Quantitative character dynamics: Gametic model

A gametic model of quantitative character dynamics is introduced that fills the gap between the two existing models: genic and zygotic/phenotypic. In this model, a gamete is treated as the elementary unit of evolution, all biological processes at the levels below gametic remain unspecified, and a gamete is characterized by its effect on the quantitative character rather than by the genotype. The hereditary and developmental processes are accounted for in a generalized form by gametogenetic and developmental functions defined for a pair of gametic effects representing an individual. A parameterization of these functions is suggested that imposes constraints on the heredity of quantitative characters similar to the constraints imposed by traditional genic models. It is shown that this parameterization can be derived for some polygenic additive models. General expressions for the dynamics of the mean and variance of additive quantitative characters are obtained, and the dynamics under random mating for sex-independent, sex-controlled, and sex-linked characters are considered. Comparisons with the dynamics predicted by genic models are made.     

Gamete types, sex determination and stable equilibria of all-hybrid populations of diploid and triploid edible frogs (Pelophylax esculentus)

Background  

Triploid individuals often play a key role in speciation by hybridization. An understanding of the gamete types (ploidy and genomic content) and stability of hybrid populations with triploid individuals is therefore of importance for exploring the role of hybridization in evolution. The all-hybrid populations of the edible frog, Pelophylax esculentus, are unique in their composition and genetic dynamics: Diploid (genotype LR) and triploid (LLR and LRR) hybrids depend on each other's different gamete contributions for successful reproduction and maintenance of the populations, as the parental genotypes P. lessonae (LL) and P. ridibundus (RR) are absent among adults. This study provides data and interpretations on gamete types and sex determination that are essential for understanding the function, evolutionary potential and threats of this intriguing system.     

Germline Selection: Population Genetic Aspects of the Sexual/Asexual Life Cycle

Population geneticists make a distinction between sexual and asexual organisms depending on whether individuals inherit genes from one or two parents. When individual genes are considered, this distinction becomes less satisfactory for multicellular sexual organisms. Individual genes pass through numerous asexual mitotic cell divisions in the germline prior to meiosis and sexual recombination. The processes of mitotic mutation, mitotic crossing over, and mitotic gene conversion create genotypic diversity between diploid cells in the germline. Genes expressed in the germline whose products affect cell viability (such as many "housekeeping" enzymes) may be subjected to natural selection acting on this variability resulting in a non-Mendelian output of gametes. Such genes will be governed by the population genetics of the sexual/asexual life cycle rather than the conventional sexual/Mendelian life cycle. A model is developed to investigate some properties of the sexual/asexual life cycle. When appropriate parameter values were included in the model, it was found that mutation rates per locus per gamete may vary by a factor of up to 100 if selection acts in the germline. Sexual/asexual populations appear able to evolve to a genotype of higher fitness despite intervening genotypes of lower fitness, reducing the problems of underdominance and Wright's adaptive landscape encountered by purely sexual populations. As might be expected this ability is chiefly determined by the number of asexual mitotic cell divisions within the germline. The evolutionary consequences of "housekeeping" loci being governed by the dynamics of the sexual/asexual life cycle are considered.     

A mixed polyploid model for linkage analysis in outcrossing tetraploids using a pseudo-test backcross design.

Based on how chromosomes pair at meiosis, the nature of polyploids can be described by bivalent polyploids, multivalent polyploids, and mixed polyploids. In bivalent polyploids, only two chromosomes pair, during which two more similar chromosomes have a higher pairing probability (preferential pairing) than two less similar chromosomes, whereas in multivalent polyploids more than two chromosomes pair at a time, which results in double reduction. Preferential chromosome pairings and double reduction affect the frequencies of gamete formation and, therefore, linkage analysis of polymorphic markers in bivalent and multivalent polyploids, respectively. For mixed polyploids, in which both bivalent and multivalent formations occur simultaneously, linkage analysis is affected by both preferential pairings and double reduction. In this study, we develop a hierarchical maximum likelihood model for discerning gamete genotypes derived from different pairing mechanisms and different formation modes. The first-stage model in the hierarchy is formulated to characterize the relative frequencies of bivalent and multivalent pairing configurations in terms of the preferential pairing factor. The second-stage model is derived to rule out identical gamete genotypes into their different formation modes with relative probabilities determined by the recombination fraction. The first-stage pairing mechanism and second-stage formation mode are integrated to provide the simultaneous maximum likelihood estimates of the preferential pairing factor, the frequency of double reduction, and the recombination fraction, by implementing the EM algorithm. We performed extensive simulation studies to demonstrate the statistical properties of our hierarchical model for linkage analysis in tetraploids. The implications of our model for polyploid linkage mapping are discussed.     

