Inbreeding, Self-Fertilization, Lethal Genes and Genomic Coalescence

Heredity 68 (1992) 449—456 Received 24 May 1991 Genetical Society of Great Britain

Inbreeding, self-fertilization, lethal genes and genomic coalescence

S. H. JAMES Botany Department, The University of Western Australia, Nedlands, Western Australia, 6009

A deterministic computer model was used to investigate the elevation in frequency of coalesced genomic heterozygotes, i.e. heterozygotes with reduced numbers of independently assortingsuper- genic units at meiosis, in inbred populations in which every supergenic unit carried a recessive lethal gene. Inbreeding was manipulated in terms of s,theproportion of self-fertilizations per generation, and F, Wright's Inbreeding Coefficient which measures the degree of relatedness between individuals within a population. It was found that where F was greater than about 0.19, coalesced heterozygotes were lifted to high frequencies (>50 per cent) in the population in the absence of self-fertilization. Coalesced heterozygotes were lifted to high frequencies in populations with F less than 0.19 by appropriate levels of self-fertilization. Populations with fewer independently segregating supergenic units at meiosis were more sensitive to the effects of inbreeding than those with larger numbers of such units. The possible significance of these observations in terms of the evolution of genetic systems and in conservation practice is briefly discussed.

Keywords:evolution,genomic coalescence, inbreeding, lethal genes, permanent hybridity, self- pollination.

