Structure of the R r tandem duplication in maize

Isolation by distance in populations with power-law dispersal

Limited dispersal of individuals between generations results in isolation by distance, in which individuals further apart in space tend to be less related. Classic models of isolation by distance assume that dispersal distances are drawn from a thin-tailed distribution and predict that the proportion of the genome that is identical by descent between a pair of individuals should decrease exponentially with the spatial separation between them. However, in many natural populations, individuals occasionally disperse over very long distances. In this work, we use mathematical analysis and coalescent simulations to study the effect of long-range (power-law) dispersal on patterns of isolation by distance. We find that it leads to power-law decay of identity-by-descent at large distances with the same exponent as dispersal. We also find that broad power-law dispersal produces another, shallow power-law decay of identity-by-descent at short distances. These results suggest that the distribution of long-range dispersal events could be estimated from sequencing large population samples taken from a wide range of spatial scales.

A spatial approach to jointly estimate Wright's neighborhood size and long-term effective population size

Spatially continuous patterns of genetic differentiation, which are common in nature, are often poorly described by existing population genetic theory or methods that assume panmixia or discrete, clearly definable populations. There is therefore a need for statistical approaches in population genetics that can accommodate continuous geographic structure, and that ideally use georeferenced individuals as the unit of analysis, rather than populations or subpopulations. In addition, researchers are often interested describing the diversity of a population distributed continuously in space, and this diversity is intimately linked to the dispersal potential of the organism. A statistical model that leverages information from patterns of isolation-by-distance to jointly infer parameters that control local demography (such as Wright's neighborhood size), and the long-term effective size (Ne) of a population would be useful. Here, we introduce such a model that uses individual-level pairwise genetic and geographic distances to infer Wright's neighborhood size and long-term Ne. We demonstrate the utility of our model by applying it to complex, forward-time demographic simulations as well as an empirical dataset of the Red Sea clownfish (Amphiprion bicinctus). The model performed well on simulated data relative to alternative approaches and produced reasonable empirical results given the natural history of clownfish. The resulting inferences provide important insights into the population genetic dynamics of spatially structure populations.

Rearrangement with the nkd2 promoter contributed to allelic diversity of the r1 gene in maize (Zea mays)

The maize red1 (r1) locus regulates anthocyanin accumulation and is a classic model for allelic diversity; changes in regulatory regions are responsible for most of the variation in gene expression patterns. Here, an intrachromosomal rearrangement between the distal upstream region of r1 and the region of naked endosperm 2 (nkd2) upstream to the third exon generated a nkd2 null allele lacking the first three exons, and the R1-st (stippled) allele with a novel r1 5' promoter region homologous to 5' regions from nkd2-B73. R1-sc:124 (an R1-st derivative) shows increased and earlier expression than a standard R1-g allele, as well as ectopic expression in the starchy endosperm compartment. Laser capture microdissection and RNA sequencing indicated that ectopic R1-sc:124 expression impacted expression of genes associated with RNA modification. The expression of R1-sc:124 resembled nkd2-W22 expression, suggesting that nkd2 regulatory sequences may influence the expression of R1-sc:124. The r1-sc:m3 allele is derived from R1-sc:124 by an insertion of a Ds6 transposon in intron 4. This insertion blocks anthocyanin regulation by causing mis-splicing that eliminates exon 5 from the mRNA. This allele serves as an important launch site for Ac/Ds mutagenesis studies, and two Ds6 insertions believed to be associated with nkd2 mutant alleles were actually located in the r1 5' region. Among annotated genomes of teosinte and maize varieties, the nkd2 and r1 loci showed conserved overall gene structures, similar to the B73 reference genome, suggesting that the nkd2-r1 rearrangement may be a recent event.

