Global analysis of a two-allele mating system

The global analysis of a two-allele mating system is provided. One allele is dominant to the other. Mating is random, but mating between unlike phenotypes has a lower fertility than that between like phenotypes. The generations are discrete and non-overlapping. The population is considered to be infinite, and the model is deterministic. There are three equilibria of the difference equations. Two of the equilibria are the (two) homozygous states, and these are asymptotically stable. The third equilibrium is polymorphic but is unstable. It is proven that almost all populations converge to one of the two homozygous states. The remaining populations converge to the unstable equilibrium, and lie on a curve that separates the basins of attraction for the other two equilibria. This curve is shown to satisfy some simple properties.     

Regular systems of inbreeding

Regular systems of inbreeding with discrete, nonoverlapping generations and the same number of individuals and mating pattern in every generation are studied. The matrix Q that specifies the recursion relations satisfied by the probabilities of identity is expressed in terms of the matrix M that describes the mating system. Necessary and sufficient conditions for convergence to genetic uniformity are given, and it is determined which probabilities of identity approach one. If the mating system has certain symmetries and these are imposed initially, then a matrix R, of lower dimension than Q, specifies the recursion relations. For such a mating system, for generic initial conditions, the condensed matrix R suffices for determining whether convergence to uniformity occurs and which probabilities of identity approach one. If Q is irreducible, the maximal eigenvalue of R is the same as that of Q. If Q is also aperiodic, this implies that the asymptotic rate of convergence to homogeneity of the condensed system is the same as that of the complete one. The above results apply to autosomal loci in monoecious (with or without selfing) and dioecious populations and to X-linked loci. As an example, all the eigenvalues and right and left eigenvectors of Q for circular mating are found.Supported by National Science Foundation Grant BSR-8512844     

A genetic perspective on mating systems and sex ratios of parasitoid wasps

Parasitoid sex ratios are influenced by mating systems, whether complete inbreeding, partial inbreeding, complete inbreeding avoidance, or production of all-male broods by unmated females. Population genetic theory demonstrates that inbreeding is possible in haplodiploids because the purging of deleterious and lethal mutations through haploid males reduces inbreeding depression. However, this purging does not act quickly for deleterious mutations or female-limited traits (e.g., fecundity, host searching, sex ratio). The relationship between sex ratio, inbreeding, and inbreeding depression has not been explored in depth in parasitoids. The gregarious egg parasitoid, Trichogramma pretiosum Riley, collected from Riverside, CA (USA) produced a female-biased sex ratio of 0.24 (proportion of males). Six generations of sibling mating in the laboratory uncovered considerable inbreeding depression (∼ 20%) in fecundity and sex ratio. A population genetic study (based upon allozymes) showed the population was inbred (F _it = 0.246), which corresponds to 56.6% sib-mating. However, average relatedness among females emerging from the same host egg was only 0.646, which is less than expected (0.75) if ovipositing females mate randomly. This lower relatedness could arise from inbreeding avoidance, multiple mating by females, or superparasitism. A review of the literature in general shows relatively low inbreeding depression in haplodiploid species, but indicates that inbreeding depression can be as high as that found in Drosophila. Finally, mating systems and inbreeding depression are thought to evolve in concert (in plants), but similar dynamic models of the joint evolution of sex ratio, mating systems, and inbreeding depression have not been developed for parasitoid wasps. Received: November 13, 1998 /Accepted: January 8, 1999     

Incorporating mating preferences into a host-parasite model

Mating preferences are incorporated into a host-macroparasite system. Mating preferences of the host and/or parasite can affect the outcome of the host-parasite relationship if certain genotypes of the host are more (or less) affected by the parasite induced death rate than others. Several examples illustrate the situations that can occur.     

Complete chaos in a simple epidemiological model

A first-order difference equation which constitutes a simple model for a lethal parasite-host interaction is studied. Completing a study initiated by May and Anderson, the dynamics are shown to be completely chaotic.     

Coexistence for systems governed by difference equations of Lotka-Volterra type

The question of the long term survival of species in models governed by Lotka-Volterra difference equations is considered. The criterion used is the biologically realistic one of permanence, that is populations with all initial values positive must eventually all become greater than some fixed positive number. We show that in spite of the complex dynamics associated even with the simplest of such systems, it is possible to obtain readily applicable criteria for permanence in a wide range of cases.     

