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Summary Some male and female plants of dioecious populations of seven Cotula species are strictly unisexual, or constant; other plants of the same populations are inconstant, with a low proportion of florets of the opposite sex (minority-sex florets) which function normally. The distribution of minority-sex florets among heads of male and female plants is shown by rank-frequency curves. The average inconstancies of males and females are quantified as the proportions of genes transmitted via gametes of the minority-sex florets, estimated by the proportions of minority-sex florets. The average inconstancy of males is 9.9 × 10−4; that of females is 4.3 × 10−4. The Primary Sex Index, 0.9993, is the average constancy (1—inconstancy) of all individuals. This provides a measure of the degree of separation of male and female gamete functions in the two sexes, on a scale from 0.5 (sexual monomorphism) to 1.0 (complete separation of the sexes). The sex Asymmetry Index, male inconstancy–female inconstancy/male inconstancy + female inconstancy, + 0.39, measures the relative magnitude of inconstancies of the two sexes on a scale from –1.0 (androdioecy) to + 1.0 (gynodioecy). Male and female heads differ in several secondary characters. The progeny of experimental crosses show that females are heterogametic and males are homogametic for sex-determining chromosomes. Males and females occur in equal numbers in the progeny of male × female crosses and in natural populations. The distribution and experimental manipulation of sex inconstancies provide considerable information on the origin and genetic maintenance of dioecy. The evolution of dioecy in Cotula has been accomplished by divergence in the sexes of the timing of the switch from male floret to female floret formation during head development, rather than by the introduction of male- and female-sterility genes. No genes essential for female reproduction are restricted to the Y chromosome. A polyploid series in the dioecious populations (2n= 52 to 2n=c.312) indicates an ‘active Y’ mechanism, and may have been facilitated by the regeneration of sexual dimorphism from inconstant females with new chromosome numbers.

Algebraic models of gynodioecy show that the effects on the equilibrium sex ratio of the relative survival and seed production of the sexes and of inbreeding of male-fertile plants are identical for all genic modes of inheritance, provided that different genotypes among male-fertile plants (or among females) do not differ in average fitness. The effects of three modes of inbreeding on equilibrium sex ratios are examined. If there is competition between self- and cross-fertilization of male-fertile individuals, a stable sexual dimorphism can be maintained by an outbreeding advantage of females if both the proportion of cross-fertilized seeds among those borne on male-fertile individuals,t, and the inbreeding depression (fitness inbred/outbred seeds),i, are less than one half. A lower frequency of females is obtained for the same values oft andi if self-fertilization precedes cross-fertilization. If self-fertilization follows cross-fertilization, gynodioecy cannot be maintained by an outbreeding advantage of females. When the sex phenotypes of gynodioecious populations are determined by cytoplasmic inheritance, females need only a slight advantage over males in survival, ovule production or outbreeding to persist at equilibrium. When determined by nuclear genes, androdioecy can be maintained by greater fecundity or a higher survival rate of males than of female-fertile plants, but not by an outbreeding advantage. Androdioecy cannot be maintained with cytoplasmic inheritance of sex. The models suggest explanations for the more frequent occurrence of gynodioecy than of andrdioecy, the high frequency of gynodioecy in Hawaii and New Zealand, and the origin of gynodioecy from hermaphrodite but not from monoecious ancestors.

Sex ratios in 35 inflorescence and plant counts of perennial, sexually dimorphic Umbelliferae vary from 0·96 to 87·33 times as many males as females. The ranges of ratios are similar in dioecious and gynodioecious populations. In 10 populations in which both the inflorescences and plants were counted, the male/female ratios are approximately one in populations in which the plants produce only one inflorescence per year and increase as the average number of inflorescences increases. The interpretation offered is that the sex ratio is approximately one until reproduction begins, and in subsequent years increasingly male-biased ratios develop because sexual reproduction utilises more of the available resources of females than of males. Following reproduction, male plants survive longer and grow more and so become predominant. In dioecious Angiosperms generally, male-biased ratios are characteristic of long-lived repeatedly flowering species and may be partly due to differential post-reproductive growth. It is postulated that male preponderance is not directly selected for, but is a secondary consequence of separate competition among males and among females during sexual reproduction. The seed set and fitness of total populations may actually decrease with the development of marked male preponderance.