Ghosts of a Structured Past: Impacts of Ancestral Patterns of Isolation-by-Distance on Divergence-Time Estimation

Isolation-by-distance is a widespread pattern in nature that describes the reduction of genetic correlation between subpopulations with increased geographic distance. In the population ancestral to modern sister species, this pattern may hypothetically inflate population divergence time estimation due to allele frequency differences in subpopulations at the ends of the ancestral population. In this study, we analyze the relationship between the time to the most recent common ancestor and the population divergence time when the ancestral population model is a linear stepping-stone. Using coalescent simulations, we compare the coalescent time to the population divergence time for various ratios of the divergence time over the population size. Next, we simulate whole genomes to obtain single nucleotide polymorphisms (SNPs), and use the Bayesian coalescent program SNAPP to estimate divergence times. We find that as the rate of migration between neighboring demes decreases, the coalescent time becomes significantly greater than the population divergence time when sampled from end demes. Divergence-time overestimation in SNAPP becomes severe when the divergence-to-population size ratio < 10 and migration is low. Finally, we demonstrate the impact of ancestral isolation-by-distance on divergence-time estimation using an empirical dataset of squamates (Tropidurus) endemic to Brazil. We conclude that studies estimating divergence times should be cognizant of the potential ancestral population structure in an explicitly spatial context or risk dramatically overestimating the timing of population splits.

The unusual dRemp retrotransposon is abundant, highly mutagenic, and mobilized only in the second pollen mitosis of some maize lines

The frequent mutations recovered recently from the pollen of select maize lines resulted from the meiotic mobilization of specific low-copy number long-terminal repeat (LTR) retrotransposons, which differ among lines. Mutations that arise at male meiosis produce kernels with concordant mutant phenotypes in both endosperm and embryo because the two sperms that participate in double fertilization are genetically identical. Those are in a majority. However, a small minority of kernels with a mutant endosperm carry a nonconcordant normal embryo, pointing to a postmeiotic or microgametophytic origin. In this study, we have identified the basis for those nonconcordant mutations. We find that all are produced by transposition of a defective LTR retrotransposon that we have termed dRemp (defective retroelement mobile in pollen). This element has several unique properties. Unlike the mutagenic LTR retrotransposons identified previously, dRemp is present in hundreds of copies in all sequenced lines. It seems to transpose only at the second pollen mitosis because all dRemp insertion mutants are nonconcordant yet recoverable in either the endosperm or the embryo. Although it does not move in most lines, dRemp is highly mobile in the Corn Belt inbred M14, identified earlier by breeders as being highly unstable. Lastly, it can be recovered in an array of structures, ranging from solo LTRs to tandem dRemp repeats containing several internal LTRs, suggestive of extensive recombination during retrotransposition. These results shed further light on the spontaneous mutation process and on the possible basis for inbred instability in maize.

Isolation-by-distance-and-time in a stepping-stone model

With the great advances in ancient DNA extraction, genetic data are now obtained from geographically separated individuals from both present and past. However, population genetics theory about the joint effect of space and time has not been thoroughly studied. Based on the classical stepping-stone model, we develop the theory of Isolation by distance and time. We derive the correlation of allele frequencies between demes in the case where ancient samples are present, and investigate the impact of edge effects with forward-in-time simulations. We also derive results about coalescent times in circular and toroidal models. As one of the most common ways to investigate population structure is principal components analysis (PCA), we evaluate the impact of our theory on PCA plots. Our results demonstrate that time between samples is an important factor. Ancient samples tend to be drawn to the center of a PCA plot.

Dying on the way: the influence of migrational mortality on neutral models of spatial variation

Migrational mortality is introduced into the classical Malécot model for migration, mutation, and random genetic drift. To assess the influence of mortality, its effect on the backward migration rates and on the probabilities of identity in allelic state are studied. Perhaps surprisingly, some of the former may increase, but as is intuitive, their sum always decreases. As expected, in the island model, mortality does not change the migration pattern, but it decreases the migration rate. Furthermore, it decreases the expected heterozygosity, but increases the genetic diversity and differentiation. The circular habitat and the unbounded, linear stepping-stone model also illustrate the general results. Arbitrary migration is also analyzed. If migration is sufficiently weak, then mortality diminishes every migration rate; it decreases the expected heterozygosity and the genetic similarity between demes. In the strong-migration limit, mortality may raise or lower the probability of identity in state. Perhaps unexpectedly, under mild and reasonable biological assumptions, mortality does not alter the diffusion limit of the probabilities of identity.

