variability and genetic load (Weller and Sakai, 1990; Maki, 1992).Pollen flow can influence female advantage independently of its effects on hermaphro-dite outcrossing rate (Kikuzawa, 1989; Widen and Widen, 1990). In self-incompatibleChapter 1. Introduction^ 20species, clogging of self pollen on the stigmatic surface can cause fertilization deficits inhermaphrodites, and consistent, site-specific variation in clogging rates could result insex-ratio variation. In contrast, in cases where fertilization of female (and outcrossedhermaphrodite) ovules is pollen-limited, any female advantage, regardless of its source,can be reduced or eliminated in sites with low cross-pollination rates. Clearly, low pollendispersal can have countervailing effects on female advantage and sex ratio, and its con-sequences may be difficult to predict in practice.1.4 Dioecy and SubdioecyTo be selectively favored, any loss of successful ovules in a hermaphrodite must be morethan compensated by a gain in successful pollen. Successful pollen, however, is a complexfunction of female frequency, selfing rate, pollen limitation, and inbreeding depression(Charlesworth and Charlesworth, 1978).1.4.1 Theory of Male InvasionA rare modified hermaphrodite that has traded a proportion T of successful ovules fora pollen fertilization advantage T relative to hermaphrodites will experience a geneticfitness F when invading a gynodioecy equilibriumFht (total available outcrossed ovules per hermaphrodite)(1 T)▪ (2)(selfed ovules produced by hermaphrodite)(1 — 7)▪ (outcrossed ovules produced by hermaphrodite)(1 — T)[(1^k) f + (1— s)1(1^T) -F [28(1^+ (1 — s)](1 — r).1 — f[(1 + k)f + -^+ 7-) + (1 + s — 2sd)(1 — 7).1 — f(1.23)Chapter 1. Introduction^ 21Substituting Equation 1.15 here, and setting F1', = Fh, where Fh = F for 7^T^0,gives the threshold fertilization advantage T necessary for invasion of a fully or partiallyfemale-sterile individual1 + - 2sdT = 7 k -F2sd — s'(1.24)1 sdassuming1 + k <0.5, required for gynodioecy.This equation assumes that all male-sterile individuals are female fertile, which willoccur if both sterility mutations are recessive regardless of linkage, or if the two loci arelinked, one mutation is dominant and the other recessive, and female sterility is intro-duced in a male-fertile individual. If these conditions are unmet (e.g., if both mutationsare dominant regardless of linkage), then the fertility threshold for male invasion will behigher to an unknown extent. In the case of linkage and reciprocal dominance, however,either subdioecy or dioecy is possible depending on the value of IT. The theory is notyet sufficiently developed to provide an expression for the threshold T necessary to pusha population from subdioecy to dioecy. In case of pollen limitation, T will be larger forgiven 7, but because there is no explicit solution for f, the precise amount is unspecifiablein general.These equations of course assume that males are invading a nuclear gynodioecy equi-librium, which is not generally necessary and may not be commonly true. The theoryagain is not sufficiently developed to provide even numerical conditions for male inva-sion of a pre-equilibrium nuclear or nucleo-cytoplasmic gynodioecy in specific cases; nonumerical models of male invasion into F-S or S-S gynodioecy have yet been explored.Furthermore, the ability of nucleo-cytoplasmic gynodioecy to evolve to dioecy hasbeen questioned by theoreticians. The details of nuclear control of dioecy have beendemonstrated in a large number of angiosperm species (Chattopadhyay and Sharma,1991). However, a large proportion, perhaps a majority, of the known male-sterilityChapter I. Introduction^ 22loci in hermaphrodite species appear to reside in the cytoplasm (in the mitochondrialgenome in the known cases) (Edwardson, 1970; Kheyr-Pour, 1981; Couvet, et al., 1986;Van Damme, 1986). Given that gynodioecy is a theoretically probable intermediate statein the evolution from hermaphroditism to dioecy, these observations call into questionthe evolutionary significance of nucleo-cytoplasmic gynodioecy: if dioecy is controlled bynuclear genes, can its male-sterility function be served by cytoplasmic genes?Several authors answer in the negative, under the assumption that, because incor-poration of cytoplasmic DNA into the nuclear genome is unlikely, any nuclear controlof sterility is likely to have originated in the nucleus. Thus, Ross (1978) distinguishesbetween stable and unstable gynodioecy: "stable gynodioecy often shows cytoplasmicinheritance, and it probably does not evolve towards dioecy because linkage cannot de-velop between nuclear female sterility and cytoplasmic male sterility." This view hasbeen reiterated recently by Richards (1986) and Sakai et al. (1989).However, loss of the cytoplasmic polymorphism, in the presence of nuclear restor-ers, will result in full nuclear control over male sterility. In the F-S model, fixation ofthe sterile cytoplasm in the absence of any restorer pleiotropy (or after the evolutionof modifier alleles that negate the pleiotropy) eliminates the cytoplasmic component ofnucleo-cytoplasmic gynodioecy, converting it into fully nuclear gynodioecy. This accom-plishes the "linkage" required by Ross (1978), and converts the population from "stable"to "unstable" gynodioecy (sensu Ross), a state now capable of evolving into full dioecy.This suggests that the few known cases of nuclear gynodioecy (e.g., Weller and Sakai,1991; Eckhart, 1992; perhaps Kohn, 1988) might have evolved through cytoplasmic mu-tations now fixed but with their expression controlled by the nuclear genome.However, some well-studied cases of nucleo-cytoplasmic gynodioecy appear ecolog-ically stable (e.g., Van Damme, 1986). A joint polymorphism in both cytoplasm andnucleus can be perpetuated by population instability in either the F-S or S-S model (forChapter 1. Introduction^ 23an extension of the S-S model see Frank, 1989), by antagonism between different nuclearrestorer loci in the S-S model (Gouyon, et al., 1991), or by pleiotropic effects of restorerand cytoplasm (Charlesworth, 1981, Delanney, 1981). However, in each of these cases, iffemales enjoy a fitness advantage then their frequency may be transiently or periodicallyhigh prior to an increase in restorer alleles, because in their absence the sterile cytoplasmwill increase until female seed fitness drops, as a result of pollen limitation, to a valueequal to hermaphrodite seed fitness. If restorer alleles appear at about the same timeor after female-sterility alleles, then abundant females during this transient period of"cytoplasmic runaway" might constitute a strong selective force favoring males, and thismight accelerate the evolution to dioecy. In this scenario, elimination of all but a singlemale-sterile cytoplasm might then occur simultaneously with the evolution of dioecy.1.4.2 Sources of Male AdvantageAs shown above, hermaphrodite selfing and inbreeding depression can be sufficient tomaintain females in a gynodioecious (or subdioecious) population. But as Equation 1.24shows, although inbreeding depression lowers the male fertility threshold for male invasionof a hermaphrodite or gynodioecious population, inbreeding depression will generally notbe sufficient for such invasion. The fitness of a male genotype (7 = 1) is expressedsolely through fertilization propensity (T) relative to other pollen-bearing genotypes.Inbreeding depression could cause higher fertility of males relative to hermaphroditesonly if the average male enjoyed lower genetic load than the average hermaphrodite. Thiswould occur only if males predominated in outcrossed progeny. However, males cannotpredominate in outcrossed progeny without superior fertility. Of course, the possibilityalways exists that such superiority is a result of chance linkage between female-sterilityalleles and the deleterious alleles at the load loci, making genetic load an indirect causeof male advantage, but such linkage is unlikely either to originate or persist for long.Chapter 1. Introduction^ 24However, though load in itself is not likely to cause a male fertility advantage, it doesreduce the advantage needed by males for invasion, regardless of the presence or frequencyof females. This is simply because, for any selfing rate, genetic load reduces the totalfitness of hermaphrodites relative to males. As shown in Equation 1.24, for low selfing,regardless of inbreeding depression, a roughly twofold fertility advantage of males isnecessary to compensate for loss of one of the two near-equal avenues of fitness (dependingon the value of k). For low inbreeding depression and high selfing rate, a virtually infinitemale advantage is necessary to compensate for the scarce outcrossed ovules, throughwhich any advantage must be exercised. For selfing rate and inbreeding depression bothapproaching unity, hermaphrodites are de facto males, and will thus compete for femaleovules on equal footing with true males: any fertility advantage in the latter will nowallow them to invade. But in any case, some fertility advantage in males, independent ofinbreeding depression, is necessary. If that advantage is sufficiently high, and if femalex male progeny contain no hermaphrodites or neuters, then hermaphrodites will beeliminated permanently and dioecy established. If male fertility advantage is moderate,or if female x male progeny contain hermaphrodites regardless of male fertility, thenhermaphrodites can persist permanently at low frequencies with males and females.Low or nonexistent pollen limitation creates sexual asymmetry in which an increasein an individual's attractiveness to pollinators raises its successful pollen grains whilehaving little or no effect on its ovule success. So whereas greater attractiveness is likelyto buy little female advantage over hermaphrodites, it can buy a large male advantage.For a steep pollinator learning curve, pollinators might avoid hermaphrodites and seekout the greater nectar and pollen rewards afforded by males. For a 1:10 ratio of males: hermaphrodites, a pollinator load of 1:1 male : hermaphrodite pollen represents atenfold male advantage. In the presence of discriminating pollinators, males could gainthis advantage with only a moderate transfer of formerly female resources to increasedChapter I. Introduction^ 25nectar, pollen, and other attractions.Like females, males can also gain advantage through higher survivorship and gameteproduction, but for the same reasons, these are not likely to be sufficient in themselvesfor invasion. Unlike females, males cannot gain an advantage through overall progenyquality, because there is no male parental investment. Males of course will benefit byfertilizing higher quality female ovules, but not more than hermaphrodites without afertilization advantage.1.5 Conclusions from TheoryIf sterility alleles are nuclear, then females will invade a hermaphrodite population only iftheir ovule fitness at introduction is more than twice that of hermaphrodites. Sufficientlyfertile females will increase on a sigmoid curve to an equilibrium frequency that increaseswith increasing female advantage and with decreasing pollen limitation. Outcrossingadvantage can double female ovule output, but only for high hermaphrodite selfing andinbreeding depression. These conditions will persist only in the absence of genetic vari-ation favoring higher outcrossing rates, and only if mutation rates to load alleles arehigh enough to balance their selective loss, whose rate is a positive function of selfingrate. Of course, intermediate developmental and outcrossing advantages can provide asufficient total ovule advantage to allow female invasion to high frequency (< 0.5) in ahermaphrodite population.The selective conditions for male invasion of a gynodioecious population are morecomplex, and depend on linkage, dominance, selfing rate of the hermaphrodites, femaleadvantage, and pollen limitation. Of course, males cannot invade unless they enjoy afertilization advantage over hermaphrodites. But in general, the threshold advantagedecreases as any female advantage over hermaphrodites increases. The only exceptionChapter 1. Introduction^ 26to this rule is hermaphrodite selfing rate. If inbreeding depression is less than 0.5, thenthe threshold male advantage increases with selfing rate, and as the former approachesone, the latter increases virtually without limit. If both hermaphrodite selfing rate andinbreeding depression are high, then hermaphrodites are nearly male, and a comparativelysmall pollen fertility advantage can compensate for loss of female function.Because outcrossing ovules are necessary for the expression of male fertilization ad-vantage and hence for the invasion of males, invasion generally occurs more easily ina gynodioecious than a hermaphrodite population. However, if male advantage is suf-ficiently high, then conversion to dioecy can occur even if female fertility is less thandouble that of hermaphrodites. In general, the fertility of males required for invasion ofa gynodioecious population will be roughly 1.5-5 times that of hermaphrodites for bio-logically realistic regions of the parameter space (Charlesworth and Charlesworth, 1978,but this model assumes no female selfing or pollen limitation), depending on linkage,dominance, and the degree of female advantage.Although inbreeding depression facilitates male invasion, it is never sufficient for theevolution of subdioecy or dioecy. At the very least, a pollen-fertility advantage is neces-sary for males, and this may be due to selective behavior of pollinators, resource transferduring sporogenesis, or both. Developmental advantages are unlikely to double the suc-cessful ovules of females without the interaction of other species. Such interaction mightinclude frugivore selection of female fruit, and herbivore selection of hermaphrodite in-dividuals. In the absence of such doubling, gynodioecious or even dioecious species canrevert to hermaphroditism easily, with changing pollinator communities and increasingoutcrossing rates.Chapter 1. Introduction^ 271.6 ObjectivesIn this thesis I intended to address both theoretical and empirical questions in the evo-lution of unisexuality in angiosperms. One of the most interesting theoretical questionsstill unanswered in the late 1980s concerned the evolution of dioecy through an inter-mediate stage of gynodioecy with nucleo-cytoplasmic male sterility: can such evolutionoccur, and under what conditions?In Chapter 2 I answered this question by constructing several numerical populationgenetic models, deterministic and stochastic, using standard population-genetics recur-sion equation theory. These models, built with the Pascal programming language, allowarbitrary specification of the magnitude of selfing rate, inbreeding depression, pollen lim-itation, mutation rates at all loci, effective population size, and independent fitnessesassociated with every genotype, and address dynamics of any number of cytoplasm typesand three nuclear loci with arbitrary linkage and any number of alleles per locus. I usedthese models to determine (1) the threshold pollen fertility necessary for the spread ofmales into equilibrium nuclear- and cytoplasmic-nuclear gynodioecy of both the F-S andthe S-S system, (2) the threshold pollen fertility necessary for the conversion of thesesytems of gynodioecy into dioecy, and (3) the pre-equilibrium dynamics of such spread,to explore the relative rates of spread into nuclear and cytoplasmic-nuclear systems.In Chapters 3 and 4 I report the results of empirical studies of sex ratio and femaleadvantage in Hawaiian species of the Composite genus Bidens, B. sandvicensis and B.cervicata. The conditions promoting evolution of unisexuality in the Hawaiian archipelagois of special interest because of the high frequency of gynodioecy and dioecy in the nativeflora (Carlquist, 1980). Although many gynodioecious species show various intermediatestates of male sterility (Boutin, et al., 1989; Agren and Willson, 1991; Atlan, et al.,1992), male sterility in Bidens is complete. Previous work on the genetics of theseChapter I. Introduction^ 28species showed no evidence of any cytoplasmic polymorphism within taxa, and in Bidenssandvicensis male sterility appears to be unlinked digenic recessive (Sun, 1987). Femalesof different taxa fertilized by the same hermaphrodite often yield different progeny sexratios, suggesting differences in inheritance of male sterility among taxa; these differencescan be explained by the existence of two sterile cytoplasms, only one of which occurs inany gynodioecious species of Hawaiian Bidens.Chapter 3 reports the results of studies of sex-ratio correlates in four populationcenters of these species along the western ridge of Waimea Canyon, Kauai, to determinethe degree to which among-population variation in sex ratio (over the four years of thisstudy) is explained by (1) 1989 outcrossing rate as estimated using maximum likelihoodanalysis of isozyme markers, (2) local site characteristics, (3) taxon of the population,and (4) any morphological gender dimorphism.Chapter 4 reports results of fitness experiments performed to determine (1) whetherthe female advantage is sufficient to explain the observed female frequencies under nu-clear male-sterility and complete dominance, (2) the proportion of any advantage toopen-pollinated progeny of females attributable to inbreeding depression in hermaphro-dites, and (3) any female superiority in survivorship or fecundity. These questions areanswered through the measurement of (a) the total inbreeding depression in hermaphro-dite families of Bidens sandvicensis, subspecies sandvicensis and confusa, expressed asone minus the self:outcross performance in seed set in the glasshouse, germination ratein the open-air nursery on Kauai, and survivorship/fecundity in the field adjacent tonatural populations of Bidens sandvicensis; (b) the total effect of maternal sex on fitnessof open-pollinated progeny of females and hermaphrodites collected from natural popula-tions and monitored for germination in the growth chamber, and survivorship/fecundityunder the same field conditions as the selfs and outcrosses; (c) the relative survivorship offemales and hermaphrodites in natural populations; and (d) the relative fitness of femalesChapter I. Introduction^ 29and hermaphrodites of known parentage in the field plots.Chapter 2Theoretical Dynamics of Female Sterility2.1 The ModelsFour' families of models were constructed (Table 2.1). The F-S-D model consisted of a fer-tile cytoplasm F, a restorable male-sterile cytoplasm S, and a non-restorable male-sterilecytoplasm D. A nuclear restorer locus codes for two alleles: a restorer that completelyrestores male fertility in the S cytoplasm, and a maintainer allele that fails to restoremale sterility in the S cytoplasm. Linked to this locus is a female-sterility locus carryinga sterility and fertility allele. The F-S model is equivalent to the F-S-D minus the Dcytoplasm, and is the same model as that of Delanney et al. (1981) and Charlesworth(1981), but with a female-sterility locus added. The S model is equivalent to the F-Smodel minus the F cytoplasm; i.e., entirely nuclear male-sterility. The S-S model followstwo restorable male-sterile cytoplasms Si and S2, and three nuclear loci. Unlinked lociN and M code for restorer (N, M) and maintainer alleles (n, m) for Si only and S2 onlyrespectively. Locus F, linked (with arbitrary recombination rate) to locus N, codes for afemale-sterility (F) and a female-fertility (f) allele. The S-S model is the same model asthat of Gouyon et al. (1991), but with a female-sterility locus added. In all models, thefemale sterility allele acts in all cytoplasms independently of the presence or absence ofrestorer alleles."Antagonism" in the S-S model is defined simply as the condition wr < 1 (see Table2.2); the term is used synonymously with the term "cost of restoration" used previously'This chapter has been accepted for publication in the journal Evolution.30Chapter 2. Theoretical Dynamics of Female Sterility^ 31ModelSterilecytoplasmsFertilecytoplasmsRestorablecytoplasmNuclearrestorerlocusF locuslinked toS S None S M MF-S S F S M MF-S-D S, D F S M MS-S Si, S2 None 51, S2 N, M NTable 2.1: Description of the models.(Gouyon, et al., 1991) but avoided here because a cost of possessing a restorer alleledoes not necessarily occur in all genotypes, but rather only in individuals already malefertile. Since these individuals by definition already contain a restorer allele, the costof restoration occurs only in individuals with both restorer alleles (M and N); thus thecost of restoration can be conceived as an antagonism between these alleles. Althoughantagonism could be modelled to affect any fitness component, in the present treatmentit is assumed to reduce male fertility only (as shown in Table 2.2).In all models, the plant species is assumed to have non-overlapping generations, andgenotype frequencies are calculated with standard recursion equations. The relativefrequency of genotype k in generation t +1 isPk,t+1 = q Epi,tpiok.iiaibj (1 _ si) + (1 _ Epbiij[31(1 — d)^(1 — si)q},^(2.25)IiEPi,tPJ,taibigk./3 where i and j represent hermaphrodite maternal and hermaphrodite or male paternalparents respectively, 1 represents female maternal parents, pi,t is the proportion of geno-type i in generation t, gjj is the proportion of genotype k in the progeny of the crossi x j, ai and b3 are the female and male fertility respectively of genotypes i and j, si isthe selfing rate of genotype i, q is the proportion fertilized of outcrossed ovules, 1 — dChapter 2. Theoretical Dynamics of Female Sterility^ 32F— if(51) MN/-- 0 1Wr Wm Wr(51) mN/m— 0 1w, 1(Si) Mn/—n 0 wf0 0(Si) mn/mn 0 wf0 0(S2) MN/-- 0 1Wr Wm Wr(S2) mN/m— 0 wf0(S2) Mn/—n 0 1wrn 1(S2) mn/mn 0 wf0 0Table 2.2: Fitness values of genotypes in the S-S model, multiplicative male fitness.Dominant male-sterility restorers M of S2, N of Si. Dominant female-sterility F. Uppercell: female; lower cell: male. The parameters wf and Wm represent the phenotypic effectof male sterility on ovule fitness and of female sterility on pollen fitness, both relative tohermaphrodites. For non-multiplicative male fitness (Figure 2.3) replace ?Donn, with wr.The terms "antagonism" and "cost of restoration" are defined as 1 — wr, and representa loss of male function in individuals possessing both restorer alleles (N and M), relativeto hermaphrodites. As this table shows, the cost of restoration is assumed to be paidentirely through loss of male fertility.is the relative fitness of selfed progeny (d = inbreeding depression), and the ph,t+i arescaled to sum to unity. Selfing rates were assumed to by determined by sex phenotypealone, while male and female fertilities (as shown in Tables 2.3 and 2.2) were assumed toresult from the product of genetic and phenotypic components.Several parameters were varied: hermaphrodite selling rate (sh ), female "selfing" rate(sf), inbreeding depression (d), phenotypic fertility contributions (wf and Wm), genotypicfertility contributions (w7, and we affecting female fertility in the F-S model, and wraffecting male fertility in the S-S model), recombination rate (r) between the nuclearChapter 2. Theoretical Dynamics of Female Sterility^ 33F— ff(S) M— 0 ?linWm 1(S) mm 0 wf0 0(F) M— 0 wnwcWm 1(F) mm 0 wcWm 1Table 2.3: Fitness values of genotypes in the F-S model. Dominant male-sterility restorerM, dominant female sterility F. Upper cell: female; lower cell: male. The parameters wfand w, defined as in Table 2.2. The parameters tan and w, represent the genotypic effectsof the restorer allele and the fertile cytoplasm on ovule fitness, relative to females (whichlack both the restorer and the fertile cytoplasm). Phenotypic and genotypic effects areassumed to combine multiplicatively.male and female sterility loci, and pollen limitation (q). Pollen limitation is modelledassuming n independent pollinator visits per plant, female frequency f in the population,and pollinator efficiency of fertilization c, such that the proportion q of outcrossed ovulesfertilized isq = 1— [1 —c(1 — f)]Th . (2.26)This assumes a linear relationship of slope c between frequency of pollen-bearing plantsand the proportion of ovules fertilized per pollinator visit of the plant. The female"selfing" rate S f represents a level of biparental inbreeding sufficient to account for a lossof fitness equal to 1 — dsf. Assuming 8/ > 0 simply alters the relative fitness of femalegenotype 1; one could alternatively incorporate this component into the fertility terms.Moreover, if 8/ is the same for all females, then the results are not affected if 8/ is set tozero in Equation 2.25 and si is replaced withSi(1 — Sf)Si.adj — 1 — dS f(2.27)where s is the selfing rate of hermaphrodite genotype i, sf is the effective female selfingChapter 2. Theoretical Dynamics of Female Sterility^ 34rate (the same for all females), and d is the inbreeding depression, assumed the same infemales and hermaphrodites.Stochastic runs were done to demonstrate the effect of random genetic drift on theconsequences of male invasion in the S-S model, and to provide a rough initial corrobora-tion of the differences observed in rates to evolution in the deterministic runs. Genotypesof individuals in the stochastic runs were assigned by comparing a randomly drawn num-ber in the interval [0,1] to the theoretical frequency of each genotype calculated eachgeneration. Mutations were incorporated after a random number in the same intervalwas drawn for each of the alleles, nuclear and cytoplasmic, for each of 200 individuals,and compared to the set mutation rates. Random numbers were generated with a com-monly used subroutine yielding an unknown period greater than 109 ("rand3" in Dewand James, 1983). In all stochastic runs, the initial population consisted entirely of thehomozygous hermaphrodite.In the stochastic runs of models S, F-S, and F-S-D, for each set of parameters popu-lations were allowed to evolve for 5, 10, 20, 40, 60, 80, 100, 150, 200, 400, and sometimes500 generations, and the mean frequency and variance for each genotype over the pop-ulations calculated at the end of each interval. For runs from 5 to 150 generations 50populations were followed; for runs above 150 generations 20 populations were followed.Each run was independent of the previous; i.e., 50 populations were allowed to evolve 5generations; a second, independent group of 50 populations were allowed to evolve for 10generations; a third, independent group of 50 populations were allowed to evolve for 20generations, and so on. Hence, the results represent not 50 (or 20) evolving populationssampled at each time interval, but rather 400+ populations evolving, in separate groupsof 50 (or 20), to each time endpoint. In cases of non-restored cytoplasmic male-sterility,occasional extinctions occurred due to fixation of females. In these cases the numberof extinctions was tallied, new runs were made until 50 (or 20) populations survivedChapter 2. Theoretical Dynamics of Female Sterility^ 35to the end of the interval, and genotype frequency statistics were calculated for thesepopulations only.2.2 Results2.2.1 Cytoplasmic Runaway and Rates of EvolutionIn the absence of mutation and drift, evolution to dioecy can be over 50 times as fastthrough a shift from fertile to sterile cytoplasm than when only the sterile cytoplasm ispresent (Figure 2.1 and Table 2.4). This result holds for numerous parameter combina-tions in both the S-S and the F-S models, and for numerous genotype starting frequencies(Table 2.4). The only obvious exception occurs under large negative pleiotropy of the re-storer allele in the F-S model (and the fertility allele in the S model) (Table 2.6, footnotei).20 40 60 80—0— (Si) Mnf/Mnf-F(S1)MNF/Mnf-M—0— (Si) MNf/Mnf-H(S2)Mnf/Mnf-H1.00.8 -0.6 -0.4 -0.2 -0.0010 200a) 0.40.20.01.0—0-- (S) mf/mf-F(S) MF/mf-M(F) mf/mf-H0.8 -"0.61.0—.0— mf/mf-FJ. MF/mf-MMf/Mf-HMf/mf-H0.4 -0.2 -0.0100^200Generation3000.8 -0.6 -Chapter 2. Theoretical Dynamics of Female Sterility^ 36Figure 2.1: Trajectories to dioecy, deterministic models. S-S, F-S, and S models: Dom-inant restorer and female-sterility; recessive male-sterility. sh = 0.7, sf^0.2, d = 0.9,wf = 1.0, Wm = 2.5, wn =^= 1, € = 0.005, n = 600, no mutation, no drift, noextinctions. a: S-S model. Start with 0.99 (S2) Mnf/Mnf, 0.005 (SO mNf/mNf, 0.005(Si) mNF/mNf. b: F-S model. Start with 0.985 (F) mf/mf, 0.005 (F) Mf/mf, 0.005 (F)MF/mf, 0.005 (5) mf/mf. c: S model. Start with 0.99 Mf/Mf, 0.005 Mf/mf, and 0.005MF/Mf, S cytoplasm only. Appended F, M, H: female, male, hermaphrodite.Chapter 2. Theoretical Dynamics of Female Sterility^37Parameters Generations to DioecySh,Sf,d,c, W f n WmMalesheterogameticFemalesheterogameticF-S S S-S F-S Swr = 0 wr = 0.5sh = 0, - 2.1 10119 770 13\18 20\23 27 2434S f = 0,d = 0,c = 1,2.53.03.591188118811859150145611\1310\1310\4713\1412\1211\122117161466983740WI = 3. 4.0 8118 429 10\43 11\11 15 595sh = 0.5, 1 3.5 T15011157' T202 T210' Tb T860' T240'S f = 0,d = 0,c = 1,24.02.12.5T17511185cG1441111040'61711513hT210'G6100'925hT200'G1830'1210hTdG1G'T680'Gg1447hT220'G3570'971hWf = 3. 