The coalescent and the genealogical process in geographically structured population

We shall extend Kingman's coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two-population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration.     

Waiting with and without Recombination: The Time to Production of a Double Mutant

R. A. Fisher and H. J. Muller argued in the 1930s that a major evolutionary advantage of recombination is that it allows favorable mutations to be combined within an individual even when they first appear in different individuals. This effect is evaluated in a two-locus, two-allele model by calculating the average waiting time until a new genotypic combination first appears in a haploid population. Three approximations are developed and compared with Monte Carlo simulations of the Wright–Fisher process of random genetic drift in a finite population. First, a crude method, based on the deterministic accumulation of single mutants, produces a waiting time of 1/with no recombination and 1/with recombination between the two loci, whereμis the mutation rate,Nis the haploid population size, andRis the recombination rate. Second, the waiting time is calculated as the expected value of a heterogeneous geometric distribution obtained from a branching process approximation. This gives accurate estimates forNμlarge. The estimates for small values ofNμare considerably lower than the simulated values. Finally, diffusion analysis of the Wright–Fisher process provides accurate estimates forNμsmall, and the time scales of the diffusion process show a difference betweenR=0 and forR?0 of the same order of magnitude as seen in the deterministic analysis. In the absence of recombination, accurate approximations to the waiting time are obtained by using the branching process for highNμand the diffusion approximation for lowNμ. For lowNμthe waiting time is well approximated by 1/. WithR?0, the following dependence onNμis observed: ForNμ>1 the waiting time is virtually independent of recombination and is well described by the branching process approximation. ForNμ≈ the waiting time is well described by a simplified diffusion approximation that assumes symmetry in the frequencies of single mutants. ForNμ?1 the waiting time is well described by the diffusion approximation allowing asymmetry in the frequencies of single mutants. Recombination lowers the waiting time until a new genotypic combination first appears, but the effect is small compared to that of the mutation rate and population size. For largeNμ, recombination has a negligible effect, and its effect is strongest for smallNμ, in which case the waiting time approaches a fixed fraction of the waiting time forR=0. Free recombination lowers the waiting time to about 45% of the waiting time for absolute linkage for smallNμ. Selection has little effect on the importance of recombination in general.     

The strong-migration limit for the genealogical process in geographically structured populations

In this article we assume that the entire population is subdivided into a finite number of panmictic colonies, each of which consists of a respective number of haploid individuals. We also assume that random genetic drift occurs in each colony and migration among colonies, which is independent of time and ergodic. We study the genealogical process of sampled genes from geographically structured populations. We prove that if the actual total population number is replaced by the effective population number, the mean coalescence time converges to that in a panmictic population in the strong migration limit. We also obtain the geographical distribution of the common ancestor.     

Inference from gene trees in a subdivided population

This paper studies gene trees in subdivided populations which are constructed as perfect phylogenies from the pattern of mutations in a sample of DNA sequences and presents a new recursion for the probability distribution of such gene trees. The underlying evolutionary model is the coalescent process in a subdivided population. The infinitely-many-sites model of mutation is assumed. Ancestral inference questions that are discussed are maximum likelihood estimation of migration and mutation rates; detection of population growth by likelihood techniques; determining the distribution of the time to the most recent common ancestor of a sample of sequences; determining the distribution of the age of the mutations on the gene tree; determining in which subpopulation the most recent common ancestor of all the sequences was; determining subpopulation ancestors, where they were, and times to them; and determining in which subpopulations mutations occurred. A computational technique of Griffiths and Tavaré used is a computer intensive Markov chain simulation, which simulates gene trees conditional on their topology implied by the mutation pattern in the sample of DNA sequences. The software GENETREE, which implements these ancestral inference techniques, is available.     

When and where was the most recent common ancestor?