Divergence of gene regulation through chromosomal rearrangements

BACKGROUND

The molecular mechanisms that modify genome structures to give birth and death to alleles are still not well understood. To investigate the causative chromosomal rearrangements, we took advantage of the allelic diversity of the duplicated p1 and p2 genes in maize. Both genes encode a transcription factor involved in maysin synthesis, which confers resistance to corn earworm. However, p1 also controls accumulation of reddish pigments in floral tissues and has therefore acquired a new function after gene duplication. p1 alleles vary in their tissue-specific expression, which is indicated in their allele designation: the first suffix refers to red or white pericarp pigmentation and the second to red or white glume pigmentation.

RESULTS

Comparing chromosomal regions comprising p1-ww[4Co63], P1-rw1077 and P1-rr4B2 alleles with that of the reference genome, P1-wr[B73], enabled us to reconstruct additive events of transposition, chromosome breaks and repairs, and recombination that resulted in phenotypic variation and chimeric regulatory signals. The p1-ww[4Co63] null allele is probably derived from P1-wr[B73] by unequal crossover between large flanking sequences. A transposon insertion in a P1-wr-like allele and NHEJ (non-homologous end-joining) could have resulted in the formation of the P1-rw1077 allele. A second NHEJ event, followed by unequal crossover, probably led to the duplication of an enhancer region, creating the P1-rr4B2 allele. Moreover, a rather dynamic picture emerged in the use of polyadenylation signals by different p1 alleles. Interestingly, p1 alleles can be placed on both sides of a large retrotransposon cluster through recombination, while functional p2 alleles have only been found proximal to the cluster.

CONCLUSIONS

Allelic diversity of the p locus exemplifies how gene duplications promote phenotypic variability through composite regulatory signals. Transposition events increase the level of genomic complexity based not only on insertions but also on excisions that cause DNA double-strand breaks and trigger illegitimate recombination.

The influence of partial panmixia on neutral models of spatial variation

Partial panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into neutral models of geographical variation is investigated. The monoecious, diploid population is subdivided into randomly mating colonies that exchange gametes independently of genotype. The gametes fuse wholly at random, including self-fertilization. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus; every allele mutates to new alleles at the same rate. Introducing some panmixia intensifies sufficiently weak migration. A general formula is derived for the migration effective population number, N(e), and N(e) is evaluated explicitly in a number of models with nonconservative migration. Usually, N(e) increases as the panmictic rate, b, increases; in particular, this result holds for two demes, and generically if the underlying migration is either sufficiently weak or panmixia is sufficiently strong. However, in an analytic model, there exists an open set of parameters for which N(e) decreases as b increases. Migration is conservative in the island and circular-habitat models, which are studied in detail. In the former, including some panmixia simply alters the underlying migration rate, increasing (decreasing) it if it is less (greater) than the panmictic value. For the circular habitat, the probability of identity in allelic state at equilibrium is calculated in a nonlocal, continuous-space, continuous-time approximation. In both models, by an efficient, general method, the expected homozygosity, effective number of alleles, and differentiation of gene frequencies are evaluated and discussed; their monotonicity properties with respect to all the parameters are determined; and in the model of infinitely many sites, the mean coalescence times and nucleotide diversities are studied similarly. For the probability of identity at equilibrium in the unbounded stepping-stone model in arbitrarily many dimensions, introducing some panmixia merely replaces the mutation rate by a larger parameter. If the average probability of identity is initially zero, as for identity by descent, then the same conclusion holds for all time.