MHC-linked susceptibility to a bacterial infection, but no MHC-linked cryptic female choice in whitefish

Non-random gamete fusion is one of several potential cryptic female choice mechanisms that have been postulated and that may enhance the survival probability of the offspring. Previous studies have found that gamete fusion in mice is influenced by genes of the major histocompatibility complex (MHC) region. Here we test (i) whether there is MHC-dependent gamete fusion in whitefish (Coregonus sp.) and (ii) whether there is a link between the MHC and embryo susceptibility to an infection by the bacterium Pseudomonas fuorescens. We experimentally bred whitefish and reared sibships in several batches that either experienced or did not experience strong selection by P. fluorescens. We then determined the MHC class II B1 genotype of 1016 surviving larvae of several full sibships. We found no evidence for MHC-linked gamete fusion. However, in one of seven sibships we found a strong connection between the MHC class II genotype and embryo susceptibility to P. fluorescens. This connection was still significant after correcting for multiple testing. Hence, the MHC class II genotype can considerably influence embryo survival in whitefish, but gamete fusion seems to be random with respect to the MHC.     

Genetic demographic description of the Ust-Aldan rural population of Sakha Republic (Yakutia): migrations and marriage structure

Migrations, dynamics of the gametic structure of rural populations, and marriage structure with respect to birthplaces and inbreeding estimated from isonymy have been studied in the Ust-Aldan ulus (administrative district) of Sakha Republic (Yakutia). The villages studied (Byadi, Dyupsya, and Cheriktey) are characterized by intense migration; however, the migration radius is small (most migrations occur within the district). The rural populations studied differ in the intensities and directions of gamete flows and their dynamics. There is no substantial gamete flow into the Ust-Aldan population from outside Sakha Republic. About 50% of marriages contracted in this population are homolocal (between residents of the same district); the endogamy is low (15%). In most cases of heterolocal marriages (contracted between residents of different districts), one of the spouses is a local resident. The inbreeding estimated from isonymy is FTT = 0.002930 in Yakuts; it is mainly accounted for by the nonrandom component (FIS = 0.002232 and FST = 0.000700).     

完达山东部地区东北虎主要猎物种群的时空动态模拟

基于能体现直接与间接人为干扰的不同意外死亡率和环境容纳量情景,使用景观尺度的动物种群模型（LAPS）模拟了1990—2009年完达山东部地区东北虎主要猎物种群的时空动态,研究了意外死亡率和环境容纳量对种群动态的影响,并直观展现了研究区内动物集群的时空分布状况,比较了不同生境斑块类型中个体密度的差异.结果表明：意外死亡率对研究区动物种群动态的影响较环境容纳量大;灌丛中动物种群的密度高于阔叶林中的密度.研究结果为有效进行东北虎主要猎物的保护与管理提供了科学依据,但相关的定量验证还需深入研究.     

Covariances between Arbitrary Relatives in Autotetraploids with Panmictic Disequilibrium

In random mating autopolyploid populations which have not reached equilibrium, two alleles may be interdependent as a result of the phenomenon of gametic recombination, i.e. the maintenance through successive gamete generations of an association of two alleles from the same gamete in a source reference generation. Any two alleles are dependent by this relationship if they derive by descent from the same ancestral gamete in the source population. Applied with the classical notion of identity by descent, the concept thus defined identifies new coefficients of dependence between arbitrary relatives. Coefficients of dependence are probabilities attached to the drawing of genes from two zygotes such that there are certain relationships amongst them. Applying the concept to autotetraploids, consideration of the states of dependence between the genes of a zygote or of a pair of zygotes leads to the definition of new parameters bearing on population means, variances and covariances, for arbitrary inbreeding. The absence of epistasis is supposed. Some applications of interest in artificial selection are briefly envisaged, with simplifying restrictions on genetic effects. The particular case of diallelism is also considered.     

The spread of infectious diseases in spatially structured populations: an invasory pair approximation

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.     

