Establishment in a new habitat by polygenic adaptation.

Maladapted individuals can only colonise a new habitat if they can evolve a positive growth rate fast enough to avoid extinction, a process known as evolutionary rescue. We treat log fitness at low density in the new habitat as a single polygenic trait and use the infinitesimal model to follow the evolution of the growth rate; this assumes that the trait values of offspring of a sexual union are normally distributed around the mean of the parents' trait values, with variance that depends only on the parents' relatedness. The probability that a single migrant can establish depends on just two parameters: the mean and genetic variance of the trait in the source population. The chance of success becomes small if migrants come from a population with mean growth rate in the new habitat more than a few standard deviations below zero; this chance depends roughly equally on the probability that the initial founder is unusually fit, and on the subsequent increase in growth rate of its offspring as a result of selection. The loss of genetic variation during the founding event is substantial, but highly variable. With continued migration at rate M, establishment is inevitable; when migration is rare, the expected time to establishment decreases inversely with M. However, above a threshold migration rate, the population may be trapped in a 'sink' state, in which adaptation is held back by gene flow; above this threshold, the expected time to establishment increases exponentially with M. This threshold behaviour is captured by a deterministic approximation, which assumes a Gaussian distribution of the trait in the founder population with mean and variance evolving deterministically. By assuming a constant genetic variance, we also develop a diffusion approximation for the joint distribution of population size and trait mean, which extends to include stabilising selection and density regulation. Divergence of the population from its ancestors causes partial reproductive isolation, which we measure through the reproductive value of migrants into the newly established population.

The infinitesimal model: Definition, derivation, and implications.

Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, …. We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Simulations suggest that in some cases the convergence may be as fast as 1∕M.

Spread of pedigree versus genetic ancestry in spatially distributed populations.

Ancestral processes are fundamental to modern population genetics and spatial structure has been the subject of intense interest for many years. Despite this interest, almost nothing is known about the distribution of the locations of pedigree or genetic ancestors. Using both spatially continuous and stepping-stone models, we show that the distribution of pedigree ancestors approaches a travelling wave, for which we develop two alternative approximations. The speed and width of the wave are sensitive to the local details of the model. After a short time, genetic ancestors spread far more slowly than pedigree ancestors, ultimately diffusing out with radius ∼ t rather than spreading at constant speed. In contrast to the wave of pedigree ancestors, the spread of genetic ancestry is insensitive to the local details of the models.

Coalescent simulation in continuous space: algorithms for large neighbourhood size.

Many species have an essentially continuous distribution in space, in which there are no natural divisions between randomly mating subpopulations. Yet, the standard approach to modelling these populations is to impose an arbitrary grid of demes, adjusting deme sizes and migration rates in an attempt to capture the important features of the population. Such indirect methods are required because of the failure of the classical models of isolation by distance, which have been shown to have major technical flaws. A recently introduced model of extinction and recolonisation in two dimensions solves these technical problems, and provides a rigorous technical foundation for the study of populations evolving in a spatial continuum. The coalescent process for this model is simply stated, but direct simulation is very inefficient for large neighbourhood sizes. We present efficient and exact algorithms to simulate this coalescent process for arbitrary sample sizes and numbers of loci, and analyse these algorithms in detail.

Inference in two dimensions: allele frequencies versus lengths of shared sequence blocks.

We outline two approaches to inference of neighbourhood size, N, and dispersal rate, σ(2), based on either allele frequencies or on the lengths of sequence blocks that are shared between genomes. Over intermediate timescales (10-100 generations, say), populations that live in two dimensions approach a quasi-equilibrium that is independent of both their local structure and their deeper history. Over such scales, the standardised covariance of allele frequencies (i.e. pairwise FST) falls with the logarithm of distance, and depends only on neighbourhood size, N, and a 'local scale', κ; the rate of gene flow, σ(2), cannot be inferred. We show how spatial correlations can be accounted for, assuming a Gaussian distribution of allele frequencies, giving maximum likelihood estimates of N and κ. Alternatively, inferences can be based on the distribution of the lengths of sequence that are identical between blocks of genomes: long blocks (>0.1 cM, say) tell us about intermediate timescales, over which we assume a quasi-equilibrium. For large neighbourhood size, the distribution of long blocks is given directly by the classical Wright-Malécot formula; this relationship can be used to infer both N and σ(2). With small neighbourhood size, there is an appreciable chance that recombinant lineages will coalesce back before escaping into the distant past. For this case, we show that if genomes are sampled from some distance apart, then the distribution of lengths of blocks that are identical in state is geometric, with a mean that depends on N and σ(2).

