An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distribution

A large offspring-number diploid biparental multilocus population model of Moran type is our object of study. At each time step, a pair of diploid individuals drawn uniformly at random contributes offspring to the population. The number of offspring can be large relative to the total population size. Similar “heavily skewed” reproduction mechanisms have been recently considered by various authors (cf. e.g., Eldon and Wakeley 2006, 2008) and reviewed by Hedgecock and Pudovkin (2011). Each diploid parental individual contributes exactly one chromosome to each diploid offspring, and hence ancestral lineages can coalesce only when in distinct individuals. A separation-of-timescales phenomenon is thus observed. A result of Möhle (1998) is extended to obtain convergence of the ancestral process to an ancestral recombination graph necessarily admitting simultaneous multiple mergers of ancestral lineages. The usual ancestral recombination graph is obtained as a special case of our model when the parents contribute only one offspring to the population each time. Due to diploidy and large offspring numbers, novel effects appear. For example, the marginal genealogy at each locus admits simultaneous multiple mergers in up to four groups, and different loci remain substantially correlated even as the recombination rate grows large. Thus, genealogies for loci far apart on the same chromosome remain correlated. Correlation in coalescence times for two loci is derived and shown to be a function of the coalescence parameters of our model. Extending the observations by Eldon and Wakeley (2008), predictions of linkage disequilibrium are shown to be functions of the reproduction parameters of our model, in addition to the recombination rate. Correlations in ratios of coalescence times between loci can be high, even when the recombination rate is high and sample size is large, in large offspring-number populations, as suggested by simulations, hinting at how to distinguish between different population models.     

Multiple merger gene genealogies in two species: Monophyly, paraphyly, and polyphyly for two examples of Lambda coalescents

Probabilities of monophyly, paraphyly, and polyphyly of two-species gene genealogies are computed for modest sample sizes and compared for two different Λ coalescent processes. Coalescent processes belonging to the Λ coalescent family admit asynchronous multiple mergers of active ancestral lineages. Assigning a timescale to the time of divergence becomes a central issue when different populations have different coalescent processes running on different timescales. Clade probabilities in single populations are also computed, which can be useful for testing for taxonomic distinctiveness of an observed set of monophyletic lineages. The coalescence rates of multiple merger coalescent processes are functions of coalescent parameters. The effect of coalescent parameters on the probabilities studied depends on the coalescent process, and if the population is ancestral or derived. The probability of reciprocal monophyly tends to be somewhat lower, when associated with a Λ coalescent, under the null hypothesis that two groups come from the same population. However, even for fairly recent divergence times, the probability of monophyly tends to be higher as a function of the number of generations for coalescent processes that admit multiple mergers, and is sensitive to the parameter of one of the example processes.     

The coalescence time of sampled genes in the structured coalescent model

The aim of this article is to investigate the distribution of the coalescence time (T) for sampled genes in the structured coalescent. We obtain some exact solutions for small samples and approximate distributions for n sampled genes in strong and weak migration. We also conduct computer simulation to evaluate efficiencies of these approximations and show the dependency of the distribution of the coalescence time on the geographical structure and the intensity of migration. In a panmictic population, we prove that the conditional distribution of the coalescence time given the number of segregating sites (S) among sampled genes is given by the weighted mean of the convolution of gamma distributions. We also study the joint distribution of T and S in the structured coalescent model and show some exact solutions.     

The distribution of coalescence times and distances between microsatellite alleles with changing effective population size

We investigate the effects of past changes of the effective population size on the present allelic diversity at a microsatellite marker locus. We first derive the analytical expression of the generating function of the joint probabilities of the time to the Most Recent Common Ancestor for a pair of alleles and of their distance (the difference in allele size). We give analytical solutions in the case of constant population size and the geometrical mutation model. Otherwise, numerical inversion allows the distributions to be calculated in general cases. The effects of population expansion or decrease and the possibility to detect an ancient bottleneck are discussed. The method is extended to samples of three and four alleles, which allows investigating the covariance structure of the frequencies f(k) of pairs of alleles with a size difference of k motifs, and suggesting some approaches to the estimation of past demography.     

Estimation of divergence times in cnidarian evolution based on mitochondrial protein-coding genes and the fossil record

The phylum Cnidaria is comprised of remarkably diverse and ecologically significant taxa, such as the reef-forming corals, and occupies a basal position in metazoan evolution. The origin of this phylum and the most recent common ancestors (MRCAs) of its modern classes remain mostly unknown, although scattered fossil evidence provides some insights on this topic. Here, we investigate the molecular divergence times of the major taxonomic groups of Cnidaria (27 Hexacorallia, 16 Octocorallia, and 5 Medusozoa) on the basis of mitochondrial DNA sequences of 13 protein-coding genes. For this analysis, the complete mitochondrial genomes of seven octocoral and two scyphozoan species were newly sequenced and combined with all available mitogenomic data from GenBank. Five reliable fossil dates were used to calibrate the Bayesian estimates of divergence times. The molecular evidence suggests that cnidarians originated 741 million years ago (Ma) (95% credible region of 686-819), and the major taxa diversified prior to the Cambrian (543 Ma). The Octocorallia and Scleractinia may have originated from radiations of survivors of the Permian-Triassic mass extinction, which matches their fossil record well.     

Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress–strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress–strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress–strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress–strain behavior.     

Division of labour and social insect colony performance in relation to task and mating number under two alternative response threshold models

Some social insects exhibit an exceptionally high degree of polyandry. Alternative hypotheses exist to explain the benefits of multiple mating through enhanced colony performance. This study critically extends theoretical analyses of the hypothesis that enhanced division of labour confers fitness benefits to the queen that are sufficient to explain the observed mating frequencies of social insects. The effects of widely varying numbers of tasks and matings were systematically investigated in two alternative computer simulation models. One model was based on tasks that have to be performed to maintain an optimal trait value, while the other model was based on tasks that only have to be sufficiently performed to exceed a minimum trait value to confer full fitness returns. Both model versions were evaluated assuming a broad and a narrow response threshold distribution. The results consistently suggest a beneficial effect of multiple mating on colony performance, albeit with quickly diminishing returns. An increasing number of tasks decreased performance of colonies with few patrilines but not of more genetically diverse colonies. Instead, a performance maximum was found for intermediate task numbers. The results from the two model versions and two response threshold distributions did not fundamentally differ, suggesting that the type of tasks and the breadth of response thresholds do not affect the benefit of multiple mating. In general, our results corroborate previous models that have evaluated simpler task/patriline scenarios. Furthermore, selection for an intermediate number of tasks is indicated that could constrain the degree of division of labour. We conclude that enhanced division of labour may have favoured the evolution of multiple mating but is insufficient to explain the extreme mating numbers observed in some social insects, even in complex task scenarios.     

No direct selection to increase offspring number of bet-hedging strategies in large populations: Simons' model revisited

In mixed or 'bet-hedging' strategies, offspring phenotypes are taken randomly from a distribution determined by the genotype and shaped by evolution. Offspring of a single parent represent a finite sample from this distribution, and therefore are subject to variability because of sampling. Contrary to a recent article by A.M. Simons (2007; J. Evol. Biol.20: 813-817), I show that selection does not favour the production of many offspring just to reduce sampling variability when such mixed strategies are used in large populations.     

The trade-off between number and size of offspring in humans and other primates

Life-history theory posits a fundamental trade-off between number and size of offspring that structures the variability in parental investment across and within species. We investigate this 'quantity-quality' trade-off across primates and present evidence that a similar trade-off is also found across natural-fertility human societies. Restating the classic Smith-Fretwell model in terms of allometric scaling of resource supply and offspring investment predicts an inverse scaling relation between birth rate and offspring size and a (-1/4) power scaling between birth rate and body size. We show that these theoretically predicted relationships, in particular the inverse scaling between number and size of offspring, tend to hold across increasingly finer scales of analyses (i.e. from mammals to primates to apes to humans). The advantage of this approach is that the quantity-quality trade-off in humans is placed into a general framework of parental investment that follows directly from first principles of energetic allocation.     

On the interpretation and application of mean times to extinction

As a metric of population viability, conservation biologists routinely predict the mean time to extinction (MTE). Interpretation of MTE depends on the underlying distribution of times to extinction (DTE). Despite claims to the contrary, all information regarding extinction risk can be obtained from this single statistic, the MTE, provided the DTE is exponential. We discuss the proper interpretation of MTE and illustrate how to calculate any population viability statistic when only the MTE is known and the DTE is assumed to be exponential. We also discuss the restrictive assumptions underlying the exponential DTE and the conditions under which alternative models for the DTE are preferable to the conventional (exponential) model. Despite superficial similarities between the exponential and alternative DTEs, several key differences can lead to substantially different interpretations of the MTE.     

Population differentiation and migration: coalescence times in a two-sex island model for autosomal and X-linked loci

Evolutionists have debated whether population-genetic parameters, such as effective population size and migration rate, differ between males and females. In humans, most analyses of this problem have focused on the Y chromosome and the mitochondrial genome, while the X chromosome has largely been omitted from the discussion. Past studies have compared F_ST values for the Y chromosome and mitochondrion under a model with migration rates that differ between the sexes but with equal male and female population sizes. In this study we investigate rates of coalescence for X-linked and autosomal lineages in an island model with different population sizes and migration rates for males and females, obtaining the mean time to coalescence for pairs of lineages from the same deme and for pairs of lineages from different demes. We apply our results to microsatellite data from the Human Genome Diversity Panel, and we examine the male and female migration rates implied by observed F_ST values.     

Estimation of population parameters and their application to the development of fishery management models in two African rivers

The dynamics of fish populations in two African rivers are being investigated with a view to developing fishery management models for tropical non-floodplain rivers. Preliminary work was carried out in the Rufiji River, East Africa, to establish growth and mortality rates along with L _∞ and K for six species in a river where fishing mortality is zero. These parameters, derived from scale-reading and length frequency analysis, also allowed the development of phased management plans for the fishery resulting from impoundment.
A subsequent investigation has begun on a West African river, the Taia in Sierra Leone, to pursue observations over four seasons, two of which are now complete. A systematic daily sampling programme is being carried out of the whole community, to accumulate similar but more extensive data to those obtained previously. In the Taia, however, fishing mortality must also be estimated from catch surveys, and analysis is carried out using the recently developed ELEFAN programs which can be compared with results obtained by other methods such as scale-reading.     

