Selection with gene-cytoplasm interactions. I. Maintenance of cytoplasm polymorphisms

General conditions for the protectedness of gene-cytoplasm polymorphisms are considered for a biallelic model with two cytoplasm types and under the assumption that nuclear polymorphisms cannot be maintained in the presence of only one cytoplasm type. Analytical results involving male fertilities, female fertilities, viabilities and selfing rates are obtained, and numerical results show spiral and cyclic behavior of population trajectories. It is shown that a maternally inherited cytoplasmic polymorphism cannot be maintained in the absence of a nuclear polymorphism, and that a gene-cytoplasm polymorphism can only be maintained if the population shows sexual asymmetry, i.e. , if the ratio of male to female fertility varies among genotypes. Thus, the classical viability selection model does not allow gene-cytoplasm polymorphisms.     

Selection in plant populations of effectively infinite size. V. Biallelic models of trioecy

A one-locus two-allele model of trioecy (presence of hermaphrodites, males and females in one population) is considered, in order to study the conditions for the persistence of this system. All possible assignments of the three sex types to the three genotypes are considered. This leads to three different modes of inheritance of trioecy, namely (a) females heterozygous, (b) males heterozygous and (c) hermaphrodites heterozygous, where in each mode each of the remaining two sex types is homozygous for one of the alleles. For mode (c) trioecy is always persistent, and the dependence of the sex ratio (for the three sex types) on the ovule and pollen fertilities and on the hermaphrodite selfing rate is specified. For the other two modes, (a) and (b), trioecy is not protected, i.e., it may not persist for any fertilities, viabilities or selfing rates. Thus, in this situation it is important to study the conditions under which the "marginal" systems of sexuality of trioecy, i.e., hermaphroditism, dioecy and gynodioecy in mode (a), and hermaphroditism, dioecy and androdioecy in mode (b), may become established. The results show that each marginal system may evolve from each other via trioecy. The evolution of dioecy is easier in mode (a) than in (b), so that female heterogamety would be expected to occur more often than male heterogamety in the present model. Under some conditions the breeding system obtained in equilibrium populations may depend on the initial genotype frequencies.—The necessity of considering modes of inheritance for sexual polymorphisms is demonstrated by comparing our results with those obtained from an evolutionary stable strategy (ESS) analysis of a purely phenotypic model.     

Selection in plant populations of effectively infinite size: IV. The maintenance of males among hermaphrodites for a biallelic model

Conditions for the maintenance of males in androdioecious populations (populations with both male and hermaphrodite individuals) have been derived for four different one-locus two-allele models of inheritance of androdioecy. The results are not in general accordance with those already known: depending on the mode of inheritance, males can be maintained irrespective of their fertilities. If males are sufficiently fertile, it may happen that they are maintained only for intermediate selfing rates of the hermaphrodites. A result already found for gynodioecy is confirmed for androdioecy, namely, that a 11 sex ratio is immediately established among zygotes if hermaphrodites appear as heterozygotes only.     

The effect of positive assortative mating at one locus on a second linked locus

Summary Considerations proceed from a model of positive assortative mating based on genotype at one locus, with an arbitrary number of alleles, assuming no selection, mutation, or migration, hypothetically infinite population size, and discrete non-overlapping generations. From these conditions, inferences are made about the genotypic structure at a linked locus, as well as about the corresponding 2-locus gametic structure.The following main results are presented: in the course of the generations, the genotypic structure at the second locus and the 2-locus gametic structure always tend to a limit responsive to the initial conditions concerning the joint genotypic structure at the two loci and the degree of assortativity and linkage. A complete, analytical representation of the limits is given. In particular, if assortative mating is only partial and at the same time linkage is not complete, a population is not able to maintain a permanent deviation of the gametic structure from linkage equilibrium, and thus the genotypic structure at the second locus tends to Hardy-Weinberg proportions. On the other hand, if initial linkage disequilibrium is combined with partial assortative mating and complete linkage (or with complete assortative mating and unlinked loci) the population maintains this disequilibrium and thus the genotypic structure at the second locus need not tend to Hardy-Weinberg proportions. It turns out that the conditions not only of complete linkage, but also of unlinked loci together with complete assortativity, imply no change in gametic structure from the initial structure.In order to demonstrate the influence of several parameters on the speed of convergence to and the magnitude of the respective limits, several graphs are included.     

The effect of positive assortative mating at one locus on a second linked locus

Summary A model for positive assortative mating based on genotype for one locus is employed to investigate the effect of this mating system on the genotypic structure of a second linked locus as well as on the joint genotypic structure of these two loci. It is shown that the second locus does not attain a precise positive assortative mating structure, but yet it shares a property that is characteristic of positive assortative mating, namely an increase in the frequency of homozygotes over that typically found in panmictic structures. Given any arbitrary genotypic structure for the parental population, the resulting offspring generation possesses a structure at the second locus that does not depend on the recombination frequency, while the joint structure of course does. In case assortative mating as well as linkage are not complete, there exists a unique joint equilibrium state for the two loci, which is characterized by complete stochastic independence between the two loci as well as by Hardy-Weinberg proportions at the second locus. For the second locus alone, Hardy-Weinberg equilibrium is realized if and only if gametic linkage equilibrium and an additionally specified condition are realized.     