3.0 121111 147 24\37 44\181 365 1565 2.1 12211100 1076 202\270 T3 800 12322.5 171113 227 35\45 56\123 142 2463.0 10119 126 17\22 29\36 62 12910 2.1 991169 1021 160\202 511k 283 11602.5 171112 225 34\43 54\120 58 2433.0 10119 125 16\22 29\36 29 128sh = 0.5, 1 3.5 6116 42 9\40 10\11 22 81S f = 0,d = 0.8,c = 1,wf = 3.24.02.12.53.06116911871177116397354468\3614\2010\1710\4210\1119\2314\1610\1218332418682361591145 2.1 9117 72 14\20 19\22 23 2472.5 7117 53 10\17 13\16 18 1673.0 6116 45 9\40 10\12 15 12010 2.1 9117 72 13\20 19\22 21 2482.5 7117 53 10\17 13\16 17 1683.0 6116 45 9\40 10\12 14 120sh = 0.7, 600 2.5 131111 256 15\22 33\38 101 303S f = 0.2,d = 0.9,c = 0.005,wf = 1.10003.02.53.011111012111010111015122414112\1515\2212\1515\1833\3815\18394726156268147'Males and females constant at 0.3619 and 0.3913 respectively, by indicatedgeneration.Chapter 2. Theoretical Dynamics of Female Sterility^ 38bMales and females constant initially (240-280 generations) at 0.3619 and 0.3913respectively, then regular oscillations between the two cytoplasms. Total femalesoscillate between 0.29 and 0.54, males between 0.02 and 0.33; period about 55generations.'Males and females constant at 0.4156 and 0.4286 respectively by indicatedgeneration.dOscillation of increasing period between near-dioecy (0.4156 males and 0.4286females) and near-gynodioecy (0.0741 males and 0.1743 females).'Males and females constant at 0.0414 and 0.258 respectively by indicatedgeneration.Males fail to invade.g No male invasion by 10,000 generations, but f allele still present at low frequency.h Males and females constant at 0.468 and 0.480 by indicate-d generation.iTemporary initial phenotypic dioecy (males = 0.468, females = 0.480), butmales lost by 900 generations. Undamped oscillation by 2500 generations, femalesroughly 0.38.JComplex oscillation of males and females around roughly 0.28 and 0.47respectively.kTime at which hermaphrodite frequency falls below 0.05; neuters remain atequilibrium frequency of 0.192.Table 2.4: Generations to dioecy under nuclear and nucleo-cytoplasmic gynodioecy.Dioecy defined as the frequency of the final male and final female genotype each greaterthan 0.4, and the sum of the two greater than 0.95. In the case of the S-S model, totalfrequency of all males plus all females often exceeded 0.95 before genotypic equilibriumwas reached. For this model, the first figure indicates time when total males plus totalfemales exceeded 0.95, while each exceeded 0.4; the second indicates time that dioecy (asdefined above) was reached. For the F-S models equilibrium was reached a few genera-tions after total frequency of all males plus all females exceeded 0.95. In the F-S modelwith males heterogametic, starting frequencies were 0.985 (F) mf/mf, 0.005 (F) Mf/mf,0.005 (F) MF/Mf, 0.005 (S) mf/mf to the left of the vertical parallel lines, and the sameexcept that (F) MF/Mf was replaced with (F) MF/mf to the right of the parallel lines. Inthe S model with males heterogametic, starting frequencies were 0.99 (S) Mf/Mf, 0.005(S) Mf/mf, 0.005 (5) MF/Mf. In the F-S model with females heterogametic, startingfrequencies were 0.985 (F) MF/MF, 0.005 (F) MF/mF, 0.005 (F) MF/mf, 0.005 (5)MF/MF. In the S model with females heterogametic, starting frequencies were 0.99 (5)mF/mF, 0.005 (S) mF/mf, 0.005 (5) MF/mF. In the S-S model, starting frequencies were0.99 (S2) Mnf/Mnf, 0.005 (Si) mNf/mNf, 0.005 (Si) mNF/mNf. If dioecy is not reachedwithin 10,000 generations, "T" indicates males, females, and hermaphrodites present,each at a frequency greater than 0.1, and "G" indicates female and male frequency re-spectively greater than 0.1 and less than 0.05. In all shown cases in the F-S model,w, = wri = 1; consequently equilibrium nucleo-cytoplasmic gynodioecy is not possible.This assumption is not generally necessary for the accelerating effect, however (see TableChapter 2. Theoretical Dynamics of Female Sterility^ 392.6).However, in the stochastic versions of these models, the accelerating effect is somewhatlost. If male sterility is a dominant nuclear trait and only a single (sterile) cytoplasm ispossible, then high mutation rates at both nuclear loci (e.g., iuN = 0.01) create a mutationpressure that more than compensates for the high selective force exerted by females in theF-S dominant model, and evolution to dioecy is at least as rapid. For a recessive restorer,nuclear mutation rates 0.001, cytoplasm mutation rates 0.01, an effective population sizeof 200, and other parameters as in Figure 2.1, the double-heterozygous female genotypereaches only 0.0184 (s.d. 0.0908) in frequency after 400 generations, as compared to0.1841 (s.d. 0.234) in a single-cytoplasm population with dominant male-sterility. Fornuclear mutation rates reduced to 10-4, the rate of female invasion is slowed somewhatin the S model, but this rate is still not lower than for the F-S model.In contrast, if male sterility is recessive, then high mutation rates are less effectivein accelerating dioecy, and the speeding effect of high initial female frequencies gains inimportance. With parameters as above, except that nuclear mutation rates equal 10,female and male frequencies reach respectively 0.472 and 0.442 (s.d. 0.0946 and 0.1355)by 400 generations in the F-S model with dominant restorer, but respectively 0.191 and0.151 (s.d. 0.213 and 0.211) in the S model with recessive male-sterility. This differenceis due presumably to the wider zone of attraction of the dominant allele.The accelerating effect may also disappear under the stochastic version of the S-Smodel, if initialized with 100% hermaphrodite (S2) Mnf/Mnf, and all other genotypesare introduced through random mutation. This is because selection for any particularmale is highly dependent on the relative frequency of the two classes of females, which mayvary greatly in an undamped oscillation (Figure 2.2). If the appropriate male genotypeis present at the peak frequency of the same-cytoplasm female, then evolution to dioecy—0— Total Female Steriles—U-- Female Sterile (Si) mNF/mnfAI— Male Sterile Si—0- Male Sterile S24444.410.607525 1000.40..,cf`'ao:cr.r..0.200.00o 50GenerationChapter 2. Theoretical Dynamics of Female Sterility^ 40Figure 2.2: Loss of males introduced out of phase, S-S Model. Dominant restorer andfemale-sterility; recessive male-sterility. sh = 0.7, sf = 0, d = 0.9, wf = 1.0, Wm = 2.5,c = 0.005, n = 600, wr = 0.5, no recombination between N and F. Started with allgenotypes as in the Si trough, but in addition the male Si mNF/mnf at 0.005. Theseparameters give rapid evolution to dioecy if the Si male is introduced at the first peak ofthe Si female frequency. Antagonism is dominant over the phenotypic effect of maleness;i.e., fertility of males with both restorers (M and N) is wr rather than wrwm.Chapter 2. Theoretical Dynamics of Female Sterility^ 41can occur in several generations. However, if it appears out of phase, evolution to dioecywill be slower, and for some parameter sets will not occur at all (Figure 2.2). Withantagonism, the greater average time required for evolution to dioecy under the stochasticversion of the S-S model is simply due to the time needed for the appropriate malegenotype to appear in phase; when it does, dioecy is reached quickly.How quickly dioecy is reached depends on the fitness relationship between femalesterility and the restorer alleles. If male fitness is the product tarnwr of a phenotypiceffect and one minus the antagonism (suffered only in individuals bearing the restorerallele at each of the two loci, Table 2.2), then the advantage of female sterility is greaterand the evolution to dioecy faster than if the relative male fitness were simply equal toone minus the antagonism (wr in Table 2.2). In the latter case, time to evolution todioecy can be strongly correlated with antagonism (negatively) and with the advantageof the cytoplasm (Si) restored by the locus linked to the female sterility locus (posi-tively) (Figure 2.3a). Each point on the graph of Figure 2.3a represents the mean offive stochastic runs; if any of the runs failed to reach dioecy by 1000 generations, thepoint is not plotted. The advantage of the Si cytoplasm is expressed here entirely asan ovule fertility advantage of the genotype (Si) mnf/mnf. Multiple regression analysisyielded standard regression coefficients of 0.63 and -0.28 (residual d.f. = 497, p < 0.001)respectively for the antagonism and fertility of (Si) mnf/mnf. The apparent reason isthat the amplitude of the oscillation in female frequency increases with cost, and higherpeak female frequencies constitute a stronger selective force for males. In the case of mul-tiplicative male fitness, the stronger advantage of the female-sterility allele overpowersthe accelerating effect caused by a cost of restoration (Figure 2.3b).In the F-S and S models, when mutation rates in both directions are large at all loci(e.g., ttN = 2), a new equilibrium is possible with males, females, and the heterozygoushermaphrodite genotype. With parameters as in Figure 2.1 and all mutation rates 0.01,Chapter 2. Theoretical Dynamics of Female Sterility^ 4210008006004174 400200Fertility of (Si) mnf/mnf—A— 1.02—El — 1.06- .41) - 1.10- -*- - 1.14- - 1.18a, \-^\ \0.2^0.4Antagonism0.6^08600500 -0.1CO0)g" 4'00 -o4 300 –.2ro^4%.• 200 - ■ "..^,C.7.4^N1 00 IF:"^rSi Antagonism--43— 0.8—El — 0.6- - 0.4- -* - - 0.2- - 00.2^0.4^0.6^08S2 AntagonismFigure 2.3: Antagonism and rate of evolution to dioecy, S-S model. Dominant restorerand female sterility; recessive male-sterility. sh = 0.7, s f = 0, d = 0.9, N = 200, wf = 1.0,Wm = 2.5, w5 = 0.5, c = 0.005, n = 600, all mutation rates 0.001, no recombinationbetween N and F, no extinctions. Start with 200 (S2) Mnf/Mnf. a: Fitness of genotype(Si) mnf/mnf varied, cost of restoration the same in the two cytoplasms; each pointrepresents the mean of five runs. b: cost or antagonism in cytoplasm Si varied againstcost in S2; each point represents a single run.Chapter 2. Theoretical Dynamics of Female Sterility^ 43subdioecy occurred with the heterozygous hermaphrodite reaching a mean frequency of0.130 (s.d. 0.047) in the F-S model by about 30 generations and 0.142 (s.d. 0.048) in theS model by about 80 generations. This subdioecy equilibrium is maintained by mutationrates high enough to outbalance the low rate of loss of the homozygous hermaphroditeunder borderline conditions favoring dioecy, and occurs whether the restorer (F-S model)and female fertility (S-model) alleles are dominant or recessive.2.2.2 Conditions for Male InvasionFate of Males in the Presence of a Non-Restorable CytoplasmIn general, a non-restorable male-sterile cytoplasm can easily invade a population at anystage in its evolution from hermaphroditism to full dioecy, and in a fully dioecious popu-lation (no hermaphrodites possible either by mutation or recombination), the probabilityof extinction due to fixation of non-restorable male-sterility is independent of pollen lim-itation. In general, males will fail to invade or will invade temporarily, after which boththe female-sterility and the restorer alleles will be lost. Assuming a dominant female-sterility allele F, a dominant male-sterility restorer M, and three cytoplasms: F malefertile, S restorable male-sterile, and D non-restorable male-sterile, the final populationcomposition is the same for a wide range of initial conditions that allow production ofhermaphrodites with either F or S cytoplasm.For example, if the starting population is 100% hermaphrodite (genotype (F) mf/mf),and if conditions favor evolution to dioecy (female advantage due to high hermaphroditeselfing and inbreeding depression, and unspecified male-fertility advantage), then evolu-tion is rapid towards a simple cytoplasmic polymorphism of the female (D) Mf/Mf andhermaphrodites dominated by the genotype (5) Mf/Mf.Chapter 2. Theoretical Dynamics of Female Sterility^ 44The final frequency of the D cytoplasm may be approximated by11—Os(1—sd)17-;6 + 1-0s(1-s)PD=^ 7 (2.28)where Os is the ovule production of S individuals relative to D, and s is the hermaphroditeselfing rate. If Os = 1 then selfing rate becomes irrelevant and the middle term in thenumerator reduces to di/n. The equilibrium in the face of mutation rate /IDS from D toS and psi) from S to D may be obtained from the recursion equationPDiisttsp + pp (1 — tips)] q [Maps + Ps (1 — lisp)] [8(1 — d) (1 — s)q] 0 swhere ps = 1 — pp, and q is from Equation 2.26. This equation, however, assumes thatall individuals with the D cytoplasm are female, and all those with the S cytoplasm arehermaphrodite; hence it applies only near equilibrium under the present assumptions.Essentially the same result occurs if the population is initially dioecious (genotypes (S)mf/mf and (5) MF/mf), and either mutation rates or recombination rate between maleand female sterility loci are nonzero. In either case, hermaphrodite genotypes appearoccasionally at the start, but eventually the hermaphrodite genotype (S) Mf/Mf codom-inates with the female (D) Mf/Mf in the same final equilibrium as above (Figure 2.4a).However, if the population starts at dioecy (genotypes (S) mf/mf and (S) MF/mf), andall mutation rates are zero except S to D and back, then the D cytoplasm can invadeto the equilibrium frequency p /(SD \PDS + is). For psDN > 0.2 equilibrium is reachedin less than 100 generations. In this case,and consequent extinction of the population is almost inevitable by generation 400. Thisresult is dependent only on population size and relative rates of mutation, and assumesequal fitness and pollen limitation on all females.[PS itSD PD (1 PDS)] q ,^(2.29)if^> 10frup5 and N < 200, fixation of D(S) Mf/Mf-H(S) mf/Mf-H(D) Mf/Mf-F(D) mf/mf-F50 150100 2001.0—0— (S) mf/mf-F(S) MF/mf-M—13-- Proportion Extinct— 0— (S) mf/mf-F—6-- (S) MF/mf-M- (D) mf/mf-F(D) MF/mf-F100^200^300Generation0.8-a) 0.6-a-n);-1 0.4 -P•Ti0.2-0.01.0400 5000.800.6gl" 0.44.0.20.0Chapter 2. Theoretical Dynamics of Female Sterility^ 45Figure 2.4: Invasion of D cytoplasm into dioecious population. F-S-D model. Domi-nant restorer and female-sterility; recessive male-sterility. sh = 0.7, sf = 0.2, d = 0.4,N = 200, wf = 1, Win = 2.5, wn = w = 1, c = 0.005. Start with 1:1 (S) mf/mf : (5)MF/mf. a: d = 0.4, n = 1000, ,usr) = //Ds = 0.01, all other cytoplasmic mutation rates0, all nuclear mutation rates 0.001, no recombination. Essentially the same trajectoriesoccur with recombination rate = 0.001, /LSD = tips = 0.001, and all other mutationrates 0. b: d = 0.9, n = 300, fisp = 0.01, lips = 0.001, all other mutation rates 0, norecombination.Chapter 2. Theoretical Dynamics of Female Sterility^ 46If the product of population size and combined mutation rate from S or F to D is low(e.g., 0.004 or less), then random drift prevents the D cytoplasm from invading either adioecious or a hermaphrodite population, and evolution from hermaphroditism to dioecyproceeds at a normal rate (trajectory not shown).Restorable Sterile CytoplasmsThe F-S model allows nucleo-cytoplasmic gynodioecy under pleiotropy of the restorerallele and the sterile cytoplasm (Charlesworth, 1981; Delanney, et al., 1981; Ross andGregorius, 1985). Equilibrium nucleo-cytoplasmic gynodioecy occurs in a boundary zonebetween the portion of the cytoplasm/restorer fitness plane where the cytoplasmic poly-morphism is lost (regardless of the outcome of the nuclear polymorphism), and theportion where the nuclear polymorphism is lost (and the cytoplasmic retained). Thisgenerally occurs for negative fitness pleiotropy of the restorer allele (regardless of thecytoplasm in which the allele occurs) and for positive pleiotropy of the sterile cytoplasm(regardless of the presence of the restorer allele); i.e., both wn and w, generally less thanunity. The lower the relative fitness of the restorer allele, the lower the fitness the fertilecytoplasm must be to maintain a nucleo-cytoplasmic polymorphism, and the lower thefemale fitness, the lower the value of /I), must be. Results of several thousand deter-ministic and stochastic runs over the restorer-cytoplasm fitness plane show that malescan generally invade regardless of the relative cytoplasm frequencies, but dioecy fails toestablish under sufficiently low relative fitness of the sterile cytoplasm, and low femaleadvantage within the sterile cytoplasm (Figures 2.5 and 2.6).The threshold pollen fertility for male invasion of an equilibrium nucleo-cytoplasmicgynodioecious population is similar to, and in many cases slightly lower than, the thresh-old needed for invasion of an equilibrium nuclear gynodioecious population, for the sameset of fitness parameters (Tables 2.5 and 2.6). Of course the lack of a general analytical1.201.000.80Wn 0.600.400.20_^.^.....• a^HFS-HFS-HFS ^HS-HS-HSCN-CN-SubCNN-N-DN-D-DHF-HF-AFCN-CN:AFN-SubCN-AFCN-SubCN-SubCNC-C-AF.C-SubCN-SubCN1.201.000.80Wn 0.600.400.20CN: •Chapter 2. Theoretical Dynamics of Female Sterility^ 47.^. .b^HFS-HFS-HFS^_HS-HS-HA. .^•HF- •AFCN-CN-AF^•CN-CN-SubCN'^N-N-D CN-Sub^-.^N-SubSN-D AF^.CN-SubCN-SubCN* C-^-N-D-D ubCIS'. AF.0.00 ^0.000.00 0.20 0.40 0.60 0.80 1.00 1.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20We^ We1.201.00"HS-HS"-HSN-N-D0.80N-SubSN-DWn 0.60N-D-D0.400.20 CN-SubCN-SubCN0.00 • •0.00 0.20 0.40 0.60 0.80 1.00 1.20we0.80 1.00 1.20 1.40 1.60 1.80 2.00WfFigure 2.5: Cytoplasm-restorer fitness pleiotropy and stable subdioecy, F-S model. Dom-inant restorer and female-sterility; recessive male-sterility. Start with 0.985 (F) mf/mf,0.005 (F) Mf/mf, 0.005 (F) MF/mf, 0.005 (S) mf/mf, add 0.005 (5) MF/mf after 1000generations. First abbreviation is the state at generation 999, second is the state atgeneration 2000 with wm, = 2.5, and third is the state at generation 2000 with Wm = 104.a-c: sf = 0, sh = 0.7, wf = 1.25, a: d = 0.1. b: d = 0.4. c: d = 0.7. c = 1, n = 1, nomutation, no drift, no extinctions. d: s f = 0, .sh = 0.2, w, 1.25, 'ton = 0.8, € = 1, n = 1,no mutation, no drift, no extinctions. N: nuclear gynodioecy; CN: cytoplasmic-nucleargynodioecy; HF: hermaphroditism F cytoplasm only; HS: hermaphroditism S cytoplasmonly; HFS: hermaphroditism both cytoplasms; Sub: subdioecy, both restorer and main-tainer present; SubSN: S cytoplasm only; SubCN: both cytoplasms; AF: androdioecy, Fcytoplasm only; D: dioecy.0.40N-N-D1.201.000.80Wu 0.600.400200.001.01^1.05^1.10^1.15Wc.•a.• .HF-AF-AF.CN-D-D,.N. 'CN-SubCN-D. CN-SubSN-D I'' CN-D-D• D-'D• N-D-D :• . .^.^. .1.20^1.24^00 0.20 0.40 0.60 0.80 1.00 1.20.^......... weHFS-HFHS-HS-HSHF- 'HF-AF •CN-CN-AF •N-SubSN-D0.20.N-D-DCN-SubCN-AF:1.201.000.80.0.601.00.80.60.40.21.00.80.60.40.20.0 ^•^•^...... ^0.01 2 3 4 5 6 7 8 9 II 10000^1 2^4 5 6 7 8 9 II 0000Chapter 2. Theoretical Dynamics of Female Sterility^ 48w„,Figure 2.6: Cytoplasm-restorer fitness pleiotropy, overdominance, and stable sub dioecy,F-S model. Dominant restorer and female-sterility; recessive male-sterility. Start with0.985 (F) mf/mf, 0.005 (F) Mf/mf, 0.005 (F) MF/mf, 0.005 (5) mf/mf, add 0.005 (S)MF/mf after 1000 generations. No mutation, drift, extinctions. a-b: Abbreviations as inFigure 2.5; c-d: condition after 2000 generations. sf = 0, d 0, wf = 1.25, wr„ = 2.5,= 1. a: sh =- 0, n = 1. b: sh = 0.99, n = 107. c-d: sf = 0, sh = 0.5, wf = 1.25,w„ w, = 1, € = 1, n = 2. H, A, S, G, D: hermaphroditism, androdioecy, subdi-oecy, gynodioecy, dioecy. c: No overdominance at the male-sterility locus. Dioecy afterhermaphroditism occurs because females have not been entirely eliminated. d: Over-dominance: heterozygote Mm is twice as fit as either homozygote, for each cytoplasm.The same results occur in the absence of the F cytoplasm. Dashed line is point at whichfemale fitness is double the ovule fitness of hermaphrodites.Chapter 2. Theoretical Dynamics of Female Sterility^ 49treatment means that only a subset of the parameter space can be explored, but thisresult appears to hold over a wide range of selfing rates, pollen limitation, and pleiotropyof cytoplasm and restorer in the F-S model. In particular, male invasion is considerablyeasier into a cytoplasmic polymorphism where the fitness parameters produce gynodioecyin the presence of both cytoplasms, but hermaphroditism in the presence of only the Scytoplasm, especially if selfing rate is high (Tables 2.5 and 2.6).Chapter 2. Theoretical Dynamics of Female Sterility^ 50ParametersInvasionThresholdWmDioecyThresholdWmResultw, =10, 000aNeuterfrequencys d w f wr r S S1S2 S S1S2 S1S2 S1S20.9 0.5 1.5 0.7 0 3.2 3.5 6.5 7.7 D(S1)c 0.0270.9 0.5 1.5 0.3 0 3.2 3.5 6.5 - T(S1S2) 0.240.9 0.5 1.5 0.7 0.5 5.1 4.6 - - T(51S2) 0.0770.9 0 2.5 0.7 0 4.5 4.6 32.8 - T(S1S2) 0.120.9 0 2.5 0.3 0 4.5 4.2 32.8 - T(S152) 0.200.9 0 2.5 0.7 0.5 7.3 6.0 - - T(5152) 0.0310.7 0.7 1.2 0.7 0 2.6 2.6 3.4 4•06 MFN(S1S2) 0.00510.7 0.7 1.2 0.3 0 2.6 2.7 3.4 4•16 MFN(S1S2) 0.200.7 0.7 1.2 0.7 0.5 3.0 2.9 - - T(51S2) 0.0800.5 0.5 1.8 0.7 0 2.3 2.3 2.8 3.0 D(S1)c 0.00290.5 0.5 1.8 0.3 0 2.3 2.5 2.8 3•46 MFN(S1S2) 0.0890.5 0.5 1.8 0.7 0.5 2.7 2.7 - - T(5152) 0.0940.5d 0 1.7 0.5 0 4.0 3.5 - - T(5152) 0.130.5 0 1.7 0.5 0.5 4.0' 3.7 T(5152) 0.0320 0 2.5 0.6 0 1.7 1.7 1.7 1.86 D(S1)c 0.00320 0 2.5 0.3 0 1.7 1.9 1.7 1•96 MFN(S1S2) 0.1150 0 2.5 0.6 0.5 2.0 2.0 - - T(S1S2) 0.17'State of population after 2000 generations for specified male fertility.bThreshold to eliminate hermaphrodites; neuters still persist.'Low frequency of cytotype 52.dParameters as in Figure 2.9.6No females.Table 2.5: Threshold male fertility for invasion or conversion to dioecy, S-S model. In-vasion defined as total male frequency greater than 10-6 at 2000 generations. Dioecydefined as total frequency of males and females greater than 0.95, and each greater than0.45. Columns as in Table 2.6, except for last column, which indicates equilibrium fre-quency of neuters under Wm = 10,000. In all cases, in the absence of males equilibriumgynodioecy includes both sterile cytotypes Si and S2. S: Entirely nuclear male-sterility.Start with 0.995 (5) Mf/Mf, 0.005 (5) mf/mf; male (5) MF/Mf introduced at frequency0.005 after 500 generations. 5152: S-S model. Start with 0.995 (S2) Mnf/Mnf and 0.005(Si) mNf/mNf; male (Si) mNF/mNf added after either single point limit reached (ifwr = 0.7 or 0.6), or at peak of oscillating S2 female frequency (if wr = 0.3). In allcases, c = 1 and n = 2; i.e., pollen limitation is moderate. r is the recombination rateChapter 2. Theoretical Dynamics of Female Sterility^ 51between the female-sterility locus and the male-sterility locus (locus N in the S-S model).Recombination rate between loci M and N in the S-S model is 0.5. In Result column:T: subdioecy; D: dioecy; MFN: males, females, and neuters; (51): cytotype Si presentat equilibrium; (S1S2) both cytotypes present at equilibrium. In all cases with r = 0.5,both cytotypes present at equal frequency at final equilibrium.Chapter 2. Theoretical Dynamics of Female Sterility^ 52ParametersInvasionThresholdWmDioecyThresholdWmResultWm =10,000wn we s d 'ix f n r S F-S S F-S S F-S0.7 0.9 0.99 0 1.25 107 0 199.1" 4.378 - - Hb H(F)b0.5 199.1' 8.702 - - Hb H(F)b0.3 0.8 0.99 0 1.25 107 0 1.880 1.570 1.925 - D H(F)b0.5 3.770 3.156 - T H(F)b0.8 1 0.7 0.1 1.25 1 0 6.139' 3.580 - A A(F)0.5 6.139' 5.351 - - A A(F)0.4 0.7 0.7 0.1 1.25 1 0 2.556 2.229 7.555' D T(FS)0.5 3.979 3.775 - T T(FS)0.3 0.9 0.7 0.4 1.25 1 0 1.593 1.422 1.870 - D T(FS)0.5 2.846 2.729 - - T T(FS)0.7 1.05 0.4 0.1 1.25 1 0 3.142 2.145 - - T A(F)0.5 3.165 3.138 - - T A(F)0.8 1.25 0.2 0.5 1.6 1 0 2.002 1.928 2.452 2.452 Dd D(S)0.5 2.209 2.221 - - T T(FS)0.8 1.25 0.2 0.5 1.6 100 0 1.966 1.908 2.041 2.020 De D(S)0.5 2.190 2.192 - - Tf T(FS)f0.6 1.2 0 0 1.25 1 0 1.965f 1.478 2.077 1.845 Dg D(S)0.5 1.990f 1.984 - - Af T(FS)0.6 1.2 0 0 1.25 100 0 1.965f 1.478 2.077 1.845 Dh D(S)0.5 1.990f 1.984 - - Af T(FS)0.3 1.228 0 0 1.25 1 0 1.293 1.204 1.323 1.235 Di D(S)0.5 1.979 1.981 - - T T(FS)a0 females.b Low males.'Same threshold exists if followed for 10,000 rather than 2000 generations.dFor turn = 2.5, dioecy reached in 426 generations under S, and in 40 generationsunder F-S.'For wm = 2.5, dioecy reached in 283 generations under S, and in 26 generationsunder F-S.f Low females.g For win = 2.5, dioecy reached in 655 generations under S, and in 203 generationsunder F-S.h For w, = 2.5, dioecy reached in 655 generations under S, and in 203 generationsunder F-S.'For Wm = 2.5, dioecy reached in 81 generations under S, and in 465 generationsunder F-S.Chapter 2. Theoretical Dynamics of Female Sterility^ 53Table 2.6: Threshold male fertility for invasion or conversion to dioecy, F-S model. In"Invasion Threshold" column, the minimum male fertility (relative to hermaphrodites)for spread of males in the population. In "Dioecy Threshold" column, the minimummale fertility for conversion to dioecy by 2000 generations. Invasion defined as totalmale frequency greater than 10-6 at 1000 generations. Dioecy defined as total frequencyof males and females greater than 0.95, and each greater than 0.45. Male (S) MF/Mfintroduced at frequency 0.005 after 500 generations. S: Entirely nuclear male-sterility.Start with 0.995 (S) Mf/Mf, 0.005 (S) mf/mf. FS: F-S model. Start with 0.99 (F)mf/mf, 0.005 (F) Mf/mf, and 0.005 (5) mf/mf. In the latter case, both cytoplasmswere present at male introduction. In the absence of males, all parameter combinationslead to a joint nuclear-cytoplasmic polymorphism, though some with low equilibriumfemales. In all cases, c = 1. r is the recombination rate between the female sterilitylocus and the male-sterility locus. In "Result" column: state of the population after2000 generations for specified male fertility. D: dioecy; T: subdioecy; A: androdioecy; H:hermaphroditism; (F): F cytoplasm present at 1000 generations; (S): S cytoplasm presentat 1000 generations. High final frequency of neuters in most cases where r = 0.5.In the S-S model, the invasion threshold for males is less predictable, but still generallycomparable to that for nuclear gynodioecy in the portion of the parameter space explored(Table 2.5). The only apparent pattern is a tendency for the threshold to be lowerinto a population with both cytoplasms (Si and S2) than into a nuclear gynodioeciouspopulation when male and female-sterility loci are unlinked (r = 0.5). Otherwise, maleinvasion appears to be slightly more difficult into the S 1/S2 cytoplasmic polymorphismover most of the parameter space. However, ease of invasion is almost equal if selfingrate is zero, as is the case in what appears to be the best natural approximation of theS-S model, the genus Plantago (Van Damme and Van Delden, 1982; Van Damme, 1983).In both F-S and S-S models, male invasion of a gynodioecious population need notlead to evolution of dioecy, even with proper linkage of sterility loci and unlimited maleadvantage. The major barriers to dioecy allowed by the F-S model are low relativefitness of the sterile cytoplasm and overdominance at the restorer locus (the latter, how-ever, is equally effective in the S model). In the first case, the proportion of the cyto-plasm/restorer fitness plane over which the barrier occurs increases as the selfing rateChapter 2. Theoretical Dynamics of Female Sterility^ 54increases, and includes some portions where the fitness of the fertile cytoplasm exceedsthat of the sterile (Figures 2.5 and 2.6). As the relative fitness of the sterile cytoplasmdecreases, the maintainer allele becomes fixed, and nuclear control of male function is lostand dioecy is of course impossible. If the relative fitness of the fertile cytoplasm exceedsthe phenotypic female advantage (regardless of selfing and inbreeding depression) thenfemales are lost entirely.Overdominance at the male restorer/sterility locus ironically facilitates male invasionto subdioecy at the same time that it hinders evolution to dioecy (Figure 2.6c-d). Thisresult occurs regardless of the initial presence or absence of the F cytoplasm, and canoccur even when the female fitness is over twice the ovule fitness of the homozygoushermaphrodite. The generality of these effects under w, and wn 1 needs to be explored.In the S-S model, high antagonism or low female fitness can prevent the evolution ofdioecy (Table 2.5, line two). For reasons unclear, antagonism tends to result in a mod-erately high final frequency of neuters or hermaphrodites, even under conditions thatwould lead to rapid evolution of dioecy under nuclear male-sterility. This occurs eventhough the presence of males with effectively infinite fertility can convert an oscillatingequilibrium into a (different) single point equilibrium (trajectories not shown). Antago-nism, however, does not greatly affect the male threshold for the evolution of subdioecyin the parameter regions examined.A high antagonism can maintain an oscillating gynodioecy even if the female fitnessis less than double the ovule fitness of hermaphrodites (Figure 2.9). In this case malescan invade more easily than they can an equivalent single-cytoplasm population (Table2.5), but the low female fitness is a barrier to dioecy independent of the high antagonism(Table 2.5). If female fitness is increased in Figure 2.9, hermaphrodites can be eliminatedby sufficiently fertile males, though a low frequency of neuters persists (not shown).Chapter 2. Theoretical Dynamics of Female Sterility^ 55Females are maintained in such a population through a process of alternating cyto-plasmic runaway (Gouyon, et al., 1991). As either cytoplasm begins to dominate, itselects against the restorer of the other cytoplasm. As this restorer becomes rare, fe-males of the rare cytoplasm can invade. In the process of invading they convert thepopulation to the other sterile cytoplasm, now favoring hermaphrodites of this cyto-plasm over females, and females may then fall to low frequency. But the high frequencyof the new cytoplasm again selects against the restorer for the other cytoplasm, andthe cycle continues. Hence each female peak alternates in cytoplasm and occurs as theuncommon cytoplasm invades.Because antagonism is the strength of selection against the restorer of the rare cyto-plasm, both amplitude and frequency of the oscillation in total female frequency increasewith antagonism. Without it oscillation ceases and the equilibrium female frequency isthe same as for a single-cytoplasm gynodioecy. However, since female fitness has thesame effect on amplitude and frequency of the oscillation as antagonism (not shown),relative female fitness must be greater than about 1.5 for females to remain permanentlyin the population over most of the parameter space.Besides influencing evolution of dioecy in the deterministic version of the S-S model,antagonism between restorer alleles in the stochastic version can result in long-termtransient states that cannot be predicted from the deterministic trajectories. Under highantagonism, dioecy is easily invadable by either sterile cytoplasm (Figure 2.7). Invasiontransiently shifts the genotype frequency array towards males and females of the invadingcytoplasm, and recombination between nuclear restorer and female sterility loci in thiscytoplasm produces hermaphrodites. If male advantage is marginal (but still sufficientto produce dioecy in a deterministic model) then invasion of temporarily non-restoredfemales can nearly eliminate males for many generations, and temporarily convert tooscillating gynodioecy (Figure 2.8).1.0Cytoplasm S2Total FemalesTotal Males^f. ^•.^. 01".1^-^ai & , .0 . 