Genetic hitchhiking in spatially extended populations.

When a mutation with selective advantage s spreads through a panmictic population, it may cause two lineages at a linked locus to coalesce; the probability of coalescence is exp(-2rT), where T∼log(2Ns)/s is the time to fixation, N is the number of haploid individuals, and r is the recombination rate. Population structure delays fixation, and so weakens the effect of a selective sweep. However, favourable alleles spread through a spatially continuous population behind a narrow wavefront; ancestral lineages are confined at the tip of this front, and so coalesce rapidly. In extremely dense populations, coalescence is dominated by rare fluctuations ahead of the front. However, we show that for moderate densities, a simple quasi-deterministic approximation applies: the rate of coalescence within the front is λ∼2g(η)/(ρℓ), where ρ is the population density and ℓ=σ2/s is the characteristic scale of the wavefront; g(η) depends only on the strength of random drift, η=ρσs/2. The net effect of a sweep on coalescence also depends crucially on whether two lineages are ever both within the wavefront at the same time: even in the extreme case when coalescence within the front is instantaneous, the net rate of coalescence may be lower than in a single panmictic population. Sweeps can also have a substantial impact on the rate of gene flow. A single lineage will jump to a new location when it is hit by a sweep, with mean square displacement σeff(2)/σ(2)=(8/3)(L/ℓ)(Λ/R); this can be substantial if the species' range, L, is large, even if the species-wide rate of sweeps per map length, Λ/R, is small. This effect is half as strong in two dimensions. In contrast, the rate of coalescence between lineages, at random locations in space and on the genetic map, is proportional to (c/L)(Λ/R), where c is the wavespeed: thus, on average, one-dimensional structure is likely to reduce coalescence due to sweeps, relative to panmixis. In two dimensions, genes must move along the front before they can coalesce; this process is rapid, being dominated by rare fluctuations. This leads to a dramatically higher rate of coalescence within the wavefront than if lineages simply diffused along the front. Nevertheless, the net rate of coalescence due to a sweep through a two-dimensional population is likely to be lower than it would be with panmixis.

A coalescent dual process in a Moran model with genic selection.

A coalescent dual process for a multi-type Moran model with genic selection is derived using a generator approach. This leads to an expansion of the transition functions in the Moran model and the Wright-Fisher diffusion process limit in terms of the transition functions for the coalescent dual. A graphical representation of the Moran model (in the spirit of Harris) identifies the dual as a strong dual process following typed lines backwards in time. An application is made to the harmonic measure problem of finding the joint probability distribution of the time to the first loss of an allele from the population and the distribution of the surviving alleles at the time of loss. Our dual process mirrors the Ancestral Selection Graph of [Krone, S. M., Neuhauser, C., 1997. Ancestral processes with selection. Theoret. Popul. Biol. 51, 210-237; Neuhauser, C., Krone, S. M., 1997. The genealogy of samples in models with selection. Genetics 145, 519-534], which allows one to reconstruct the genealogy of a random sample from a population subject to genic selection. In our setting, we follow [Stephens, M., Donnelly, P., 2002. Ancestral inference in population genetics models with selection. Aust. N. Z. J. Stat. 45, 395-430] in assuming that the types of individuals in the sample are known. There are also close links to [Fearnhead, P., 2002. The common ancestor at a nonneutral locus. J. Appl. Probab. 39, 38-54]. However, our methods and applications are quite different. This work can also be thought of as extending a dual process construction in a Wright-Fisher diffusion in [Barbour, A.D., Ethier, S.N., Griffiths, R.C., 2000. A transition function expansion for a diffusion model with selection. Ann. Appl. Probab. 10, 123-162]. The application to the harmonic measure problem extends a construction provided in the setting of a neutral diffusion process model in [Ethier, S.N., Griffiths, R.C., 1991. Harmonic measure for random genetic drift. In: Pinsky, M.A. (Ed.), Diffusion Processes and Related Problems in Analysis, vol. 1. In: Progress in Probability Series, vol. 22, Birkhäuser, Boston, pp. 73-81].