Are geographic populations equivalent to genetic populations in biennial species? A study usingVerbascum virgatum(Scrophulariaceae)

Geographic populations are not necessarily equivalent to genetic populations. Electrophoretic isozyme analysis shows that in the biennial,Verbascum virgatum, not only is spatial distribution a factor creating isolated populations, but time also is an isolating mechanism. Thus, in the biennial situation there is a possibility that selection can be rejected as the probable cause of variation, much as can random drift in cases involving spatial distributions. The magnitudeof difference infrequency of alleles between the odd and even year colonies studied was too large to be explained by random drift in populations of the size and short duration of those we observed. Similarly, it is unlikely that random fluctuations in selection intensity on one age class would produce a difference as large as that observed. It is possible, however, that variation was introduced (mutation or founder) when the population was much smaller and that the difference was trapped at a relatively high level when the population rapidly increased in size. Simulations and algebraic theory do not refute this idea. They also show that colony differentiation can occur with migration rates considerably greater than previously predicted.

Genetic drift on networks: ploidy and the time to fixation

Genetic drift in finite populations ultimately leads to the loss of genetic variation. This paper examines the rate of neutral gene loss for a range of population structures defined by a graph. We show that, where individuals reside at fixed points on an undirected graph with equal degree nodes, the mean time to loss differs from the panmictic value by a positive additive term that depends on the number of individuals (not genes) in the population. The effect of these spatial structures is to slow the time to fixation by an amount that depends on the way individuals are distributed, rather than changing the apparent number of genes available to be sampled. This relationship breaks down, however, for a broad class of spatial structures such as random, small-world and scale-free networks. For the latter structures there is a counter-intuitive acceleration of fixation proportional to the level of ploidy.

Distribution of Activator (Ac) throughout the maize genome for use in regional mutagenesis

A collection of Activator (Ac)-containing, near-isogenic W22 inbred lines has been generated for use in regional mutagenesis experiments. Each line is homozygous for a single, precisely positioned Ac element and the Ds reporter, r1-sc:m3. Through classical and molecular genetic techniques, 158 transposed Ac elements (tr-Acs) were distributed throughout the maize genome and 41 were precisely placed on the linkage map utilizing multiple recombinant inbred populations. Several PCR techniques were utilized to amplify DNA fragments flanking tr-Ac insertions up to 8 kb in length. Sequencing and database searches of flanking DNA revealed that the majority of insertions are in hypomethylated, low- or single-copy sequences, indicating an insertion site preference for genic sequences in the genome. However, a number of Ac transposition events were to highly repetitive sequences in the genome. We present evidence that suggests Ac expression is regulated by genomic context resulting in subtle variations in Ac-mediated excision patterns. These tr-Ac lines can be utilized to isolate genes with unknown function, to conduct fine-scale genetic mapping experiments, and to generate novel allelic diversity in applied breeding programs.

Activator mutagenesis of the pink scutellum1/viviparous7 locus of maize

The transposable elements Activator/Dissociation (Ac/Ds) were first discovered in maize, yet they have not been used extensively in their native host for gene-tagging experiments. This can be attributed largely to the low forward mutation rate and the propensity for closely linked transpositions associated with Ac and its nonautonomous deletion derivative Ds. To overcome these limitations, we are developing a series of nearly isogenic maize lines, each with a single active Ac element positioned at a well-defined location. These Ac elements are distributed at 10- to 20-centimorgan intervals throughout the genome for use in regional mutagenesis. Here, we demonstrate the utility of this Ac-based gene-tagging approach through the targeted mutagenesis of the pink scutellum1/viviparous7 (ps1/vp7) locus. Using a novel PCR-based technique, the Ps1 gene was cloned and Ac elements positioned precisely in each of the seven alleles recovered. The Ps1 gene is predicted to encode lycopene beta-cyclase and is necessary for the accumulation of both abscisic acid and the carotenoid zeaxanthin in mature maize embryos. This study demonstrates the utility of an Ac mutagenesis program to efficiently generate allelic diversity at closely linked loci in maize.

The coalescent in a continuous, finite, linear population

In this article we present a model for analyzing patterns of genetic diversity in a continuous, finite, linear habitat with restricted gene flow. The distribution of coalescent times and locations is derived for a pair of sequences sampled from arbitrary locations along the habitat. The results for mean time to coalescence are compared to simulated data. As expected, mean time to common ancestry increases with the distance separating the two sequences. Additionally, this mean time is greater near the center of the habitat than near the ends. In the distant past, lineages that have not undergone coalescence are more likely to have been at opposite ends of the population range, whereas coalescent events in the distant past are biased toward the center. All of these effects are more pronounced when gene flow is more limited. The pattern of pairwise nucleotide differences predicted by the model is compared to data collected from sardine populations. The sardine data are used to illustrate how demographic parameters can be estimated using the model.