0 f.ii • 0 • 0^, . . ..k, . • . L 3^1. „AnRi. a t ^A_ L ....g, 3"1 ^0 ,,, A, r^. . f^.200^400 600^800Generation0.00 1000Chapter 2. Theoretical Dynamics of Female Sterility^ 56Figure 2.7: Dioecy and cytoplasmic polymorphism, S-S model, stochastic. Dominantrestorer and female-sterility; recessive male-sterility. sh = 0.7, sf^0, d = 0.9, N = 200,wf = 1.0, wn, = 2.5,^= 0.005, n = 600, wr = 0.5, all mutation rates 0.001, norecombination between N and F, no extinctions. Start with 200 (S2) Mnf/Mnf. Theseparameters give permanent dioecy in the deterministic equivalent, with only negligiblehermaphrodites at any time.1Cytotype S2Total FemalesTotal Males11,0.2_rbt 400^600Generation800^1000Chapter 2. Theoretical Dynamics of Female Sterility^ 57Figure 2.8: Sporadic invasion of hermaphrodites into dioecious population, S-S model,stochastic. Dominant restorer and female-sterility; recessive male-sterility. sh = 0.5,sf = 0, d = 0, N = 200, wf = 3.0, w, 2.9, c 1, n = 2, wr = 0.5, all mutation rates0.001, no recombination between N and F, no extinctions. Start with 0.99 (S2) Mnf/Mnf,0.005 (51) mNf/mNf, and 0.005 (51) mNF/mNf. These parameters give permanentdioecy in the deterministic equivalent.200 800 1000400^600Generationf^. tiCytotype S2Total FemalesTotal Males10.8 -:1Chapter 2. Theoretical Dynamics of Female Sterility^ 58Figure 2.9: Repeated invasion of unrestored cytotypes, S-S model. Dominant restorerand female-sterility; recessive male-sterility. sh = 0.5, .5 f = 0, d 0, N = 200, wf = 1.7,Wm = 3.0, c = 1, n = 2, tor = 0.5, all mutation rates 0.001, no recombination betweenN and F, no extinctions. Start with 0.99 (S2) Mnf/Mnf, 0.005 (Si) mNf/mNf, and0.005 (51) mNF/mNf. These parameters give oscillating gynodioecy, minimum femalefrequency > 0.074, in the deterministic equivalent. Threshold for male invasion in thedeterministic equivalent is Wm = 3.5; threshold for single cytoplasm, same parameters, isWm = 4.0 (see Table 2.5).If male advantage is too low to produce a permanent dioecy in a deterministic model,then males can invade to an oscillating subdioecy that may occasionally shift to a tran-sient dioecy (not shown).As previous authors have shown for a single-cytoplasm system (cf. Ross, 1978), maleinvasion and dioecy are greatly hindered by high hermaphrodite selfing rates when in-breeding depression is low (Figure 2.6a and b). In this case, males can invade a nucleo-cytoplasmic gynodioecy as easily as a nuclear gynodioecy (to low frequencies), but evo-lution to dioecy may not be possible. For the parameters examined, males of effectivelyChapter 2. Theoretical Dynamics of Female Sterility^ 59infinite fertility cause evolution from nucleo-cytoplasmic gynodioecy to androdioecy inthe fertile cytoplasm (though with very low frequencies of males).Generally the results reported here for the F-S-D, F-S, and S models are largelyindependent of starting genotype frequencies, and trajectories either settle into a single-point limit cycle or are non-cyclic, although wide, undamped oscillations can occur insome boundary regions of the parameter space of the F-S model. However, the trajectoriesin the S-S model are more sensitive to starting frequencies and to small variation in theparameters. More exploration of this model is needed, particularly its behavior under(1) an expanded definition of antagonism that includes effects on both sexual functions,and (2) fitness pleiotropy of the sterile cytoplasms.2.3 Discussion2.3.1 Rates of EvolutionThese models clearly indicate that not only can a cytoplasmic male-sterility gene servethe male sterility function in dioecy, but that in many instances evolution from herma-phroditism to dioecy can be greatly accelerated if such a gene is available. In order forsuch acceleration to occur, populations must be perturbed away from equilibrium of therestorer allele, or in oscillation, such that female frequencies are initially or periodicallyhigh. The extent to which such conditions have occurred in nature is unknown. However,female frequencies often exceed 50% in some nucleo-cytoplasmic gynodioecious species,and this may be caused by population instability such that colonization by a particularsterile cytoplasm without its corresponding restorer allele is not uncommon (Belhassen,et al., 1989). Under these conditions, if the restorer is introduced linked to a femalesterility allele, evolution to dioecy can occur in a few generations. In other populationsChapter 2. Theoretical Dynamics of Female Sterility^ 60at equilibrium at the restorer locus, the same male introduction may require several hun-dred generations to cause conversion to dioecy, providing mutation rate is sufficientlyhigh to prevent loss to drift.2.3.2 "Stable" Breeding SystemsThe presence of gynodioecy in a taxon in which dioecy is rare or lacking (e.g., the Plan-taginaceae [Ross, 1970a, 1970b]) suggests a barrier to the evolution of dioecy in thetaxon. Such gynodioecious species may be evolutionarily "stable." However, there isno a priori reason that such stability should persist over the long term, since genetic,developmental, and selective conditions could eventually change in a way that removesany barrier. In the immediate term, however, gynodioecy may be stable in the followingsense. A female-sterility mutant, regardless of its nuclear locus, and regardless of its fit-ness advantage over hermaphrodites, cannot invade the population. Similarly, subdioecymay be stable in the sense that a female-sterility mutant, regardless of its nuclear locusor fertility advantage, cannot cause the population to evolve to dioecy.There appear to be at least four types of barrier to the evolution to dioecy in gyno-dioecious or subdioecious populations. There may be (1) no nuclear control over malesterility; (2) multilocus nuclear control; (3) single locus nuclear control with only minimalfemale advantage (and any number of cytoplasms); and (4) single locus nuclear controlwith large female advantage, but fertile cytoplasm selectively maintained. Of these, onlythe first and last require a cytoplasmic locus controlling male sterility, but in neither isthat locus a barrier to male invasion.1. No nuclear control of male sterility. In this case, females are due to a non-restorablemale-sterile cytoplasm with any advantage over hermaphrodites, and the equilibrium sexratio is determined by the advantage and the degree of pollen limitation. In this case it isvirtually impossible for males to eliminate hermaphrodites regardless of fitness, and evenChapter 2. Theoretical Dynamics of Female Sterility^ 61if they could, males themselves would be eliminated the next generation. Nevertheless, afemale-sterility allele can invade a polymorphism in cytoplasm only, and ease of invasionto subdioecy is similar to that for a single-cytoplasm population if the allele is linked toa male-fertility allele. For males with high relative fertility, such invasion may eliminatefemales entirely, leaving androdioecy. With no nuclear control over male fertility, condi-tions for male invasion can be even more stringent than those for androdioecy, since someof the progeny of males will be neuters, resulting from the fertilization of unrestorablefemales.Although the present models show that an unrestorable cytoplasm can easily invadea hermaphrodite, gynodioecious, subdioecious, or dioecious population and convert itrapidly to cytoplasmic gynodioecy, this class of population may be rare or transient innature: in all well-studied examples of cytoplasmic male-sterility, nuclear genes havebeen found that restore male fertility in the sterile cytoplasm or cytoplasms. Neverthe-less, since cytoplasmic mutations that restore male fertility in a nuclear gynodioeciouspopulation are likely to be rare, invasion of an unrestorable cytoplasm is generally nec-essary for the establishment of nucleo-cytoplasmic gynodioecy.2. Multilocus nuclear control of male sterility. Dioecy requires complete linkagebetween male fertility and female sterility and vice-versa. If male sterility is controlledby two or more polymorphic unlinked loci, then regardless of the location of the female-sterility locus hermaphrodites can occur in the female x male progeny. Dioecy can evolveonly if the female-sterility allele is linked to the fertility allele at one of the male-steril-ity loci (with both alleles either dominant or recessive), and if the sterility alleles at allthe other male-sterility loci then become fixed. This effectively transfers control of themale function onto that single locus linked to the female-sterility locus. Although thissituation has not yet been modelled, it seems likely that, with complete dominance andno pleiotropic effects of the male fertility alleles, such fixation should occur in concertChapter 2. Theoretical Dynamics of Female Sterility^ 62with the invasion of suitably fertile males, with dioecy the probable end result. However,if some of the fertility alleles have positive side effects, or are overdominant, then theymight be difficult to eliminate and strict dioecy impossible to achieve. Nevertheless, thiscannot prevent the invasion of males. Although the fertility thresholds for male invasionof such a population are unknown, single-locus models suggest that they will tend to belowered by overdominance at the male-sterility loci.3. Single-locus nuclear control and female advantage minimal, with or without cyto-plasmic polymorphism. This situation can occur in at least three ways. If male sterilityis single-locus recessive, then females can be maintained through heterozygote advan-tage even if they have no advantage over hermaphrodites. Alternatively, the S-S modeldescribed here can give an undamped oscillation between the two restorable cytoplasmsand their corresponding female genotypes even if the female relative fitness is less thantwice that of hermaphrodites. This perpetual oscillating runaway occurs only if the twonuclear restorer alleles are antagonistic; i.e. complete restoration is prevented when bothare present. In this case, simultaneous reversion to hermaphroditism in both cytoplasmsis impossible, because conditions required for full restoration of one allow invasion of theother's female genotypes.Finally, females can be maintained in the F-S model in a complex nucleo-cytoplasmicpolymorphism that results from a fitness pleiotropy of the restorer allele or the sterilecytoplasm. Where the female fitness is less than twofold, however, the equilibrium femalefrequency is generally low.Although in these three cases female-sterility alleles cannot accomplish evolution todioecy regardless of their fertilization advantage over hermaphrodites, they can invade toa subdioecious equilibrium. In the case of an F-S or S-S gynodioecy, if female fitness istoo low to allow gynodioecy in the absence of cytoplasmic polymorphism, male invasionthreshold will generally be much smaller into a nucleo-cytoplasmic gynodioecy. In theChapter 2. Theoretical Dynamics of Female Sterility^ 63case of overdominance at the male-sterility locus, with recessive male-sterility and lowfemale advantage, overdominance facilitates invasion of both females and males at thesame time as it prevents or hinders evolution to strict dioecy.4. Large female advantage, cytoplasmic polymorphism selectively maintained. In theF-S model, females may enjoy a twofold advantage within the restorable sterile cytoplasm,yet a female-sterility allele cannot cause evolution to dioecy because fitness pleiotropy ofthe restorer allele or sterile cytoplasm allows the persistence of the fertile cytoplasm. Inthe S-S model, high antagonism can prevent the complete elimination of hermaphroditesor neuters even in the presence of highly fit females and linked males. The cytoplasmof the neuters is that restored by the locus unlinked to the female-sterility locus; this isthe rare cytoplasm in these cases. This effect of antagonism has a stochastic as well asa deterministic component. Drift in restorer frequencies can allow sporadic invasion ofalien females into a dioecious population in the S-S model, and subsequent recombinationto hermaphrodites. Again, although these conditions prevent elimination of cytoplasmicpolymorphism and hermaphrodites, they leave the threshold for male invasion largelyunaffected.In general, however, a polymorphism in both cytoplasm and nucleus should not persistover evolutionary time. If a mutant restorer occurs that lacks any negative pleiotropyor antagonism, it will eliminate the old restorer(s) and convert the system to nucleargynodioecy (if females have a twofold fitness and the sterile cytoplasm is at least as fitas the fertile), or to hermaphroditism.These considerations may shed some light on examples in nature of apparently stablenucleo-cytoplasmic or nuclear gynodioecy. In none of the models of these two situationsare barriers to dioecy simultaneously barriers to subdioecy. Moreover, in none of themodels is any hindrance to subdioecy unique to populations with nucleo-cytoplasmicmale-sterility. In all models males can invade with a sufficient fertilization advantage overChapter 2. Theoretical Dynamics of Female Sterility^ 64hermaphrodites, with the threshold advantage being smaller if the female-sterility locus islinked to the male-sterility (i.e., restorer) locus and the female sterility allele introducedin coupling. Even in the case of cytoplasmic polymorphism, if there are nuclear restorerloci, then the conditions for male invasion to an intermediate equilibrium are virtuallythe same as for an entirely nuclear gynodioecy. If the conditions for dioecy are met withinany single sterile cytoplasm, then over large portions of the parameter space, dioecy willevolve after or during the elimination of all but that sterile cytoplasm. And in somecases, strict dioecy can occur with two coexisting sterile cytoplasms and their respectiverestorers.These results, then, suggest that the cytoplasmic polymorphism observed in many gy-nodioecious populations of flowering plants is by no means a barrier to males. Rather, ifnuclear restorer loci exist, then the factors controlling evolution to maleness are virtuallythe same as for an entirely nuclear system of gynodioecy; these are primarily selfing rateand ovule fitness ratio of females to hermaphrodites. Non-restorable male-sterile cyto-plasms or fertile cytoplasms may be able to invade and distort the sex ratio, but they willgenerally not prevent evolution to subdioecy. The absence of males in nucleo-cytoplasmicgynodioecious populations may then be due to the same structural or functional factorsinvolved in nuclear gynodioecious populations. For example either female-sterility mu-tations appropriately linked to the restorer locus are rare or impossible, or males simplydo not benefit from a sufficient fertilization advantage. The latter could be due to de-velopmental constraints that prevent males from recouping much on the loss of femalefunction, or to ecological constraints on pollination.Three of the four listed barriers to dioecy in a gynodioecious population are likely tobe uncommon or transient in nature, while the fourth, small female advantage, may bean occasional but recurrent result of hybridization and introgression. In two subspeciesor races separated over evolutionary time, mutations in both cytoplasm and nucleus mayChapter 2. Theoretical Dynamics of Female Sterility^ 65accumulate in a way that eventually creates a distinct, unique coadaptation between thetwo genomes in each subspecies. If these then hybridize in both directions, the result-ing mismatches between cytoplasm and alien nucleus could result in regulatory errors,e.g., by nuclear genes acting on mitochondrial genes. A consequence might be a re-duced mitochondrial efficiency during the energetically demanding process of microsporedevelopment, resulting in abortion of the process and male sterility. Each of the two"sterile" cytoplasms will be restored by regulatory alleles in one or more loci from thenuclear genome in its parental taxon; these will be among the "coadapted" alleles thataccumulated during the prior period of separation. That nucleo-cytoplasmic male steril-ity might be a common consequence of hybridization is suggested by its occurrence inrecent artificial hybrids in Phacelia (Levy, 1991), and the fact that all genetically well-understood cases of nucleo-cytoplasmic male sterility in agricultural species originatedfrom hybridization (Edwardson, 1970). If the recombinant de facto females enjoy only asmall fecundity advantage, then males will have difficulty invading, and generally couldnot eliminate hermaphrodites if that advantage were less than twofold. If females dofortuitously benefit by more than doubling their fitness, and if selfing rate is low, thenmales will invade more easily to a subdioecious equilibrium. Of course, if male steril-ity is a multilocus quantitative trait, elimination of hermaphrodites will be difficult orimpossible.However, without antagonism between the two suites of restorer loci, this introgressivegynodioecy should revert to hermaphroditism rapidly if females have less than doublethe ovule fitness of hermaphrodites: restorer alleles for both cytoplasms will becomefixed in the hybrid population, and females eliminated. As the S-S model shows (in thecase of a single restorer locus for each cytoplasm), antagonism can maintain a perpetualoscillation of females even for a moderate female advantage. Such antagonism mightalso be expected to follow introgressive hybridization. Since the two suites of restorerChapter 2. Theoretical Dynamics of Female Sterility^ 66loci evolved separately, the products of these genes may interfere in a way that fails tofully restore male fertility. Alternatively, each suite of restorer loci may be linked toits own suite of nuclear alleles from its parental nuclear genome, and these two suitesof linked alleles may themselves be antagonistic, again due to divergent evolution andlack of coadaptation (this latter possibility, however, was not explored in the present S-Smodel, which assumed that antagonism affected male sterility only).But such a population may not persist for long. If non-antagonistic restorer allelesappear, or if a single allele appears that restores both cytoplasms, then females willbe lost immediately. However, repeated episodes of hybridization could still reestablishenclaves of oscillating de facto gynodioecy, which would last until immigration of thesuperior restorer alleles.Regardless of how nucleo-cytoplasmic gynodioecy becomes established, it might beargued that purely genetic constraints in such populations tend both to increase thefertility threshold for male invasion, and to prevent evolution to dioecy. In nucleo-cytoplasmic male-sterility, the nuclear restorer alleles most likely perform some regulatoryfunction on cytoplasmic genes, and hence are probably not involved in the direct control ofany aspect of floral development. As a result, they may not be in any position to becomelinked to a locus that controls female fertility. In contrast, loci directly involved in theorganization of the inner floral whorls might be controlled by a single regulatory gene,which could be mutable in two independent ways: one halting androecium developmentwithout eliminating the gynoecium, and the other vice-versa. Linkage between malesterility and female fertility (and vice-versa) could then be made possible by tandemduplication of this gene, or by the specific function of the mutations themselves withoutany duplication of the locus.The recently proposed combinatorial model of floral whorl development in Arabidop-sis and Antirrhinum (Meyerowitz and Coen, 1991) suggests a simple means wherebyChapter 2. Theoretical Dynamics of Female Sterility^ 67linkage and reciprocal dominance of male- and female sterility could be achieved. If asingle gene regulates the expression of the b domain genes (those controlling identity ofthe second and third whorls), then both male- and female-sterility mutations may bepossible within this single locus. A mutation that extended the expression of b genesinto the fourth floral whorl would produce the sequence sepals, petals, stamens, and sta-mens. This female-sterility/male-fertility mutation constitutes a gain of function in theb genes. Conversely, a mutation at the regulatory locus that truncated the expression ofb genes to just the second whorl would produce the sequence sepals, petals, carpels, andcarpels. This male-sterility/female-fertility mutation constitutes a loss of function in theb genes. Because one of these mutations is a loss, and the other a gain in function, oneis likely to be dominant over the other; if the regulatory gene encoded a repressor thenthe female-sterility/male-fertility mutation would be recessive. Assuming complete dom-inance, heterozygotes at this locus would be one sex, and homozygous recessives the othersex, and matings between the two would produce a 1:1 sex ratio. Hence if the respec-tive fertilities of the resulting male and female phenotypes exceeded the thresholds fordioecy, these two mutations would be sufficient to cause evolution from hermaphroditismto dioecy.A possible canditate for such a regulatory locus is the FLO10 or SUPERMAN genein A rabido psis, which encodes a DNA-binding protein and appears to regulate expressionof b genes at the level of transcription (Schultz, et al., 1991). A recessive mutation hasbeen found at this locus that causes a variable floral phenotype usually involving thereplacement (complete or incomplete) of carpels by stamens and the overproduction ofstamens. The converse mutation, that causing replacement of stamens by carpels, hasnot yet been manufactured.Another possible location for this pair of sterility mutations is the promoter of a bgene itself, depending on the nature of the interaction between the two b loci (AP3 andChapter 2. Theoretical Dynamics of Female Sterility^ 68PI in Arabidopsis). That the extended expression of one of the b alleles is sufficient toproduce female-sterility/male-fertility is suggested by the fact that constitutive expres-sion of AP3, achieved by splicing the gene to the cauliflower mosaic virus promoter andintroducing it into Arabidopsis, causes the partial to complete replacement of carpels bystamens (T. Jack and E.M. Meyerowitz, unpublished data). This implies that a pro-moter mutation in this gene that produced the same expression would be dominant. Theconverse mutation in the promoter of a b gene that reduces its expression to the secondwhorl only is hypothetical. That such a mutation would be recessive is suggested by thefact that mutations in AP3 that completely block its expression are completely reces-sive; these produce the male-sterile/female-fertile phenotype sepals, sepals, carpels, andcarpels. Hence two types of alteration in the expression of AP3 have been experimentallydemonstrated that, if produced by mutations in a single population, very likely wouldsatisfy the genetic requirements for dioecy with maleness dominant and males the het-erogametic sex. Besides the ideal mutation of restricting AP3 expression to the secondwhorl, the shortcoming of lack of petals in the male-steriles thus produced might be elim-inated by a mutation that simply reduced AP3 expression without changing its domainof expression. This might sufficiently interfere with stamen development to produce ster-ile microspores, but not sufficiently interfere with petal development to eliminate them.Such reduction, however, might reduce the size of petals, a phenotype observed in femalesof most gynodioecious species.If homeotic genes are often involved in controlling sex expression in diclinous species,then the threshold for spread of female-sterility mutants might be lower into nuclear-than nucleo-cytoplasmic gynodioecious populations, since such mutants may be morelikely to arise linked to the nuclear restorer locus in the former populations. Ironically,this would constitute a linkage constraint as originally hypothesized by Ross, but of anentirely different kind.Chapter 2. Theoretical Dynamics of Female Sterility^ 69However, this difference appears to be moderate over most of the parameter space,especially for the F-S versus S models. Examination of Table 2.6 shows that the maleinvasion threshold for the F-S model with r = 0.5 is greater in most cases than thethreshold for the S model with r = 0. But in some cases the difference is only 10-11%,and in one the two thresholds are nearly identical; in none is the difference over 70%. Thesame comparison for the S-S versus S models shows a greater but still moderate difference,and as low as 16%. For a species whose relative allocation of energy and materialsto female function is on the order of 200%, an difference of 10-20% can probably beconsidered moderate. In any case, little evidence exists that homeotic genes homologousto those described in Arabidopsis control sex expression in any diclinous species, andthe side effects of known mutations at these loci have apparently not been reported inany diclinous species. Moreover, male sterility mutations appear to be possible at manyunlinked nuclear restorer loci in most species.In summary, the present models provide little support for the concept of stable gyno-dioecy, as defined conservatively here. However, they do provide support for a concept ofstable subdioecy, independent of any linkage constraint. Unstable gynodioecious popu-lations may evolve to dioecy rapidly, and under some conditions a cytoplasmic polymor-phism greatly accelerates the evolution of dioecy. In those cases of nucleo-cytoplasmicgynodioecy with a large female advantage, an absence of males most likely is not causedby the cytoplasmic polymorphism, but rather by fitness or genetic/developmental barri-ers that prevent a sufficient gain of pollen fertility in males. These factors might then beresponsible for the general rarity of dioecy (and subdioecy) in some gynodioecious taxa.Chapter 3Correlates of Female Frequency3.1 MethodsThe Bidens populations studied occupied steep (often greater than 100% slope), unstable,eroded ridges on the western side of Waimea Canyon or the north slope of Makaha Ridge,Kauai, U.S.A. All field studies were conducted within four major population centers: A,B, C, and D in Figures 3.11 and 3.12 and Table 3.7. Smaller-scale studies of sex ratiofrom 1989 to 1992 inclusive, or sex ratio and outcrossing rate in 1988, were conductedwithin centers A, B, and C, on a total of 14 subpopulations (Table 3.7). Centers Aand B occurred in a Lowland Dry Shrublands plant community (Wagner et al., 1990),from 370 to 600m in elevation and receiving 675 to 750mm annual rainfall. Commonassociates included Dodonaea viscosa, Heteropogon contortus, Wilkesia gymnoxiphium,Grevillea robusta, Psidium guajava, and Opuntia ficus-indica. Center C occurred in aLowland Mesic Shrublands community, at 880m elevation and receiving about 1000mmannual rainfall. Common associates included Dodonaea viscosa, Wilkesia gymnoxiphium,Myopo rum sandwicense, and Met rosideros polymorpha. Center D occurred on the erodedor roadcut margins of a Pinus plantation within a Lowland Mesic Forest dominated byMetrosideros polymorpha. Boundaries of subpopulations were topographically definedand enclosed regions ranging from 5000 to 10,000 square meters in area and separatedby 50-100 meters; population centers constituted clumps of subpopulations ranging from10,000 to 50,000 square meters in area, and separated by several kilometers. Center A70Chapter 3. Correlates of Female Frequency^ 71occupied about 10,000 square meters, and the mating system here was not studied onany smaller scale.Sex ratios were monitored in all 14 subpopulations during the flowering season from1989 to 1992 inclusive, and outcrossing rates measured for the 1988 season. In four sub-populations in centers A and B I measured plant height, total capitulum production,mean seed-set per capitulum, total length of primary branches, and for each measuredindividual, counted the hermaphrodites within a 5 meter radius; results of morpholog-ical comparisons are displayed graphically as box plots (see Figure 3.10). I also logged30 hours of pollinator visitation and approach observations at three subpopulations atthe same two population centers in 1991. Preliminary surveys showed no difference innumber of flowers per capitulum between the two sexual morphs (females 16.31, s.d. 2.2;hermaphrodites 16.38, s.d. 2.3 in subpopulations B2 and B3), and further counts werenot made.For the 1989 flowering season, I used isozyme markers in wild-collected progenies tomeasure outcrossing rates at the four centers, with subsampling at centers B and C (Table3.7). Out of a preliminary review of 20 glycolytic loci, a total of three were sufficientlyvariable to provide estimates of outcrossing rate; these were phosphoglucoisomerase (2loci) and shikimate dehydrogenase (one locus). In each subpopulation, 10 progeny, fromeach of 20-50 hermaphrodite maternal parents, were scored for genotype at these loci.Electrophoretic techniques generally followed those of Soltis et al. (1983), Haufler(1985), and Wendel and Weeden (1989), with minor variations. I sterilized achenesin 3% (w/w) sodium hypochlorite for 10 minutes, followed by 30 seconds in 70% (v/v)ethanol, and sowed them on Murashige-Skoog growth medium suspended in sterile agar incylindrical jars 10cm in diameter and 10cm high. Given 12 hours of alternating light anddark, and constant 25°C, the first achenes germinated in about one week, and germinationcontinued over 1.5 month, to rates over 90% in most families by about two months. I-4— Median of observationsgreater than grand median = mh-4— Grand median...41-- Median of observationsless than grand median = ml'F.-----..„ Value of smallest observation(excluding outliers)Chapter 3. Correlates of Female Frequency^ 72Value of largest observation(excluding outliers)95% confidenceinterval forthe medianFigure 3.10: Anatomy of a box plot. An observation is defined as an outlier if greaterthan mh + (1.5)(mh — ml) or less than ml — (1.5)(mh — ml). Outlying observations areplotted as asterisks, or as open circles if greater than rnh + (3)(mh — ml) or less thanml — (3)(mh — ml).Chapter 3. Correlates of Female Frequency^ 73Figure 3.11: Location of Bidens population centers A, B, C, and D, on the island of Kauai,Hawaii, U.S.A. Contours indicate elevation in feet (1000 feet per contour interval).Chapter 3. Correlates of Female Frequency^ 74Subpop. Taxon El. (m) AspectAl Bisasa 370 NEA2 Bisasa 370 NEA3 Bisasa 370 NEB1 Bisasa 570 SEB2 Bisasa 600 SWB3 Bisasa 580 NEB4 Bisasa 550 SEB5 Bisasa 550 SEC1-1 Bisaco 880 EC1-2 Bisaco 880 EC2-1 Bice 880 EC2-2 Bice 880 EC3 Bisasa 880 ED Bice 760 NWTable 3.7: Attributes of 14 subpopulations of Bidens studied in population centers A,B, C, and D. Outcrossing rates were calculated for A, Bl, B2, B3, B4, Cl, C2, C3,and D; small-scale variation within A, Cl, and C2 was not addressed. Bisasa: Bidenssandvicensis ssp. sandvicensis. Bisaco: Bidens sandvicensis ssp. confusa. Bice: Bidenscervicata.Chapter 3. Correlates of Female Frequency^ 75Figure 3.12: Location of Bidens population centers A, B, C, and D, on the island ofKauai, Hawaii, U.S.A. Contours indicate annual rainfall in inches.extracted tissues of the first true leaves during weeks 3 and 4 after sowing; time constraintsprevented any approximation of a random sampling of seedlings germinated over the twomonths. This would have been difficult in any case, since early germinators often came todominate late germinators, which not uncommonly remained suppressed or died beforeproducing true leaves.I submerged approximately one square centimeter of fresh leaf material in 3-4 dropsof extraction buffer in spot wells placed on ice, and macerated the tissue with a plastic-tipped pestle attached to a power drill bit. Extraction buffer consisted of 0.1% v/v2-mercaptoethanol, 0.001 M EDTA (ethylenediaminetetraacetic acid, tetrasodium salt),0.010 M potassium chloride, 0.010 M magnesium chloride hexahydrate, and 20% w/vPVP 40,000 (polyvinylpyrrolidone) in 0.10 M Tris[hydroxymethyl}aminomethane-HC1buffer, pH 7.5. The extraction buffer was stored minus the PVP and mercaptoethanolChapter 3. Correlates of Female Frequency^ 76Electrode Buffer Gel Buffer Enzymes1^0.40 M citric acid,trisodium salt;0.020 M histidine-HC1;1.0 M NaOH to pH 7.0F16DP G3PDG6PD (PGI)PGM SkDH6^0.10 M NaOH;0.30 M boric acid,pH 8.60.015 M Tris; 0.004 Mcitric acid, pH 7.8AAT GDH PGIPGM8^0.039 M Li0H;0.263 M boric acid,pH 8.00.033 M Tris; 0.005 Mcitric acid; 0.004 MLi0H; 0.030 M boricacid; 1.0 M HC1 topH 7.6ADH ALDAMP ESTHEX (IDH)LAP (SkDH)TPI9^0.065 M L-histidine;0.015 approx.citric acid, topH 5.70.009 M L-histidine;0.002 M citric acidSkDHMorph.^0.04 citric acid;0.068 M approx.N- (3-aminopropy1)-morpholine to pH 6.21 part electrodebuffer: 25 parts water(ACO) IDHMDH MEPGM SkDHTable 3.8: Electrode and gel buffers used to resolve 18 enzyme systems in Bidens cervicataand B. sandvicensis. Enzymes marginally resolved are listed in parentheses.at 4°C, and these ingredients were added just before extraction to a 12.5 ml aliquot ofthe stock, which was made fresh weekly in batches of 125 ml.I absorbed the supernatant portion of the tissue-buffer homogenate onto wicks (3 x10 mm) of Whatman 3MM filter paper, blotted the wicks on paper towels, and loaded30-35 wicks onto each 12.5% starch gel, cooled during extraction to 4°C. I prepared geland electrode buffers as in Table 3.8.Enzymes assayed during preliminary surveys were aspartate aminotransferase (AAT),aconitase (ACO), alcohol dehydrogenase (ADH), aldolase (ALD), aminopeptidase (LAP),Chapter 3. Correlates of Female Frequency^ 77esterase (EST), fructose-1,6-diphosphatase (F16DP), glucose-6-phosphate dehydrogenase(G6 PD), glutamate dehydrogenase (GDH), glyceraldehyde-3-phosphate dehydrogenase(G3PD), hexokinase (HEX), isocitrate dehydrogenase (IDH), malate dehydrogenase (MDH),malic enzyme (ME), phosphoglucoisomerase (PGI), 6-phosphogluconate dehydrogenase,phosphoglucomutase (PGM), shikimate dehydrogenase (SKDH), and triose phosphateisomerase (TPI). These are listed in Table 3.8 according to the buffer system that re-solved them best.Staining protocols proposed by Soltis et al. (1983) were generally successful, withsome exceptions. LAP, SKDH, and PGI were stained in the dark at 37°C, with thestaining buffers pre-heated to that temperature. LAP often showed increased stainingwhen removed to 4°C for several hours after about 0.5 hour incubation at 37°C.The only enzyme systems showing appreciable within-population variation were LAP,SKDH, and PGI; LAP, however, was excluded from the analysis, since it exhibited onlymarginal variation, and staining/resolution was generally unreliable.PGI behaved as a dimeric enzyme with both cytosolic (cathode) and plastid (anode)forms. The anode region contained three evenly-spaced bands, intensity ratio (anode-cathode) roughly 3 : 2: 1, in every individual assayed. Banding patterns in the cathoderegion varied in a manner expected for two-loci nuclear control, with four alleles at thefast locus (1), and three at the slow (2), with overlapping migration rates for two allelesat each locus. The fastest allele at locus one, however, was rare; see Figure 3.13 forall possible patterns for the remaining six alleles. About 20% of the observed bandingpatterns could have been produced by more than one genotype. In more than halfthese cases, only one genotype was logically possible given the genotypes of other familymembers. In the remaining ambiguous cases the most common alleles were assumed.SKDH behaved as a monomeric enzyme coded at three non-overlapping loci. Bandingat the anode region was consistent with single-locus control of four alleles (Figure 3.14),1 4 1 1 4 1 4 1 1 14 2 2 4 4 24. 