Introduction genomes that are visible to natural selection in the Genomiccoalescence may be defined as the evolu- short-term, and which tend to drive lineages into risk tionary rearrangement of the genotype in diploid and extinction. sexual organisms into fewer linkage groups or into The natural tendency for linkage to increase was linkage groups which exhibit reduced levels of recom- first noted by Fisher (1930) and the phenomenon has bination. It is supergene formation and may be been the centre of considerable discussion since. A reflected by a reduction in chromosome number, by variety of theoretical situations have been described in structural hybridity, by the alteration of position and which the tendency may be promoted or countered frequency of chiasmata, by epistatic linkage in the for- (e.g. Turner, 1967; Maynard Smith, 1977), but the dis- mation of coadapted gene complexes, and by devices cussion has not examined extreme situations in which which promote the polarized segregation of chromo- coalesced genomes are clearly advantageous. Of parti- somes at meiosis. Because related taxa often differ with cular interest is the role of linkage in inbred popula- respect to chromosome structure and other attributes tions carrying high frequencies of recessive lethal modulating recombination, genomic coalescence may genes. be a common outcome of micro-evolutionary pro- It is commonly held that the equilibrium frequencies cesses. If, however, genomic coalescence reduces the of deleterious alleles, such as recessive lethals, will be recombinational capability of its products, it may lower in inbreeding populations than in outcrossing thereby expose them to an increased risk of extinction. populations. Charlesworth eta!.(1990), in agreement Lineages which avoid genomic coalescence should with Lande & Schemske (1985), contend that 'this con- maintain their recombinational potential and the evolu- clusion is quite correct for recessive lethals and sub- tionary capability generated by that potential; they are lethals'. Indeed, it is the expectation arising from more likely to be successful as ancestors of future classical population genetic theory which demonstates generations. While the advantages of free recombina- that recessive lethal genes will be reduced in fre- tion may account for the long-term evolutionary suc- quencies to levels maintained by mutation pressure. cess of lineages which avoid genomic coalescence, However, deleterious recessives and lethal genes are there must be advantages associated with coalesced common in many plant populations. Substantial levels 449 450 S. H. JAMES of seed abortion resulting from recessive lethal poly- (06) association. The 06 consisted of three inter- morphisms in natural populations characterize many changed chromosomes forming an N complex and the diploid sexual plants (Sorensen, 1969; Ledig, 1986; three homologous chromosomes with primitive struc- Weins et a!., 1987; Burbidge & James, 1991). It ture forming the complementary S complex. Thus, in appears, however, that the phenomenon is often the N.S 06 hybrids, the number of independently segre- ignored. Because plants exhibiting very low levels of gating units was reduced to five and the genome may seed set following self-pollination would need to be be considered to have been coalesced from seven to heterozygous for quite large numbers of lethals if the five. The models also recognized a reduced fecundity incompatibility was postzygotic, the incompatibility is (73 per cent) in the 06 due to their irregular behaviour often presumed to be prezygotic (e.g. see Kendrick & at meiosis which would be significant in determining Knox, 1989). Standard population genetic theory, the relative fertility of the heterozygotes as seed which indicates that natural selection would reduce the parents. The models assumed that all supergenic alleles frequency of any recessive lethal gene to very low were recessively lethal, that is, each chromosome was levels, may well be valid in panmictic systems where considered to carry one or more mutations that would the individual recessive lethal genes may be so diluted prevent its homozygote from contributing to the next in the population as to be essentially invisible. With generation. It was also assumed that all products of self-fertilization, however, the probability of individ- crosses, apart from those homozygous for the inter- ually rare recessive lethals becoming associated as changed chromosome arrangement N, were viable; that homozygotes is elevated. With very large numbers of is, apart from the interchanged ring-of-six, the value of loci polymorphic for recessive lethals, and with high F (Wright's Inbreeding Coefficient) at all supergenic levels of inbreeding, only a small proportion of the loci was 0.0. The two models differed in that in one zygotes produced may be viable. This would place case, the N complex was fully transmitted in both intense positive selection pressure on devices mini- pollen and embryosac while in the second, the N mizing the proportion of inviable zygotes produced. complex was pollen non-transmissible. It was found Plants may respond by coalescing the genome. This that both models elevated the frequency of the 06 may ultimately concentrate the genome into two super- interchange heterozygotes in the population to high genic alleles held in permanent hybridity, thereby levels where the frequency of self-pollination, s, was reducing the frequency of inviable zygotes to 50 per very high (>97per cent). cent as, for example, in autogamic complex hybrids It may be anticipated that recurrent self-pollination such as Oenothera lamarckiana and Isotoma petraea, may elevate the frequency of the 06 even more which are maintained by balanced post-zygotic lethal effectively in more inbred populations, that is, in popu- systems. lations characterized by F values greater than 0.0. In In Isotoma petraea, a member of family Lobeliaceae order to examine the effect of the levels of inbreeding (Angiospermae), the ability to cross-pollinate is in terms of F and s on genomic coalescence conjointly, dependent upon the protrusion of the stigma from the the nascent complex hybridity model, with free trans- anther tube. The frequency of flowers with retained mission of N in both pollen and embryosacs, is genera- stigmas thus provides a minimum estimate of the fre- lized in this paper. quency of self-pollination within plants. In some populations, this frequency approaches 100 per cent, of the model permitting the analysis of population genetic architec- Description ture under conditions of very high inbreeding levels. Themodel is illustrated in Table 1. x is a genome com- These populations exhibit elevated levels of genetic posed of n independently assorting supergenic units. n heterozygosity, polymorphism for seed aborting reces- is visualized as approximating the haploid chromo- sive lethal genes, and have evolved complex hybridity. some number plus the mean number of chiasmata per Recently, two deterministic models purporting to cell that are not terminally localized; it approximates simulate the fixation of a doubly interchanged genome the 'recombination index' (Darlington, 1958). N is a as nascent 06 complex hybrids in a population of derivative genome which reduces the number of inde- isotoma petraea have been described (James et a!., pendently assorting units in N.x heterozygotes to m. N 1990). The models recognized seven independently is of monophyletic origin in the population so that all segregating supergenic loci in the ancestral forms alleles of N are identical by descent. Each chromosome corresponding to seven pairs of homologous chromo- is recessively lethal. Only those selfed progeny hetero- somes which exhibited terminal chiasma localization. zygous for all n or m independently assorting units are Three of the erstwhile independently assorting super- viable. The frequency of N.x heterozygotes and x.x genes were combined by interchange into a ring-of-six homozygotes in the adult population is P and Q, GENOMIC COALESCENCE 451

Table I Explanation of the population model. See text for detail

Female Male parent parent Contributionto next generation

Disjunction Pollination Type Frequency frequency type/frequency Type Frequency N.ax ax ax

s N.x 1 (1/2)' 0 N.x P D N.x P (1F)m (1—F)"