 The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = τ, the distribution of Z is Gaussian with mean zero and variance 2τ. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension. Received: 1 May 2001 / Revised version: 2 September 2001 / Published online: 8 February 2002     

Geographical Distribution of Phacellaria Benth. (Santalaceae) and its Hosts

Based on the geographical distribution of the species of Phacellaria and its host plants in the world, we speculated on the possible time, sites, and migration of the origin of Phacellaria. The host plants of Phacellaria mainly belong to Loranthaceae. Plants of Phacellaria and their hosts are mainly distributed in tropical and subtropical areas. The plants of Phacellariamight have originated from a tropical area in the south of China before the Tertiary. Their ancestors were parasitic on the ancestors of some plants of Loranthaceae by chance during the Tertiary. It possibly took them millions of years to form a sturdy relationship with their hosts. Translated from Guihaia, 2005, 25(2) (in Chinese)     

Factors influencing seasonal absconding in colonies of the African honey bee,Apis mellifera scutellata

Summary This study investigated the effects of colony growth and development, food storage, foraging activity and weather on the migration behavior of African honey bees in the Okavango River Delta, Botswana. Four observation colonies were studied during the honey bee migration season (November–May), at which time the availability of blooming species was reduced. Two of the colonies (colonies 1 & 2) migrated during the study period, while the remaining two (colonies 3 & 4) did not. During the 4–6 weeks preceding the onset of migration preparations, colonies 1 & 2 exhibited increasing population sizes, high levels of brood production with low brood mortality, relatively large stores of food, and increasing mass. In contrast, the populations of colonies 3 & 4 did not increase, brood-rearing activity was erratic and lower, brood mortality was higher, food stores became depleted and colony mass declined. Both colonies 3 & 4 ceased rearing brood, and colony 3 died of starvation. Colony foraging activity was examined by monitoring waggle-dance activity 2–3 days each week. For 4–6 weeks before the onset of migration in colonies 1 & 2, daily foraging areas and mean daily foraging distances became increasingly large and variable. Colonies 3 & 4 exhibited foraging patterns similar to those observed for colonies 1 & 2 preceding migration. There was no clear association between 7 weather parameters examined and migration behavior. These data suggest that migration is influenced by an interaction of intra-colony demographics, food reserves and foraging patterns. Migration may be feasible only for those colonies that possess (1) a population of appropriate size and age structure to compensate for the natural attrition of older workers during the emigration process, and (2) sufficient food reserves for long-distance travel and the establishment of a new nest. Changing foraging patterns may reflect a deteriorating foraging environment, which may trigger the onset of migration preparations, provided that colony demographics and food reserves are conducive. Colonies that show decreased brood production, higher brood mortality and reduced food stores may be incapable of migrating, even when experiencing deteriorating foraging conditions. Rather, such colonies may have a greater chance of survival if they attempt to persist in a given area.     

Spatial distribution of bacterial colonies in a model cheese

In most ripened cheeses, bacteria are responsible for the ripening process. Immobilized in the cheese matrix, they grow as colonies. Therefore, their distribution as well as the distance between them are of major importance for ripening steps since metabolites diffuse within the cheese matrix. No data are available to date about the spatial distribution of bacterial colonies in cheese. This is the first study to model the distribution of bacterial colonies in a food-type matrix using nondestructive techniques. We compared (i) the mean theoretical three-dimensional (3D) distances between colonies calculated on the basis of inoculation levels and considering colony distribution to be random and (ii) experimental measurements using confocal microscopy photographs of fluorescent colonies of a Lactococcus lactis strain producing green fluorescent protein (GFP) inoculated, at different levels, into a model cheese made by ultrafiltration (UF). Enumerations showed that the final numbers of cells were identical whatever the inoculation level (10(4) to 10(7) CFU/g). Bacterial colonies were shown to be randomly distributed, fitting Poisson's model. The initial inoculation level strongly influenced the mean distances between colonies (from 25 μm to 250 μm) and also their mean diameters. The lower the inoculation level, the larger the colonies were and the further away from each other. Multiplying the inoculation level by 50 multiplied the interfacial area of exchange with the cheese matrix by 7 for the same cell biomass. We finally suggested that final cell numbers should be discussed together with inoculation levels to take into account the distribution and, consequently, the interfacial area of colonies, which can have a significant influence on the cheese-ripening process on a microscopic scale.     