2 .L4 2 4 4 2 4 4 2 4 4 21 4 2 j. 1 1 4 34 , 5 5,6 6,36,6 4, 6 ja. 2 2 21414111411lclb 2cla 2b2aChapter 3. Correlates of Female Frequency^ 781^1 1^11 C2lb 2c N6 1 1^13,5^6,5^5,5la 2b 1 fi?m^ 106 1 Kim1,3^3,3^3,6^2,3 5,3^4,31,5 2,5 1,6 ori.2,62a1,2^1, 1^3,1^3,4^2, ^2,1^3,2^6,1^5,4^6,4^5,2^4,1^4,2^6,2^1,4 2,4 4,4Figure 3.13: Banding patterns and intensities observed for phosphoglucoisomerase, withgenotypes coded numerically in the format required by MLT, the multilocus estimationprogram, below each lane. One- and three-band patterns above; five- to seven-bandpatterns below. Locus and associated allele indicated to the left: both locus 1 and 2contain three alleles, designated a, b, and c. Genotypes coded at the two loci as follows:1: aa; 2: ab; 3: bb; 4: ac; 5: cc; 6: bc. The first number codes locus one, and thesecond locus two; e.g., 3, 5: lbb2cc. Some banding patterns can be produced by severalgenotypes; these are listed on separate lines.Chapter 3. Correlates of Female Frequency^ 79ldlclbla1 2 3 4 5 6 UnenteredFigure 3.14: Banding patterns observed for shikimate dehydrogenase. Genotype codes aslisted in Figure 3.13. The last two (rare) genotypes were ignored due to capacity limitsof the estimation program.of which the fastest was rare. The cathodal region contained two poorly-resolved bands,each presumably from a different locus, in nearly all individuals assayed.I processed genotypes at the three loci with MLT, the multilocus maximum-likeli-hood program for the estimate of plant mating systems (Ritland, 1990). Each of the fourpopulation centers was defined as the "population" in the analysis, and mean outcrossingrates were calculated for each of the centers, and for seven of the eight subpopulationswithin centers B and C by averaging the outcrossing rates given for the individualscollected in those subpopulations. Standard error of the estimate at each populationcenter was calculated from 100 bootstrap estimates. Standard error at the subpopulationsat centers B and C was calculated as the standard error of the mean individual outcrossingrate within those subpopulations.I fitted the counts of females and hermaphrodites at the 14 subpopulations to three-factor loglinear models. Each subpopulation was scored for elevation, aspect, taxon,population center, and outcrossing rate (above or below 0.70), and each of these environ-mental factors was subjected separately to analysis of sex-ratio variation independentlyof year, in a three-factor model (sex ratio, year, and environmental factor; in this discus-sion "taxon" is included as an "environmental factor" for semantic convenience). Ideally,Chapter 3. Correlates of Female Frequency^ 80all factors should be included in a full, loglinear model. However, such an analysis wouldbe impossible in this case, since only a minority of all possible combinations of categorylevels were observed in the study populations, leaving all but a few model cells empty.I tested the significance of the environmental factor x sex ratio interaction by fit-ting the model year x factor + year x sex ratio, and subtracting the G statistics ofthis fit from those obtained by fitting the model with all three two-factor interactions.The difference then yields the G statistics (the "between" G) for the added two-factorinteraction beween environmental factor and sex ratio. The same procedure was used toobtain the interaction between subpopulation and sex ratio. The difference between thesubpopulation x sex ratio G and the environmental factor x sex ratio G gives another G(the "within" G) that tests the significance of subpopulation variation in sex ratio withineach level of the environmental factor. In analogy with standard procedures of analysisof variance, I then tested whether the environmental factor x sex ratio interaction wassignificantly larger than would be expected from random variation among subpopulationsin sex ratio, by forming an F ratio of "between" G to "within" G, each divided by itsdegrees of freedom.3.2 Results3.2.1 Outcrossing Rates, Aspect, Elevation, and TaxonFrequencies of females ranged from 0.05 at subpopulation B1 in 1992 to 0.49 in sub-population Al in 1990 (Figure 3.15). Sex ratio varied significantly by year, both amongsubpopulations (G(3) = 7.81, p = 0.05) and among population centers (G(3) = 9.33, p< 0.05). This effect is primarily due to an abrupt increase in female frequency at centerA in 1990.Sex ratio variation among subpopulations was significant independent of year (G(13) =c0 a0.50.40.1cm^co .4-CO CO COC\Ilf)^I03 1— 1—0 00ccChapter 3. Correlates of Female Frequency^ 81SubpopulationFigure 3.15: Female frequency in 14 Bidens subpopulations from 1989 to 1992. Er-ror bars in these and subsequent figures computed from the binomial standard error,.V[f(1— f)/(n —1)](N —n)/N, where f, N, and n are respectively female frequency,total flowering population, and total individuals scored. Unless otherwise indicated, thesame error is plotted for the following figures.Chapter 3. Correlates of Female Frequency^ 82122.03, p < 0.001). Sex-ratio variation among population centers (subpopulations ig-nored) was also significant independent of year (G(3) = 69.04, p < 0.001). Sex-ratio vari-ation among subpopulations within population center also varied significantly (G(10) =52.99, p < 0.001; obtained by difference between the above G statistics); this variationconsiderably reduces the observed strength of the among-center effect. This conclusion isobtained by calculating the following F ratio (analogous to a ratio of among- to within-centers mean squares):F(310) = 52.99/1069.04/3= 4.34; p(one-tail) = 0.0334.'This effect can be considered equivalent to the elevation effect, since the four populationcenters occurred at four separate elevations.The 1989 outcrossing rates for nine of the subpopulations averaged 0.62 (s.e. 0.21)and ranged from 0.37 (s.e. 0.10) to 0.87 (s.e. 0.076). The pooled outcrossing rates at thefour population centers were 0.503 (s.e. 0.112), 0.552 (s.e. 0.070), 0.755 (s.e. 0.085), and0.705 (s.e. 0.064); female frequencies at these four centers averaged respectively 0.33 (s.e.0.075), 0.27 (s.e. 0.018), 0.14 (s.e. 0.038), and 0.18 (s.e. 0.010) (Figures 3.26-3.28).Although the "between" G statistics suggest highly significant effects of all environ-mental factors on sex ratio, the "within" statistics also show highly significant variationwithin levels of each factor, and this variation reduces the probability level for each ef-fect (Table 3.9). The effect of outcrossing rate is entirely eliminated at a small spatialscale: variation in subpopulation sex ratio is not explained by variation in subpopulationout crossing rate, when each subpopulation is scored as high- or low out crossing indepen-dently of the other subpopulations at that population center ("small scale" in Table 3.9).However, if each subpopulation is scored according to the overall outcrossing rate of itspopulation center, variation in population-center outcrossing rate explains a significantamount of the variation in population-center sex ratio ("medium scale" in Table 3.9).Chapter 3. Correlates of Female Frequency^ 83Source G StatisticsBetween^WithinF Statistics ProbabilityAspectd.f.93.62**428.41**97.414,90.0063Centerd.f.69.04**352.99**104.343, 100.0334Taxond.f.51.13**270.90**113.972, 110.0505Out. Rate (small scale)Out. Rate (med. scale)d.f.16.47**49.18**1105.56**72.85**121.8728.1011, 120.1970.0148Table 3.9: Associations between environmental factors and female frequency, computed inthree-factor log-linear models (sex, year, and environmental factor) estimated separatelyfor each environmental factor. ** p < 0.001The analysis in Table 3.9 is meaningful only to the extent that different individualplants are scored in the different years. This condition is nearly met for the two popula-tions of B. cervicata, since this taxon approaches an annual life-history here with over 80%annual mortality of adult plants. However, the other populations consist of short-livedperennials, with annual adult mortality rates roughly 20 to 40%. Some double-scoringwas prevented by the fact that less than half the adult plants of a population were flow-ering at the time of sexing, and not all of these were scored. Nevertheless, one expectsthat an average scored plant was scored between once and twice over the four floweringseasons in the B. sandvicensis populations.Chapter 3. Correlates of Female Frequency^ 84Year Source Factorscontrolled BetweenG Statisticsd.f.^Within d.f.F StatisticF^Prob.Aspect 24.144** 4 15.728N5 9 3.45 0.057Center 3.68NS 2 15.58* 8 0.945 NSTaxon 6.39N5 4 13.36N5 7 0.837 NSOut.Rate 5.30N5 3 15.66* 8 0.903 NS1989 Center 20.613** 3 19.259* 10 3.57 0.055Aspect 0.15NS 1 15.58* 8 0.077 NSTaxon 2.86NS 3 16.89* 8 0.452 NSOut.Rate 2.03N5 2 18.93* 9 0.483 NSTaxon 20.127** 2 19.745* 11 5.61 0.0210Aspect 2.37NS 2 17.38* 9 0.614 NSCenter 2.37NS 2 17.38* 9 0.614 NSOut.Rate 1.91N5 2 17.84* 9 0.482 NSOutrate 18.747** 1 21.297* 12 10.466 0.0072Taxon 0.58N5 1 19.17* 10 0.303 NSAspect 45.606** 4 8.15N5 9 12.591 0.0068Center 10.03* 2 7.74N5 8 5.183 0.036Taxon 33•34** 4 7.74N5 7 7.538 0.0112Outrate 22.27** 3 8.15N5 8 7.287 0.01131990 Center 35.991** 3 17.765N5 10 6.753 0.0091Aspect 0.41N5 1 7.74N5 8 0.420 NSTaxon 23.73** 3 17.35* 8 3.647 0.0636Outrate 14.46** 2 15.96N5 9 4.077 0.055Taxon 12.677* 2 41.079** 11 1.697 0.228Aspect 0.41N5 2 40.67** 9 0.0454 NSCenter 0.41N5 2 40.67** 9 0.454 NSOut.Rate 0.25N5 2 40.83** 9 0.0276 NSOutrate 16.024** 1 33•457** 12 7.875 0.0159Taxon 4.79* 1 36.29** 10 1.320 0.278Chapter 3. Correlates of Female Frequency^ 85Year Source Factorscontrolled Between d.f.G StatisticsWithin d.f.F StatisticF^Prob.Aspect 27.782** 4 6.082NS 9 10.278 0.0021Center 8.90* 2 6NS 8 5.933 0.0263Taxon 16.42* 4 4.49NS 7 6.400 0.0172Outrate 11.93* 3 5.92NS 8 5.374 0.02551991 Center 18.962** 3 14.902NS 10 4.241 0.0356Aspect .08NS 1 6NS 8 0.107 NSTaxon 7.60NS 3 13.31NS 8 1.523 0.2815Outrate 5.12 2 12.73NS 9 1.810 0.2185Taxon 12.954* 2 20.91* 11 3.407 0.071Aspect 1.60NS 2 19.31* 9 0.373 NSCenter 1.60NS 2 19.31* 9 0.373 NSOut.Rate 1.58NS 2 19.33* 9 0.368 NSOutrate 11.376** 1 20.108* 12 8.209 0.0142Taxon 0.01NS 1 20.9* 10 .00478 NSAspect 1.621NS 4 14.414NS 9 0.253 NSCenter 0.19NS 2 13.41NS 8 0.0567 NSTaxon 1.30NS 4 13.09NS 7 0.174 NSOutrate 0.99NS 3 14.41NS 8 0.183 NS1992 Center 2.433NS 3 13.602NS 10 0.596 NSAspect 1.00NS 1 13.41NS 8 0.597 NSTaxon 2.11NS 3 12.28NS 8 0.458 NSOutrate 1.80NS 2 13.6S 9 0.132 NSTaxon 1.644NS 2 14.391NS 11 0.628 NSAspect 1.33NS 2 13.06NS 9 0.458 NSCenter 1.33NS 2 13.06NS 9 0.456 NSOutrate 1.21NS 2 13.18NS 9 0.413 NSOutrate 0.453NS 1 15.437NS 12 0.465 NSTaxon 0.03 1 14.36NS 10 0.021 NSTable 3.10: Associations between environmental factors and female frequency, computedseparately for each year. First line for each factor in the "Source" column indicates pooledeffect; subsequent lines indicate effect with indicated factors controlled in three-factor log-linear analyses. * p < 0.05; ** p < 0.001.To minimize this problem I re-fitted the data for each year to separate two-factormodels (the first line in each block in Table 3.10), and combined these probability levelsChapter 3. Correlates of Female Frequency^ 86Source G, d.f. ProbabilityAspect 28.06, 8 < 0.001Center 21.87, 8 0.0052Taxon 15.97, 8 0.0443Out. Rate 26.66, 8 < 0.001Table 3.11: Combined probability values from within-year two-factor log-linear models(sex and environmental factor) from Table 3.10. Each G is calculated as —2 E lnp„ wherep, are the probability values, for each year, of the environmental factor x sex interactionuncontrolled by any other factor (Sokal and Rohlf, 1981, pp. 779-782).over the four years for each environmental effect (Table 3.11). Overall, the most impor-tant effects were aspect and outcrossing rate, followed by population center/elevation.The taxon effect is substantially smaller, and not statistically significant over the fouryears.In addition, I attempted to control statistically for interactions among environmentalfactors with three-factor models (sex and all combinations of two environmental factors)within each year (the lines following the first for each year in Table 3.10). In these analysesthe effects of the environmental factors on sex ratio almost completely disappeared.This occurred most likely because of the loss of statistical power as effects are addedto a loglinear model. Obviously, only 14 subpopulations are not sufficient for a fullcategorization along four separate dimensions (plus sex ratio), and constitute a smallsample size even for two dimensions. The data are insufficiently crossed for any four-factor model, and for all three-factor models that include outcrossing rate, sex ratio, andanother environmental factor, unless that factor is taxon (hence only this line is listed inTable 3.10).The aspect x sex ratio effect is problematic, since it varies significantly by year(G(12) = 21.50, p = 0.0435, for the model containing all two-factor interactions of year,aspect, and sex). But overall, female frequency tends to be higher on northeast-facing andChapter 3. Correlates of Female Frequency^ 87NE^SE^SW^NWAspectFigure 3.16: Female frequency of subpopulations, pooled by predominate compass aspectof the site.southwest-facing slopes (Figure 3.16). The taxon x sex ratio effect is stable over time,and female frequencies are higher in Bidens sandvicensis subsp. sandvicensis populationsthan in B. sandvicensis subsp. confusa or B. cervicata populations (Figure 3.17). Overthe medium scale, outcrossing rate again varies inversely with female frequency. Overthe small (subpopulation) scale, however, there is no significant relationship between thetwo, and these calculations were not included in Tables 3.10 and 3.11. Female frequencyis negatively correlated with elevation (Figure 3.18).0BiceBisacoTaxonBisasa0.3Chapter 3. Correlates of Female Frequency^ 88Figure 3.17: Female frequency of subpopulations, pooled by taxon. Abbreviations as inTable 3.7.ei 1989o 19900 19910 1992-I..IM-Chapter 3. Correlates of Female Frequency^ 89460^610^760^910Elevation (meters)Figure 3.18: Female frequencies of subpopulations, pooled by elevation.Chapter 3. Correlates of Female Frequency^ 90I^I^I^ I^i^i^i^I I^t^I2^6^10^14^18Number Hermaphroditeswithin 5 mFigure 3.19: Mean seed set per capitulum (three replicates per plant) versus number ofhermaphrodites within a radius of 5 meters, for females and hermaphrodites in nature.For females (solid line) r2 = 0.018; for hermaphrodites (dashed line) r2 = 0.032.3.2.2 Pollen Flow and Sexual DimorphismSeed set per capitulum was positively correlated with the number of hermaphroditeindividuals within a five-meter radius, and the regression coefficient for females was notsignificantly different from that of hermaphrodites (Figure 3.19, Tables 3.12 and 3.13).Analysis of covariance also indicated a significantly lower seed set of hermaphroditesindependent of population, size class, and proximity of other hermaphrodites (Table3.13). However, the significant population effect on mean seed-set appeared independentof mean female frequency over the four years, as indicated by the analysis of variance inChapter 3. Correlates of Female Frequency^ 91Source SS d.f. MS F PNo. Near 40.311 1 40.311 8.710 0.004Height 15.923 1 15.923 3.440 0.065Sex 69.362 1 69.362 14.986 0.000Pop. 24.687 3 8.229 1.778 0.154Pop. xNo. Near 20.808 3 6.936 1.499 0.217Sex xNo. Near 0.697 1 0.697 0.151 0.699Pop. xHeight 13.439 3 4.480 0.968 0.410Sex xHeight 1.549 1 1.549 0.335 0.564Sex xPop. 16.328 3 5.443 1.176 0.321Error 726.651 157 4.628Table 3.12: Model I analysis of covariance among mean seed set per capitulum, numberof hermaphrodites within a 5 m radius, and height, by population and sex, square-roottransformed data.Source SS d.f. MS F PNo. Near 18.974 1 18.974 4.115 0.044Size 7.497 1 7.497 1.626 0.204Sex 466.951 1 466.951 101.275 0.000Pop. 113.726 3 37.909 8.222 0.000Error 774.601 168 4.611Table 3.13: Model I analysis of variance among mean seed set per capitulum, numberof hermaphrodites within a 5 m radius, and size of individual, by population and sex,square-root transformed data.Chapter 3. Correlates of Female Frequency^ 92Source SS d.f. MS F PNo. Near 26.574 1 26.574 5.087 0.025Size 2.115 1 2.115 0.405 0.525Sex 415.820 1 415.820 79.603 0.000Fem. Freq. 0.305 1 0.305 0.058 0.810Error 888.023 170 5.224Table 3.14: Model I analysis of covariance among mean seed set per capitulum, numberof hermaphrodites within a 5 m radius, female frequency in the population, and size ofindividual, by sex, square-root transformed data.which female frequency was replaced for the population effect (Table 3.14, Figure 3.20;simple = 0.224, s.e.. 2.7, p = 0.933).The primary visitors of B. sandvicensis subsp. sandvicensis at the sites observed wereintroduced syrphids in the genus Allograpta, which constituted over 70% of the plantapproaches; endemic wasps in the genera Odynerus and Pachodynerus; and introducedhoneybees Apis mellifera. Occasional visitors included an introduced wasp Polistes, anintroduced moth Vaga blackburni, and 3-4 uncommonly observed, unidentified dipterans.In addition, larvae of a tenthridinid not uncommonly parasitized the anthers of herma-phrodites in most of the observed populations. Although no information exists on therelative effectiveness of the potential pollinators, it appears that both Allograpta andOdynerus have low rates of pollen pickup; both lack specialized anatomical features forcollection, and the former is small, while the latter consumes pollen and nectar primarilyin the absence of aphids, its preferred prey. Apis, on the other hand, is potentially ahighly efficient pollinator, but appears to be a less-common visitor.The total number of visitors to a plant over a two-hour interval varied little betweensexes, among individuals within a sex, among populations, or according to how manycapitula were open and receptive (Table 3.15). However, variation among individualChapter 3. Correlates of Female Frequency^ 93Al 0.38-0.49B2 0.25-0.38B3 0.26-0.42B5 0.18-0.250^5^10^15^20Mean Seed SetFigure 3.20: Box plots of mean seed set per capitula (three replicates per plant) by sexand subpopulation, with range of female frequency from 1989 to 1992 indicated.Chapter 3. Correlates of Female Frequency^ 94Source SS d.f. MS F PFInd 0.081 1 0.081 0.269 0.620HInd 0.264 1 0.264 0.879 0.380Sex 0.377 1 0.377 1.252 0.300Capitula 1.153 1 1.153 3.832 0.091Pop. 1.274 2 0.637 2.117 0.191Error 2.107 7 0.301Table 3.15: Nested analysis of covariance between total number of insects visiting aplant in a two-hour period and number of capitula open, by female and hermaphroditeindividual (nested within sex), sex, and population, square-root transformed data. Alltwo-factor interactions with number of capitula were non-significant.hermaphrodites was significant, and hermaphrodites tended to receive more visits overall.The total number of capitula visited per plant approach was greater for hermaphrodites,and varied among the three subpopulations, with slightly lower capitula visitation ratesobserved in the population with the highest female frequency (Table 3.16, Figure 3.21).No significant relationship appeared to exist between either total approaches of a plantor number of capitula visited per approach, and the female frequency of the populationcontaining the plant (Table 3.17), although total mean approaches was nearly significantlypositively correlated with female frequency.Separate two-factor analyses of variance showed no evidence for a sex x subpopula-tion interaction in number of capitula produced, total height, or total length of primarybranches, over the subpopulations Al, Bl, B2, B3, and B5 (Tables 3.18 to 3.20).However, all three attributes varied significantly among the five subpopulations, primar-ily due to smaller size of individuals in subpopulation B2. While between-sex variation innumber of capitula and perhaps height was not significantly greater than within-sex vari-ation, the total branch length was significantly greater in hermaphrodites (Table 3.20).Although these variables failed to pass the Kolmogorov-Smirnov normality test whetherSource SS d.f. MSNumber of Approaches per PlantRegressionResidual0.0170.046 1120.0170.0044.407 0.058Number of Capitula Visits per ApproachRegressionResidual0.0000.2730.0000.0040.037 0.848169Chapter 3. Correlates of Female Frequency^ 95Source SS d.f. MS F pFind 0.013 1 0.013 0.154 0.697Hind 0.174 1 0.174 2.067 0.156Sex 0.727 1 0.727 8.615 0.005Pop. 0.912 2 0.456 5.403 0.007Capitula 0.024 1 0.024 0.282 0.598Sex xCapitula 0.813 1 0.813 9.632 0.003Pop. xCapitula 0.997 2 0.498 5.905 0.005Error 5.147 61 0.084Table 3.16: Nested analysis of covariance between number of capitula visited per plantvisit, and number of capitula open at time of visit, by female and hermaphrodite indi-vidual (nested within sex), sex, population, data transformed to the 1/4 power.Table 3.17: Regression of mean female frequency of a population on (1) mean numberof insect approaches per hour of a plant contained in the population, and (2) meannumber of capitula visited per approach, square-root transformed data. Both regressioncoefficients positive.Chapter 3. Correlates of Female Frequency^ 960.38-0.490.26-0.420.18-0.250^10^20^30No. capitula visitedFigure 3.21: Box plots of number of capitula visited per plant visit, by sex and subpop-ulation, with range of female frequency from 1989 to 1992 indicated.Source SS d.f. MS F pSexPop.Error0.24028.336165.740141980.2407.0840.8370.2878.4630.5930.000Table 3.18: Model I analysis of variance in log-transformed number of capitula per plant,between sexes and among five subpopulations. No interaction was found between thetwo factors (F(4,194) = 0.565, p = 0.688).Chapter 3. Correlates of Female Frequency^ 97Source SS d.f. MS F PSexPop.Error397.7515406.62729989.93314189397.7511351.657158.6772.5078.5180.1150.000Table 3.19: Model I analysis of variance in plant height between sexes and among fivesubpopulations. No interaction was found between the two factors (F(4,185) = 1.420, p= 0.229).Source SS d.f. MS F PSexPop.Error0.6261.30715.368141600.6260.3270.0966.5193.4010.0120.011Table 3.20: Model I analysis of variance in square root-transformed total primary branchlength per plant, between sexes and among five subpopulations. Little or no interactionwas found between the two factors (F(4,156) = 1.935, p 0.107).Chapter 3. Correlates of Female Frequency^ 98Variable Source Statistic Value Ties ProbabilityHeight Sex Z -1.989 36 0.0467Height Pop. H 8.368 36 0.079Capitula Sex Z -0.685 33 0.4931Capitula Pop. H 24.47 33 0.0001Branch Sex Z -1.982 7 0.0475Branch Pop. H 7.406 7 0.06Table 3.21: Nonparametric single factor analyses of variance in plant height, number ofcapitula, and total branch length by sex or population. Z: Mann-Whitney U Test; H:Kruskal-Wallis Test.transformed or not, these results were reasonably corroborated by nonparametric tests(Mann-Whitney and Kruskal Wallis), except that height variation was not significantamong populations, and branch length variation was marginal (Table 3.21). These, how-ever, are single-factor tests.Despite the nonsignificance of the sex x population interactions, the box plots suggestmoderate interactions, primarily due to differences in subpopulation Al, where femalefrequencies were highest (Figures 3.22 to 3.24). Generally, branching is greater in herma-phrodites, but females apparently produce more capitula per unit branch length, so thattheir total capitula production is the same. At Al, however, mean branch length andcapitula number are greater in females, and mean female height is greater than all othersites for either morph, despite the fact that hermaphrodites are slightly larger overall.No sex x subpopulation interaction was significant for any of the measured morpho-logical traits, and no regression of mean sexual dimorphism in a subpopulation againstthe mean female frequency of that subpopulation was significant (Tables 3.22 and 3.23).AlB2B3B5Chapter 3. Correlates of Female Frequency^ 990^Iv^-P.^01^CO0 0 00^0^0 Number of CapitulaFigure 3.22: Box plots of number of capitula by sex and subpopulation, with range offemale frequency from 1989 to 1992 indicated.00.26-0.42 0.18-0.25Chapter 3. Correlates of Female Frequency^ 1000.38-0.490.25-0.38AlB2B3B5I^I^I^ I^J-P.^CC _.,^ND^ND0^0^ND^CD -P.CD p CD 0Height (cm)Figure 3.23: Box plots of plant height by sex and subpopulation, with range of femalefrequency from 1989 to 1992 indicated.1^2^3^4^5^6AlB2B3B5Chapter 3. Correlates of Female Frequency^ 101Branch Length (m)Figure 3.24: Box plots of branch length by sex and subpopulation, with range of femalefrequency from 1989 to 1992 indicated.Chapter 3. Correlates of Female Frequency^ 102Subpop. Seed Set Visits Branch Height Cap. Fern. Freq.Al 4.04 2.97 0.17 1.00 22.50 0.4261.55 2.34 1.08 1.02 1.11B2 2.68 - -0.34 2.80 -7.50 0.2921.26 0.81 1.07 0.93B3 3.78 -4.18 -0.75 -6.50 -55.90 0.3491.41 0.39 0.66 0.86 0.67B5 3.77 -2.76 -0.64 -9.50 -34.00 0.2021.47 0.50 0.74 0.82 0.85Table 3.22: Sexual dimorphism in seed set per capitulum, number of capitula visitsper plant visit, total primary branch length, number of capitula, by population. Ineach cell, first quantity is the mean difference in indicated variable between female andhermaphrodite; second quantity is the mean ratio of female to hermaphrodite.Seed Set Visits Branch Height Cap.Diff. 0.11 0.396 0.436 0.308 0.2481.386 0.707 0.693 0.693 0.693Ratio 0.109 0.532 0.413 0.241 0.1620.693 0.707 0.693 0.693 0.693Table 3.23: Regression of sexual dimorphism in seed set, capitulum visits per plant visit,primary branch length, height, and number of capitula, on mean female frequency in thefour subpopulations Al, B2, B3, and B5. First quantity in cell: r2 in simple regression;second quantity: Z of Spearman's correlation. All slopes were positive, but none weresignificantly different from zero in either parametric or nonparametric tests. Differencesand ratios as in Table 3.22.Chapter 3. Correlates of Female Frequency^ 1033.3 DiscussionIf male sterility is controlled entirely by nuclear genes, then equilibrium frequency offemales (f) can be calculated simply from inbreeding depression (d, assumed the same infemales and hermaphrodites), outcrossing rates of females (1 — sf) and hermaphrodites(1 — sh ), intrinsic female advantage (k), and pollen limitation (1 — q), from Equations1.15, 1.17, and 1.21:1 d[tS f (q qk) — 2sh] 2sh(1 — q) -F q(1 — k)(3.30)2^d[s f (q — qk) — sh}-F sh(1 — q) — qk^•Inbreeding depression in Bidens sandvicensis approaches 100%, due to greater embryoabortion, lower germination rates, slower growth, lower survivorship, and lower repro-ductive output the first flowering season (Chapter 4). There is no strong evidence of anintrinsic female advantage (k > 0) in either survivorship or fecundity. The survivorshipof females and hermaphrodites was not significantly different either in nature or in fieldplots when compared within parentage classes (Chapter 4). The 30-40% higher seed setin females reported here is also a probable result of inbreeding depression in hermaphro-dites. If this difference were caused by seed abortion due to greater energetic limitationsin hermaphrodites, seed set would not be dependent on proximity of other hermaphro-dites, which suggests limitation not by resource but by pollen availability. Inbreedingdepression has been suggested as a cause of lower seed set in hermaphrodites of othergynodioecious angiosperms (Sakai, et al., 1989; Agren and Willson, 1991; Sastad, 1991;De Jong, et al., 1992), as well as resource limitation in hermaphrodites (Shykoff, 1988;Klinkhamer, et al., 1991), and pollen clogging in a self-incompatible species (Kikuzawa,1989). In some cases, seed set in hermaphrodites is so low (presumably due to inbreedingdepression) that hermaphrodites are nearly functional males (Sastad, 1991).Chapter 3. Correlates of Female Frequency^ 104If inbreeding depression eliminates progeny prior to electrophoretic assay, the calcu-lated selfing rate (em) will be underestimated to the extent that the relative survivorshipof selfed embryos (la) falls below unity, and the true selfing rate of fertilized ovules willthen beshla + 8, (l — la)In terms of is, relative seed set of females will beq(lssf + 1 - S f ko)r = ^issh^q(1^sh)(3.31)(3.32)where ko is the component of intrinsic female advantage affecting seed set. For ko = 0,q = 1, r = 1.4, sm = 0.4, and sf = 0.1 (Sun and Ganders, 1988), these equations give0.45 as the survival of selfed embryos to seed, relative to outcrossed, and 0.60 as thetrue selfing rate. If q = 0.8 (i.e., only 80% of the outcrossed ovules of both morphs arefertilized), and the other parameters are as above, then the relative survival of selfedembryos will be 0.38, and the true selfing rate 0.64.Substitution of Equation 3.31 into Equation 3.30 expresses equilibrium f in terms ofthe measured selfing rate:2AB'^ (3.33)whereA = {[(1 k)s f la — (1 + k)s f 2] d (1 — k)l, — 1 +— (1 + k)s flscl — (1 — k)15, andB = {[(1 k)s f la — (1 + k)s f 1] d — kl, +^— (1 + k)s flscl + kis.This assumes q = 1 or that pollen limitation reduces the ovule fitness of femalesand hermaphrodites equally, as suggested in the present case (Figure 3.19). The lattercan be approached (1) if survivorship of selfed embryos is low, (2) if the tendency ofChapter 3. Correlates of Female Frequency^ 105pollenivorous pollinators to avoid females is more pronounced the more recently theyvisited a hermaphrodite, so that fertilization rate of outcrossed hermaphrodite ovulesdrops more steeply as pollen availability decreases, or (3) if low pollinator activity tendsto reduce the fertilization rate of selfed ovules to the same extent as outcrossed ovules,which is to be expected if selfing is entirely geitonogamous. An equal pollen limitationin the two sexual morphs has not been previously reported. However, pollen limitationhas been demonstrated in one gynodioecious species (Widen and Widen, 1990), whosefemale fecundity is dependent on distance from pollen source. Hand pollinations of otherspecies fail to show any pollen limitation even though in some of these cases visitationrates to hermaphrodite inflorescences was observed to be substantially higher, as in thepresent study (Eckhart, 1991; Klinkhamer, et al., 1991; Delph and Lively, 1992). Thegreater attractiveness of hermaphrodites in some cases appears due in part to a highervolume of nectar, or more concentrated nectar (Ashman and Stanton, 1991; Klinkhamer,et al., 1991; Delph and Lively, 1992), and this difference has been postulated to resultfrom sexual selection on male function (Delph and Lively, 1992). Female flowers ingynodioecious species are almost always smaller than hermaphrodite flowers (e.g., Dorr,1990; Delph, 1990b; Agren and Willson, 1991; Ashman and Stanton, 1991; GarnockJones, 1991; Klinkhamer, et al., 1991), and this dimorphism may also be due to sexualselection, or both smaller size and lower nectar content may alternatively be pleiotropiceffects of male sterility. Female flowers are smaller than those of hermaphrodites in Bidensbut no information exists on sexual dimorphism in nectar volume or concentration, orthe role of pollen on the greater visitation rates to hermaphrodites.The selfing rate of hermaphrodites at each of the four Bidens population centers in1989 predicts the mean female frequency over the four years in close accordance withEquation 3.33, with all other parameters held constant (Figures 3.26 to 3.28). Interest-ingly, the same inbreeding depression in seed set (60-70%) required to explain the sexChapter 3. Correlates of Female Frequency^ 106I^.