Summary Four geographic races of Leavenworthia crassa and one race of L. alabamica are described as self-incompatible, since the average frequencies of fruit set and of pollen tube growth into the style are significantly lower after self-pollination than after cross-pollination. The frequency of successful self-pollination in individual plants of these races varies from zero to 100%, and is positively correlated with the average number of seeds in self-pollinated siliquas. Eleven races of L. crassa and three races of L. alabaimca are adapted to self-pollination and are described as self-compatible, although self-pollinations succeed 2% less frequently than cross-pollinations. Self-pollinated siliquas of these races contain an average of 12% fewer seeds than cross-pollinated siliquas; this is probably an expression of cryptic self-incompatibility and not the result of the exposure of seed lethals on inbreeding. There is, therefore, no absolute distinction between self-incompatibility and self-compatibility in Leavemcorthia. The growth of pollen tubes is compared in successful and unsuccessful pollinations of the same type, in self- and cross-pollinations of the same individuals, and in self-incompatible and self-compatible races. Pollen grains react with the stigma even in unsuccessful pollinations and some pollen grains are inhibited in successful pollinations. In both self-incompatible and self-compatible races, the average number of emptied pollen grains on the stigmata of successful pollinations (an estimate of the number of pollen tubes in the styles) is similar after self- and cross-pollinations. But the average number of emptied pollen grains is lower in self-incompatible races than in self-compatible races. The results are interpreted in terms of the response of pollen grains to an essential growth substance supplied by the stigma.

Six plants of a self-incompatible population ofLeavenworthia crassa were grown from seed collected in nature and cross-pollinated in all combinations. The incompatibility relationships between sibs were determined in eleven of the F1 families. A one-locus sporophytic incompatibility system was established. None of the parents was homozygous at the S locus. At least five, and possibly all six, of the parents did not share an S allele. Only one pair of alleles was shown to have different interactions in the pollen and stigmata. The identity and expression of the S alleles were determined in six families. Eight pairs of alleles were independently expressed in both the pollen grains and the stigmata. Sixteen pairs of alleles showed dominance of one allele over the other in the pollen grains or the stigmata or both.

A model is presented which expresses the seed production of dioecious and gynodioecious animal-pollinated Angiosperms in terms of the relative seed-fecundity of the sexes, the number of pollinator visits to each flower and the sex ratio. The model predicts that the maximum seed set occurs when females predominate, providing the pollinators visit each flower more than once and the seed set of males is not high. There is strong evidence that a marked preponderance of females in species of four genera is due to more frequent fertilisation by female-determining pollen nuclei than by male-determining nuclei. Two hypotheses have been proposed to explain this differential fertilisation. Several objections are raised to the hypothesis of Lewis (1942), Mulcahy (1967) and Kaplan (1972) that female-predominant sex ratios have been selected because they maximise the total seed production of populations. It is considered that the hypothesis of Smith (1963) that the differential fertilisation is a consequence of the genetic differentiation of sex chromosomes offers a more likely explanation of female-predominant sex ratios.

The genetic contributions of individual males and females in dioecious and gynodioecious angiosperms

Summary The distribution of male and female florets in heads of monoecious populations is represented by a curve joining points on a graph of percentage of female florets against rank in the same percentage. Comparison of curves for samples from different origins in Cotula minor and C. atrata subsp. atrata shows that sex expression is not greatly influenced by macro-environmental differences. Much of the total intra-population variation in sex expression appears in the heads collected at one time from a single plant. The rank-frequency curves show marked differences between species in the percentages of male and female florets. The average percentage of female florets in seventeen monoecious species is negatively correlated with the floret length, a measure of adaptation to outbreeding. In three species, the seed set and subsequent germination percentages are slightly lower after self-pollination than after cross-pollination. Self-fertilization probably occurs in varying degrees in the monoecious species. Monoecy has arisen independently in sections Leptinella and Strongylosperma.