Chromosomes and the origins of apes and australopithecins

Comparison of molecular data suggests that the higher apes (Gorilla, Pan) and humankind (Homo) are closely related and that they diverged from the common ancestor through two speciation events situated very closely together in time. Examination of the chromosomal formulas of the living species reveals a paradox in the distribution of mutated chromosomes which can only be resolved by a model of trichotomic diversification. This new model of divergence from the common ancestor is characterized by the transition from (1) a monotypic phase to (2) a polytypic phase of three sub-species — pre-gorilla, pre-chimpanzee and preaustralopithecine. The quadruped ancestors ofAustralopithecus appear to have been one of the three components of the common ancestor. The question is whetherramidus is an australopithecine or a pre-australopithecine representative of the common ancestor. The new model of diversification of the common ancestor is resituated in the paleogeographic and paleoclimatic context which, through the north-south pattern of extension of aridity, provides a coherent scenario for the formation of extant species and subspecies of theGorilla andPan genera.     

The evolution of embryogeny in seed plants and the developmental origin and early history of endosperm

For almost a century, the formation of endosperm from a second and distinctive fertilization event has been viewed as a unique feature of flowering plants. However, until recently, the evolutionary origin of this unique embryo-nourishing entity remained a mystery. Based upon comparative developmental analysis of reproduction among basal angiosperms and their closest extant relatives, the Gnetales (Ephedra, Gnetum, and Welwitschia), it is possible to construct an explicit hypothesis of the events that led to the evolutionary establishment of double fertilization and endosperm. The formulation of this historical record is derived entirely from and dependent upon the determination of reproductive features that are likely to have characterized the common ancestors of angiosperms and Gnetales. Current evidence is most congruent with the concept that a process of double fertilization first evolved in a common ancestor of the Gnetales and angiosperms. Initially, however, the second fertilization product was diploid and yielded a supernumerary embryo. Subsequent to the divergence of the angiosperm lineage from its closest relatives (which include the Gnetales), modification of the development of the supernumerary embryo (derived from the second fertilization event) led to the establishment of an embryo-nourishing endosperm. Comparative analysis of patterns of embryogeny within Gnetales and angiosperms establishes that embryo development in the ancestors of flowering plants (with a rudimentary process of double fertilization) was ab initio cellular, and not free nuclear, as had previously been assumed. Thus, it is likely that the earliest flowering plants displayed an ab initio cellular pattern of endosperm development, whose expression was inherited from that of the supernumerary embryo of the ancestors of flowering plants.     

A test of adaptive hypotheses for rapid nest construction in a swarm-founding wasp

Most social insect species enlarge their nests gradually and in close correlation with the growing need for space for brood and/or stored food. In contrast, some species of swarm-founding eusocial wasps construct the nest rapidly to a final size in the first two to three weeks of the founding stage. We considered four hypotheses on the functions of rapid nest construction in the wasp Polybia occidentalis and directly tested two of them. The first hypothesis is that rapid construction maximizes output of the worker force when there are few other work demands; it predicts that construction rate remains high until the first eggs begin to hatch, following which it declines as increasing amounts of worker effort are allocated to the feeding of larvae. The second says that rapid nest construction minimizes the time the adults in the swarm are exposed to predation and the elements; it predicts that nest-construction rate should drop steeply after the nest is large enough to house all the adults in the swarm. We measured pulp-foraging rates for the first 12 days of the founding stage in control colonies and in colonies whose nests we manipulated to prevent housing of the swarm. The treatment and control groups did not differ in construction rate for several days following the housing event, contradicting the adult-protection hypothesis. Late in nest construction, treatment colonies were building at significantly higher rates than were control colonies. If demand for brood care were a major factor in determining construction rate, both groups would have responded to the eclosion of larvae in the same way and shown a parallel decline in construction rate, but this did not happen. Instead, the patterns of nest construction rate we observed provided indirect support for the two remaining hypotheses. The first of these is that rapid construction minimizes exposure of the brood to natural enemies and desiccation. The second is that rapid construction promotes competition among queens by providing empty cells for oviposition, thereby facilitating the selecting out of the less fecund of the multiple reproductive females. Also consistent with this hypothesis is the apparent absence of explosive nest construction in monogynous, eusocial bees. Received 13 October 2007; revised 31 March 2008; accepted 6 April 2008.     