^,^I^•^1^1^1^I^I•^I^1^1^1^I^1^1^1^I^1^1^I^'0.5^0.6^0.7^0.8 0.9Measured Outcrossing RateFigure 3.25: Total female frequency at the four population centers from 1989 to 1992versus mean 1989 outcrossing rate at each center, with Equation 3.33 plotted ford = 1.0, k = 0.15, is = 0.3, and sf = 0.1.difference in seed set per capitulum is also required to produce the observed female fre-quencies, under the low measured selfing rates. However, small-scale variation in selfingfails to explain small-scale variation in female frequency according to the equation, unlessother parameters are varied as well (Figure 3.29). The lack of small-scale correlation hasat least three plausible explanations. First, wide annual variation in mean hermaphro-dite selfing rate in a subpopulation might cause annual variation in the sex ratio of newrecruits in the flowering population, as observed at centers A and D. The selfing rate inany given season may not measurably affect female frequency for one or two years in theB. sandvicensis populations, and this effect may be diluted by the effects of the selfingrate in previous years. For perennial species with varying selfing rates, Equation 3.33may not be adequately testable on a small scale without monitoring of the mating systemChapter 3. Correlates of Female Frequency^ 1070.5 I^I^I I^t^1^11111 10 ^0.4sf = 0d = 1.0k = 0.2ls varying0.90.5^0.6^0.7^0.8^0.9Measured Outcrossing Rateo ObservedTheoryFigure 3.26: Mean female frequency at the four population centers from 1989 to 1992versus mean 1989 outcrossing rate at each center, with Equation 3.33 plotted for theindicated parameter values. Error bars in female frequency are the standard deviation infemale frequency within each site over the four years; the same error is plotted in Figures3.27 and 3.280.5o Observed^sf =0— Theory^1, = 0.5d = 1.0k varying0.80.60.2^0.40 r^ I^T^1^I^F^I^-1 1 " 1 "0.4^0.5^0.6^0.7^0.8Measured Outcrossing Rate0.9Chapter 3. Correlates of Female Frequency^ 108Figure 3.27: Mean female frequency at the four population centers from 1989 to 1992versus mean outcrossing rate at each center, with Equation 3.33 plotted for the indicatedparameter values.I^•^I^i^I^I^I^•^Io Observed^sf =0•2— Theory 1, = 0.5d = 1.0k varying0.80^0.2^0.4^0.6I^I^I^I^I^I^I0.5o ^0.5^0.6 0.7^0.80.4 0.91,0Chapter 3. Correlates of Female Frequency^ 109Measured Outcrossing RateFigure 3.28: Mean female frequency at the four population centers from 1989 to 1992versus mean 1989 outcrossing rate at each center, with Equation 3.33 plotted for theindicated parameter values.Chapter 3. Correlates of Female Frequency^ 1100.50.4 —U'Zcu 0.3 —0-1ca)er.-■(i)0.2 —'7da.)4-1 0.1 —it• 1989^ i• 1990• 1991• 1992^•B2 C3 AB11---i--1^4B4 C2 B3 C1D^;-–_-1-4-1^ i 1-11-1I-I-^I^I^1^,^.^ I^11-^I^I^•0.2 0.4 0.6 0.8 1.0Measured Outcrossing RateFigure 3.29:^Female frequency at nine subpopulations from 1989 to 1992versus medium scale 1989 out crossing rate, with Equation 3.33 plotted ford = 1.0, k = 0.15, is = 0.3, and sf = 0.1. Outcrossing rate calculated defining eachof the four population centers as a population, and computing mean outcrossing rate offamilies within each subpopulation.Chapter 3. Correlates of Female Frequency^ 111over several years in several populations. Over the medium scale, however, mean selfingrates may be sufficiently stable that the annual small-scale variation in female frequencycancels out within a population center; see the variation in sex ratio at centers B and Cin comparison to that at the smaller centers A and D (Figure 3.25).Second, the true selfing rates of the subpopulations at centers B and C might be tem-porally invariant, but not accurately measurable because of among-subpopulation varia-tion in abortion rates of selfed embryos, even if this latter variation is also stable in time.Inbreeding depression at later developmental stages has been shown to be environmen-tally variable in many species (e.g., Waller, 1985; Dudash, 1990; Schmitt and Ehrhardt,1990; Eckert and Barrett, 1993), but little information exists on environmental corre-lates at these early stages. Under this hypothesis, the significant among-subpopulation,within-center variation in female frequency may be caused simply by variation in selfingrate and hence expression of inbreeding depression, but the measured variation in sellingrate is largely an artifact of spatial variation in relative rate of abortion of selfed em-bryos. The significant correlation of the small-scale variation in female frequency withenvironment (e.g., aspect) may still be explained by a correlation between environmentand pollinator species composition/foraging behavior.Third, the small-scale variation could simply be the result of random genetic drift. Ifmost members of a subpopulation are full- or half-sibs, they do not represent statisticallyindependent occurrences of their sex, and the sample size for the estimate of sex ratio willbe artificially inflated, leading to spurious variation in the sex ratio. This possibility isperhaps the most parsimonious explanation of the phenomenon, since drift undoubtedlyoccurs to some extent, and could be sufficient to account for the observed variation.Neither behavioral component of insect visitors in a Bidens subpopulation (totalapproaches or visits per approach) was correlated with frequency of females in the sub-population, although the positive relationship of female frequency and approaches wasChapter 3. Correlates of Female Frequency^ 112nearly significant. This lack of correlation could be explained either by the low totalhours devoted in this study to insect observation, or by large annual variation in pol-linator behavior and resulting selfing rate in hermaphrodites. Two of the four mostcommon insect visitors, Odynerus and Pachodynerus, are native to the Hawaiian archi-pelago. That native wasps in these genera were the primary pre-contact pollinators ofHawaiian Bidens is suggested by their occurrence on all islands and all species of Bidensclosely observed (Ganders, unpublished). Hence the pollinating conditions in this studydiffered from the likely conditions under which gynodioecy originally evolved only in thepresence of introduced Apis mellifera and various flies. Although the precise pre-contactconditions are difficult to ascertain, the apparent lack of any intrinsic female advantage inB. sandvicensis suggests that the original female advantage was primarily an outcrossingadvantage; in any case, the behavior of the past pollinators, whether native or not, isirrelevant to the current maintenance of females.In conclusion, pollen limitation exists in these populations of Bidens sandvicensis andprobably B. cervicata, but it appears to operate about equally in the two sexual morphs,so that, theoretically, its effect on sex ratio should be neutral. Evidence for environment-mediated variation in sex allocation is marginal, with no statistically significant variationin measured sex dimorphism among four subpopulations, but some clear differences atsubpopulation Al that favor females at this high female-frequency site. Overall, femalefrequency is strongly correlated with hermaphrodite selfing rate, and hence also pollinatorefficiency in pollen transfer and outcrossing, although no pollinator behavioral correlateswith female frequency were evident. Larger and more detailed studies of pollinatorbehavior would be useful, as well as more extensive studies of sex allocation patternsat site Al.Chapter 4Inbreeding Depression and Maternal Parentage4.1 MethodsIn four major Bidens sandvicensis population centers along the western rim of WaimeaCanyon, Kauai, I collected open-pollinated seed from over 500 hermaphrodites in May1989, and from over 200 each of hermaphrodites and females in May 1990. In Novem-ber 1989, after surface-sterilizing the 1989 seeds in 70% (v/v) ethanol and 3% (w/w)sodium hypochlorite, I planted a sample from each parent in sterile agar fortified with3% (w/w) sucrose, Murashige-Skoog medium, and vitamins, in 10cm x 10cm glass jars.Jars were placed in growth chambers at constant 25°C, and alternating 12 hours of lightand darkness.In January 1990, I potted the seedlings in a sterile mixture of peat, perlite, soil,and osmocote (1 : 1 : 1 : 1/50 by volume) and transferred one individual for each of100 families to the glasshouse at the South Campus facility of the University of BritishColumbia, where they were maintained at a constant 21°C and received ambient levelsof light.Plants began flowering by June, and each individual remained flowering for abouttwo weeks. Fewer than about five individuals flowered together at any time from Juneto January, and only after mid-February did flowering reach a peak, when most of theremaining individuals flowered simultaneously.From June to January 1991 I performed self- and outcross pollinations on the available113Chapter 4. Inbreeding Depression and Maternal Parentage^ 114individuals, with parentage determined solely by the plants in flower. In each cross, atleast 10 pollen grains were placed on each stigma. I applied pollen directly from flowerto flower, using as donors flowers presenting pollen but whose style branches had not yetseparated to expose the stigmatic surface. All crosses were between individuals whosematernal parents were separated by at least 15m and at most about 200m. The last weekof January 1991 I sterilized seeds obtained from these crosses and from the 1990 collectionin 3% (w/w) sodium hypochlorite, and germinated them in the open-air nursery at theNational Tropical Botanical Garden in Lawai, Kauai, in an equal parts mixture of sterilesoil, peat, and perlite. For the outcrosses and selfs, two seeds were sown in each ofthe 76 wells per 12in x 24in planting flat; for the open-pollinated progeny, 10-20 seedswere sown per flat well. Seedlings were watered daily and those from open-pollinatedparents were thinned randomly in each well on a weekly basis. Germination rates for theoutcrossed and selfed seeds were measured the last week of February 1991.Sample size for the selfed/outcrossed comparison in seed set began with 14 herma-phrodite seed parents, but low seed set and germination rates (especially of selfs) reducedthe sample size for subsequent performance of selfs and outcrosses to a total of 10 par-ents, each represented on average by 40 seedlings (20 each of selfs and outcrosses). Inthe three families that set no seed in hand selfs, autoselfed seed were used; no attempt,however, was made to incorporate the low rate of autoselfs observed in each family intothe estimates of inbreeding depression in seed set. Each hermaphrodite parent was pro-duced by a different open-pollinated hermaphrodite maternal parent in nature. A totalof 20 pollen donors was used for the outcrosses, but not all 20 were used to pollinateany of the seed parents, and the paternal parentage in each of the maternal families wasnot entirely the same due to the fact that pollen was produced for less than about onemonth for any given donor. Sample size for the open-pollinated progeny comparison wasover 150 families each of females and hermaphrodites, each represented by ten seeds inChapter 4. Inbreeding Depression and Maternal Parentage^ 115the germination experiment, and by two seedlings in subsequent fitness comparisons.In this design I attempted to maximize the number of sampled families rather thanthe number of seeds per family. Preliminary studies of statistical power showed that,because family membership is a random factor in the mixed-model analyses of variancerequired to demonstrate inbreeding depression (or an effect of maternal sex on fitness),statistical power is increased more rapidly with increasing number of randomly sampledfamilies than with increasing number of individual subjects beyond about 10 each of selfsand out crosses per family, assuming moderate inbreeding depression and family variationin inbreeding depression. The total number of families for the inbreeding depressionexperiment was determined solely by the number of hermaphrodite parents co-floweringin the glasshouse (out of a sample of 100) between January 1990 and January 1991.In early March 1991 I transplanted the germinated seedlings into the field adjacentto natural populations of Bidens sandvicensis into the horizontal base of a large slump,at an elevation of 880m on the western rim of Waimea Canyon (at site B in Figures3.11 and 3.12). Plantings were done at this time to mimic the natural timing of seedrecruitment, which occurs in winter as the first extended rains break seed dormancy. Iplanted the seedlings in twelve cleared plots, four of which contained 50 each of selfed andoutcrossed individuals, and eight of which contained 50 each of open-pollinated progenyof female and hermaphrodite maternal parents from the 1990 collection. Progeny fromthe original maternal grandparents of the selfs and outcrosses were not used in the open-pollinated progeny comparison because these seed were produced in 1989, a year beforethe selfs and outcrosses, and therefore may have developed different germination behaviorthat would have prevented any comparison with the selfs and outcrosses. I planted theseedlings in hexagonal 10 x 10 arrays in which individuals were separated by 10cm andthe two progeny classes occupied alternate positions. Each self/outcross plot was pairedat random with a female/hermaphrodite progeny plot, and the two were situated adjacentChapter 4. Inbreeding Depression and Maternal Parentage^ 116to each other.I monitored survivorship and height growth of the subjects three times in 1991 (March,May, and October), and in 1992 (January, May, and August). In May 1992 I additionallymeasured length of the longest leaf; counted the number of primary branches per plant,of apical leaf pairs, and of capitula produced; and recorded the stage of developmentin plants that flowered (budding, flowers open and receptive, petals absent but seedsstill green, seeds black and mature, seeds dispersed). In addition, I monitored apparentsurvivorship of 100 each of female and hermaphrodite individuals in four populations attwo elevations from May 1991 to October 1991, January 1992, May 1992, and August1992. Survivorship was defined as the presence of photosynthetic foliage on any part ofthe individual. Fitness experiments were terminated somewhat abruptly by HurricaneIniki, which conveniently hit Kauai after the first full year of monitoring.The fitness experiment comparing open-pollinated progeny of females and hermaphro-dites was replicated on a smaller scale in standard 12in x 24in, 76-well planting flats inthe growth chamber, maintained at constant 25°C and alternating 12 hours of light anddark. For these experiments, 86 families (43 each from females and hermaphrodites) wereeach represented by 6-7 seedlings per family, germinated from a total of 60-70 plantedseeds. Seeds sterilized in 3% (w/w) sodium hypochlorite were planted and seedlingsgrown in a 1 : 1 : 1 mix of sterile soil, peat, and perlite; female and hermaphroditefamilies planted in alternating wells in the flats. I planted 10 seeds in each of the 76 wellsper flat, and discarded all germinated seedlings except the one closest to one corner ofeach well. This was done to insure that the one surviving individual in each well was arandom sample of the germinated individuals from the 10 seeds. Total germination ratewas calculated for each well to one month after planting, to compare with the same cal-culation made for outcrosses and selfs under the same planting conditions in the open-airnursery at the National Tropical Botanical Garden.Chapter 4. Inbreeding Depression and Maternal Parentage^ 117Four classes of confirmatory statistical tests were used to demonstrate either inbreed-ing depression or an effect of maternal sex. To demonstrate inbreeding depression inmeasurement variables, I used mixed-model analyses of variance in which cross effect isfixed, family effect is random, and the cross x family interaction is random. Becausesample size in cells was uneven, I used a maximum-likelihood approach to estimate thecomponents of variance (Hartley and Rao, 1967; Hartley and Vaughn, 1972; Jennrich andSampson, 1976; Harville, 1977). This technique yields estimates of the parameters of theANOVA model and their asymptotic standard errors. Significance tests of the effects inthe model are accomplished by setting each effect individually to zero, reestimating theparameters, and comparing the reestimates to those of the original model. This com-parison yields a chi-square statistic with a single degree of freedom. The result tablesfor these analysis provide the parameter estimate for each effect, its standard error, thechi-square value for the effect comparison with the complete model, and its associatedone-tail probability.To demonstrate inbreeding depression in categorical variables (e.g., germination, sur-vivorship, flowering), I used a loglinear analogue of mixed-model analysis of variancesimilar to those used to address correlates of female frequency in Chapter 3. Standardthree-factor contingency tables were generated in which the factors were cross, family,and performance (e.g., survive), and the cross x performance G was determined for thesampled families using the standard difference method (Fienberg, 1987). To determinewhether the observed cross x performance interaction could have been due to randomvariation among the sampled families in inbreeding depression, I formed the ratio of thecross x performance G to the three-factor interaction G, each divided by its degrees offreedom. If the null hypothesis of no cross effect on performance is true, then this ratioestimates an F ratio with degrees of freedom equal to the numerator and denominatordegrees of freedom of the numerator and denominator G values. Its one-tail probabilityChapter 4. Inbreeding Depression and Maternal Parentage^ 118then tests this null hypothesis given the among-family variation in cross effect. Thistechnique has not received any analytical or numerical analysis and apparently has notyet been employed in studies of inbreeding depression; it has, however, been used in atleast one other biological context (Nunney, 1990).To demonstrate a maternal-sex effect on measurement variables for the growth cham-ber experiment, I used a mixed-model nested analysis of variance in which the sex effectis fixed and the family effect (among the 86 families) is random and nested within sex.To demonstrate this effect for the field experiment, a different approach was necessitatedby the fact that the total number of families (over 300) exceeded the capacity of at leastfour standard statistical packages (SYSTAT, BMDP, MIDAS, and SAS; in some of these,however, the array size can be enlarged, but the cost of the analysis becomes prohibitivelyhigh). My alternative method was to simply perform a standard one-factor analysis ofvariance, with maternal sex the fixed effect, using family means as observations; thedrawback of this is that any two observations may not have an equal variance, dependingon the number of surviving individuals (2 or 1) in a family.To demonstrate an effect of maternal sex on categorical variables, I used a loglin-ear analogue of a nested analysis of variance similar to the one described above. Inthis approach, two two-factor contingency tables were generated. The first tabulatedperformance by maternal sex, and gave a marginal sex x performance interaction G,with families lumped. The second tabulated performance by family, and gave a familyx performance interaction G, with the two maternal sexes lumped. The among-familyvariation within either sex class was then measured by the difference between these twoG values (and their degrees of freedom). To demonstrate an effect of maternal sex onperformance greater than would be expected by random family variation, I formed theratio of the marginal sex x performance ("between") G to the difference ("within") G,Chapter 4. Inbreeding Depression and Maternal Parentage^ 119each divided by its degrees of freedom. If the null hypothesis of no sex effect on perfor-mance is true, then this ratio again estimates an F statistic whose one-tail probabilitytests the null hypothesis given the among-family variation within each sex category.The same types of statistical tests were performed to test for other random effects,such as field plot, home population, and planting flat effects. Mixed-model analyses ofvariance and covariance were performed by BMDP program 3V, and loglinear analysisof contingency tables by program 4F (Dixon, 1985); the F values were subsequently cal-culated by hand and their associated one-tail probabilities obtained from Maple V (Uni-versity of Waterloo, Waterloo Maple Software). For survivorship and flowering variables,results from the above techniques were checked with conventional analysis of variance(on arcsin root transformed proportions of the categorical variables) using the MGLHmode of SYSTAT. All variables were transformed as necessary to meet normality re-quirements; however, the results were little affected by transformation of any kind. Inparticular, results of tests for the family x cross interaction were the same for log- andsquare root-transformed data.4.2 Results4.2.1 Seed setSelfed capitula of hermaphrodites set significantly fewer seed per pollinated ovule thanoutcrossed capitula of hermaphrodites (Table 4.24). Seed set of outcrossed and selfedheads averaged respectively 26.7% (N = 154 heads, s.d. = 0.136) and 21.3% (N = 74heads, s.d. = 0.178) of pollinated ovules (S:0 0.809), for those crosses that yielded seed. Ifall crosses are included in the calculation of the mean, the total proportion of pollinatedovules that develops to seed is under 5%, the total seed set ratio of selfed to outcrossedovules falls to 53%, and the proportion seed set of selfs relative to outcrosses variesChapter 4. Inbreeding Depression and Maternal Parentage^ 120VariancecomponentEst. S. E. d.f. LikelihoodRatio X2Prob.Cross 0.035 0.016 1 3.761 0.052Family 0.002 0.003 1 0.661 0.416Familyx cross 0.001 0.002 1 0.376 0.540Error 0.036 0.004Table 4.24: Mixed-model analysis of variance in seed set per capitulum (arcsine of squareroot transformed), of experimentally outcrossed and selfed progeny of hermaphrodites.Cross effect is fixed, family effect and interaction are random. Seed set defined as pro-portion of fertilized ovules that develop to seed. Observations restricted to crosses thatyielded seed; if all crosses are included, the cross effect is greatly increased (41) = 30.52,p < 0.0005).among families from 0 to 1.057, (mean 0.502, s.e.m. = 0.0957, N = 13 families; seeFigure 4.30). The low seed sets may have been due partly to potting stress; roots rapidlyfilled the one-gallon pots, and in some plants entire heads were aborted a few days afterflowers matured. Weekly watering with 20:20:20 fertilizer appeared necessary for seedproduction.Mean mass of ten seed from open-pollinated females and hermaphrodites, outcrosses,and selfs respectively was 9.07 (s.e. 0.159), 8.95 (s.e. 0.299), 8.29 (s.e. 0.833), and 6.94(s.e. 0.608) milligrams. The difference in seed mass between outcrosses and selfs wasmarginally significant (F(1,8) = 4.891, p = 0.056, repeated-measures analysis of variancein family means, square-root transformed data); and between progeny of females andhermaphrodites non-significant (F(1,240) = 0.17, p = 0.680, factorial analysis of variancein family means, square-root transformed data).1.00-0.50-Cri^0.00 ^°-' 2.00 ^<1.)tv-s' 1.50-T)A2 A2 A2 A2 A2 B2 B5• Seed setIN Germination bEl SurvivorshipO FloweringO Fecundity1.50a1.00- 0.50:0.00 T C 1 Cl Cl Cl Cl Cl ClChapter 4. Inbreeding Depression and Maternal Parentage^ 121Population source of familyFigure 4.30: Relative performance of selfed seed progeny of 14 hermaphrodite familiesof Bidens sandvicensis. Variables are proportion fertilized ovules per capitulum thatdevelop into mature seed, one-month germination rate of seeds, survivorship in fieldplots from March 1991 to May 1992, proportion survivors that flowered by August 1992,and number of capitula produced per flowering plant. If no selfed seed were obtainedfrom hand pollinations, autoselfs were used for subsequent comparisons. a: Parents areBidens sandvicensis ssp. sandvicensis. b: Parents are Bidens sandvicensis ssp. confusa.Error bars are standard error of the mean inbreeding depression among families (seeChapter 2 for details about source populations).Chapter 4. Inbreeding Depression and Maternal Parentage^ 1224.2.2 GerminationThe one-month germination rate of open-pollinated seeds of females (46.7%) was signifi-cantly greater than that of open-pollinated seeds of hermaphrodites (34.0%; G(i) = 65.81,p < 0.001 for total sex effect; G(85) ----- 693.75 for total family effect; G(84) = 627.94, P< 0.001 for family effect within either sex; F(1,84) = 8.803, p = 0.0039 for sex effect givenfamily effect). Relative to seeds from open-pollinated hermaphrodites, seeds from open-pollinated females germinated significantly more quickly (respectively 12.63 and 14.12days to first germination in a sample of ten seeds), and exhibited faster subsequent de-velopment and growth in the growth chamber (Table 4.25). At respectively four and 10months from planting, the relative height of open-pollinated progeny of hermaphroditeswas 0.702 and 0.764, and relative dry weight at 10 months was 0.811 (86 families, over400 plants).1^1^1I^1^1^1^1^1^I^1^1^1^1^1^1^1^1^1^I^I^1^1^1^10.70^0.75^0.80^0.85^0.90 0.951^1^1^1^1^I^1^1^1^1^I^1^1^1^1^I^1^1^1^1^I^i^1^1^1Chapter 4. Inbreeding Depression and Maternal Parentage^ 1230.300.28 -t's zz 0cu 0.260.24 -(1) 0.4MI ()CU 0.22 -EC.) 0‘+-1\ 1 ci9 0.2000.18 -Relative germination rate of plantswith hermaphrodite maternal parentFigure 4.31: 1992 female frequency of source population versus germination rate in growthchamber, expressed as a ratio of plants with hermaphrodite to plants with female mater-nal parentage, by population. Seed collected from open-pollinated plants in May 1990.Regression was non-significantly negative for female frequencies in all four years, and formean female frequency from 1989 to 1992 (for 1992, r2 = 0.470).If the relative germination rate of open-pollinated seeds from hermaphrodites is calcu-lated separately for each of the four sampled populations (A, B4, B5, and Cl) from whichthe seeds were collected, the relative rate is negatively but non-significantly associatedwith the frequency of females at that population (see Figure 4.31 for the 1992 plot). Theassociation is negative (but non-significant) for all four years, and for the mean femalefrequencies over the four years (slopes for best fit lines of female frequency on relativegermination rate, respectively for 1989, 1990, 1991, and 1992, were -0.246, -0.599, -0.649,and -0.307).Joint loglinear analysis of germination, sex of maternal parent, and source populationChapter 4. Inbreeding Depression and Maternal Parentage^ 124VariancecomponentEst. S. E. d.f. LikelihoodRatio x 2Prob.Time to germinationSex -0.781 0.258 1 8.745 0.003Family 4.773 0.870 1 170.061 < 0.001Error 4.793 0.337Time to first true leafSex -0.044 0.083 1 0.279 0.597Family 0.121 0.091 1 3.389 0.066Error 2.341 0.173Time to second true leafSex -0.258 0.124 1 4.159 0.041Family 0.273 0.141 1 5.698 0.017Error 1.070 0.152Height at 4 monthsSex 0.515 0.136 1 13.204 < 0.001Family 1.315 0.243 1 167.889 < 0.001Error 1.388 0.099Height at 10 monthsSex 0.609 0.166 1 12.491 < 0.001Family 1.486 0.358 1 50.070 < 0.001Error 3.793 0.290Dry weight at 10 monthsSex 0.148 0.043 1 11.299 0.001Family 0.035 0.024 1 2.743 0.098Error 0.564 0.043Table 4.25: Mixed model nested analysis of variance in performance of plants in growthchamber by sex of maternal parent (open-pollinated progeny only). Levels of family, therandom effect, are nested within sex, the fixed effect. Negative estimate indicates greatermean in progeny of hermaphrodites.Chapter 4. Inbreeding Depression and Maternal Parentage^ 125indicated no three-factor interaction (G(3) = 4.05, p = 0.256), but a strong populationeffect on germination rate independently of sex (G(3) = 153.24, p < 0.001 for populationx germination interaction within either sex category, and F(3,82) = 7.749, p -= 0.00013for population x germination interaction given family variation within each population).This population effect was due to a higher germination rate in seed collected from pop-ulation Cl, the highest elevation site in the sample (61.3% total, as compared to 32.4%,48.6%, and 38.0% respectively for populations A, B4, and B5).The total one-month germination rate of outcrossed seed of hermaphrodites (50.6%)was significantly greater than that of selfed seed of hermaphrodites (26.0%; G(1) = 62.22,p < 0.001 for cross x germination interaction independently of family; G(10) 22.55, P= 0.0125 for family x cross x germination interaction; F(1,10)^27.592, p^0.0039 forcross effect given the family interaction). Germination rate of selfs relative to outcrossesvaried among families from 0.175 to 1.30, and averaged 0.600 (s.e.m. = 0.104, N11 families; see Figure 4.30). Germination rate of outcrosses was significantly higherthan that of open-pollinated seed of females (G(i) = 195.531, p = 0.0001 for parentagex germination interaction, families lumped; G(56) = 403.34, p < 0.0001 for family xgermination interaction, parentage lumped; F(1,55) = 51.750, p < 0.0005 for parentageeffect given the family variation within parentage class).4.2.3 SurvivorshipOpen-pollinated progeny of females had significantly greater survivorship than open-pollinated progeny of hermaphrodites during three census intervals: May to October1991, January to May 1992, and May to August 1992 (Table 4.26). This resulted ina significantly greater cumulative survivorship (H:F ratio 0.669) from the time of fieldtransplant (March 1991) to August 1992.A moderate proportion of plants with no discernable living tissue at one census pointChapter 4. Inbreeding Depression and Maternal Parentage^ 126Interval IntervalH/FCum.H/FG bet.,1 d.f.G with.,d.f.F,d.f.Prob.2/91 to 3/91 0.984 0.984 3.56NS 69.04NS 18.460 4 x 10-5358 1, 3583/91 to 5/91 0.993 0.978 0.79NS 65.55NS 4.303 0.04357 1, 3575/91 to 10/91 0.928 0.907 5.30* 362.00NS 5.212 0.02356 1, 35610/91 to 1/92 0.987 0.925 0.84NS 132.45NS 2.156 0.1340 1, 3401/92 to 5/92 0.840 0.782 19.65** 385.85* 17.366 6 x 10-5341 1, 3415/92 to 8/92 0.827 0.669 14.05** 350.18* 12.518 6 x 10'312 1, 312Table 4.26: Loglinear analysis of survivorship of seed progeny of open-pollinated femalesand hermaphrodites during specified time intervals. Columns are time interval, relativesurvivorship of progeny of hermaphrodites during the interval, cumulative relative sur-vivorship since transplant at the beginning of 3/91, G statistic for departure of intervalrelative survivorship from 1:1, G statistic for family variation in survivorship within ei-ther progeny class, and F statistic, with associated one-tail probability, for the parentageeffect on survivorship independent of family variation. *p = 0.05; **p = 0.001.Chapter 4. Inbreeding Depression and Maternal Parentage^ 127Interval IntervalH/FG bet.,1 d.f.G with.,d.f.F,d.f.Prob.3/91 to 5/91 0.359 0.52NS 18.22NS 1.513 0.4553 1,535/91 to 10/91 NoSUTV.10/91 to 1/92 0.771 0.72N5 163.07NS 0.623 0.4141 1,1411/92 to 5/92 0.814 0.05NS 32.02N5 0.195 0.6125 1,1255/92 to 8/92 0.578 2.13NS 137.82NS 2.581 0.1167 1,167Table 4.27: Loglinear analysis of regeneration in seed progeny of open-pollinated femalesand hermaphrodites during the specified time interval. Columns are time interval, relativenumber of progeny of hermaphrodites regenerating foliage during the interval, G statisticfor parentage effect on regeneration, G statistic for family variation in regeneration withineither progeny class, and F statistic, with associated one-tail probability, for parentageeffect given family variation. Subjects restricted to individuals with no discernable livingtissue at the beginning of each interval.regenerated living tissue by the next census point (up to 21% from October 1991 to Jan-uary 1992). The proportion regenerating was in all periods greater for open-pollinatedprogeny of females (H:F ratio ranged from 0.359 to 0.814), but in no period was thisdifference significant (Table 4.27), nor was the overall sex x regeneration interactionsignificant (G(i) = 2.88, p = 0.09, loglinear analysis of census interval, sex, and regen-eration). Regeneration propensity was greatest during the wet fall and winter months(G(3) = 34.47, p < 0.001 for census interval x regeneration interaction independently ofsex in loglinear analysis of census interval, sex, and regeneration; see Table 4.28), and theseasonal effect on regeneration propensity was not dependent on sex of maternal parent(G(3) = 0.53, p = 0.913, for three-factor interaction, Table 4.28).Both total survivorship and survivorship of progeny of open-pollinated hermaphro-dites relative to those of females were greatest during the wet fall and winter monthsChapter 4. Inbreeding Depression and Maternal Parentage^ 128Model d.f. G Prob.Survive x season,Survive x sex6 4.02 0.6744Survive x sex,Season x sex6 35.00 0.0000Season x sex,Survive x season4 3.41 0.4918Survive x season,Survive x sex,Season x sex3 0.53 0.9129Table 4.28: Loglinear models of regeneration by sex of open-pollinated maternal parentand time interval, families ignored. Subjects restricted to individuals with no discernableliving tissue at the beginning of each time interval.