Testing models of parental investment strategy and offspring size in ants

Parental investment strategies can be fixed or flexible. A fixed strategy predicts making all offspring a single ‘optimal’ size. Dynamic models predict flexible strategies with more than one optimal size of offspring. Patterns in the distribution of offspring sizes may thus reveal the investment strategy. Static strategies should produce normal distributions. Dynamic strategies should often result in non-normal distributions. Furthermore, variance in morphological traits should be positively correlated with the length of developmental time the traits are exposed to environmental influences. Finally, the type of deviation from normality (i.e., skewed left or right, or platykurtic) should be correlated with the average offspring size. To test the latter prediction, we used simulations to detect significant departures from normality and categorize distribution types. Data from three species of ants strongly support the predicted patterns for dynamic parental investment. Offspring size distributions are often significantly non-normal. Traits fixed earlier in development, such as head width, are less variable than final body weight. The type of distribution observed correlates with mean female dry weight. The overall support for a dynamic parental investment model has implications for life history theory. Predicted conflicts over parental effort, sex investment ratios, and reproductive skew in cooperative breeders follow from assumptions of static parental investment strategies and omnipresent resource limitations. By contrast, with flexible investment strategies such conflicts can be either absent or maladaptive. Electronic Supplementary Material Supplementary material is available for this article at     

Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

肠道菌群及内毒素在多器官功能不全综合征时的变化

目的　探讨肠道菌群及内毒素在多器官功能不全综合征( MODS)时的变化。方法　取SD大鼠,腹腔注射无菌酵母多糖A制备MODS模型,检测大鼠肠道菌群、外周血和门静脉血中的内毒素以及肠道游离内毒素含量,并进行定量分析。结果　模型组大鼠肠道专性厌氧菌的数量明显减少,革兰阴性杆菌和双歧杆菌的比例倒置,内毒素含量明显增加,与对照组比差异有显著性( P<0 .0 5 )。结论　MODS时肠道细菌微生态发生明显改变,肠道内毒素池与肠道革兰阴性杆菌的变化密切相关     

Collaborative production and experimental labor: two models of dissertation authorship in the eighteenth century

This article examines two early modern models of dissertation authorship that both relied on extensive collaboration between the degree candidate and his supervisor. The dissertation conducted on the traditional model, practiced until the eighteenth century at German universities, was a joint product of the supervisor, who prepared the thesis in writing, and the degree candidate, who defended it in the oral disputation. The two collaborators shared the credit for a successfully defended thesis in different forms: right for public recognition and rights to use and reproduce the thesis. Instead of sharing the credit as two equal partners, each of them took advantage of his credit in ways that benefited his status. In the model that Albrecht von Haller introduced at Göttingen, the supervisor provided the student with a laboratory and experimental training, while the degree candidate wrote a thesis by himself based on the experiments he carried out, and defended the thesis without the supervisor chairing the disputation. The Haller model reveals two new elements that heralded the development of modern scientific education: divisibility of laboratory labor between the student’s experimentation and the research program to which it belongs; and feasibility of the requirement of experimental work in return for the exclusive authorship of the doctoral thesis.     

Spatial distribution of resting stages,rate of emergence from diapause and times to adulthood and to the appearance of the first clutch in 3 species of cyclopoid copepods

The spatial distribution of dormant copepodids of 3 species of cyclopoid copepods — Cyclops vicinus, Mesocyclops leuckarti and Thermocyclops crassus — was studied in 4 small lakes in South Germany. The rate of emergence from diapause and times from the resting stage to adulthood and from adulthood to the appearance of the first clutch was studied at 4 constant temperatures (5, 10, 15, 20 °C) in the laboratory. Resting stages of C. vicinus were always concentrated in the deepest parts of the lakes and were found relatively deep in the mud. M. leuckarti- and T. crassus-copepodids preferred shallow areas in deep lakes but were concentrated in the deep areas in shallow lakes. Copepodids of both species were always concentrated in the uppermost mud layers.Rate of emergence from diapause was strongly temperature-dependent. At high temperatures (20 °C) copepodids of all species under study emerged within 2 weeks. At lower temperatures C. vicinus copepodids showed the highest rate of emergence. At 5 to 10 °C only few M. leuckarti- and T. crassus-copepodids had emerged after the investigation period (7 weeks). Both C. vicinus and T. crassus showed the highest rate of emergence at the natural end of diapause but even at that time only few T. crassus-copepodids emerged at 5 °C. Times to adulthood at 5 °C were shortest in C. vicinus. At higher temperatures this species was passed by M. leuckarti. Times from adulthood to the appearance of the first clutch at 5–15 °C were shortest in C. vicinus. T. crassus produced no clutch at 5 and 10 °C.