一阶泛函差分方程解振动的充分和必要条件

得到具有多个时滞的差分方程：An l-An m^∑i=1piAn-ki=0解振动的充分和必要条件,这里pi全是正数,ki是正整数,i=1,2,3,…,m,(或pi是负数,ki是负整数)。     

Host mating system and the spread of a disease-resistant allele in a population

The model presented here modifies a susceptible-infected (SI) host–pathogen model to determine the influence of mating system on the outcome of a host–pathogen interaction. Both deterministic and stochastic (individual-based) versions of the model were used. This model considers the potential consequences of varying mating systems on the rate of spread of both the pathogen and resistance alleles within the population. We assumed that a single allele for disease resistance was sufficient to confer complete resistance in an individual, and that both homozygote and heterozygote resistant individuals had the same mean birth and death rates. When disease invaded a population with only an initial small fraction of resistant genes, inbreeding (selfing) tended to increase the probability that the disease would soon be eliminated from a small population rather than become endemic, while outcrossing greatly increased the probability that the population would become extinct due to the disease.     

Inbreeding depression and mixed mating in Leptosiphon jepsonii: a comparison of three populations

BACKGROUND AND AIMS: Inbreeding depression is thought to play a central role in the evolution and maintenance of cross-fertilization. Theory indicates that inbreeding depression can be purged with self-fertilization, resulting in positive feedback for the selection of selfing. Variation among populations of Leptosiphon jepsonii in the timing and rate of self-fertilization provides an opportunity to study the evolution of inbreeding depression and mating systems. In addition, the hypothesis that differences in inbreeding depression for male and female fitness can stabilize mixed mating in L. jepsonii is tested. METHODS: In a growth room experiment, inbreeding depression was measured in three populations with mean outcrossing rates ranging from 0.06 to 0.69. The performance of selfed and outcrossed progeny is compared at five life history stages. To distinguish between self-incompatibility and early inbreeding depression, aborted seeds and unfertilized ovules were counted in selfed and outcrossed fruits. In one population, pollen and ovule production was quantified to estimate inbreeding depression for male and female fitness. KEY RESULTS: Both prezygotic barriers and inbreeding depression limited self seed set in the most outcrossing population. Cumulative inbreeding depression ranged from 0.297 to 0.501, with the lowest value found in the most selfing population. Significant inbreeding depression for early life stages was found only in the more outcrossing populations. Inbreeding depression was not significant for pollen or ovule production. CONCLUSIONS: The results provide modest support for the hypothesized relationship between inbreeding depression and mating systems. The absence of early inbreeding depression in the more selfing populations is consistent with theory on purging. Differences in male and female expression of inbreeding depression do not appear to stabilize mixed mating in L. jepsonii. The current estimates of inbreeding depression for L. jepsonii differ from those of previous studies, underscoring the effects of environmental variation on its expression.     

Actin in mating structures of Chlamydomonas eugametos gametes

The presence of actin in Chlamydomonas eugametos mating structures was studied using monoclonal anti-actin antibodies. Immunofluorescent labelling of mating gametes clearly stained their mating structures and this was confirmed at the electron microscope level by immunogold labelling of sections. Anti-actin labelling also strongly stained the flagella at the flagellar collar regions and weakly stained the rest of the flagella. Treatment of gametes with 6–8% ethanol induced mating structures which protruded as large 'balloons'. Balloons stained brilliantly with anti-actin antibodies and weakly with FITC-phalloidin, a fluorescent reagent that stains F-actin. Isolated mating structure balloons and flagella were analyzed using western blotting. A prominent 43 kDa band, co-migrating with actin in erythrocyte ghosts, reacted with anti-actin antibodies. The results indicate that actin is present in mating structures and flagella of both mating types of C, eugametos .     

Positive assortative mating with selection restrictions on group coancestry enhances gain while conserving genetic diversity in long-term forest tree breeding