(Figure 4.32, Table 4.26, Figure 4.34). The relationship between the relative survivorshipand total survivorship of individuals of female maternal parentage appeared significantlypositive (regression coefficient = 1.015, s.e. = 0.265, r2 = 0.83, p = 0.0313; see Figure4.34).The relative survivorship of open-pollinated progeny of hermaphrodites was non-sig-nificantly negatively associated with the frequency of females at that population (seeFigure 4.35 for the 1992 plot). The association was negative (but non-significant) for allfour years, and for the mean female frequencies over the four years (slopes for best fitlines of female frequency on relative survivorship, respectively for 1989, 1990, 1991, and1992, were -0.238, -0.112, -0.128, and -0.144).In the growth chamber, survivorship of open-pollinated progeny of females to 10months (86.6%) was also significantly greater than that of open-pollinated progeny ofhermaphrodites (67.0%; G(1) = 30.41, p < 0.0001 for parental sex x survivorship inter-action, G(85) = 210.21, p < 0.0001 for family x survivorship interaction, G(84) = 179.80,p < 0.0001 for family x survivorship interaction within either sex class, and F(1,84) =Chapter 4. Inbreeding Depression and Maternal Parentage^ 129• F 1E HO 0 0.8O s• 0.617)(;-,o-,-,^0.4>p-,v).- 0.2>;—,ci)--'^0March to May to Oct. 91^Jan. to^May toMay 91^Oct. 91 to Jan. 92 May 92 Aug. 92Census intervalFigure 4.32: Total survivorship of open-pollinated progeny of females and hermaphro-dites, and out crossed and selfed progeny of hermaphrodites, in field plots during indicatedtime intervals. Error bars computed from the binomial standard error, V/(1 — 1)/(n — 1),where 1 and n are respectively survivorship and total living individuals in each of thefour parental classes at the start of each interval. F and H: open-pollinated progeny offemales and hermaphrodites; 0 and S: hand-pollinated outcrossed and selfed progeny ofhermaphrodites.10.6• 0.40.2U0Chapter 4. Inbreeding Depression and Maternal Parentage^ 130May 91 Oct. 91 Jan. 92 May 92 Aug. 92Time of censusFigure 4.33: Cumulative survivorship of open-pollinated progeny of females and herma-phrodites, and outcrossed and selfed progeny of hermaphrodites, in field plots at specifiedcensus points. Error bars computed from the binomial standard error, 0(1 — /)/(n — 1),where 1 and n are respectively survivorship and total number of seedlings transplantedto the field plots in each of the four parental classes. F and H: open-pollinated progenyof females and hermaphrodites; 0 and S: hand-pollinated outcrossed and selfed progenyof hermaphrodites.Chapter 4. Inbreeding Depression and Maternal Parentage^ 1311.00_^0.957.sn,0.90.b" 5› --,.›--. (1) 0.85-^•-1 ^;4.cu^0 80,'() °...6•I:^75^0.757rics0.70:_.0.65^0.80I^I^I^I^I^I^I^I^I^I^I^I^I^0.85 0.90 0.95Total survivorship during census interval(female maternal parent or outcrossed)1.00Figure 4.34: Mean relative survivorship within a census interval versus total survivorshipin that interval, and best-fit regression lines. Relative survivorships are selfed/outcrossedprogeny of hermaphrodites (dashed line) or open-pollinated seed progeny of hermaphro-dites/of females (solid line). Horizontal axis is the total survivorship of outcrossedprogeny (dashed line) or open-pollinated seed progeny of females (solid line). Foropen-pollinated progeny, r2 =- 0.83, p = 0.0313; for outcrosses and selfs, 1.2 = 0.956,p = 0.004.,T^II^I^I^I^TITS^-I^II^I^1^I^I^i^U '^I'0.9 1.00.7^0.80.5^0.6II^I^II^1^II^11111111^II^1111111Chapter 4. Inbreeding Depression and Maternal Parentage^ 132Relative survivorship of plants withhermaphrodite maternal parentMarch 1991 to May 1992Figure 4.35: 1992 female frequency of source population versus survivorship from March1991 to May 1992, expressed as a ratio of plants with hermaphrodite to plants withfemale maternal parentage by population. Seed collected from open-pollinated plants inMay 1990. Regression was non-significantly negative for female frequencies in all fouryears, and for mean female frequency from 1989 to 1992 (for 1992, r2 = 0.125).Chapter 4. Inbreeding Depression and Maternal Parentage^ 13314.207, p = 0.00030 for parental sex x survivorship interaction given family variationwithin parental sex).The parental sex >< survivorship interaction varied significantly by planting flat (G(7) =15.08, p = 0.0349 for flat x parental sex x survivorship, loglinear model), but theparental sex effect within flats was significant even given the flat variation (G(i) = 32.00,p < 0.0001 for parental sex x survivorship interaction within flats, F(1,7) = 14.85, p= 0.00626 for parental sex x survivorship interaction given flat effect). Since differentfamilies occupied different flats, it was impossible to separate the family effect from a trueflat effect. In all flats but one, relative survivorship of individuals of hermaphrodite seedparentage was less than unity; in one flat it was 1.04, but survivorship of both classeswas over 93%.Outcrossed progeny of hermaphrodites had significantly greater survivorship thanselfed progeny of hermaphrodites during the same three census periods as above (Table4.29), resulting in a significantly greater cumulative survivorship to August 1992 (S:0ratio 0.401). Survivorship of selfs relative to outcrosses from field transplant to firstflowering (May 1992) varied among families from 0 to 1.5 (mean = 0.582, s.e.m. = 0.156,N = 11 families; see Figure 4.30). Survivorship of outcrosses was not significantly greaterthan that of open-pollinated progeny of females (G(i) = 2.20, p = 0.1376 for parentagex survivorship interaction, families lumped).Height in May 1991 had a significant positive effect on survivorship from May 1991to May 1992, within each of the four progeny classes (G(i) = 17.6, p < 0.001 for heightx survivorship interaction within progeny class, families lumped; G(373) = 520.56 forfamily x survivorship interaction within progeny class; G(372) = 502.96, p < 0.001 forfamily x survivorship interaction within progeny and height class; F(1,372) = 13.017, p= 0.0004 for height x survivorship interaction within progeny class, given family effect),but a cross effect persisted independently of the height effect (G(1) = 29.23, p < 0.001Chapter 4. Inbreeding Depression and Maternal Parentage^ 134Interval Interval Cum. G„,,,,, G3F, F, Prob.S/O S/0 1 d.f. d.f. d.f.2/91 to 3/91 0.948 0.948 0.15NS 6.12NS 0.0735 0.8043 1,33/91 to 5/91 0.977 0.932 1.19NS 16.45* 0.434 0.5346 1,65/91 to 10/91 0.809 0.753 28.1** 15.17* 12.966 0.008737 1,710/91 to 1/92 0.969 0.771 0.15NS 11.01NS 0.0817 0.7856 1,61/92 to 5/92 0.762 0.593 18.03** 20.18* 7.148 0.02828 1,85/92 to 8/92 0.653 0.401 8.48* 10.32NS 5.752 0.04767 1,7Table 4.29: Loglinear analysis of survivorship of experimentally outcrossed and selfedseed progeny of hermaphrodites during specified time intervals. Columns are relativesurvivorship of selfs during the interval, cumulative relative survivorship since transplantin 2/91, G statistic for departure of interval relative survivorship from 1:1, G statistic forthree factor interaction of cross, family, and survivorship, and F statistic, with associatedone-tail probability, for the cross effect on survivorship independent of family variationin the cross effect. *p = 0.05; **p = 0.001.Chapter 4. Inbreeding Depression and Maternal Parentage^ 135for cross x survivorship interaction within height class, outcrosses and selfs only, familieslumped; G(14) = 38.88 for family x survivorship interaction within height class; G(13) =9.65, p = 0.53 for family x survivorship interaction within progeny and height class;F(1,14) = 39-377, P = 2 x 10-5 for cross x survivorship interaction within progeny class,given family effect; G(i) = 16.48, p < 0.001 for parentage x survivorship interactionwithin height class for open-pollinated progeny only, families lumped; family effects notmeasured due to BMDP capacity limit).As in the open-pollinated progeny, both total and relative survivorship were greatestduring the wet season (Figure 4.32, Table 4.29, Figure 4.34). The relationship betweenthe relative survivorship of selfs, and total survivorship of outcrossed progeny, appearedsignificantly positive (regression coefficient = 0.956, s.e. = 0.344, r2 = 0.956, p = 0.004;see Figure 4.34).As in the open-pollinated progeny, regeneration of foliage occurred in the selfed andoutcrossed progeny, primarily during the wet season (33% in outcrossed individuals fromOctober 1991 to January 1992). The proportion regenerating was in all periods greaterfor outcrossed progeny of hermaphrodites (S:0 ratio ranged from 0.308 to 0.583), but inno period was this difference significant (Table 4.30), nor did the combined probabilitiesyield a significant difference overall (G(8) = 6.815, p > 0.5).The parentage x survivorship interaction from March 1991 to May 1992 did not varysignificantly among the field plots for either the open-pollinated progeny (G(6) = 1.17, p =0.978 for three-factor interaction in loglinear model of survivorship, plot, and sex of seedparent) or the experimental selfs versus outcrosses (G(4) = 5.57, p = 0.234 for three-factorinteraction in loglinear model of survivorship, plot, and cross). Survivorship independentof parentage class, however, varied significantly among the field plots (G(6) = 57.13, p<0.001 for plot x survivorship interaction in loglinear model of parentage, survivorship,and plot for open-pollinated progeny; G(4) = 38.74, p < 0.001 for plot x survivorshipChapter 4. Inbreeding Depression and Maternal Parentage^ 136Interval IntervalS/OG,.,1 d.f.G3F,d.f.F,d.f.Prob.3/91 to 5/91 Nosurv.5/91 to 10/91 0.308 0.23NS 1.23NS 0.187 0.7401 1,110/91 to 1/92 0.583 1.23NS 10.86* 0.453 0.5384 1,41/92 to 5/92 0.330 2.88NS 0.12NS 24.00 0.1281 1,15/92 to 8/92 0.500 0.35NS 5.83NS 0.240 0.6504 1,4 _,Table 4.30: Loglinear analysis of regeneration of outcrossed and selfed seed progenyof hermaphrodites during the specified time interval. Columns are relative number ofselfed progeny regenerating foliage during the interval, G statistic for cross effect onregeneration (independently of family), G statistic for the family x regeneration x crossinteraction, and F statistic, with associated one-tail probability, for cross effect givenfamily interaction. Subjects restricted to individuals with no discernable living tissue atthe beginning of each interval. *p = 0.05; **p = 0.001.interaction in loglinear model of parentage, survivorship, and plot for selfs and outcrossesonly). Total survivorship varied from 54.0% to 64.0% at the four relatively xeric plotlocations, and from 72.1% to 86.7% at the four mesic locations.For individuals that survived, flowered, and could be sexed in May 1992, sexes ofprogeny of open-pollinated females and hermaphrodites were respectively 8:12 and 2:9female to hermaphrodite, and of outcrossed and selfed progeny of hermaphrodites re-spectively 2:23 and 1:5 female to hermaphrodite; sex ratio thus varied from 8.0% femalein outcrossed progeny of hermaphrodites to 40.0% female in open-pollinated progenyof females. The sex ratio x parentage interaction was not significant (G(3) = 6.98, p= 0.073, all four parentage classes). Independently of parentage (selfed, outcrossed,open-pollinated female or hermaphrodite maternal parent), female and hermaphroditeindividuals in the field plots did not differ significantly in apparent survivorship fromChapter 4. Inbreeding Depression and Maternal Parentage^ 137Model d.f. G Prob.Population x survive,Sex x survive 6 4.55 0.603Sex x survive,Sex x population 6 20.00 0.003Sex x population,Population x survive 4 1.72 0.788Population x survive,Sex x survive,Sex x population 3 1.08 0.782Table 4.31: Loglinear models of apparent survivorship from May 1991 to May 1992, bysex and population (for populations A, B2, B3, and Cl).May 1992 (the earliest time sex could be determined) and August 1992 (G(i) = 0.54,p = 0.48 for survive x sex of progeny interaction in loglinear model of sex, survivor-ship, and parentage). Total survivorship for females and hermaphrodites over this periodwas respectively 66.7% and 81.6%; among only open-pollinated progeny of females, totalsurvivorship of females and hermaphrodites in this period was respectively 62.5% and75.0%.Total survivorship of adult females and hermaphrodites in the four natural popula-tions, respectively 75.6% and 73.0% from May 1991 to May 1992, was not significantlydifferent (G(1) = 0.64, p -= 0.30 for sex x survive interaction independently of population,in three-factor loglinear analysis; see Table 4.31). Total survivorship, however, did varysignificantly by population, due primarily to population B2 (G(3) = 18.92, p < 0.001 forpopulation x survive interaction independently of sex, in three-factor loglinear analysis;see Table 4.31); total survivorship in populations A, B2, B3, and Cl was respectively88.2%, 53.1%, 83.0%, and 72.0% (Figure 4.36).B21.00.8° Female° Hermaphrodite0.60.40.2LL) 1.0zct0-, 0.80.60.41.00.80.65/92 10/91 1/92 5/92 8/92Time of Census0.61.00.8Chapter 4. Inbreeding Depression and Maternal Parentage^ 138Figure 4.36: Survivorship of female and hermaphrodite individuals in four natural pop-ulations (A, B2, B3, and Cl) from May 1991 to August 1992. Error bars computedfrom the binomial standard error, -0/(1 — 1)/(n —1)1(N — n)/N, where 1, N, and n arerespectively survivorship, total flowering population, and total individuals scored.Chapter 4. Inbreeding Depression and Maternal Parentage^ 1394.2.4 Flowering and fecundityA slightly greater proportion of surviving open-pollinated progeny of females than ofhermaphrodites flowered the first season (respectively 16.3% and 15.5% by August 1992),but this difference was not significant (G(i) = 0.06, p = 0.812 for parental sex x floweringinteraction, G(313) = 335.01, p = 0.188 for family x flowering interaction). No individualsflowered in 1991. The mean number of capitula per flowering plant was also greater foropen-pollinated progeny of females (21.1, s.d. = 21.0, N = 48) than of hermaphrodites(17.0, s.d. = 12.4, N = 32, Table 4.32, Figure 4.37), but this difference was not significantin either an analysis of variance (Table 4.33) or analysis of covariance with seedling heightat field transplant the covariate (Table 4.34).Chapter 4. Inbreeding Depression and Maternal Parentage^ 140GrazestatusParentage N Mean S. D. C. V.Height 5/91 (cm)G F 129 8.069 2.592 0.321H 65 6.469 1.731 0.2680 64 9.070 2.962 0.327S 21 7.761 2.718 0.350NG F 239 7.087 2.383 0.336H 256 5.873 2.196 0.3740 129 6.655 2.360 0.355S 156 5.307 2.195 0.414Tot. F 372 7.435 2.489 0.335H 326 6.006 2.109 0.3510 208 7.413 2.774 0.374S 193 5.564 2.349 0.422Height 5/92 (cm)G F 113 22.274 18.073 0.811H 47 18.489 14.192 0.7680 62 35.000 24.378 0.697S 20 26.150 11.595 0.443NG F 177 22.468 18.909 0.842H 154 18.616 15.591 0.8380 108 30.370 22.443 0.739S 80 16.762 10.906 0.651Tot. F 294 22.707 18.695 0.823H 206 18.766 15.277 0.8140 183 32.322 23.570 0.7295 108 19.037 12.036 0.632Chapter 4. Inbreeding Depression and Maternal Parentage^ 141GrazestatusParentage N Mean S. D. C. V.Flower 5/92G F 113 0.212 0.415 1.956H 48 0.187 0.395 2.1120 62 0.371 0.488 1.316S 20 0.35 0.487 1.393NG F 177 0.119 0.319 2.683H 154 0.136 0.347 2.5550 109 0.284 0.449 1.581S 81 0.160 0.369 2.306Tot. F 294 0.163 0.377 2.314H 207 0.154 0.360 2.3360 184 0.320 0.326 1.017S 109 0.211 0.209 0.990No. capitulaG F 24 15.916 11.963 0.752H 9 14.111 7.606 0.5390 23 32.434 26.455 0.816S 7 11.428 2.878 0.252NG F 21 27.904 27.940 1.001H 21 18.619 14.350 0.7710 31 27.483 15.472 0.563S 13 10.000 4.600 0.460Tot. F 48 21.104 20.978 0.994H 32 16.968 12.397 0.7310 59 29.372 20.198 0.688S 23 10.869 5.841 0.537Chapter 4. Inbreeding Depression and Maternal Parentage^ 142GrazestatusParentage N Mean S. D. C. V.No. primary branchesG F 108 2.388 0.852 0.357H 42 2.166 0.960 0.4430 51 2.215 0.807 0.364S 12 1.583 0.668 0.422NG F 148 2.831 1.306 0.461H 125 2.248 0.921 0.4100 54 1.833 1.004 0.548S 30 1.533 0.776 0.506Tot. F 256 2.644 1.155 0.437H 168 2.220 0.931 0.4190 111 1.963 0.933 0.475S 46 1.521 0.722 0.475No. apical leaf pairsG F 88 2.579 0.840 0.326H 38 2.368 0.882 0.3720 38 2.552 0.860 0.337S 15 2.266 1.099 0.485NG F 159 3.031 1.182 0.390H 133 2.541 0.900 0.3540 79 3.063 1.029 0.336S 66 2.106 0.704 0.334Tot. F 247 2.870 1.092 0.380H 172 2.494 0.901 0.3610 125 2.856 1.005 0.352S 86 2.127 0.779 0.366Chapter 4. Inbreeding Depression and Maternal Parentage^ 143GrazestatusParentage N Mean S. D. C. V.Leaf length (cm)G F 112 3.258 1.487 0.456H 46 3.108 1.448 0.4660 60 3.316 1.420 0.428S 20 2.600 1.046 0.402NG F 178 3.904 2.229 0.571H 153 3.137 1.892 0.6030 107 4.102 2.009 0.490S 80 2.400 1.228 0.512Tot. F 294 3.649 1.985 0.544H 204 3.132 1.785 0.5700 180 3.794 1.823 0.480S 109 2.412 1.156 0.479Survive 5/92G F 129 0.876 0.329 0.376H 65 0.738 0.443 0.6010 66 0.939 0.244 0.260S 22 0.909 0.295 0.325NG F 243 0.728 0.452 0.621H 267 0.577 0.490 0.8500 138 0.783 0.411 0.525S 171 0.468 0.497 1.062Tot. F 376 0.781 0.407 0.521H 337 0.611 0.496 0.8110 220 0.831 0.371 0.446S 219 0.493 0.488 0.991Table 4.32: Means and standard deviations of morphological traits and survivorship fromFebruary 1991 to May 1992 in grazed and ungrazed individuals of all four parental classes(open-pollinated female, open-pollinated hermaphrodite, outcrossed hermaphrodite, andselfed hermaphrodite). Traits analyzed are height in May 1991 and 1992, proportion flow-ering, number of capitula (if nonzero), number of primary branches (if nonzero), numberof apical leaf pairs, length of largest leaf, and proportion surviving to May 1992. Columnsare grazed status (grazed or not grazed), parentage (open-pollinated female or hermaphro-dite maternal parent, outcrossed or selfed progeny of hermaphrodites), total number ofindividuals, mean, standard deviation, and coefficient of variation (s.d./mean). All traitsmeasured in May 1992 except as indicated.Chapter 4. Inbreeding Depression and Maternal Parentage^ 144Source d.f. SS MS F PNo. capitula per flowering plantSexError1633.5158139.10823.51582.20811.5923 0.2117No. primary branchesSexError12740.880922.72250.88090.082910.6228 0.0013No. apical leaf pairsSexError12780.572516.59390.57250.05979.5910 0.0022StageSexError1600.00005.90790.00000.09850.0000 0.9994Leaf lengthSexError13101.504968.75871.50490.22186.7850 0.0096Table 4.33: Analysis of variance of family means of morphological variables (square roottransformed) measured in 5/92, by sex of maternal parent (open-pollinated progeny only).All means greater for plants of female maternal parentage.Chapter 4. Inbreeding Depression and Maternal Parentage^ 145Source d.f. SS MS F PNo. capitula per flowering plantSex 1 2.9465 2.9465 1.3158 0.256Ht. 2/91 1 0.2729 0.2729 0.1219 0.728Error 62 138.8353 2.2393Ht. 2/91x Sex 1 0.1428 0.1428 0.0628 0.803Error 61 138.6925 2.2736No. primary branchesSex 1 1.2538 1.2538 15.5083 0.000Ht. 2/91 1 0.6519 0.6519 8.0636 0.005Error 273 22.0706 0.0808Ht. 2/91x Sex 1 0.0209 0.0209 0.2572 0.612Error 272 22.0497 0.0811No. apical leaf pairsSex 1 0.6606 0.6606 11.1326 0.001Ht. 2/91 1 0.1560 0.1560 2.6281 0.106Error 277 16.4379 0.0593Ht. 2/91x Sex 1 0.1863 0.1863 3.1641 0.076Error 276 16.2516 0.0589Chapter 4. Inbreeding Depression and Maternal Parentage^ 146Source d.f. SS MS F PStageSex 1 0.0200 0.0200 0.2172 0.643Ht. 2/91 1 0.4657 0.4657 5.0487 0.028Error 59 5.4422 0.0922Ht. 2/91x Sex 1 0.0710 0.0710 0.7661 0.385Error 58 5.3712 0.0926Leaf lengthSex 1 4.333 4.333 20.551 0.000Ht. 2/91 1 0.039 0.039 0.187 0.666Ht. 2/91x Sex 1 3.8059 3.8059 18.0493 0.000Error 308 64.9459 0.2109Table 4.34: Analysis of covariance between family means of morphological variables mea-sured in 5/92, and height of seedling at time of field transplant (2/91), by sex of the ma-ternal parent (open-pollinated progeny only). Variables are number of capitula producedper flowering plant, number of main branches per branching plant, number of live apicalleaf pairs per living plant, stage of maturity of flowering plant at time of assessment, andlength of the largest leaf. All analyses are of square root transformed variables. Becausethe interaction was significant for leaf length, main effects for that variable are expressedover the interaction error. Plants of female maternal parentage had higher adjusted meansfor all variables.The relative capitula production of open-pollinated progeny of hermaphrodites wasnon-significantly negatively associated with the frequency of females at that popula-tion (see Figure 4.38 for the 1992 plot), although capitulum production was actually(non-significantly) greater for open-pollinated progeny of hermaphrodites in two of thepopulations. The association was negative (but non-significant) for all four years, andfor the mean female frequencies over the four years (slopes for best fit lines of femalefrequency on relative capitulum production, respectively for 1989, 1990, 1991, and 1992,were -0.013, -0.174, -0.031, and -0.019).F H F H1 00F H F H7680601al 406Z201 00.0**e+Chapter 4. Inbreeding Depression and Maternal Parentage^ 147Maternal Parent SexFigure 4.37: Box plots, by sex of open-pollinated maternal parent, of number capitulaproduced per flowering plant, length of largest leaf, number of apical leaf pairs, andnumber of primary branches per branching plant. See Figure 3.10 for interpretation ofbox plots._I_Chapter 4. Inbreeding Depression and Maternal Parentage^ 1480.260.24 -c.)z 0cu cict 0.22cr4-1 0(2.) ray 0.20 -("3CI)^0.180N cnCS'■ 0 0.16 -0.0^1.0^2.0^3.0^4.0^5.0Relative capitulum production ofplants with hermaphroditematernal parentFigure 4.38: 1992 female frequency of source population versus total number of capit-ula produced per plant in May 1992, expressed as a ratio of plants with hermaphro-dite to plants with female maternal parentage, by population. Seed collected fromopen-pollinated plants in May 1990. Regression was non-significantly negative for fe-male frequencies in all four years, and for mean female frequency from 1989 to 1992 (for1992, r2 = 0.739).Chapter 4. Inbreeding Depression and Maternal Parentage^ 149A significantly higher proportion of outcrossed than selfed progeny of hermaphroditesflowered the first season (respectively 32.0% and 21.1%, Table 4.32; G(i) = 12.76, p< 0.001 for cross x flowering interaction within family; G(6) = 5.26, p = 0.511 for crossx flowering x family interaction, F (1,6) = 14.555, p = 0.0088 for cross effect on floweringgiven family variation in cross effect). The proportion of surviving selfs flowering relativeto outcrossed varied among families from 0 to 1 (mean = 0.420, s.e.m. = 0.148, N = 8families; see Figure 4.30).Outcrosses also were significantly more likely to flower the first season than open-pollinated progeny of females (G(i) = 15.79, p = 0.0001 for parentage x flowering inter-action, families lumped; G(188) = 272.56, p = 0.0001 for family x flowering interaction,parentage lumped; F(1,187) = 11.499, p < 0.001 for parentage effect given the familyvariation within parentage class).Height in May 1992 had a highly significant positive effect on flowering probabilitywithin each of the four progeny classes (G(i) = 281.16, p < 0.001 for height x floweringeffect within progeny class), and there was no parentage effect on flowering probabilityindependently of the height effect (G(i) = 0.5, p = 0.26 for cross x flowering effect withinheight class, outcrosses and selfs only, families lumped; G(1) = 3.00, p = 0.063 for sameeffect, open-pollinated progeny only, families lumped).The mean number of capitula per flowering plant was also significantly greater foroutcrossed (29.4, s.d. = 20.2, N = 59) than selfed (10.9, s.d. = 5.84, N = 23) progeny ofhermaphrodites (Tables 4.32 and 4.35); within families, mean ratio of selfed to outcrossedwas 0.323, s.e.m. = 0.0853, N = 4 families).Chapter 4. Inbreeding Depression and Maternal Parentage^ 150VariancecomponentEst. S. E. d.f. LikelihoodRatio X2Prob.Leaf lengthCross 0.203 0.047 1 13.980 < 0.001FamilyFamily0.000 0.018 1 0.000 0.982x cross 0.028 0.022 1 5.154 0.023Error 0.152 0.014Apical leaf pairsCross 0.105 0.020 1 14.685 < 0.001Family 0.001 0.002 1 0.202 0.653Familyx cross 0.000 0.000 1 0.000 1.000Error 0.061 0.006CrossFamilyFamilyX CrossErrorNumber of primary branches^0.063^0.0350.016^0.0120.005^0.0090.060^0.0071^2.784^0.0951^1.623^0.2031^0.604^0.437StageCrossFamilyFamilyX CrossError-0.0380.0200.0010.1060.4561.8640.0010.5000.1720.9710.051^10.022^10.018^10.0191CrossFamilyFamilyX CrossError< 0.0010.285<0.0010.048< 0.001Number of capitula0.446^0.093^1^7.473^0.0060.301^0.151^1^2.348^0.1250.999Chapter 4. Inbreeding Depression and Maternal Parentage^ 151Table 4.35: Mixed-model analysis of covariance in morphological variables (square roottransformed), measured in May 1992, of experimentally outcrossed and selfed progeny ofhermaphrodites. Cross effect is fixed, family effect and interaction are random. Covariateis height before field transplant in February 1991. Positive cross estimate indicates greatermean of outcrosses, and negative indicates greater mean of selfs.This difference was evident in both analysis of variance and in analysis of covariance inwhich the covariate was height at field transplant (Table 4.35). Total capitulum produc-tion was significantly correlated with total height at flowering (for flowering outcrossesand selfs only: F(1,79) = 14.343, p = 0.0003, square-root transformed data); neverthelessthe difference in capitulum production between outcrosses and selfs persists when heightat flowering is controlled in an analysis of covariance (likelihood ratio 41) = 5.032, p= 0.025, for cross effect on capitulum production, square-root transformed data, flow-ering plants only, model otherwise as in Table 4.35). Outcrosses produced significantlymore capitula than open-pollinated progeny of females (likelihood ratio 41) = 6.634,p = 0.010, mixed model nested analysis of variance in which cross/parentage effect isfixed, family and interaction effects are random, and families are partially nested withincross/parentage).Independently of their membership in the four parentage classes (outcrossed, selfed,open-pollinated progeny of females and hermaphrodites), female and hermaphrodite indi-viduals in the field plots did not differ significantly in capitulum production (Table 4.36),although sample size was minimal because few individuals survived to flower. The ca-pitulum production of females and hermaphrodites respectively was 33.9 (s.e.m. = 13.8,N = 8) and 23.4 (s.e.m. = 6.8, N = 12) among open-pollinated progeny of females, and15.0 (s.e.m. 10.6, N = 2 ) and 25.8 (s.e.m. = 5.4, N = 23) among outcrossed progenyof hermaphrodites.Chapter 4. Inbreeding Depression and Maternal Parentage^ 152VariancecomponentEst. S. E. d.f. LikelihoodRatio X2Prob.Leaf lengthSexError0.0530.1430.0660.0261 0.647 0.421Apical leaf pairsSexError0.0720.0100.0630.0051 1.228 0.268Number of primary branchesSexError0.0180.0510.0400.0091 0.193 0.660StageSexError0.0270.1070.0580.0201 0.221 0.638Number of capitulaSexError0.0132.9450.2840.5291 0.002 0.964Total height growth 2/91 to 5/92SexError0.0900.2880.1200.0801 0.523 0.470Table 4.36: Mixed-model analysis of variance in morphological variables (square roottransformed), measured in May 1992, of all sexed subjects in field plots. Effects analyzedwere sex of individual (fixed), parentage (fixed; all four parental categories), and family(random). For all variables the family effect was non-significant (41) <0.1 and p > 0.99for all variables except total height growth, for which 41) = 1.850 and p = 0.174). Thesex effect is also non-significant in two-factor analyses of variance (sex and parentage)for all variables.Chapter 4. Inbreeding Depression and Maternal Parentage^ 1534.2.5 MorphologyFor every measured attribute, open-pollinated progeny of females exceeded open-polli-nated progeny of hermaphrodites in both mean and variance (see Table 4.32). In log-or square-root transformed data, however, the difference in variance was generally notstatistically significant (e.g., F(1,696) = 1.51, p = 0.212 for variance in height in May 1992,female versus hermaphrodite maternal parentage, square-root transformed data).For plants in the field plots, the ratio of the means (progeny of hermaphrodites toprogeny of females) for number of primary branches, number of apical leaf pairs, lengthof longest leaf, and height in May 1992 was respectively 0.840, 0.869, 0.858, and 0.826(see Table 4.32). The ratio of variances in these same attributes was respectively 0.650,0.681, 0.809, and 0.668 (see Table 4.32).The difference between the two open-pollinated classes was significant for number ofprimary branches, number of apical leaf pairs, leaf length, and total height growth in allcensus intervals, as demonstrated both by analysis of variance (Tables 4.33 and 4.37; seeFigures 4.37 and 4.39), and by analysis of covariance, with height at field transplant thecovariate (Tables 4.34 and 4.38). Mean height of seedlings at field transplant was alsogreater for females (5.81cm) than hermaphrodites (5.29cm; F(1,351) = 13.481, p = 0.0003in single-factor analysis of variance in family means of height, square-root transformed).Chapter 4. Inbreeding Depression and Maternal Parentage^ 154Source d.f. SS MS F P2/91 to 5/92SexError13111.600976.19121.60090.24506.5345 0.01112/91 to 3/91SexError13540.01760.67400.01760.00199.2240 0.00263/91 to 5/91SexError13530.02070.76130.02070.00229.6135 0.00215/91 to 10/91SexError13380.11043.23740.11040.009611.5244 0.000810/91 to 1/92SexError13330.065611.14060.06560.03351.9608 0.16241/92 to 5/92SexError13090.425431.13840.42540.10084.2217 0.0407Table 4.37: Analysis of variance of mean height-growth in a maternal family (square roottransformed) during specified time interval, by sex of maternal parent (open-pollinatedprogeny only). All means greater in plants of female maternal parentage.Chapter 4. Inbreeding Depression and Maternal Parentage^ 155Source d.f. SS MS F P2/91 to 3/91Sex 1 0.0195 0.0195 10.2308 0.002Ht. 2/91 1 0.0024 0.0024 1.2700 0.261Error 353 0.6715 0.0019Ht. 2/91x Sex 1 0.0007 0.0007 0.3643 0.547Error 352 0.6708 0.00193/91 to 5/91Sex 1 0.0217 0.0217 10.0647 0.002Ht. 2/91 1 0.0010 0.0010 0.4727 0.492Error 352 0.7603 0.0022Ht. 2/91x Sex 1 0.0045 0.0045 2.0985 0.148Error 351 0.7557 0.00225/91 to 10/91Sex 1 0.1099 0.1099 11.4449 0.001Ht. 2/91 1 0.0006 0.0006 0.0613 0.805Error 337 3.2368 0.0096Ht. 2/91x Sex 1 0.0347 0.0347 3.6457 0.057Error 336 3.2021 0.0095Chapter 4. Inbreeding Depression and Maternal Parentage^ 156Source d.f. SS MS F P10/91 to 1/92SexHt. 