—' "'1 x.x Q ( 1 —F)in ( 1 —F)n_1(1 — F)'— s x.x 1 0 (1/2)" xx Q 1 N.x P (1 —F)"1 (1—F)'(1—F)""'

x.x Q 0 (1—F)'

x =thestandard genome with n independently segregating supergenic units. x.x =theprimitive homozygote. N the coalescing genome; N.N homozygotes are excluded from the population by zygotic lethality. N.x =thecoalesced heterozygote with m independently assorting supergenic units. P= the population frequency of N.x, and Q =1 —P. D =therelative gametic fertility of the N.x heterozygote as seed parent. s =therecurrent selfing rate, and t= 1—s. All genomic components are freely transmissible through both pollen and embryosacs. For the cases examined in this paper, in which m =n—1,the frequency of the N.x heterozygote in the next generation is given by I PsD/2' +PID(1 —F)(fl_/2+PQt(1 —F)(_ — — — [PsD/2"+PtD(1 —F)"/2 +PQt(1—F)"'+tD(1F)"/4+ PQD(1 —F)'72 +Qs/2"+PQI(1 —F)72 +Q2t(1F)"]

respectively. Since N.Nhomozygotesare always coalesced heterozygote to a frequency of 0.5 is pre- inviable, P+ Q= 1. The relative seed fecundity of x.x sented in Fig. 1a. Courses of the 50-generation cycles homozygotes is 1, and that of N.x heterozygotes D. The following stepwise variations of each parameter about recurrent selfing rate is s. The inbreeding coefficient of the value used in Fig. la are presented in Fig. lb—e. It the population is F so that the probability of choosing can be seen that a sufficient level of inbreeding will two alleles of a supergene (apart from alleles of N) elevate the frequency of the coalescent genome hetero- carrying identical recessive lethals is F. All N.N homozygotes within the population. The necessary level of zygotes are lethal, whether they be produced from inbreeding may be generated by recurrent self-fertiliza- crosses or selfs. tion (s, Fig. ib), by a sufficiently high level of genetic The value of F' (the value of P in the next genera- relatedness between individuals within the population tion) was determined according to the equation given (F, Fig. ic), or by a combination of both. The effectivity in the legend to Fig. 1. of the coalescing device will also be dependent upon the relative fitness of the heterozygote, symbolized in this model by D, the relative ovule fecundity or meiotic disjunction frequency (Fig. id). The level of inbreeding Results necessary to elevate a coalesced heterozygote to a Themodel was run for particular values of s, F, D, n particular frequency in a population also decreases as and m. Only cases where m =n—1(equivalent to a the original number of independently assorting super- single interchange or chromosome fusion) are reported genes, n, decreases (Fig. le), and the level of inbreed- here. In any run, the population was started with ing capable of inducing genomic coalescence from n to P=0.01 and Q=0.99 and cycled across 50 genera- n —1would induce coalescence from n —1to n —2 tions. Two series of experiments are reported here. even more rapidly. Genomic coalescence, therefore, Results for the first series of experiments are would be a self-reinforcing or orthogenetic tendency. summarized in Fig. 1. The parameters and course of a In the second series of experiments, the level of self- 50-generation cycle leading to the elevation of the fertilization, s, necessary to elevate the frequency of a 452 S. H. JAMES

(0)

4 a 4,

i0 0.5 0' 0 4, I6)

(b) Id) a

I.0 0.96 0.92 0.88 0.84 0.80

le) 2 4

Fig. 1 Coalesced heterozygote frequencies across 50 sequential generations calculated according to the model presented in Table 1. (a) The course of a single model run with the following parameter values. s =recurrentselling rate (0.98); F= inbreeding coefficient of population (0.01); D =relativeovule fertility of heterozygote (0.95); n =originalnumber of independently assorting supergenic units (7). In these runs, the coalesced heterozygote had n —1independently segregating supergenic units. (b—e) Model runs with one parameter stepped as indicated at right of each figure, the remaining parameters constant, with values as in (a). coalesced heterozygote to 0.5 for particular values of F value, high levels of self-fertilization were necessary to within the population, for D as given in Fig. 1 a, was elevate the frequency of coalescent heterozygotes determined for a range of n, with m =n—1.The results above 0.5, but the population response to self-fertiliza- of this exercise are presented in Fig. 2. It can be seen tion was highly dependent upon n, the number of inde- that when F is greater than about 0.19, coalescent pendently assorting supergenes. In general, providing F heterozygotes will be raised to 0.5 even without any was less than the critical value (about 0.19), popula- self-fertilization, i.e. under conditions of complete pan- tions in which n was greater than about 7 were reason- mixia. With population levels of F below this critical ably resistant to self-fertilization. GENOMIC COALESCENCE 453