A model for genetic relationship in areally continuous plant populations

Representations are based on plant populations, continuously distributed over their habitats according to specified density patterns. Migration of genetic material takes place via pollen and seed dispersal. Monoecious plants with arbitrary rates of self-fertilization and dioecious plants are considered. The model was constructed with the intention of determining coefficients of inbreeding and kinship for all locations within the seed population after its dispersal over the habitat, assuming the respective genetic relationships of the parental generation to be known. To display the consequences of single components hidden in the general result, the following specifications have been treated: finite population size combined with random dispersal of seed, equilibrium states for hypothetically infinite population size with “limited” dispersal of pollen and seed, random dispersal of pollen, and random dispersal of seed.     

HER-2 DNA and protein vaccines containing potent Th cell epitopes induce distinct protective and therapeutic antitumor responses in HER-2 transgenic mice

Overexpression of the growth factor receptor HER-2 (c-erbB-2, neu) has transforming potential and occurs in approximately 20-30% of breast and ovarian cancers. HER-2 is a self Ag, but Abs and T cells specific for HER-2 have been isolated from cancer patients, suggesting HER-2 may be a good target for active immunotherapy. We constructed rat HER-2 DNA and protein vaccines containing potent Th cell epitopes derived from tetanus toxin and studied their potency in two strains of mice transgenic for the rat HER-2 molecule. Vaccination with HER-2 DNA protected nontransgenic mice from tumor challenge, but induced only moderate protection in one of the tumor models. However, vaccination with the modified HER-2 protein resulted in almost complete protection from tumor challenge in both tumor models. This protection could be mediated by Abs alone. In addition, protein vaccination efficiently eliminated pre-established tumors in both models, even when vaccination occurred 9 days after tumor implantation. These data demonstrate the potential of HER-2-based vaccines as therapeutic agents for the treatment of cancers overexpressing HER-2.     

The effect of genetic incompatibility of demes on total population development

The change of absolute deme frequencies in a discrete-time model of multiple, mutually genetically incompatible subpopulations (demes) which are still in mating contact has been studied. The attempt was made to answer the question of which initial conditions concerning deme frequencies lead to extinction or survival of certain demes. A complete answer could be given for the density-independent model and, with some restrictions, for a particular kind of density-dependent model assuming essentially complete niche overlap. For a more general model of density dependence, necessary initial conditions for deme extinction have been derived. Some implications for pest control have been briefly outlined.     

Selection in plant populations of effectively infinite size II. Protectedness of a biallelic polymorphism

The biologically important problem of protectedness of genetic polymorphisms in monoecious plant populations exhibiting genotypically determined variation in rates of self-fertilization and sexually asymmetrical fertilities has hitherto escaped exact, analytical treatment for the reason that appropriate mathematical techniques relying on allelic frequencies do not seem to exist. For the particular case of one locus and two alleles it was possible to develop such a technique which provides conditions of high precision for protectedness of an allele. A comparison of the results with those already known from models that appear to be specializations of the present model showed that some of the earlier conclusions can be generalized, while others have to be handled with great care or should even be rejected. Above all, this concerns the role of self-fertilization, which is frequently considered to counteract the establishment of genetic polymorphisms. However, it turned out that increasing the heterozygote selfing rate also increases protectedness for both alleles in all situations. Moreover, even if the amount of self-fertilization is the same for all genotypes, asymmetry in the production of ovules and pollen, which is more the rule than an exception, may imply protectedness only for comparatively large selfing rates. The probably most outstanding finding is that, depending on the ovule and pollen fertilities, protectedness may be realized only within small ranges of selfing rates, and these ranges may vary from arbitrarily low to arbitrarily high rates. On the other hand, if the ovule fertilities show strong overdominance for the heterozygote—more precisely, if the heterozygote produces more than twice as many ovules as either of the homozygotes—both alleles are protected irrespective of the pollen fertilities and rates of self-fertilization; this generalizes earlier results obtained for more specific models.     

Partitioning of trait variation among communities: measures of apportionment and differentiation based on binary sampling

The notion that trait variation is partitioned among communities essentially rests on the supposition that the total variation in the metacommunity exceeds the variation within the communities due to differences between their trait distributions (the partitioning principle). Two elementary perspectives of partitioning can be distinguished: apportionment (members of the same community tend to hold the same trait state) and differentiation (members of different communities tend to hold different trait states). While the apportionment perspective reaches its extreme when each community is monomorphic (fixation), the differentiation perspective does so if communities share no trait states. Even though both perspectives can be shown to be involved in the analysis of community dynamics, their assessment is still almost completely limited to the apportionment perspective (chiefly G _ST and its relatives). To overcome this limitation, methods of quantifying both partitioning perspectives are developed for qualitatively and quantitatively varying traits, where variation is represented by the differences in type resulting from sampling two individuals. It is shown that the validity of the partitioning principle and the design of corresponding measures crucially depend on proper specification of the modes of sampling and specification of differences between types that follow a concavity principle. This approach allows comparison between measures of apportionment and measures of differentiation. Such comparisons enable conclusions about the share that random (drift) and directional (selection, migration) processes have in the partitioning of variation among communities. One of the more far-reaching conclusions is that effects of forces apportioning variation outperform the effects of forces of differentiation, if the average similarity within communities exceeds the average difference between them.