Genetic Demographic Description of the Ust-Aldan Rural Population of Sakha Republic (Yakutia): Migrations and Marriage Structure

Migrations, dynamics of the gametic structure of rural populations, and marriage structure with respect to birthplaces and inbreeding estimated from isonymy have been studied in the Ust-Aldan ulus (administrative district) of Sakha Republic (Yakutia). The villages studied (Byadi, Dyupsya, and Cheriktey) are characterized by intense migration; however, the migration radius is small (most migrations occur within the district). The rural populations studied differ in the intensities and directions of gamete flows and their dynamics. There is no substantial gamete flow into the Ust-Aldan population from outside Sakha Republic. About 50% of marriages contracted in this population are homolocal (between residents of the same district); the endogamy is low (15%). In most cases of heterolocal marriages (contracted between residents of different districts), one of the spouses is a local resident. The inbreeding estimated from isonymy is F _IT = 0.002930 in Yakuts; it is mainly accounted for by the nonrandom component (F _IS = 0.002232 and F _ST = 0.000700).     

Efficiency of gamete usage in nature: sperm storage, fertilization and polyspermy

Gamete production for both males and females can be energetically expensive such that selection should maximize fertilization opportunities while minimizing fertilization costs. In laboratory studies of Drosophila reproduction, however, the failure of eggs to yield adult progeny can be quite high, suggesting that female control over gamete utilization is surprisingly inefficient. We examined gamete utilization in D. pseudoobscura from nature and compared our observations to those for laboratory populations. In natural populations 100% of oviposited eggs effectively produce adult progeny, and fertilization is exclusively monospermic, indicating that in nature, D. pseudoobscura females maintain a very strict control over their reproduction such that gamete usage is extremely efficient. The potential reasons for the inefficient gamete utilization in the laboratory, as well as the potential impact on laboratory studies of sperm competition, sexual conflict, and the evolution of reproductive barriers are discussed. Furthermore, in this sperm-heteromorphic species, our observations show definitively that in nature, as well as in the laboratory, only the long sperm morph participates in fertilization.     

Note on the effects of maternal selection in biological populations

The dynamics of the genetic structure of populations under various selection factors are considered. The effect of selection by way of the maternal genotype through fecundity, favorable placement of eggs and such factors as are dependent on the character of the maternal parent is emphasized. This factor can lead to a stable equilibrium with genotype frequencies which would appear to be unstable. A similar result can be obtained as a result of differences in mating probabilities which may arise due to differences in maturation rates. A number of cases are treated to illustrate the dynamics as well as conditions for stable equilibrium.     

Allelopathy of bacteria in a lattice population: Competition between colicin-sensitive and colicin-producing strains

We analyse the population dynamics of two strains of bacteria (Escherichia coli): one strain produces a toxin (called colicin) that increases the mortality of a colicin-sensitive strain in the neighbourhood, but does not harm the colicin-producing strain itself. On the other hand, in the absence of colicin in the environment, the colicin-sensitive strain enjoys a higher population growth rate. The model is closely related to the evolutionary dynamics of social interaction. It has been established previously that a perfectly mixing population shows bistability; that is, whichever strain dominates initially tends to defeat the other. On the other hand, empirical and computer simulation results in lattice structured populations show neither co-existence nor bistability of the two strains. In this paper, we analyse the lattice model based on pair approximation (forming a system of ordinary differential equations of global densities and local densities), and by the direct c omputer simulation of the spatial stochastic model. Both the pair approximation dynamics and the computer simulation show that, for most regions of parameter values, one strain defeats the other, irrespective of the initial abundance. However, the pair approximation analysis also suggests a relatively narrow parameter region of bistability, which should disappear when the model is considered on a lattice of infinitely large size. The biological implications of the results and the relationship of the present model with other models of the evolution of spite or altruistic behaviours are discussed. This suggests that the dynamics reflected by the spatially explicit lattice model may be sufficient, perhaps even necessary, to support the evolution of colicin.     

Sexual selection at the protein level drives the extraordinary divergence of sex-related genes during sympatric speciation

An increasing number of molecular studies are indicating that, in a wide variety of species, genes directly related to fertilization evolve at extraordinarily high rates. We try to gain insight into the dynamics of this rapid evolution and its underlying mechanisms by means of a simple theoretical model. In the model, sexual selection and sympatric speciation act together in order to drive rapid divergence of gamete recognition proteins. In this process, intraspecific competition for fertilizations enlarges male gamete protein variation by means of evolutionary branching, which initiates sympatric speciation. In addition, avoidance of competition for fertilizations between the incipient species drives the rapid evolution of gamete recognition proteins. This mechanism can account for both strong stabilizing selection on gamete recognition proteins within species and rapid divergence between species. Moreover, it can explain the empirical finding that the rate of divergence of fertilization genes is not constant, but highest between closely related species.     