lethal polymorphism, to elevate the frequency of coale- Discussion scent genome heterozygotes in populations. Themodel described in this paper indicates that in a Genomic coalescence may be driven into popula- population in which each supergenic allele carries a tions having appropriate levels of inbreeding and lethal recessive lethal gene, inbreeding, due either to self- polymorphism by natural selection because, under the circumstances given, the coalesced heterozygote, N.x, may be fitter than the primitive uncoalesced homozygote, x.x. On selfing, x.x. will produce 1/2's viable zygotes while N.x will produce 1/2 XDviable a zygotes, where D is the relative ovule fecundity of N.x. a, Providing that n and m are integars with n> m and that C D is more than 1/2( in)N.xwill produce more viable a, t0 zygotes than x.x. C 0) Although of short-term adaptive utility in elevating aU the proportion of viable zygotes above 1/2" in highly inbreeding populations fraught with recessive lethal polymorphisms, genomic coalescence would reduce the recombinational diversity of the lineage. This, in Inbreeding coefficient (F) turn, must reduce the adaptability and long-term evolu- Fig.2 These graphs describe the levels of recurrent selfing, tionary potential of the lineage and thereby increase its s, and the population inbreeding coefficient, F, necessary to risk of extinction. In addition, the model ignores muta- elevate the population frequency of coalesced heterozygotes tion. Genomic degradation and recurrent mutation of with n —1independently segregating supergenic units rela- competent genes to deleterious and even lethal mutants tive to the n independently segregating supergenic units of is a constant attribute of DNA-based life and is mini- the primitive forms, to 50 per cent, for n =2(lower left), 4, 6, mized by a variety of DNA repairing mechanisms. 8 and 10 (upper right), according to the model described in Biparental sexual reproduction involving recombina- Table 1. tion mechanisms provides a system whereby deleterious mutations may be removed from corrupted fertilization (s) or to relatedness of individuals within genomes. Where genomic coalescence is driven into a the population (F), or both, will lead to an increased genetic system already encumbered with high levels of frequency of coalescent genome heterozygotes in the inbreeding and a ubiquity of recessive lethal genes, this population. What is modelled then, is the procedure by aspect of sexual reproduction must be inhibited and which autogamy, systems of reduced recombination, the genome must be pushed towards further degrada- and lethal polymorphisms are associated into per- tion. Thus, lineages responding positively to selection manent hybrid genetic systems. If F was greater than for genomic coalescence risk decreasing survivability about 0.19, the frequency of coalescent genome and orthogenetic progress towards extinction. heterozygotes would increase even in the absence of The tendency towards genomic coalescence, risk self-fertilization. The critical value of F, here approxi- and extinction may well provide an engine which drives mating 0.19, is obviously directly dependent upon the evolutionary progress by eliminating those lineages value of P, here set at 0.5, chosen to define the isopleth; which do not, perhaps serendipitously, incorporate lower values of F and/or s would be required to elevate adaptations that insulate against the forces of genomic the frequency of the coalescent genome heterozygotes coalescence into their genetic systems. Such adapta- to levels less than 0.5. tions may affect s, F or n, they may accommodate the The model presented maintained F constant over high genetic load through elevated levels of seed pro- generations that were characterized by constant levels duction, or they may direct maternal resources pre- of self-fertilization. However, a constant level of self- ferentially to heterozygous progeny. fertilization would influence F, so that an inbreeding Adaptations affecting s include those structural and equilibrium, in which F= (1 —t)/( 1+t) = s/(2—s), mechanical modifications of the flower that prevent or should be established. Thus, for s greater than about modulate the frequency with which self and cross 0.32, we might expect F to exceed 0.19 and the fre- pollen grains arrive at the stigma, and the physiological quency of coalesced heterozygotes should increase, discrimination between those two types of pollen. regardless of subsequent values of s. Consequently, the Dicliny, including dioecy, and prezygotic self-incom- model presented must underestimate the power of patibility, may represent the most effective systems inbreeding, in association with high levels of recessive modifying s. Adaptations