Summary Five classes of sex expression are distinguished in Cotula on the basis of the degree of separation of male and female gametes on different flowers and plants. These classes are divided into sexually monomorphic and dimorphic systems. The order–monocliny, gynomonoecy, monoecy, subdioecy, dioecy–places the five classes in a linear sequence of increasing dependence for fertilization on the transfer of pollen between flowers and plants. Four of the five major taxonomic groups in Cotula and five species have more than one class of sex expression. The four monoecious and gynomonoecious species tested are self-compatible. The morphology of hermaphrodite, male and female florets are compared. Seven additional characters are associated with sex expression in New Zealand species. In general, the extent of protogyny, brightness of flowers, degree of retraction of stigmas and anthers, floret length, head diameter, peduncle length and the number of pollen grains increase from gynomonoecious through monoecious to dimorphic (dioecious or subdioecious) populations. But within each kind of sex expression there is considerable variation in these ancillary characters. A MAS (measurements associated with sex expression) index is calculated from the four quantitative characters for each New Zealand species (or part-species where there are two kinds of sex expression in a species). The MAS index reflects the expenditure of energy on adaptations to cross-pollination and provides an approximate measure of the relative frequency of outbreeding. The MAS indices of the species and part-species indicate a continuous array in the expression of adaptations to cross-pollination and the frequency of outbreeding. The different kinds of sex expression occupy characteristic but overlapping segments of this array and ought to be considered as convenient classes which only specify the breeding system approximately.

Summary The taxonomic position, status, and characters of Cotula, and its subdivision into three sections are briefly described. Section Leptinella is considered a well-defined taxon and its characters and relationships are discussed. Twenty-five species from New Zealand, the Subantarctic islands, and South America are described and classified into two series, Elongata and Radiata. The following new taxa and names are described: series Oligoleima (from Australia and New Guinea), Elongata and Radiata; five new species, C. dispersa, C. serrulata, C. calcarea, C. intermedia, and C. nana; two new names, C. albida and C. membranacea; five new combinations, C. rotundata, C. traillii subsp. pulchella, C. pectinata subsp. villosa, C. pectinata subsp. willcoxii, and C. pyrethrifolia var. linearifolia; four new subspecies, C. dispersa subsp. rupestris, C. dioica subsp. monoica, C. squalida subsp. mediana, and C. atrata subsp. luteola.

The following parameters affecting the frequency of male and female plants in sexually dimorphic Angiosperms are defined: relative fecundity (as seed parent), F, differential survival, S, and gamete success, G, all as male/female quotients, and the probability of fertilisation of ovules on female plants, in terms of the number of pollinator visits to the flowers, x. Four different modes of inheritance of gynodioecy and dioecy are examined: The equilibrium frequencies of females and (for three models) the rates of change in female frequency per generation at non-equilibrium frequencies are expressed in terms of the controlling parameters. The conditions necessary for sexual dimorphism and the changes in frequencies of the sex genotypes as the number of pollinator visits increase and the relative seed fecundity decreases towards zero (dioecy) are derived for each model. Differential survival of the sexes (and differential gamete success in the heterozygous male model) cause an increase at equilibrium in the sex surviving more frequently or the sex derived from the more successful gamete. In a dioecious population, the ratio of the sexes is equal to their relative survival or their relative gamete success. Populations at non-equilibrium frequencies return more rapidly to equilibrium with the heterozygous male model than with the heterozygous female and cytoplasmic models. In the extreme case when females are lost from a population, with the heterozygous female and cytoplasmic models extinction or loss of sexual dimorphism occurs, but with the heterozygous male and dual male models sexual dimorphism is regenerated. The ability of systems with heterozygous males to regenerate dimorphism may explain the prevalence of such systems in both gynodioecious and dioecious populations.

Many genera of Angiosperms contain closely related self-incompatible (si) and self-compatible (sc) taxa. In attempting to cross such taxa, it has often been found that the pollen of the self-incompatible plants grows successfully through the styles of the self-compatible plants, but the pollen tubes of the self-compatible plants are inhibited in the styles of the self-incompatible plants, in a manner similar to the self-incompatibility inhibition (Harrison and Darby, 1955; Lewis and Crowe, 1958). Several hypotheses have been proposed to account for the occurrence of "unilateral incompatibility" in some si x sc crosses and its absence from others. Lewis and Crowe (1958) pointed out that the exceptional self-compatible species whose pollen is not inhibited in self-incompatible styles are only recently derived from selfincompatible ancestors. They proposed that self-compatibility and unilateral incompatibility are due to changes in pollenstyle interactions resulting from mutations at the S locus. Anderson and de Winton (1931) and Pandey (1964) observed that pollen tubes of the self-compatible species Nicotiana langsdorfii were inhibited in styles of the self-incompatible species N. alata containing certain S alleles, but were not inhibited in styles containing other alleles. Pandey postulated that the two types of S alleles differ by a mutation at a sub-locus of the S locus. In contrast, Martin (1964) Grun and Aubertin (1966) and others, have found that the inheritance of unilateral incompatibility in their material is complex and conditioned by a