Selection and mating principles in a closed breeding population (BP) were studied by computer simulation. The BP was advanced, either by random assortment of mates (RAM), or by positive assortative mating (PAM). Selection was done with high precision using clonal testing. Selection considered both genetic gain and gene diversity by "group-merit selection", i.e. selection for breeding value weighted by group coancestry of the selected individuals. A range of weights on group coancestry was applied during selection to vary parent contributions and thereby adjust the balance between gain and diversity. This resulted in a series of scenarios with low to high effective population sizes measured by status effective number. Production populations (PP) were selected only for gain, as a subset of the BP. PAM improved gain in the PP substantially, by increasing the additive variance (i.e. the gain potential) of the BP. This effect was more pronounced under restricted selection when parent contributions to the next generation were more balanced with within-family selection as the extreme, i.e. when a higher status effective number was maintained in the BP. In that case, the additional gain over the BP mean for the clone PP and seed PPs was 32 and 84% higher, respectively, for PAM than for RAM in generation 5. PAM did not reduce gene diversity of the BP but increased inbreeding, and in that way caused a departure from Hardy-Weinberg equilibrium. The effect of inbreeding was eliminated by recombination during the production of seed orchard progeny. Also, for a given level of inbreeding in the seed orchard progeny or in a mixture of genotypes selected for clonal deployment, gain was higher for PAM than for RAM. After including inbreeding depression in the simulation, inbreeding was counteracted by selection, and the enhancement of PAM on production population gain was slightly reduced. In the presence of inbreeding depression the greatest PP gain was achieved at still higher levels of status effective number, i.e. when more gene diversity was conserved in the BP. Thus, the combination of precise selection and PAM resulted in close to maximal short-term PP gain, while conserving maximal gene diversity in the BP.Communicated by O. Savolainen     

Simulation modeling of ligand receptor interactions at non-equilibrium conditions: processing of noisy inputs by ionotropic receptors

The first event in signal transduction at a synapse is the binding of transmitters to receptors. Because of rapidly changing transmitter levels this binding is unlikely to occur at equilibrium. We describe a mathematical approach that models complex receptor interactions in which the timing and amplitude of transmitter release are noisy. We show that exact solutions for simple bimolecular interactions and receptor transitions can be used to model complex reaction schemes by expressing them in sets of difference equations. Results from the difference equation method to describe binding and channel opening at extended time points compare well with standard solutions using ordinary differential equations. Because it is applicable to noisy systems we used the difference method to investigate the information processing capabilities of GABA receptors and predict how pharmacological agents may modify these properties. As previously demonstrated, the response to a single pulse of GABA is prolonged through entry into a desensitized state. During trains of stimuli the signal to noise ratio can change, and even increase progressively, but the overall transmitted fidelity of the signal decreases with increased driving frequency. The GABA modulator chlorpromazine (primarily affects agonist on and off rates) is predicated to increase receptor signal to noise ratio at all frequencies whereas pregnenolone sulfate (affects receptor desensitization) completely inhibits information transfer.     

Ecological balance in the native population dynamics may cause the paradox of pest control with harvesting

We analyze a time-discrete mathematical model of host-parasite population dynamics with harvesting, in which the host can be regarded as a pest. We harvest a portion of the host population at a moment in each parasitism season. The principal target of the harvesting is the host; however, the parasite population may also be affected and reduced by a portion. Our model involves the Beverton-Holt type density effect on the host population. We investigate the condition in which the harvesting of the host results in an eventual increase of its equilibrium population size, analytically proving that the paradoxical increase could occur even when the harvesting does not directly affect the parasite population at all. We show that the paradox of pest control could be caused essentially by the interspecific relationship and the intraspecific density effect.     

Evolution of disassortative and assortative mating preferences based on imprinting

A two-locus haploid model of sexual selection is investigated to explore evolution of disassortative and assortative mating preferences based on imprinting. In this model, individuals imprint on a genetically transmitted trait during early ontogeny and choosy females later use those parental images as a criterion of mate choice. It is assumed that the presence or absence of the female preference is determined by a genetic locus. In order to incorporate such mechanisms as inbreeding depression and heterozygous advantage into our haploid framework, we assume that same-type matings are less fertile than different-type mating. The model suggests that: if all the females have a disassortative mating preference a viability-reducing trait may be maintained even without the fertility cost of same-type matings; a disassortative mating preference can be established even if it is initially rare, when there is a fertility cost of same-type matings. Further, an assortative mating preference is less likely to evolve than a disassortative mating preference. The model may be applicable to the evolution of MHC-disassortative mating preferences documented in house mice and humans.     