affecting F include those 454 S. H. JAMES concerned with dispersal, the size and shape of the quency of allosyndesis at meiosis. Polyploidy may be individuals and their spatial relationships. Adaptations regarded as an alternative response to conditions affecting s and F are likely to have significant otherwise likely to lead to genomic coalescence (see, ecological impacts not solely linked to the properties of for example Banyard & James, 1979). genetic systems. In this regard, boundaries between In a plant heterozygous for deleterious recessives at ecological and genetical relevance may be quite n independently assorting supergenic loci, the 1/2's obscured and the relevance to population genetics of fully heterozygous progeny genotypes expected on self- adaptations with obvious ecological implications may ing may be a small proportion of the zygotes produced. be overlooked. For example, the ephemeral annual However, the absolute numbers of fully heterozygous species of Slylidium, which tend to occur in dense progeny genotypes produced may be quite substantial, carpet-like populations of small, relatively few- if the ovule fecundity is sufficiently high. Thus, in flowered plants, do not exhibit the genomic coalesc- orchids which characteristically have thousands of ence (dysploid chromosome number reduction) that ovules per ovary and minimal amounts of maternal characterizes their larger racemose-inflorescenced per- resources invested into individual seeds, seed wastage ennial congeners (Burbidge & James, 1991). Ecol- on self-pollination would not be as disastrous as in ogical and habit differences evidently affect the species that produce fewer larger seeds. In species with breeding systems and cytoevolutionary responses of fewer larger seeds, the wastage of maternal resources in the two groups. Furthermore, well developed adapta- the construction of genetically inadequate seed may be tions promoting cross-pollination may result from the minimized by introducing early-acting, seed-aborting, strong selection pressures that arise from high levels of recessive lethal genes into the supergenic alleles. This inbreeding so that the presence of elaborate cross- has apparently occurred in the evolution of the seed- pollination mechanisms in a lineage may indicate high aborting lethal systems in the nascent 06 complex levels of self-pollination or other forms of inbreeding. heterozygotes of Isotoma petraea at Pigeon Rock This logic applies well to triggerplants (James et a!., (James et a!., 1991) and is characteristic of the peren- 1991a), the pseudocopulatory orchid Leporella nial Sylidium species in Western Australia (Burbidge fimbriata (Peakall & James, 1989) and the bird- & James, 1991). In Eucalyptus camaldulensis only pollinated Eucalyptus rhodantha (Sampson et al., about 7 per cent of the several hundred fertilized 1989). ovules per ovary succeed in forming seeds; a large Factors that affect n include interchange hybridity, majority succumb to intense competition within the which ties chromosomes together into a single linkage developing capsules. The surviving seeds, however, group, and the dysploid reduction of chromosome include an excess of heterozygotes following self- number through centromere loss. However, supergene pollination, or a preponderance of outcrosses follow- formation by a reduction in chiasma frequency, chi- ing open pollination (unpublished results). Thus, asma localization or other forms of structural hybridity, postzygotic seed selection systems, based on seed- such as inversion hybridity, may be an equivalent aborting recessive lethal genes or on competition response. Other coalescing devices may include epi- between sibs, may preferentially channel maternal statically induced linkage as may be found in internal resources to the most adequate progeny genotypes. chromosome segment transposition heterozygotes, Such devices would minimize the segregational load polarized segregation at meiosis as has been demon- associated with high frequencies of deleterious alleles strated in certain members of the Australian family and elevate the fitness of self-pollinating plants. Epacridaceae tribe Styphelieae (Smith-White, 1948, A positive response to selection for genomic 1955, 1959), apomixis, and asexuality. A larger n may coalescence may require extreme circumstances to be be achieved by increasing the chromosome number, by operating in a target population. The very high levels of increasing the numbers and randomness in the location inbreeding and the ubiquity of recessive lethal factors of chiasmata at meiosis, by minimizing structural necessary to elicit the response may seem unreal. How- hybridity and by retaining unencumbered classical ever, strong evidence for the