Consequences of foundress aggregation in the brown citrus aphid Toxoptera citricida

1. A field study was conducted in which colonies of Toxoptera citricida (Kirkaldy) were initiated with different numbers of foundresses on ungrafted citrus trees var. ‘Carrizo’ within an existing citrus grove in central Florida. 2. The growth rate, longevity, and final size of T. citricida colonies were all positively correlated with number of foundresses. 3. Colonies initiated by many foundresses produced alatae earlier than those initiated by fewer foundresses. 4. Nymphal developmental time was reduced in colonies initiated by more foundresses but the mean number of grand‐progeny per foundress was lower when only surviving colonies were compared. 5. The longevity of foundresses was unaffected by their number but foundress fecundity and nymphal survival decreased as foundress number increased. 6. The most abundant natural enemies were Diptera: Syrphidae, primarily Pseudodorus clavatus (F.), and Chamaemiidae (Leucopis sp.), followed by Coleoptera: Coccinellidae, primarily Cycloneda sanguinea (L). 7. Colonies initiated with more foundresses attracted more oviposition by dipteran predators than did colonies initiated with fewer foundresses.     

Ancestral Processes with Selection

In this paper, we show how to construct the genealogy of a sample of genes for a large class of models with selection and mutation. Each gene corresponds to a single locus at which there is no recombination. The genealogy of the sample is embedded in a graph which we call theancestral selection graph. This graph contains all the information about the ancestry; it is the analogue of Kingman's coalescent process which arises in the case with no selection. The ancestral selection graph can be easily simulated and we outline an algorithm for simulating samples. The main goal is to analyze the ancestral selection graph and to compare it to Kingman's coalescent process. In the case of no mutation, we find that the distribution of the time to the most recent common ancestor does not depend on the selection coefficient and hence is the same as in the neutral case. When the mutation rate is positive, we give a procedure for computing the probability that two individuals in a sample are identical by descent and the Laplace transform of the time to the most recent common ancestor of a sample of two individuals; we evaluate the first two terms of their respective power series in terms of the selection coefficient. The probability of identity by descent depends on both the selection coefficient and the mutation rate and is different from the analogous expression in the neutral case. The Laplace transform does not have a linear correction term in the selection coefficient. We also provide a recursion formula that can be used to approximate the probability of a given sample by simulating backwards along the sample paths of the ancestral selection graph, a technique developed by Griffiths and Tavaré (1994).     

Effect of spatial differences in growth on distribution of seasonally co‐occurring herring Clupea harengus stocks

The mechanisms most likely to determine the distribution of the two major herring Clupea harengus stocks in their common early summer feeding ground in the eastern North Sea, Skagerrak and Kattegat were investigated through analysis of acoustic survey data from six consecutive years. No change was detected in biomass of North Sea autumn spawning C. harengus (NSAS) over time, whereas the biomass of western Baltic spring spawning C. harengus (WBSS) declined severely. Analyses of centre of abundance by stock showed no change in NSAS distribution, whereas the WBSS changed to a more western distribution over time. Contrary to previous perception of the juvenile migration, NSAS were found to leave the study area at the age between 1 and 2 years and WBSS 1 year olds were encountered in the Skagerrak. The estimated parameters of von Bertalanffy growth equations showed marked differences between areas with fish in the eastern part of the area having the lowest size at age at all ages. Further, their growth conditions appeared to deteriorate progressively over the period studied. Both NSAS and WBSS showed the highest condition in the North Sea and Skagerrak while condition was substantially lower in age Kattegat. The westward movement of spring spawners over time suggests that growth rate and possibly density of conspecifics influence the migration pattern and distribution of C. harengus in the area. In contrast, there was no evidence to suggest that distribution was constant over time within stocks or that distribution reflected size‐dependent limitations on migration distance.     