2/91Ht. 2/91x SexError1113310.1990.0250.177910.94630.1990.0250.17790.03316.0270.7645.37980.0150.3830.0211/92 to 5/92Sex 1 0.3980 0.3980 3.9368 0.048Ht. 2/91 1 0.0027 0.0027 0.0270 0.870Error 308 31.1357 0.1011Ht. 2/91x Sex 1 0.0060 0.0060 0.0595 0.807Error 307 31.1297 0.10142/91 to 5/92Sex 1 1.5282 1.5282 6.2179 0.013Ht. 2/91 1 0.0014 0.0014 0.0058 0.939Error 310 76.1898 0.2458Ht. 2/91x Sex 1 0.3376 0.3376 1.3754 0.242Error 309 75.8521 0.2455Table 4.38: Analysis of covariance between mean height growth (square root transformed)in a maternal family during the specified time interval, and height of seedling just beforefield transplant (2/91), by sex of the maternal parent (open-pollinated progeny only),both heights square-root transformed. Because the interaction was significant for growthfrom 10/91 to 1/92, main effects for that interval are expressed over the interaction error.Adjusted mean growth was greater in all intervals for plants of female maternal parentage.Height at field transplant generally was not significantly correlated with morphologyin May 1992 (Tables 4.34 and 4.38; Figure 4.40), with the exceptions of leaf length (Table4.34) and height growth from October 1991 to January 1992 (Table 4.38).No relationship was found between relative rate of height growth of open-pollinated0 *3/91 to 5/91358 familiesFHF-0-5/91 to 10/91342 familiesH *F -^.10/91 to 1/92343 familiesH * * *F1/92 to 5/92314 familiesH .0 0 00* * * * 7* . 024I.1-10^-5^0^5^10^15^I * *^35E ^211-0-- *---HE^A * *=Chapter 4. Inbreeding Depression and Maternal Parentage^ 157Height growth in centimetersFigure 4.39: Box plots of height growth in open-pollinated individuals of female or her-maphrodite maternal parentage, during the indicated time intervals. Total number ofsurviving families indicated on the left, and total number of individuals whose heightgrowth exceeded 15cm indicated on the right.Chapter 4. Inbreeding Depression and Maternal Parentage^ 1582^3^4^5^6^7^8^9^10Height in centimeters 2/91Figure 4.40: Total height growth of open-pollinated individuals of female or hermaphro-dite maternal parentage versus height at time of field transplant. Neither regression issignificant; r2 < 0.05 in both cases.Chapter 4. Inbreeding Depression and Maternal Parentage^ 1591.60^I^I^•^i^•^I^I^I^I`4^1.20-E, 5Loo-b.0 00.80 -0.60-0.40-0.20 0.00^,I.,,,,...I.^.^,^I^.^.^.0.02^0.04^0.06^0.08 0.10Growth rate (cm/day) during census interval(female maternal parent or outcrossed)Figure 4.41: Mean relative height growth rate within a census interval versus totalheight growth rate in that interval, and best-fit regression lines. Relative growth ratesare selfed/outcrossed progeny of hermaphrodites (dashed line) or open-pollinated seedprogeny of hermaphrodites/of females (solid line). Horizontal axis is the total growthrate of outcrossed progeny (dashed line) or open-pollinated seed progeny of females (solidline). In neither case is the slope of the indicated best-fit regression line significantlydifferent from zero. For open-pollinated progeny, r2 = 0.382; for outcrosses and selfs,r2 = 0.493.progeny of hermaphrodites during any census interval and total height growth of progenyof females in that interval (regression coefficient = 6.624, s.e. = 4.865, 1-2 = 0.382, p= 0.267; see Figure 4.41).For every measured attribute, outcrossed progeny of hermaphrodites also exceededselfed progeny of hermaphrodites in both mean and variance (Table 4.32), although thedifference in variance generally disappeared in log- or square-root transformed data (e.g.,F(1,399) = 0.12, p = 0.732 for variance in height in May 1992, selfed versus outcrossed,Chapter 4. Inbreeding Depression and Maternal Parentage^ 160square-root transformed data).The selfed:outcrossed ratio of the means for number of primary branches, number ofapical leaf pairs, length of longest leaf, and height in May 1992 was respectively 0.775,0.745, 0.636, and 0.589 (see Table 4.32). The ratio of variances in these same attributeswas respectively 0.599, 0.601, 0.402, and 0.261 (see Table 4.32).The difference between selfs and outcrosses was significant for number of apical leafpairs, leaf length, and total height growth in all census intervals except from March 1991to May 1991, as demonstrated both by analysis of variance (not shown; see Figures 4.42and 4.43), and by analysis of covariance, with height of seedling at field transplant thecovariate (Tables 4.35 and 4.39). Mean height of seedlings at field transplant was alsogreater for outcrosses (4.66cm) than selfs (3.36cm; 41) = 9.313, p = 0.002 in maximumlikelihood estimation mixed-model analysis of variance, with cross fixed and family andinteraction random, square-root transformed data).Chapter 4. Inbreeding Depression and Maternal Parentage^ 161VariancecomponentEst. S. E. d.f. LikelihoodRatio x2Prob.2/91 to 3/91CrossFamilyFamilyX crossError0.0120.0000.0000.0030.0040.0000.0000.00011111.0593.2590.0000.0010.0711.0003/91 to 5/91Cross -0.001 0.003 1 0.025 0.875Family 0.000 0.000 1 2.370 0.124FamilyX cross 0.000 0.000 1 0.000 1.000Error 0.003 0.0005/91 to 10/91Cross 0.037 0.013 1 6.040 0.014Family 0.003 0.002 1 3.464 0.063Familyx cross 0.003 0.002 1 5.323 0.021Error 0.014 0.00110/91 to 1/92Cross 0.063 0.028 1 4.320 0.038Family 0.010 0.009 1 2.014 0.156Familyx cross 0.009 0.007 1 6.715 0.010Error 0.045 0.0041/92 to 5/92Cross 0.110 0.042 1 5.242 0.022Family 0.009 0.016 1 0.341 0.559Familyx cross 0.019 0.017 1 2.130 0.144Error 0.117 0.011Chapter 4. Inbreeding Depression and Maternal Parentage^ 162Table 4.39: Mixed-model analysis of covariance in total height growth (square root trans-formed) during five census intervals of experimentally outcrossed and selfed progeny ofhermaphrodites. Cross effect is fixed, family effect and interaction are random. Covariateis height before field transplant in February 1991. Positive cross estimate indicates greatergrowth of outcrosses, and negative indicates greater growth of selfs.Height at field transplant generally was not significantly correlated with morphologyin May 1992 (analyses not shown). No significant relationship was found between relativerate of height growth in selfs, and total rate in outcrosses (regression coefficient = —8.059,s.e. = 3.643, r2 = 0.62, p = 0.114; see Figure 4.41).For none of the measured morphological traits did the parentage effect vary signifi-cantly among the field plots (e.g., for plot x cross effect on total height growth in selfsand outcrosses, likelihood ratio Xi) = 0.296, p = 0.586 in mixed-model anova withcross effect fixed, plot and family effects random; for capitulum production in selfs andoutcrosses, 41) < 0.0, p > 0.9 for plot x cross effect in the same model).Independently of their membership in any of the four parentage groups, females andhermaphrodites in the field plots did not differ significantly in any of the morphologicalcharacters measured (Table 4.36).4.2.6 GrazingSometime between May and October 1991 goats grazed the top 30 to 50% of mostseedlings at five of the eight plot locations; at no other times did I observe any instancesof herbivory. Goats were significantly more likely to graze taller plants (F(1,1057) = 87.258,p < 0.0001, square-root transformed height in May 1991 by grazed status in October 1991,all subjects combined; see also Table 4.32).Although grazed plants were larger and exhibited greater means of the morphologicalvariables in May 1992 (Table 4.32), grazing had no effect on eventual number of capitula0 S 0 S1500Chapter 4. Inbreeding Depression and Maternal Parentage^ 163Figure 4.42: Box plots, by parentage, of number capitula produced per flowering plant,length of largest leaf, number of apical leaf pairs, and number of primary branches perbranching plant, in experimentally outcrossed and selfed seed progeny of hermaphrodites.5/91 to10/913/91 to5/9110/91 to1/921/92 to5/920000* * *o 4—A***+1.**01-4\111H.* *** 000-Chapter 4. Inbreeding Depression and Maternal Parentage^ 164-10^0^10^20^30^40^50Height growth in centimetersFigure 4.43: Box plots of height growth in outcrossed and selfed seed progeny of herma-phrodites during the indicated time intervals. A total of 14 families present during allintervals.Chapter 4. Inbreeding Depression and Maternal Parentage^ 165produced, number of primary branches, or number of apical leaf pairs independently ofthe height of the plant in May 1991 (Table 4.40). Grazing also had no effect on probabilityof flowering independent of height at May 1991 (G(i) = 1.14, p = 0.45, for graze x flowerinteraction within height class in May 1991, all subjects combined; height classes definedas in Table 4.41).Chapter 4. Inbreeding Depression and Maternal Parentage^ 166Source d.f. SS MS F PHeight 5/92Grazed 1 7.0983 7.0983 3.4899 0.062Ht. 5/91 1 579.5109 579.5109 284.9224 0.000Error 758 1541.7152 2.0339Ht. 5/91x grazed 1 5.1603 5.1603 2.5423 0.111Error 757 1536.5549 2.0298No. capitulaGrazed 1 7.6655 7.6655 2.5739 0.111Ht. 5/91 1 34.3712 34.3712 11.5410 0.001Error 145 431.8353 2.9782Ht. 5/91x grazed 1 0.9911 0.9911 0.3312 0.566Error 144 430.8442 2.9920No. primary branchesGrazed 1 0.0306 0.0306 0.3049 0.581Ht. 5/91 1 0.0492 0.0492 0.4906 0.484Error 568 56.9177 0.1002Ht. 5/91x grazed 1 0.0033 0.0033 0.0325 0.857Error 567 56.9145 0.1004Chapter 4. Inbreeding Depression and Maternal Parentage^ 167Source d.f. SS MSNo. apical leaf pairsGrazed 1 0.167 0.167 2.155 0.143Ht. 5/91 1 0.589 0.589 7.602 0.006Ht. 5/91x grazed 1 0.335 0.335 4.323 0.038Error 612 47.419 0.077Leaf lengthGrazed 1 1.8567 1.8567 7.8200 0.005Ht. 5/91 1 7.7225 7.7225 32.5256 0.000Error 753 178.7841 0.2374Ht. 5/91x grazed 1 0.2882 0.2882 1.2141 0.271Error 752 178.4959 0.2374Table 4.40: Analysis of covariance between morphological traits and height of seedling inMay 1991, in grazed and ungrazed individuals of all four parental classes (open-pollinatedfemale, open-pollinated hermaphrodite, outcrossed hermaphrodite, and selfed hermaphro-dite). Traits analyzed are height in May 1992, number of capitula produced in May 1992 (ifnonzero), number of primary branches (if nonzero), number of apical leaf pairs, and lengthof largest leaf, all square-root transformed. Because the interaction was significant fornumber of apical leaf pairs, main effects for that variable are expressed over the interactionerror.Grazing did, however, cause an increase in leaf size measured in May 1992, and mayhave increased height growth independently of height at May 1991 (Table 4.40). Grazingalso caused a moderate increase in survivorship of plants from October 1991 to May1992 (see Figure 4.44), independently of both height at May 1991 and parentage of theplant (selfed, outcrossed, female maternal parent, and hermaphrodite maternal parent),as indicated by three-factor loglinear analysis (Table 4.41).Chapter 4. Inbreeding Depression and Maternal Parentage^ 168Model d.f. G Prob.Graze x survive,Parentage x survive 6 41.46 <0.0001Parentage x survive,Parentage x graze 4 21.30 0.0003Parentage x graze,Graze x survive 6 44.11 <0.0001Graze x survive,Parentage x survive,Parentage x graze 3 10.93 0.0121Graze x survive,Height x survive 4 35.07 < 0.0001Height x survive,Height x graze 3 14.57 0.0022Height x graze,Graze x survive 4 18.02 0.0012Graze x survive,Height x survive,Height x graze 2 0.02 0.9923Table 4.41: Loglinear models of apparent survivorship from October 1991 to May1992, by grazed status October 1991, individual height in May 1991, and parentage(open-pollinated female, open-pollinated hermaphrodite, outcrossed hermaphrodite, andselfed hermaphrodite). Height classes were [0 to 4 cm), [4 to 8 cm), and 8 cm and over.Chapter 4. Inbreeding Depression and Maternal Parentage^ 169N 1.00(:3\Ln2.,--, 0.75a.o,--,§ 0.50..Eg 0.25...-,Cr) 0.00F HOS F HOS F HOS < 4cm 4-8cm > 8cmParentage by Height 5/91Figure 4.44: Survivorship of open- and experimentally-pollinated individuals from Octo-ber 1991 to May 1992 by parentage, height in May 1991, and grazed status in October1991. Error bars computed from the binomial standard error 0(1 — 1)/(n — 1), where 1and n are respectively survivorship and total individuals scored. F and H: open-pollinatedprogeny of females and hermaphrodites; 0 and S: hand-pollinated outcrossed and selfedprogeny of hermaphrodites.Chapter 4. Inbreeding Depression and Maternal Parentage^ 17010.8o 0.60"41;4 3 0.400.20Germination Survivorship Flowering^CapitulaFitness componentFigure 4.45: Total means of fitness components of open-pollinated seed progeny of fe-males and hermaphrodites, and experimentally outcrossed and selfed seed progeny ofhermaphrodites. Variables are one-month germination rate of seeds, survivorship in fieldplots from March 1991 to May 1992, proportion survivors that flowered by August 1992,and number of capitula produced per flowering plant. Error bars are standard devia-tion of performance means among families, divided by the square root of the number offamilies.4.2.7 Total Fitness DeficitsFamily means in inbreeding depression were 0.2 to 0.5 in seed set, 0.40 in one-monthgermination rate, 0.42 in first year survivorship in the field from March 1991 to May1992, 0.58 in the proportion of plants producing flowers during the first flowering season,and 0.68 in total flowering heads produced per flowering plant the first season (Figures4.30 and 4.45). The inbreeding effect on each of these components was significant atthe experiment-wise Type I error rate of 0.0102 (= 1 — [1 — 0.0511/5; see idàk, 1967)for the five components. Assuming independence of life-history stages and multiplicativeChapter 4. Inbreeding Depression and Maternal Parentage^ 171fitnesses across stages, the total mean inbreeding depression in seed set, germination,survivorship, flowering, and fecundity was 0.96 to 0.98 in the sampled Bidens sandvicensispopulations of Waimea Canyon, Kauai. In three families, survivorship of both selfs andoutcrosses to flowering allowed calculation of total first-year inbreeding depression as0.93, 0.94, and 0.93 (see Figure 4.30). These families, however, had higher than averagerelative seed set or survivorship of selfs.The total fitness of open-pollinated progeny of hermaphrodites relative to that of fe-males was 0.434 (0.73 in germination, 0.78 in survivorship from March 1991 to May 1992,0.95 in proportion flowering, and 0.80 in capitulum production); again assuming inde-pendence of life history stages and multiplicative fitnesses across stages, the total relativefitness of open-pollinated progeny of females is 2.31. The differences in germination andsurvivorship were both significant at the 0.01 experiment-wise probability level, while thedifference in flowering probability and capitulum production were non-significant at the0.05 level. The reasons for the lack of significance of the former are unclear, while lack ofsignificance of the latter is due probably to the low frequency of flowering plants and thehigh variance in capitulum production among individuals and families. Because the meanseed set per capitulum of open-pollinated hermaphrodites relative to that of females was0.75 (Chapter 3), the total observed relative fitness of hermaphrodites amounts to 0.325,and the total mean relative female fitness 3.08.4.3 DiscussionBidens sandvicensis, a gynodioecious species whose observed populations consist of fe-males in frequencies ranging from 0.05 to over 0.40, showed significant inbreeding de-pression and superior performance of open-pollinated progeny of females in all fitnesscomponents measured.Chapter 4. Inbreeding Depression and Maternal Parentage^ 172Because inbreeding depression tends to be positively associated with overall measuresof physiological stress (e.g., Waller, 1985; Dudash, 1990; Schmitt and Ehrhardt, 1990),and physiological stress was minimized during the early stages of the plants in this studyby daily watering of seedlings (during the first 2-3 weeks in flats and the first week in thefield), these estimates of inbreeding depression might err on the conservative side. Undernatural conditions, seeds are set in April and May (and to a lesser extent from March toJune), and germinate during the first extended rains of fall or winter, which may occuranytime between October and January (Schultz, personal observations). Precipitation,however, is highly variable in southwestern Kauai, and lengthy drought periods in the fallare not uncommon during extended periods of strong northeast tradewinds that preventboth the approach of cyclonic storms and Kona Coast weather, the primary sourcesof rainfall in the lee regions of Kauai (see Price, 1983). Newly-germinated seedlingsexperiencing day temperatures in the mid-20s and no rainfall for periods exceeding aweek will suffer substantial drought stress, and undoubtedly inbreeding depression aswell. By chance, field transplant was completed just before a drought period of 10 days,and massive mortality would have ensued if the seedlings had not been watered during thisperiod of establishment. Since selfed seedlings had smaller both above- and below-groundgrowth than outcrosses at time of transplant, they would have suffered higher mortalityrates, to the extent that inbreeding depression in survivorship could have exceeded 0.5during just the first few weeks after transplant. For similar reasons, natural survivorshipof newly germinated selfs might be even lower than that observed in this study.Apart from the lower seed set and germination rates of selfs, inbreeding depression forthe most part was expressed as a lower overall rate of growth and development. Selfedseedlings were slower to develop above- and almost certainly below-ground, and boththese differences probably explain most of the inbreeding depression in survivorship,flowering, and fecundity. Most inbreeding depression in survivorship occurred in theChapter 4. Inbreeding Depression and Maternal Parentage^ 173drought-prone spring and summer months, probably due to a lower root mass in selfedindividuals. However, more inbreeding depression in survivorship appeared to occurfrom May to August 1992 than from May to October 1991, when plants were smalleron average. Since August is the height of the summer drought, this "mortality" might,to a large extent, represent the temporary loss of foliar tissue, an apparent response tomidsummer drought stress in this species. A similar loss of foliage might have occurredin August 1991, but could have been reversed during subsequent rains in September andOctober.Although measured height was significantly correlated with survivorship, flowering,and capitulum production within any of the four progeny classes, the significantly smallersize of selfs nevertheless failed to completely explain their lower performance. Whenheight (respectively in May 1991 and May 1992) was statistically controlled, a significantinbreeding depression in, and effect of maternal sex on, survivorship and capitulum pro-duction still remained (the maternal-sex effect on flowering probability, independently ofheight at flowering, was marginal). This persistence of a parentage effect may be dueto a low correlation between height and overall vigor of a plant; for example, fitnesscomponents might correlate more strongly with root mass, which might correlate onlyloosely with plant height. Alternatively, a significant component of inbreeding depres-sion might be caused by internal factors unrelated to plant mass or growth rate, suchas a metabolic inefficiency in regenerating photosynthetic tissue after the midsummerdrought, or defects in the regulation of floral development.Families varied significantly in inbreeding depression in germination rate and in totalsurvivorship to May or August 1992 (as well as in survivorship during the spring andsummer census intervals). One possible explanation of such among-family variation isvariation in inbreeding coefficient among the hermaphrodite maternal parents of the selfsand outcrosses. The inbreeding coefficient of a self (is) is dependent on the inbreedingChapter 4. Inbreeding Depression and Maternal Parentage^ 174coefficient of its parent (in) according to the equation (Crow and Kimura, 1970)is = ip + (1 — in)/2^(1/2)(1 + in).This positive linear relationship, coupled with the negative relationship (shape unknown)between inbreeding coefficient and each of the measured fitness components, implies thatthe fitness of selfs should be correlated with the inbreeding coefficient of their parent.On the other hand, the fitness of outcrosses is not expected to vary in response to theparental inbreeding coefficients; if the parents are unrelated, for example, all outcrosseswill have zero inbreeding coefficient regardless of that of their parents. Hence the fitnessof selfs relative to outcrosses will also be correlated (negatively) with the inbreedingcoefficient of their parent, although the residual variance will be larger due to the addedfitness variance of the outcrosses. This argument assumes, however, that the autozygousportion of the parent's genome contributes to the lower fitness of selfs. In the presence oflarge inbreeding depression, the assumption will tend to be violated by the lower fitnessof more autozygous individuals, such that these individuals will tend to be eliminatedfrom the adult population, or represented by individuals whose autozygosity by chancehas little effect on fitness.Other possible sources of family variation in inbreeding depression are (1) fitnessvariation in outcrosses as a result of fitness variation among pollen-donors, which couldproduce variation in inbreeding depression even in the absence of among-family variationin fitness of selfs; and (2) variation in maternal effects among families. No attempt wasmade to quantify the relative contribution of either of these sources, which in any caseare not sufficiently strong to negate the large total inbreeding depression measured.Assuming that the fertilization probability of an ovule is identical in females andhermaphrodites, and that male-sterility is nuclear, this mean relative female fitness cor-responds to an equilibrium proportion 0.26 of females in a population. This frequencyChapter 4. Inbreeding Depression and Maternal Parentage^ 175lies in the midrange of that observed in the sampled populations, which varied over thefour years from less than 10% to over 40% females. That the among-population varia-tion in female frequency is explained by among-population variation in relative fitnessof open-pollinated progeny of hermaphrodites is suggested by the negative relationshipsbetween these two variables for germination, survivorship and capitulum production;none of these, however, is significant, perhaps due to the small number of populationsrepresented.The 2.31 relative fitness of open-pollinated progeny of females can be roughly decom-posed into outcrossing and non-outcrossing components by the use of Equations 1.18 or1.19. Since performance of open-pollinated progeny of females was significantly lowerthan that of experimental outcrossed progeny of hermaphrodites in germination, flower-ing, and capitulum production, the inbreeding coefficient of the former is probably higherdue to outcrossing to relatives, and Equation 1.18 must be used to estimate k. Assuminga maximum effective selfing rate of females equal to 0.25 (Sun and Ganders, 1988), aninbreeding coefficient of zero in the experimental outcrosses, and inbreeding depressionas observed, the maximum value of k calculated from Equation 1.18 separately for germi-nation, survivorship from March 1991 to May 1992, flowering probability, and capitulumproduction, is respectively 0.050, 0.025, -0.40, and -0.14.However, the last two negative values of k for flowering and fecundity are not likelyto represent the true values for at least two reasons. First, the flowering proportionin both classes of open-pollinated progeny was lower than that in either outcrosses orselfs, indicating the existence of variability in flowering from sources yet unaccounted for;such sources might also affect variability in capitula production. Second, no empiricalstudy has yet provided evidence for a negative k in any fitness component (althoughsome variables, such as flower size, are consistently smaller in females), and since thevalue of any fitness component is likely to be an increasing function of total resourceChapter 4. Inbreeding Depression and Maternal Parentage^ 176available, which if anything should be greater on average in outcrossed progeny of femalesthan outcrossed progeny of hermaphrodites, a negative k is unlikely on physiologicalgrounds. Overall, these four fitness components provide little evidence of a nonzero,non-outcrossing advantage to progeny borne of female plants. If such advantage is zero,then the performance of progeny of females relative to outcrosses in germination andsurvivorship suggests (from Equation 1.18) a minimum effective female selfing rate of0.14 to 0.19, assuming zero inbreeding coefficient of the outcrosses. This is within therange of rates estimated in previous studies (Sun and Ganders, 1988). The lack of anyseed provisioning advantage in females is further confirmed by the fact that, althoughopen-pollinated progeny of females and outcrosses were significantly larger at the timeof field transplant, height of transplant had no effect on morphology in May 1992, andparentage effects persisted when the former was statistically controlled.A relative fitness of 2.31 in seed quality of females due entirely to inbreeding depressionin hermaphrodites requires that the proportion selfed individuals in the 1990 seed progenyof hermaphrodites exceed 0.57, and that the proportion in one-month seedling transplantsexceed 0.40. The actual proportion outcrossed in these transplants may be estimatedfrom the 1989 multilocus outcrossing rates of the source populations (in seedlings 3-4weeks after sowing), weighted by the number of families sampled from each population.The weighted mean for the six 1990 source populations with known 1989 outcrossing rateis 0.61 (s.e. 0.070); outcrossing rate was not estimated for the remaining three sourcepopulations.The proportion of the seed-set advantage of females (Chapter 3) that is not at-tributable to abortion of selfed embryos in hermaphrodites is difficult to estimate. Thatabortion rates of selfed embryos are significantly larger than those of outcrossed embryosimplies that the female seed-set advantage is in part due to selfing and inbreeding depres-sion in hermaphrodites. However, the difficulty of obtaining a precise estimate of selfingChapter 4. Inbreeding Depression and Maternal Parentage^ 177rate of embryos prior to abortion, and the high observed variability of the abortion ratemakes a determination of the non-outcrossing component to this female advantage im-possible in the present study. No other advantage was demonstrated to adult femalesin nature in survivorship or any morphological attribute (Chapter 3), nor to juvenile oradult females of known parentage in the field experiments.Because grazing appeared to increase total survivorship by a small amount (prob-ably less than 10% overall), and since grazed plants were larger on average and henceconsisted primarily of outcrosses and progeny of females, grazing decreased the relativesurvivorship of selfs and of progeny of hermaphrodites by an indeterminate but smallamount. The positive effect of grazing is difficult to explain, given the historical lack ofherbivorous vertebrates in Hawaii; perhaps this represents an adaptation to insect her-bivory, or mechanical damage (as by wind). In any case the rate of goat herbivory onBidens sandvicensis is unknown but undoubtedly small, and undoubtedly of little or noimport in maintaining the gender polymorphism.The total inbreeding depression measured for Bidens sandvicensis is among the high-est documented for angiosperms, although it is comparable to many species of conifers(e.g., an inbreeding depression of 92% in Pinus taeda seedling survivorship [Bush andSmouse, 1991]; see also Charlesworth and Charlesworth, 1987), and to at least two othergynodioecious angiosperms: Schiedea salicaria and S. globosa (Sakai, et al., 1989; totalinbreeding depression in S. salicaria 0.62 to 0.94 in seed set, germination, survival, andfecundity in the glasshouse; total fitness of unknown mixture of half and full sib matingsrelative to outcrosses in S. globosa 0.51 to 1 in the same fitness components). Moreover,the individual components of inbreeding depression in B. sandvicensis are comparableto those of other angiosperms (usually measured in the glasshouse) whose total inbreed-ing depression is unknown. This includes inbreeding depression in seed set (0.5 to 0.75Chapter 4. Inbreeding Depression and Maternal Parentage^ 178in gynodioecious Geranium maculatum [Agren and Willson, 1991]; 0.31 in gynodioe-cious Thymus vulgaris [Assouad, et al., 1978]; almost 1 in hermaphroditic Campsis rad-jeans, but this is apparently due to pistillate sorting [Bertin, et al., 1989]; at least 0.26in hermaphroditic Ipomopsis aggregata [De Jong, et al., 1992]; 0.65 in hermaphroditicCrinum erubescens [Manasse and Pinney, 1991], a small proportion of which is due tolower fertilization success of selfed pollen); germination (0.34 in Thymus vulgaris [As-souad, et al., 1978]); survival (total 0.71 in seed germination and first-year survivorshipin the field of gynodioecious Cucurbita foetidissima [Kohn, 1988]); and fecundity (0-0.6in flower number and seed set per flower in hermaphroditic Limnanthes alba [Jain, 1978],but only 0.14 in flower number in only one population of gynodioecious Limnanthes albavar. rosea [Kesseli and Jain, 1984]). However, at least three gynodioecious angiospermsshow little or no inbreeding depression (Shykoff, 1988; Ashman, 1992; Eckhart, 1992), orself fertilization in hermaphrodites (Eckhart, 1992), and females appear to be maintainedthrough either a maternal effect on seed quality (Ashman, 1992) or direct developmen-tal/physiological advantage to adults that increases fecundity (Shykoff, 1988; Eckhart,1992; Delph, 1990a).Although experimental demonstrations of near-complete inbreeding depression arerare in angiosperms, population-genetic demonstrations are not uncommon. A combina-tion of appreciable selfing (s > 0.15) and inbreeding coefficient near zero (for isozyme loci)has been observed in gynodioecious members of Limnanthes (Kesseli and Jain, 1985) andPlantago (Wolff, et al., 1988), as well as hermaphroditic Decodon (Eckert and Barrett,1993) and Echium (Burdon and Brown, 1986). Assuming Hardy-Weinberg equilibrium,an inbreeding coefficient of zero implies a complete absence of inbred individuals in theadult population, which in the presence of appreciable selfing implies complete inbreedingdepression in survivorship (from Equation 1.11).Theoretical models assuming independent gametic allele frequencies at load loci, andChapter 4. Inbreeding Depression and Maternal Parentage^ 179load caused by recessive lethals and sublethals, conclude that even low rates of selffertilization generally prevent the buildup of high levels of inbreeding depression frominitially low levels (Lande and Schemske, 1985). These models imply that the inbreedingdepression observed in Bidens sandvicensis most likely accumulated during an ecologicalor morphological situation different from the current one. Because the lack of a positivek means that a high rate of self-fertilization in hermaphrodites is necessary to producethe over-twofold seed fitness of females, it is pertinent to ask why the presumed historicalcondition of a low selfing rate no longer exists: if the species were capable of revertingto the previous state of high outcrossing, male sterility would no longer be necessary asa means of reducing self fertilization.In a long-distance colonizer, at least two factors may be involved. First, high out-crossing rates may have existed in populations of the ancestral source species due tocoevolution of floral anatomy and anatomy/behavior of