process has been adduced sexual reproduction in the genetic system. from field and experimental observations of complex Polyploidy is a special case where an increase in hybridity in Isotoma petraea (James, 1965, 1970), chromosome number increases genomic redundancy especially in the Pigeon Rock 06 population in which from two, the normal diploid condition, to three, four the genetic system evidently arose (James et a!., 1990, or more in the polyploid derivatives. Polyploidy 199 ib). It has been demonstrated that populations of reduces the frequency of homozygotes in selfed pro- Stylidium in Western Australia may be highly inbred geny below the 25 per cent level for each deleterious and polymorphic for seed aborting recessive lethal allele to a level dependent upon the position of the genes at up to several hundred loci (Burbidge & James, locus in the chromosome, the ploid level, and the fre- 1991). The extreme circumstances required to drive GENOMIC COALESCENCE 455 genomic coalescence may be expected to promote of bias towards outbreeding in the estimate may well rapid evolutionary responses; failure to elevate the pro- reflect the intensity of inbreeding in the population. portion of viable zygotes from 1/2" may well mean Outbreeding populations of dioecious organisms extinction. It is possible that individual hermaphroditic and plants equipped with prezygotic self-incompati- plants, capable of self-fertilization and newly isolated bility systems would not be immune to genomic from larger populations, may generate a population in coalescence, especialy in populations in which F is which the extreme circumstances which both require greater than about 0.19. As Brown (1979) estimated and facilitate genomic coalescence may exist. The that the average F amongst outbreeders was of the important role of self-fertilization in promoting order of 0.16—0.26 (23 species, compared to 0.75 in genomic coalescence substantially decreases the rele- seven species of inbreeders), it is possible that many vance of the phenomenon in dioecious species, which outbreeders are sufficiently inbred through relatedness includes many plants and most animals, and in plants of individuals within populations so as to elevate with pre-zygotic self-incompatibility systems. The fact coalescent genome heterozygotes to significant fre- that it may be largely irrelevant in dioecious popula- quencies. Again, however, the impact of postzygotic tions, combined with anthropocentricity, may well have lethality and genomic coalescence on the estimates of F contributed to the phenomenon, and its causes, being given by Brown (1979), is unclear. largely overlooked amongst hermphroditic plants Finally, note that populations which exhibit low capable of self-fertilization. However, intense selection levels of allozyme heterozygosity may support the pressures towards genomic coalescence may be lowest levels of supergene formation and, thereby, the expected to be generated in small isolates of any most open recombination systems. Such populations, if diploid sexual species, and could give rise to dramatic they also maintain the highest adaptive and evolu- evolutionary episodes indistinguishable from the tionary capability, may be preferred targets in conser- 'transiliences' described by Templeton (1 980a,b). vation. The elevation of coalesced heterozygotes to high frequencies by inbreeding in populations highly poly- Acknowledgements morphic for recessive lethal genes provides an important structuring of gene pools. In particular, the average Thesupport of The University of Western Australia genome in such populations will be composed of a and the Australian Research Council is gratefully limited number of supergenes and these supergenes acknowledged. I thank David Coates, Michelle Way- will be held at high levels of heterozygosity. The super- cott, Margaret Byrne, Steve Carstairs and Helen Stace genes will contain marker loci, such as allozyme loci, as for their comments and discussion. well as the recessive lethal factors which underpin the polymorphisms. Marker alleles supergenically linked References to lethal genes will tend to occur as heterozygotes so B. J. AND JAMES, S. H. 1979. Biosystematic studies in that, for that allele, the observed frequency of hetero- BANYARD, the Stylidium crossifolium species complex (Stylidiceae) zygotes, H0, may be elevated over expectations, H0. Aust. J. Bot., 27, 27—37. Thus, estimates of F, [based on the relationship BROWN, A. H. D. 1979. Enzyme polymorphism in plant popula- F 1 —Ho/He]may be reduced and estimates of t tions. Theor. Pop. Biol,, 15, 1-42. — [based on the relationship t =(1F)/(1+ F) or on BURBIDGE, A. H. AND JAMES, S. H. 1991. 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