CYP2E1-catalyzed oxidation contributes to the sperm toxicity of 1-bromopropane in mice.

1-bromopropane (1-BrP) induces dose- and time-dependent reproductive organ toxicity and reduced sperm motility in rodents. The contribution of cytochrome P4502E1 (CYP2E1) to both 1-BrP metabolism and the induction of male reproductive toxicity was investigated using wild-type (WT) and Cyp2e1-/- mice. In gas uptake inhalation studies, the elimination half-life of [1,2,3-(13)C]-1-BrP was longer in Cyp2e1-/- mice relative to WT (3.2 vs. 1.3 h). Urinary metabolites were identified by 13C nuclear magnetic resonance. The mercapturic acid of 1-bromo-2-hydroxypropane (2OHBrP) was the major urinary metabolite in WT mice, and products of conjugation of 1-BrP with glutathione (GSH) were insignificant. The ratio of GSH conjugation to 2-hydroxylation increased 5-fold in Cyp2e1-/- mice relative to WT. After 1-BrP exposure, hepatic GSH was decreased by 76% in WT mice vs. 47% in Cyp2e1-/- mice. Despite a 170% increase in 1-BrP exposure in Cyp2e1-/- vs. WT mice, sperm motility in exposed Cyp2e1-/- mice did not change relative to unexposed matched controls. This suggests that metabolites produced through CYP2E1-mediated oxidation may be responsible for 1-BrP-induced sperm toxicity. Both 1-BrP and 2OHBrP inhibited the motility of sperm obtained from WT mice in vitro. However, only 2OHBrP reduced the motility of sperm obtained from Cyp2e1-/- mice in vitro, suggesting that conversion of parent compound to 2OHBrP within the spermatozoa may contribute, at least in part, to reduced motility. Overall, these data suggest that metabolism of 1-BrP is mediated in part by CYP2E1, and activation of 1BrP via this enzyme may contribute to the male reproductive toxicity of this chemical.

The effect of selection on genealogies.

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.

The distribution of surviving blocks of an ancestral genome.

What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y < 1 approaches y/log(yt/2) for log(yt) > or = 1. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants (approximately 80% of the population for a Poisson offspring number with mean two) is likely to persist for an extremely long time, in the form of a few short blocks of genome.

Asymmetric nodal signaling in the zebrafish diencephalon positions the pineal organ.

The vertebrate brain develops from a bilaterally symmetric neural tube but later displays profound anatomical and functional asymmetries. Despite considerable progress in deciphering mechanisms of visceral organ laterality, the genetic pathways regulating brain asymmetries are unknown. In zebrafish, genes implicated in laterality of the viscera (cyclops/nodal, antivin/lefty and pitx2) are coexpressed on the left side of the embryonic dorsal diencephalon, within a region corresponding to the presumptive epiphysis or pineal organ. Asymmetric gene expression in the brain requires an intact midline and Nodal-related factors. RNA-mediated rescue of mutants defective in Nodal signaling corrects tissue patterning at gastrulation, but fails to restore left-sided gene expression in the diencephalon. Such embryos develop into viable adults with seemingly normal brain morphology. However, the pineal organ, which typically emanates at a left-to-medial site from the dorsal diencephalic roof, becomes displaced in position. Thus, a conserved signaling pathway regulating visceral laterality also underlies an anatomical asymmetry of the zebrafish forebrain.

Catechol metabolites of polychlorinated biphenyls inhibit the catechol-O-methyltransferase-mediated metabolism of catechol estrogens.