pollinating insects. The originalcolonists of Hawaii are likely to have faced an entirely alien population of potential pol-linators, which may have been less efficient in pollen pick-up and transfer and hence lessefficient in cross fertilization (a similar explanation has been offered recently for diclinousHebe in high elevation habitats [Delph, 19904 and for gynodioecious Nemophila in sanddune habitat [Ganders, 1978]). Nevertheless, however true this might have been, a lowerefficiency in Hawaiian pollinators may not have been sufficient to maintain females. Thisis because, if lower outcrossing efficiency results simply from a lower fertilization rate ofoutcrossed ovules (as would be expected from a lower rate of pollen pickup and transfer),and if this lower rate occurs equally in ovules of females and hermaphrodites, then thefitness requirements for the spread of females are more strict, not less, than they wouldhave been in the mainland or source population (assuming some hermaphrodite fitnessis expressed through selfed ovules). Second, evolution of woodiness, greater longevity,and larger size is common in native Hawaiian angiosperms. A side effect of larger sizeChapter 4. Inbreeding Depression and Maternal Parentage^ 180is the presentation of larger numbers of receptive flowers per plant, which increases theopportunity for geitonogamous self-pollination (as shown recently in Ipomopsis [De Jong,et al., 1992]). If the selective advantages of larger size outweigh the disadvantages of self-ing and inbreeding depression, and if geitonogamy is difficult to prevent, then expressionof inbreeding depression might be an unavoidable cost of evolution of larger size. Thepresence of females, however, increases the total outcrossing rate and hence mean fitnessof a population; this could conceivably contribute to a competitive advantage over othernon-gynodioecious species simultaneously evolving larger size and increased rates of selffertilization.Alternatively, the theoretical assumption of moderate rates of mutation may havebeen unmet in ancestral populations of Bidens sandvicensis. If B. sandvicensis, likenumerous other native Hawaiian angiosperms, evolved greater longevity (perhaps con-comitantly with woodiness and larger size), this would have increased the mutation rateper generation, and perhaps sufficiently to allow accumulation of load alleles and highinbreeding depression. However, no evidence yet exists that any Hawaiian species ofBidens has evolved increased size or longevity since the original colonization event.More recent theoretical models that address identity disequilibrium among load loci,and allow either fully or partially recessive lethals to contribute to load, conclude thatvery high levels of inbreeding depression can accumulate under moderate selfing rates(e.g., Charlesworth, et al., 1990; Charlesworth and Charlesworth, 1990). This impliesthat inbreeding depression in Bidens might have originated under rates of self fertiliza-tion comparable to those currently, depending on the genetic architecture of inbreedingdepression. However, the latter is entirely unknown in Bidens, as is the difference (ifany) between gynodioecious and non-gynodioecious species of this genus in the geneticsources of inbreeding depression.Some researchers have suggested that the small size of colonizing populations inChapter 4. Inbreeding Depression and Maternal Parentage^ 181Hawaii, and resulting high biparental inbreeding and loss of genetic variability, mightconstitute strong selection for outcrossing mechanisms such as dioecy (see Sohmer andGustafson, 1987; Carlquist, 1980). Small population size, however, is likely to reducethe strength of such selection within populations. Loss of genetic variability in smallpopulations reduces the total genetic load, which immediately increases the mean fitnessof inbred individuals, and thus reduces any outcrossing advantage of male-sterile individ-uals. Once lost, genetic load may require hundreds of generations to rebuild. Increasedbiparental inbreeding in such populations also reduces the genetic difference betweenoutcrossed and selfed individuals, which reduces the de facto inbreeding depression (evenwithout any change in the total genetic load), and thus again reduces any advantageof outcrossing. Between-population effects, such as a lowered founding success by moreinbred colonists or higher extinction rates for more inbred populations, will select forincreased outcrossing. The time required for these kinds of events, though, is likely to befar longer than the few generations required for the loss of male steriles from a populationin which they have no advantage.If the frequent occurrence of rarity and population bottlenecks observed in the currentHawaiian flora are representative of pre-contact conditions, then such conditions willhave tended to prevent accumulation of genetic load in a larger proportion of speciesthan in continental source floras. Small population size is by no means ubiquitous in theHawaiian flora, however, as exemplified in the present study by Bidens sandvicensis. Forsome species, colonization of the archipelago might have been accompanied by a generalincrease in effective size of populations. For example, if the ancestral source was afugitive species occupying transiently available, fragmented habitat, frequent populationbottlenecks during founding events might have prevented the accumulation of appreciablegenetic load. The Hawaiian Islands, by contrast, offer extensive, continuous expanses ofuniform volcanic habitat. Colonists capable of spreading widely over competitively openChapter 4. Inbreeding Depression and Maternal Parentage^ 182habitat of this type might then experience a long-term increase in effective size, which,in the presence of appreciable outcrossing, allows accumulation of large genetic load.In any case, once inbreeding depression accumulates to high levels, self fertilizationbecomes increasingly ineffective in eliminating the load alleles, and in the extreme caseof complete inbreeding depression, the selfing rate will have no effect on the purgingrate (as may also be the case for intragametophyte selling in some homosporous ferns[Ganders, 1972]). This is because, in order for selfing to increase the selection againstan allele, it must increase the fitness variance at that locus. If few selfed individualssurvive to reproduce due to a large background inbreeding depression, selfing has littleeffect on the fitness variance at any particular load locus. In the limit of completeinbreeding depression, the population is genetically equivalent to an obligately out crossedpopulation, and selection has no opportunity to effect any evolution in any subset of the(only juvenile) selfed population.In summary, almost complete inbreeding depression was found under partially naturalconditions in Bidens sandvicensis. Further, a sufficient female advantage was found inseed quality alone to account for the presence of females in this gynodioecious species.Since the fitness of open-pollinated progeny of females was no greater than that of out-crosses, and since the fitness of open-pollinated progeny of hermaphrodites lay betweenthat of outcrosses and selfs in three of the four fitness components, inbreeding depressionand selfing in hermaphrodites appear sufficient to account for all of the female advantagein seed quality.Chapter 5Conclusions and Directions for Research5.1 TheoryIn general, a female-sterility allele can invade an equilibrium nucleo-cytoplasmic gynodi-oecy as easily as it can an equilibrium nuclear gynodioecy. This is true for both classesof nucleo-cytoplasmic gynodioecy for which models have been published to date: the F-Ssystem, in which both male-fertile and male-sterile cytoplasms coexist with a polymor-phic nuclear restorer locus, and the S-S system, in which two male-sterile cytoplasmscoexist (perhaps in oscillation) with two polymorphic nuclear restorer loci, each of whichrestores male fertility in only one sterile cytoplasm.For the portions of the parameter space investigated, the pollen-fertility threshold forinvasion of a male individual into the F-S system with dominant restorer varied from1.2 to 8.7 times that of a hermaphrodite (assuming all hermaphrodite genotypes haveidentical male fertility), and the threshold for invasion into an entirely nuclear gynodioecyvaried from 1.3 to 200 times that of a hermaphrodite, for the same parameter values.In these analyses the male- and female-sterility loci were either completely linked orunlinked, and the selfing rate was varied from 0 to 0.99, inbreeding depression from 0 to0.5, effective pollinator visits per plant from 1 (linear pollen limitation) to infinity (nopollen limitation), effect of the restorer allele on ovule fitness from 0.3 to 0.8 times thegenetic ovule fitness of the female, effect of the fertile cytoplasm on ovule fitness from0.7 to 1.25 times the genetic ovule fitness of the female, and the phenotypic fitness of the183Chapter 5. Conclusions and Directions for Research^ 184female from 1.25 to 1.6 times that of a hermaphrodite.The most pronounced difference in invasion threshold occurred for parameter val-ues that prevented the maintenance of females under nuclear male-sterility, but allowedfemales under nucleo-cytoplasmic male-sterility. In these regions the threshold pollen-fertility for male invasion of the F-S system was 0.02 to 0.6 times that required to invadethe nuclear system. Where females were maintained, the threshold pollen-fertility formale invasion of the F-S system varied from 0.7 to 1.0 times that required for invasionof the nuclear system.The pollen-fertility threshold for conversion of the F-S system to dioecy in the sterilecytoplasm varied from 1.2 to 2.4 times that of a hermaphrodite, for the subset of theparameter space that allowed evolution to dioecy. For this same subset, conversion ofthe nuclear system to dioecy required essentially the same pollen fertility of males. In aportion of the parameter space that allowed maintenance of females under the F-S system,conversion to dioecy was impossible even under very large pollen-fertility of males, andsubdioecy was maintained under pollen fertilities that caused evolution to dioecy fromnuclear gynodioecy.In general, results were similar for the S-S model, in which antagonism betweendominant restorer alleles affected male function only. The pollen fertility threshold formale invasion of the S-S system varied from 1.7 to 6.0 times that of a hermaphroditefor the parameter values studied, and the threshold for invasion into an entirely nucleargynodioecy varied from 1.7 to 7.3 times that of a completely restored hermaphroditefor the same parameter values. In these analyses the male- and female-sterility lociwere either completely linked or unlinked, and the selfing rate was varied from 0 to 0.9,inbreeding depression from 0 to 0.7, antagonism from 0 to 0.7 times the pollen-fitnessof a completely restored hermaphrodite, the phenotypic fitness of the female from 1.2to 2.5 times that of a hermaphrodite, and the effective pollinator visits per plant wasChapter 5. Conclusions and Directions for Research^ 185held constant at two (moderate pollen limitation if each visit fertilizes a proportion ofovules equal to the total frequency of hermaphrodites in the population). The thresholdrequired for male invasion of the S-S system varied from 0.8 to 1.1 times that requiredfor invasion of a nuclear system of gynodioecy.Conversion of the S-S system to dioecy required pollen fitnesses from 1.8 to 7.7 in theregion of the parameter space that allowed such conversion in both the S-S and nuclearmodels of gynodioecy, and conversion of the nuclear system to dioecy required pollenfitnesses from 1.7 to 6.5 in the same region.Pre-equilibrium dynamics showed that evolution to dioecy occurs more quickly if acytoplasmic polymorphism in male sterility is present, than if no such polymorphism ispresent (and male sterility is thus nuclear). The time required for evolution of dioecyunder completely nuclear male-sterility ranged from 3 to 90 times that required for evolu-tion to dioecy under the F-S or the S-S system, for a range of hermaphrodite selfing rates(0 to 0.7), female selfing rates (0 to 0.2), inbreeding depression (0 to 0.9), intrinsic femaleadvantage (0 to 2) pollinator relative efficiency (0.005 to 1) and effective pollinator visits(1 to 1000).For the F-S system with dominant restorer, a rate difference occurs in both determin-istic models, in which the arbitrary starting population consists of 200:1:1 homozygoushermaphrodite to heterozygous hermaphrodite to heterozygous male, and in stochasticmodels in which the starting population is entirely the homozygous hermaphrodite, andall genetic variation is introduced through random mutation, with the mutation rate tothe female sterility allele roughly equal to that to the male-fertility restorer allele. For theS-S system, a rate difference occurs in deterministic models from an arbitrary startingpopulation of 200:1:1 homozygous hermaphrodite (cytoplasm S2) to homozygous herma-phrodite (cytoplasm Si) to heterozygous male (cytoplasm Si), but is less pronouncedin stochastic models due to the oscillatory nature of the system and the resulting highChapter 5. Conclusions and Directions for Research^ 186probability that a male will be introduced when the same-cytoplasm female is in a lowfrequency phase.These results contradict the traditional notion of "stable" gynodioecy, and insteadshow that both nucleo-cytoplasmic and nuclear gynodioecy can evolve to subdioecy. Insome portions of the parameter space, however, evolution from subdioecy to dioecy isnot possible in the presence of a cytoplasmic polymorphism in male-sterility, indicatingthat such cytoplasmic polymorphism can produce a "stable" subdioecy in these regions.The major question suggested by these results is: In what proportion of dioeciousangiosperm species did male sterility originate as a cytoplasmic mutation, now fixed andcontrolled by a fertility restorer locus linked to the female sterility locus? Because theselective requirements for evolution to dioecy are generally the same under nuclear andnucleo-cytoplasmic gynodioecy, the answer to this question appears to lie in the genome,and in whatever nuclear processes exist that are capable of producing male and femalesterility loci, and of linking them together on a chromosome in the required dominancerelationship.Such linkage/dominance issues can be addressed only with research into the molecu-lar genetics of the currently unknown gender loci in dioecious and gynodioecious species,and continued research into the molecular genetics of floral development in related her-maphrodite species. For example, if a restriction fragment length polymorphism in mi-tochondrial DNA can be shown to be necessary (but not sufficient) for the expression ofmale sterility in some nucleo-gynodioecious species, then that fragment can be used as amarker for the cytoplasmic locus controlling male sterility. If the fragment is fixed in arelated dioecious species, then male sterility most likely originated in the mitochondrialgenome in that species. Alternatively, it might be possible to create a polymorphism inlength of restriction fragments of cloned nuclear restorer genes in a nucleo-cytoplasmicgynodioecious species, and show that such a fragment segregates with sex in both thisChapter 5. Conclusions and Directions for Research^ 187species and a related dioecious species. This again would confirm nucleo-cytoplasmiccontrol of male function in the dioecious species.The major shortcoming of the theoretical models in this thesis, and in all modelsof gynodioecy, androdioecy, subdioecy, and dioecy to date, is the assumption that in-breeding depression is a background constant, independent of the mating system. Inreality, the inbreeding depression loci will evolve concomitantly with the mating sys-tem loci (both the sterility loci and the loci that modify selfing rate in hermaphrodites)resulting in identity disequilibrium among load loci and between load loci and matingsystem loci. This in turn may cause differences in inbreeding depression between sex-ual morphs that affect the equilibrium sex ratio in established, stable populations. Theextent to which this phenomenon occurs is currently unknown, and will be addressedwith more complex population-genetic models that follow the evolution of all load locisimultaneously with the mating-system loci (as done for modifiers of outcrossing rate inhermaphroditic populations in Kondrashov, 1984, 1985, 1988; Holsinger, 1988; Charles-worth and Charlesworth, 1990; Charlesworth, et al., 1990, 1991, 1992; and Uyenoyamaand Waller, 1991a, 1991b, 1991c). The conclusions of the models in this thesis, however,would probably be altered little by incorporation of identity disequilibrium, since theyhold even when inbreeding depression is zero.5.2 Hawaiian Bidens5.2.1 Sex Ratio CorrelatesFemale frequencies among 14 subpopulations of Bidens sandvieensis and B. cervicataranged between 1989 to 1992 from less than 0.05 to over 0.46, and female frequencies atmost subpopulations did not vary significantly over the four seasons. The 1989 outcross-ing rates for nine of these subpopulations, estimated by applying Ritland's multilocusChapter 5. Conclusions and Directions for Research^ 188maximum-likelihood algorithm to the polymorphic loci coding for the enzymes shikimatedehydrogenase and phosophoglucoisomerase, averaged 0.62 (s.e. 0.21) and ranged from0.37 (s.e. 0.10) to 0.87 (s.e. 0.076). The pooled outcrossing rates at the four popula-tion centers were 0.503 (s.e. 0.112), 0.552 (s.e. 0.070), 0.755 (s.e. 0.085), and 0.705 (s.e.0.064); female frequencies at these four centers averaged respectively 0.33 (s.e. 0.075),0.27 (s.e. 0.018), 0.14 (s.e. 0.038), and 0.18 (s.e. 0.010). These outcrossing rates repre-sent the proportion outcrossed individuals in 3-4 week seedlings, and are overestimatesof the true outcrossing rates of fertilized ovules due to inbreeding depression in seed setand germination. Assuming a combined inbreeding depression of 0.6 from fertilizationto germination, the pooled outcrossing rates of fertilized ovules at these four centers are0.23, 0.27, 0.48, and 0.41. The last two of these rates are not sufficiently low to maintainfemales at the observed frequencies under complete inbreeding depression, but are suf-ficient under complete inbreeding depression and an additional non-outcrossing femaleadvantage of about 0.15.Loglinear contingency-table analysis showed significant correlation between femalefrequency and aspect, elevation, taxon, and outcrossing rate pooled into the four pop-ulation centers. Although full separation of these four factors was not possible, theoutcrossing rate effect was independent of taxon, and the aspect effect appeared to be in-dependent of taxon and outcrossing rate (but not elevation) in two years (1990 and 1991).Highest female frequencies occurred for subpopulations with northeast aspect (0.25 to0.38 over the four years), composed of Bidens sandvicensis ssp. sandvicensis (0.24 to0.28), situated at low elevation (0.24 to 0.40), or situated in a population center withlow pooled outcrossing rate (0.27 to 0.34). Probably the simplest explanation of thesecorrelations is a tendency for outcrossing rate to be greater (and hence female frequencylower) at higher elevations due to wetter conditions that support denser populations ofpollinating insects. The transient aspect effect may be due to a fortuitous tendency ofChapter 5. Conclusions and Directions for Research^ 189northeast-aspect sites to occupy lower elevations. Overall, the effect of outcrossing ratewas more stable over the four years than any of the other three factors.Total number of insect visits per plant and number of capitula visits per plant visitvaried significantly among the 3-4 monitored subpopulations, and hermaphrodites re-ceived more capitula visits per plant visit, presumably because they offered both pollenand nectar. However, neither the totals nor the differences in visitation rates to femalesand hermaphrodites were significantly correlated with female frequency at the monitoredsubpopulations.Seed set per capitula was significantly greater in females (F:H ratio 1.26 to 1.55),and seed set of both sexual morphs was significantly correlated with the number ofhermaphrodites within a 5-meter radius. The lower seed set of hermaphrodites maybe due entirely to selfing and inbreeding depression in embryo survivorship, or to acombination of inbreeding depression and a resource advantage in females; however, inat least two population centers, outcrossing rates were sufficiently low that no resourceadvantage is necessary to maintain the observed female frequencies under nuclear male-sterility. The effect of nearby pollen-donors on seed set is the same in females andhermaphrodites, indicating that insect visitation rates affect the setting of selfed as wellas outcrossed seed in hermaphrodites, as is expected if selfing is primarily geitonogamous.Plant size, total number of capitula produced per plant, and total length of primarybranches per plant varied significantly among the monitored subpopulations, and meansof total primary branch length were significantly greater in hermaphrodites (F:H ratio0.66 to 1.08). Although sexual dimorphism (whether significant or not) for none of thesetraits was correlated with female frequencies of the monitored populations, one low-elevation site with high frequencies of females was suggestive in showing greater meanbranch length and capitula production in females.Chapter 5. Conclusions and Directions for Research^ 1905.2.2 Inbreeding Depression and Maternal SexSignificant inbreeding depression was measured in seed set in the glasshouse (0.2 to 0.5),one-month germination in the nursery on Kauai (0.40, s.e. 0.10), first year survivorship inthe field (0.42, s.e. 0.16), flowering probability in the field (0.58, s.e. 0.15), and capitulumproduction of flowering plants in the field (0.68, s.e. 0.085), and the inbreeding depres-sion in both survivorship and capitulum production was independent of height at fieldtransplant. Total inbreeding depression from seed set to first flowering in the field wasthus over 0.95, for over 10 hermaphrodite maternal parents grown from open-pollinatedseed collected from four populations. Inbreeding depression from 0.3 to 0.4 was alsosignificant for first-year height growth, number of apical leaf pairs, and leaf length.Performance of open-pollinated seed-progeny of females was greater than that ofhermaphrodites in one-month germination (F:H ratio 1.37), first-year survivorship in thefield (1.28), flowering probability in the field (1.05), and capitulum production of floweringplants in the field (1.25), although the maternal sex effect was statistically significant onlyfor the first two components. Total relative first-year fitness of open-pollinated progenyof females was thus 2.30, an amount of sufficient magnitude to maintain nuclear male-sterility alleles in a population, but at lower female frequencies than those observed.When the 30% to 50% greater seed set per capitulum is included, however, the totalrelative female fitness is increased to at least 3.08, which predicts equilibrium femalefrequencies in excess of 25%, in the midrange of those observed. No significant differenceswere observed in either survivorship or fecundity in adult females and hermaphrodites innature, or in juveniles or adults of known parentage grown in the field plots.In all fitness components, performance of open-pollinated progeny of females was in-ferior to that of outcrossed progeny of hermaphrodites, indicating biparental inbreedingChapter 5. Conclusions and Directions for Research^ 191in females and the lack of any advantage to progeny of females not attributable to out-crossing. In order for inbreeding depression in hermaphrodites to account entirely for thematernal sex effect in open-pollinated progeny, the mean proportion outcrossed must be amaximum of 0.43 in the 1990 seed sample, and 0.60 in the sample of seedling transplants.This is in agreement with the mean 1989 isozyme outcrossing rate in 2-3 week seedlingsof 0.61 (s.e. 0.07), obtained from the outcrossing rates estimated for each of the sourcepopulations for the 1990 seed sample, weighted by the number of families contributingto the seed sample.In conclusion, at least 75% of the relative fitness of females in Bidens sandvicensisis due to the expression of inbreeding depression in the highly selfed progeny of herma-phrodites.The major unanswered questions raised by this and similar studies are (1) why hassome other means not evolved to reduce selfing rate in hermaphrodites below 50%?(2) how could a high inbreeding depression originate in the face of the observed highselfing rate, which selects against deleterious recessive alleles and hence prevents theiraccumulation? and (3) why is the apparent investment in male function so low as toprevent a large resource-compensation advantage in females?Each of these questions could be addressed by more extensive studies than thosereported here of the pollination biology of Bidens sandvicensis and B. cervicata. Onepossible reason for the high selfing rate in hermaphrodites is the difficulty, in a largeplant, of evolving morphological or phenological mechanisms of reducing geitonogamousself-fertilization, the primary mode of selfing in these species of Bidens, and the difficultyin general of evolving self incompatibility, which requires the joint occurrence of severalimprobable genetic mutations. Because geitonogamy results from the simultaneous re-ceptivity of a large number of flowers within an individual, it might be understandableas a negative side effect of an optimal solution to a size-number problem; i.e., what is theChapter 5. Conclusions and Directions for Research^ 192optimal number of ovules per flower, flowers per capitulum, and capitula per plant? Gei-tonogamy could be reduced, for example, by doubling the number of flowers per capitulumand halving the total number of capitula, since selling can be controlled phenologicallywithin capitula.The effect of this and similar morphological changes on the outcrossing rate could beascertained with estimates of pollen flow parameters, such as the mean number of pollengrains transferred between hermaphrodites in a typical visit, deposited per capitulumvisit (on both stigmatic and other surfaces), and picked up per capitulum visit; the meannumber of capitula visited per plant approach; the total number of approaches per plant;variation in visitor community composition; and total pollen-ovule ratios. More detailedknowledge of visitation parameters would also provide useful corroborating evidence forthe conclusion here that spatial variation in female frequency is largely due to variationin outcrossing rates: for this to be true, some behavioral component of pollinating insectsmust be correlated with female frequency. Pollen-flow information would also be useful inunderstanding the low or nonexistent non-outcrossing advantage of females: low rates ofpollen pickup or transfer might prevent any increases in pollen production from causingproportional increases in outcrossing rate; in the absence of large pollen production,elimination of pollen might provide little benefit. Knowledge of the fate of abortedsporogenous cells in females is also pertinent, since in order for resource compensation tooccur, the resources composing the cells and associated tissues must be reabsorbed andtranslocated in conducting tissue to appropriate sites.5.2.3 Implications for Mating System EvolutionThese results suggest that inbreeding depression, especially in species of isolated oceanicislands, can exert a profound influence on the evolution of floral structure. A possibleevolutionary sequence for species such as Hawaiian Bidens and Schiedea might include:Chapter 5. Conclusions and Directions for Research^ 1931. Ecological or evolutionary events leading to an increase in total genetic load, in-creasing the inbreeding depression above the outcrossing threshold (roughly 0.5).One possible cause of such an increase is a greater mutation rate per generation todeleterious recessive alleles as a result of the evolution of greater size and longevity.Size and longevity might be selectively favored during competition for resourcesin stable, predictable environments either in the mainland source population or inthe colonizing island population. Another possible cause of an increase in inbreed-ing depression is expansion of population size. A larger effective size will reduceboth the rate of loss of new mutations during random genetic drift, and the levelof biparental inbreeding. Reduction of biparental inbreeding in turn will increasethe mean fitness of outcrossed progeny, the de facto inbreeding depression, and theselective advantage of outcrossing.2. Evolution of floral structures promoting increased outcrossing (in response to in-breeding depression exceeding the 0.5 threshold); e.g., spatial or temporal separa-tion of male and female function within individual hermaphrodites.3. Increases in inbreeding depression as a result of lowered selfing rate. Loweredselfing reduces the strength of selection against deleterious recessive alleles, andhence allows total genetic load to increase to a new mutation-selection equilibrium.4. Gradual loss of effectiveness of self-fertilization in reducing genetic load. As inbreed-ing depression increases to near unity, selfed individuals have near-zero fitness andhence are less. capable of effecting a reduction in frequency of deleterious alleles atany locus, allowing enormous selection to continue against structures promotingselfing.Chapter 5. Conclusions and Directions for Research^ 1945. Colonization event leading to increased rates of autogamy or geitonogamy. In aspecies of an oceanic island, this could be the original colonization of the archipe-lago, or a later interisland colonization. Increase in selfing rate might result froma low outcrossing efficiency of alien pollinating vectors, biotic or abiotic.6. If selfing rate of hermaphrodites is sufficiently high, then male-sterile mutants caninvade the population, creating gynodioecy. An increased selfing rate, however,does not necessarily constitute increased selection for male steriles or females. Ifincreased selfing results simply from the same lower fertilization rate of outcrossedovules in both hermaphrodites and females, then selfing rate and pollen limitationare not independent, and the conditions for female invasion are the same or morestringent than previously. Only if loss of outcrossed ovules in hermaphrodites isproportionately greater than this loss in females will conditions for female invasionbe relaxed.7. The presence of females creates a higher frequency of outcrossed ovules, and hencereduces the requirements for the invasion of female-steriles or males and the evolu-tion of subdioecy or dioecy. The higher the product of selfing rate and inbreedingdepression in hermaphrodites, the lower the gain in pollen fitness necessary for theinvasion of males. Male invasion will produce subdioecy if the sterility loci are un-linked, and dioecy only if the loci are linked and the fertility allele of one functionand sterility allele of the other are both completely dominant.8. Evolution of either gynodioecy or dioecy reduces the mean selfing rate and strengthof selection against deleterious recessive alleles, creating a higher equilibrium ge-netic load than in the ancestral hermaphrodite population.Chapter 5. 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Thesis/Dissertation
eng
Botany
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Graduate
Evolution of gynodioecy and dioecy: theoretical issues and the case of Bidens sandvicensis and B. cervicata
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