Parthenogenetic female populations in the brown alga Scytosiphon lomentaria (Scytosiphonaceae,Ectocarpales): decay of a sexual trait and acquisition of asexual traits

In isogamous brown algae, the sexuality of populations needs to be tested by laboratory crossing experiments, as the sexes of gametophytes are morphologically indistinguishable. In some cases, gamete fusion is not observed and the precise reproductive mode of the populations is unknown. In the isogamous brown alga Scytosiphon lomentaria in Japan, both asexual (gamete fusion is unobservable) and sexual populations (gamete fusion is observable) have been reported. In order to elucidate the reproductive mode of asexual populations in this species, we used PCR‐based sex markers to investigate the sex ratio of three asexual and two sexual field populations. The markers indicated that the asexual populations consisted only of female individuals, whereas sexual populations are composed of both males and females. In culture, female gametes of most strains from asexual populations were able to fuse with male gametes; however, they had little to no detectable sexual pheromones, significantly larger cell sizes, and more rapid parthenogenetic development compared to female/male gametes from sexual populations. Investigations of sporophytic stages in the field indicated that alternation of gametophytic and parthenosporophytic stages occur in an asexual population. These results indicate that the S. lomentaria asexual populations are female populations that lack sexual reproduction and reproduce parthenogenetically. It is likely that females in the asexual populations have reduced a sexual trait (pheromone production) and have acquired asexual traits (larger gamete sizes and rapid parthenogenetic development).     

The Relationship between Host Lifespan and Pathogen Reservoir Potential: An Analysis in the System Arabidopsis thaliana-Cucumber mosaic virus

Identification of the determinants of pathogen reservoir potential is central to understand disease emergence. It has been proposed that host lifespan is one such determinant: short-lived hosts will invest less in costly defenses against pathogens, so that they will be more susceptible to infection, more competent as sources of infection and/or will sustain larger vector populations, thus being effective reservoirs for the infection of long-lived hosts. This hypothesis is sustained by analyses of different hosts of multihost pathogens, but not of different genotypes of the same host species. Here we examined this hypothesis by comparing two genotypes of the plant Arabidopsis thaliana that differ largely both in life-span and in tolerance to its natural pathogen Cucumber mosaic virus (CMV). Experiments with the aphid vector Myzus persicae showed that both genotypes were similarly competent as sources for virus transmission, but the short-lived genotype was more susceptible to infection and was able to sustain larger vector populations. To explore how differences in defense against CMV and its vector relate to reservoir potential, we developed a model that was run for a set of experimentally-determined parameters, and for a realistic range of host plant and vector population densities. Model simulations showed that the less efficient defenses of the short-lived genotype resulted in higher reservoir potential, which in heterogeneous host populations may be balanced by the longer infectious period of the long-lived genotype. This balance was modulated by the demography of both host and vector populations, and by the genetic composition of the host population. Thus, within-species genetic diversity for lifespan and defenses against pathogens will result in polymorphisms for pathogen reservoir potential, which will condition within-population infection dynamics. These results are relevant for a better understanding of host-pathogen co-evolution, and of the dynamics of pathogen emergence.     

Selection for high gamete encounter rates explains the success of male and female mating types

Sexual reproduction occurs in many small eukaryotes by fusion of similar gametes (isogamy). In the absence of distinguishable sperm and eggs, male and female mating types are missing. However, species with distinct males and females have so prospered that almost all familiar plants and animals have these mating types. Why has sexual reproduction involving sperm and eggs been so successful? An answer is obtained by considering physical limitations on encounter rates between gametes. A biophysical model based on well-established relationships produces fitness landscapes for the evolution of gamete size and energy allocation between motility and pheromone production. These landscapes demonstrate that selection for high gamete encounter rates favors large, pheromone-producing eggs and small, motile sperm. Thus, broadcast-spawning populations with males and females can reproduce at lower population densities and survive under conditions where populations lacking males and females go extinct. It appears that physical constraints on gamete encounter rates are sufficient to explain the first two steps in the isogamy-->anisogamy-->oogamy-->internal fertilization evolutionary sequence observed in several lineages of the eukaryotes. Unlike previous models, assumptions concerning zygote fitness or decreasing speed of swimming with increasing gamete size are not required.     