The catechol metabolites of estradiol, 2- and 4-hydroxyestradiol (2-OHE(2) and 4-OHE(2), respectively) are potent signaling molecules and are hypothesized to be central to estrogen-linked carcinogenesis. Methylation by catechol-O-methyltransferase (COMT) is the principal means of catechol estrogen (CE) deactivation in the liver and other tissues. The present studies were conducted to determine the effects of PCBs and catechol metabolites of PCBs on the COMT-mediated catabolism of 4-OHE(2) and 2-OHE(2) in vitro and in vivo. Liver homogenates of female Sprague-Dawley rats treated with Aroclor 1254 for 21 days (5 mg/kg/day) showed a 30 and 40% reduction of COMT activity toward 2-OHE(2) and 4-OHE(2), respectively. Incubation of [(3)H]-beta-estradiol with these same liver homogenates, followed by HPLC analysis, demonstrated an elevation of CEs and a nearly complete reduction in levels of methylated catechol estrogens. In classical enzyme kinetics studies, COMT was demonstrated to have a high affinity for catechol PCBs, with K(m)'s approximately equivalent to those of CEs. Catechol PCBs were also potent inhibitors of CE O-methylation. These data suggest that PCBs may significantly alter the metabolism of catechol estrogens in vivo and that this effect may be mediated by catechol metabolites of PCBs. It is further speculated that methyltransferase inhibition by PCB catechols may contribute to PCB-mediated endocrine effects and liver carcinogenesis.

Effect of selective phase II enzyme inducers on glucuronidation of benoxaprofen in rats.

The induction of benoxaprofen (BNX) glucuronidation in rats by intragastric administration of three nitrogen heterocycles (quinoline, 2,2'-dipyridyl, or 1,7-phenanthroline at 75 mg/kg daily for 3 days) has been investigated. BNX was administered i.v. at a dose of 20 mg/kg to bile-cannulated rats that had been induced. Blood and bile were collected over 8 h. Liver tissues were also collected at the end of the 8-h study and used to examine conjugation activity of BNX by UDP-glucuronosyl transferases and cytochrome P-450 enzyme activities in vitro. Two methods were used to characterize the true metabolic formation rates of the labile benoxaprofen glucuronide conjugate in vitro, which gave comparable mean values for K(M) and V(max). There appeared to be a trend of increase of the V(max) of BNX glucuronidation in rat liver microsomes by all three nitrogen heterocycles; however, the induction was only significant with 1,7-phenanthroline. K(M) was not noticeably altered by any of the three inducers. No change of measured hepatic microsomal cytochrome P-450 activities in the rat was found. BNX glucuronidation in rats in vivo was increased by all three nitrogen heterocycles with 1,7-phenanthroline more effective than quinoline and 2,2'-dipyridyl. The use of nitrogen heterocycles provides a means to modulate exposure to labile, reactive acyl glucuronides in vivo without apparent changes in oxidative metabolism.

Dose-dependent metabolism of benzene in hamsters, rats, and mice.

The disposition of oral doses of [14C]benzene was investigated using a range of doses that included lower levels (0.02 and 0.1 mg/kg) than have been studied previously in rat, mouse, and in hamster, a species which has not been previously examined for its capacity to metabolize benzene. Saturation of metabolism of benzene was apparent as the dose increased, and a considerable percentage of the highest doses (100 mg/kg) was exhaled unchanged. Most of the remainder of the radioactivity was excreted as metabolites in urine, and significant metabolite-specific changes occurred as a function of dose and species. Phenyl sulfate was the predominant metabolite in rat urine at all dose levels (64-73% of urinary radioactivity), followed by prephenlmercapturic acid (10-11%). Phenyl sulfate (24-32%) and hydroquinone glucuronide (27-29%) were the predominant metabolites formed by mice. Mice produced considerably more muconic acid (15%), which is derived from the toxic metabolite muconaldehyde, than did rats (7%) at a dose of 0.1 mg/kg. Unlike both rats and mice, hydroquinone glucuronide (24-29%) and muconic acid (19-31%) were the primary urinary metabolites formed by hamsters. Two metabolites not previously detected in the urine of rats or mice after single doses, 1,2,4-trihydroxybenzene and catechol sulfate, were found in hamster urine. These data indicate the hamsters metabolize benzene to more highly oxidized, toxic products than do rats or mice.

Selective inhibition of cytochrome P450 2E1 in vivo and in vitro with trans-1,2-dichloroethylene.