Persistence of species obeying difference equations

The question of persistence of interacting species is one of the most important in theoretical ecology; when the system is governed by difference equations this question is particularly difficult to resolve because of the complicated dynamics of the model. The problem has usually been tackled via the concepts of asymptotic stability and global asymptotic stability, however the first is not a strong enough restriction since only orbits starting near a rest point are guaranteed to converge to the rest point, while the second as well as usually being extremely difficult to establish is surely too strong a condition, since it rules out for example a stable limit cycle. It is proposed here that a more biologically realistic criterion, and incidentally one which turns out to be more tractable, is that of cooperativeness, where all orbits are required eventually to enter and remain in a region at a non-zero distance from the boundary (corresponding to a zero value of at least one population). A theorem is proved giving conditions for cooperativeness, and is applied to some examples of predator-prey interactions, simple conditions on the parameters being obtained even for some ranges of the parameters where the dynamics are chaotic.     

A schistosomiasis model with mating structure and time delay

A system of homogeneous equations with a time delay is used to model the population dynamics of schistosomes. The model includes the parasite’s mating structure, multiple resistant schistosome strains, and biological complexity associated with the parasite’s life cycle. Invasion criteria of resistant strains and coexistence threshold conditions are derived. These results are used to explore the impact of drug treatment on resistant strain survival. Numerical simulations indicate that the dynamical behaviors of the current model are not qualitatively different from those derived from an earlier model that ignores the impact of time delays associated with the multiple stages in parasite’s life cycle. However, quantitatively the time delays make it more likely for drug-resistant strains to invade in a parasite population.     

含阻尼项二阶泛函差分方程的振动性质

从解的渐近状态入手,应用分类讨论方法和Raccati技巧,讨论了一类广泛的二阶泛函差分方程解的振动性与非振动性,建立了四个新的振动性定理,推广并改进了已有文献中的相关结果.     

Expression of VirB2 protein-containing structures on Agrobacterium in mating cultures

Exocellular structures containing VirB2 proteins were, for the first time, localized on the surface of Agrobacterium by transmission electron microscopy. Using colloidal gold (CG)-labeled VirB2-specific antibodies, it was shown that VirB2 proteins enter into the composition of short surface pili, which emerge at the poles of acetosyringone (AS)-induced Agrobacterium cells. However, cells of the Ti plasmidless A. tumefaciens strain UBAPF-2 and cells not induced with AS were incapable of pilus synthesis. In suspension, mating Agrobacterium cells were connected together by short thick bridges. It was found that these bridges did not include as part of their structure CG-labeled VirB1 and VirB2 proteins. We did not find the tetracycline-resistant transconjugants after mating of A. tumefaciens donor cells harboring binary systems with plasmid-free A. tumefaciens GM-I 9023 in vir-induced and vir-uninduced conditions. However, the same strains can transfer pSUP106 plasmid via a vir-dependent way. We found that activated vir genes slightly stimulate pTd33 plasmid transfer via a tra-dependent pathway to plasmid-free strain UBAPF-2. It seems, that vir-induced T-DNA/plasmid DNA transfer machinery is not essential for the conjugation process between agrobacterial cells but may participate in this process.     

Testing Mendelian inheritance from field-collected parasites: Revealing duplicated loci enables correct inference of reproductive mode and mating system

Cryptic aspects of parasite population biology, e.g., mating systems, are increasingly being inferred from polymorphic and co-dominant genetic markers such as microsatellite loci. Underlying the use of such co-dominant markers is the assumption of Mendelian inheritance. The failure to meet this assumption can lead to artifactual statistics and erroneous population inferences. Here, we illustrate the importance of testing the Mendelian segregation and assortment of genetic markers and demonstrate how field-collected samples can be utilised for this purpose. To examine the reproductive mode and mating system of hermaphroditic parasites, we developed microsatellites for the cestode, Oochoristica javaensis. Among loci, we found a bimodal distribution of F_IS (a fixation index that quantifies the deviation from Hardy–Weinberg equilibrium within subpopulations) values where loci were either highly negative (close to −1) or highly positive (∼0.8). By conducting tests of Mendelian segregation from natural crosses, we determined that loci with negative F_IS values were in fact duplicated loci that were amplified by a single primer pair. Genetic crosses also provided linkage data and indicated that the duplicated loci most likely arose via tandem duplications rather than whole genome/chromosome duplications. By correcting for the duplicated loci, we were able to correctly infer that O. javaensis has sexual reproduction, but the mating system is highly inbred. To assist others in testing Mendelian segregation and independent assortment from natural samples, we discuss the benefits and limitations, and provide guidelines for particular parasite systems amenable to the methods employed here.     

Calculation of the inbreeding coefficient

Wright's rule for calculating the inbreeding coefficient for an arbitrary pedigree is proven for both autosomal and X-linked loci.Supported by NSF Grant PHY-84-16691