Dynamics of a Lactate Dehydrogenase Polymorphism in the Wood Louse PORCELLIO SCABER Latr.: Evidence for Partial Assortative Mating and Heterosis in Natural Populations

Electrophoretic separation of lactate dehydrogenase (LDH) of Porcellio scaber from 14 natural populations in California, and one each in Oregon, Delaware and Massachusetts, indicates a biallelic polymorphism. Phenotypes are recovered from laboratory matings of virgin females in frequencies agreeing with simple Mendelian inheritance, and the frequency distributions of phenotypes in natural populations are typically in agreement with the appropriate Hardy-Weinberg distributions for these same populations. The same allele predominates in all natural populations examined. Temporal stability within populations suggests that the polymorphism is at, or near, equilibrium. The spatial distribution of allele frequencies, however, is apparently mosaic. Abrupt discontinuities in gene frequency over short distances (50 m to 1 km) suggest that interpopulation migration is insufficient to swamp local differences in gene frequency. Analysis of the transmission dynamics of the polymorphism in natural populations using mother-offspring genotype comparisons suggests that the allelic frequencies of transmitted male gametes are not independent of female genotype. Specifically, the observed mating scheme in natural populations appears to be partially assortative. Comparisons of progeny genotype distributions with yearling (or adult) genotype distributions from the same populations indicate a superior post-partum viability of heterozygous individuals relative to homozygotes. The distortion of progeny genotypic distributions created by assortment is thus apparently counteracted by subsequent heterosis.     

The coevolution of long‐term pair bonds and cooperation

The evolution of social traits may not only depend on but also change the social structure of the population. In particular, the evolution of pairwise cooperation, such as biparental care, depends on the pair‐matching distribution of the population, and the latter often emerges as a collective outcome of individual pair‐bonding traits, which are also under selection. Here, we develop an analytical model and individual‐based simulations to study the coevolution of long‐term pair bonds and cooperation in parental care, where partners play a Snowdrift game in each breeding season. We illustrate that long‐term pair bonds may coevolve with cooperation when bonding cost is below a threshold. As long‐term pair bonds lead to assortative interactions through pair‐matching dynamics, they may promote the prevalence of cooperation. In addition to the pay‐off matrix of a single game, the evolutionarily stable equilibrium also depends on bonding cost and accidental divorce rate, and it is determined by a form of balancing selection because the benefit from pair‐bond maintenance diminishes as the frequency of cooperators increases. Our findings highlight the importance of ecological factors affecting social bonding cost and stability in understanding the coevolution of social behaviour and social structures, which may lead to the diversity of biological social systems.     

SEXUAL REPRODUCTION IN NAVICULA CRYPTOCEPHALA (BACILLARIOPHYCEAE)1

Homothallic sexual reproduction and auxosporulation were studied in monoclonal cultures and seminatural populations of the freshwater epipelic diatom Navicula cryptocephala Kütz. Gametangia paired via the girdle, one gamete was formed per gametangium (and hence one zygote per pair of gametangia), and gamete fusion took place without the formation of any copulation envelope or copulation canal. Superfluous nuclei from meiosis survived unusually long, so that gametes and young zygotes were probably functionally polyploid; later, all but two haploid nuclei degenerated. Expanded auxospores had a swollen center, but during formation of the initial valves, the auxospore contracted away from the perizonium to produce linear‐lanceolate valves. The pattern of reproductive behavior found in N. cryptocephala can be classified as type IIA2a auxosporulation in Geitler's system. The same type of zygote and auxospore formation seen in clonal cultures was observed in seminatural material from four lakes in Scotland and the Czech Republic. Variation in nuclear structure and auxosporulation in the N. cryptocephala species complex is discussed, as is the evolution of type II auxosporulation (one zygote per pair of gametangia) from type I auxosporulation (two zygotes per pair). The penalty of smaller numbers of zygote produced in type II may be outweighed by formation of larger auxospores (prolonging the vegetative phase) or more vigorous auxospores. The variation present among members of the N. cryptocephala complex indicates that biogeographical analyses based on use of the name N. cryptocephala, as performed recently to support the ubiquity hypothesis of protist distributions, are almost meaningless.