Application of a two-phenotype color-shift model with heterogeneous growth to a rat hepatocarcinogenesis experiment

The color-shift model (CSM) was introduced by Kopp-Schneider et al. [1] to describe formation and progression of foci of altered hepatocytes (FAH). It incorporates the field-effect hypothesis which postulates that entire colonies of altered hepatocytes simultaneously alter their phenotype. In the original CSM, FAH grow with deterministic growth rate and change their phenotype after an exponentially distributed waiting time. A modification of the original color-shift model (CSMbeta) is presented here in which the growth rate varies from focus to focus according to a beta distribution. The concept of an exponentially distributed waiting time to phenotype change is modified to the concept of a random radius at which phenotype changes and this radius is modelled as beta distributed. The original and the modified CSM are applied to data from an initiation-promotion rat hepatocarcinogenesis experiment with diethylnitrosomorpholine (DEN) and N-nitrosomorpholine (NNM), in which two phenotypes of FAH were observed in hematoxilin/eosin (H&E) stained liver sections. The Cramer-von-Mises Distance is used as a measure for the discrepancy between empirical and theoretical size distributions. Comparisons of model fit show that considerable improvement is obtained for CSMbeta compared to the original CSM.     

The time to the ancestor along sequences with recombination.

In a sample of DNA sequences where recombination can occur to the ancestors of the sample, distinct parts of the sequences may have different most recent common ancestors. This paper presents a Markov chain Monte Carlo algorithm for computing the expected time to the most recent common ancestor along the sequences, conditional on where the mutations occur on the sequences.     

When sinks become sources: Adaptive colonization in asexuals*

The establishment of a population into a new empty habitat outside of its initial niche is a phenomenon akin to evolutionary rescue in the presence of immigration. It underlies a wide range of processes, such as biological invasions by alien organisms, host shifts in pathogens, or the emergence of resistance to pesticides or antibiotics from untreated areas. We derive an analytically tractable framework to describe the evolutionary and demographic dynamics of asexual populations in a source-sink system. We analyze the influence of several factors on the establishment success in the sink, and on the time until establishment. To this aim, we use a classic phenotype-fitness landscape (Fisher's geometrical model in n dimensions) where the source and sink habitats have different phenotypic optima. In case of successful establishment, the mean fitness in the sink follows a typical four-phases trajectory. The waiting time to establishment is independent of the immigration rate and has a “U-shaped” dependence on the mutation rate, until some threshold where lethal mutagenesis impedes establishment and the sink population remains so. We use these results to get some insight into possible effects of several management strategies.     

Residency and movement patterns of Arctic charr Salvelinus alpinus relative to major estuaries

Estuarine residency and marine movements of 43 anadromous Arctic charr Salvelinus alpinus (mean ± s.d . fork length = 523 ± 97 mm) were examined using acoustic tracking in inner Frobisher Bay (IFB; 63° N; 68° W), Canada, from July to September 2008 and 2009. A mean ± s.d . migration duration of 63 ± 7 days occurred from late June to early September. Detected S. alpinus were either continuously (maximum 34 days) or intermittently present in estuarine zones, on average residing approximately one third of time tracked and returning once every 9 days. Significantly higher estuarine residency during the final 15 migration days suggested that a transition phase may occur prior to freshwater re‐entry. Low travel rates during flood tide suggested individuals staged before accessing intertidal and estuarine zones. Although the two main estuaries were c. 22 km apart, 19% of tagged individuals used both. Individuals remained relatively close to freshwater overwintering systems, although late‐migration inter‐estuarine movements may have indicated natal homing. Approximately half of the individuals exhibited extra‐estuarine travel, mostly during mid‐migration, but remained within 3 km of shore ranging < 30 km straight line distance (SLD) of either estuary. It was concluded that IFB S. alpinus (1) spent a significant portion of their migration within or adjacent to the estuaries and (2) had a restricted marine distribution within 30 km SLD of the river mouths.     

The ancestry of a sample of sequences subject to recombination

In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is approximately log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.