The effect of trans-1,2-dichloroethylene (DCE), an inhibitor of cytochrome P450 (P450) 2E1, on the catalytic activities and total content of hepatic P450 was determined in vivo and in vitro. Hepatic microsomes were prepared from groups of rats prior to dosing and at 2, 5, 12, and 24 h postdosing, and total P450 content and the activities of P450 1A2, P450 2A1, P450 2B, P450 2C6, P450 2C11, P450 2D1, P450 2E1, and P450 3A were determined. The lowest dose of DCE that yielded maximal inactivation of P450 2E1 was found to be 100 mg/kg. Significant decreases in total content of P450 or the activities of P450 1A2, P450 2A1, P450 2B, P450 2C6, P450 2C11, P450 2D1, and P450 3A were not observed during the 24 h following administration of DCE (100 mg/kg ip), but P450 2E1 activity was diminished about 65% at 2 and 5 h after DCE treatment and returned to control levels at 24 h. Additionally, there was little or no significant effect on the activities of hepatic cytosolic alcohol dehydrogenase or mitochondrial or microsomal aldehyde dehydrogenases 5 h postdosing. DCE showed the same selectivity for P450 inactivation in vitro, and P450 2E1 activity was inhibited by >80% without affecting the other isozymes. However, DCE (5 mM) also proved to be a good competitive inhibitor of the probe activities of P450 1A2 and P450 2C6. The in vivo inhibition of P450 2E1 was accompanied by decreases in the levels of the immunoreactive protein, and an additional immunoreactive band appeared at ca. 30 kDa in the Western blot of microsomes from DCE-treated rats, possibly arising from proteolytic degradation of P450 2E1 protein after covalent modification by the inhibitor. DCE is an effective, relatively nontoxic inhibitor of P450 2E1 in vivo and in vitro that has greater selectivity than other agents currently used.

Do endogenous volatile organic chemicals measured in breath reflect and maintain CYP2E1 levels in vivo?

The effect of trans-1,2-dichloroethylene (DCE), an inhibitor of cytochrome P450 (P450) 2E1 (CYP2E1), on the composition and quantity of volatile organic chemicals (VOCs) expired in the breath of male F-344 rats was determined in parallel with hepatic P450 activity and content. Hepatic microsomes were prepared from groups of rats prior to dosing and at 2, 5, 12, and 24 hr postdosing with DCE (100 mg/kg ip), and total P450 content and the activity of CYP2E1 was determined. Breath was collected from parallel groups of rats predose and at several intervals that encompassed the time points for rats euthanized for microsome preparation. Over 100 breath components were identified by GC/MS and quantitated by GC/FID. The overall change in the profile of breath VOCs resulting from administration of DCE was striking. An increase of approximately 1000% was measured in the mass of non-DCE-derived VOCs exhaled 4-6 hr after dosing, but there was no increase in hepatic lipid peroxidation. In addition to hexane, short-chain methyl ketones were particularly affected, and percentage increases in response to inhibition were inversely related to chain length, with acetone and 2-butanone > 2-pentanone >> 2-hexanone > 2-heptanone. There were no statistically significant decreases in total content of P450, but the activity of CYP2E1 was diminished about 65% at 2 and 5 hr after DCE treatment. However, 24 hr after inhibitor administration the total mass of VOCs expired was only marginally elevated above baseline and CYP2E1 activity was not significantly different from that of untreated rats. The compounds most markedly increased upon inhibition of CYP2E1 are also excellent inducers of that isozyme, and this finding is consistent with the hypothesis that these chemicals are important to the normal homeostasis of CYP2E1. The increase in breath components observed following inhibition of CYP2E1 suggests that VOCs in breath can reflect the activity of that isozyme in vivo.

The time of detection of recessive visible genes with non-random mating.

Expressions for the probability and average time of detection of a recessive visible gene in populations where there is partial selfing or partial full-sib mating are presented. A small increase in the proportion of inbred matings greatly reduces the average time until detection and increases the proportion detected. Unless the proportion of inbred matings or the population size is very small, the time and proportion detected are approximately independent of the population size.