The influence of neighborhood size and habitat shape on the accumulation of deleterious mutations

To examine the impact of genetic neighborhood size and habitat shape on genetic load and the accumulation of deleterious mutation, individual-based simulations were performed in continuously distributed habitats. The risk of extinction increased as both the area of the habitat and the neighborhood size decreased. When the neighborhood area became smaller than the habitat area, habitat shape also began to influence the risk of extinction by mutation loads, expected time to extinction being shorter in longer and narrower habitats than in a square habitat. Both the number of homozygous deleterious loci per individual and the mutation load in the population increased as the neighborhood size and total population size decreased. Neighborhood size and total population size both independently affected the average number of homozygous deleterious loci per individual. In addition, as the ratio of the long to the short side of the rectangle of a habitat increased, the average number of homozygous deleterious loci increased. When the areas of the habitats were held constant, the average number of homozygous loci and the mutation loads were smallest for a regular square and largest for the longest, narrowest habitat. These results suggest that the spatial genetic structure of an individual is an important factor in the accumulation of deleterious mutations and the risk of extinction by mutation meltdown.

A continuous migration model with stable demography

A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integro-differential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y epsilon R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x, y) = V(x - y) where V(x) approximately V(x/beta)/beta2 approaches a delta function, the equilibrium probability of identity vanishes as beta Leads to 0. The asymptotic rate at which this occurs is discussed for mutation rates u = u0 Greater than 0 and for beta approximately cua, alpha Greater than 0, and u Leads to 0.

Isolation by distance: reply to Lalouel and Morton

Lalouel's assertion that I misinterpreted Malécot's work on isolation by distance may or may not be correct. If so, my assertions of error in Malécot's derivation are wrong, although they do apply to others who have used models involving a spatial continuum. Lalouel's other claims of error in my derivations of the consequences of a spatially continuous model of population reproduction and migration are incorrect, with the exception of one isolated misprint.

Decay of genetic variability in geographically structured populations

The ultimate rate and pattern of approach to equilibrium of a diploid, monoecious population subdivided into a finite number of equal, large, panmictic colonies are calculated. The analysis is restricted to a single locus in the absence of selection, and every mutant is assumed to be new to the population. It is supposed that either the time-independent backward migration pattern is symmetric in the sense that the probability that an individual at position x migrated from y equals the probability that one at y migrated from x, or it depends only on displacements and not on initial and final positions. Generations are discrete and nonoverlapping. Asymptotically, the rate of convergence is approximately (I-u)2t[I-(2NT)-1]t, where u, NT, and t denote the mutation rate, total population size, and time in generations, respectively; the transient part of the probability that two homologous genes are the same allele is approximately independent of their spatial separation. Thus, in this respect the population behaves as if it were panmictic.

The effect of population subdivision on two loci without selection

This paper is devoted to the study of the effects of population subdivision on the evolution of two linked loci. Two simple deterministic models of population subdivision without selection are investigated. One is a finite linear ‘stepping stone’ model and the other is a finite linear stepping stone chain of populations stretching between two large populations of constant genetic constitution. At equilibrium in the first model the gene frequencies in each population are equal and there is linkage equilibrium in each population. The rate of decay to zero of the linkage disequilibrium functions is the larger of (1 –c) and, where λ1is the rate of convergence of the gene frequencies to equilibrium and c is the recombination frequency. In the second model at equilibrium there will be a linear cline in gene frequencies connecting the two large constant populations. This cline will be accompanied by a ‘cline’ of linkage disequilibria. The rate of convergence to this equilibrium cline is independent of the recombination frequency, and, in fact, the gene frequencies and the linkage disequilibria converge to equilibrium at the same rate.

The decay of genetic variability in geographically structured populations

The geographical structure of a population distributed continuously and homogeneously along an infinite linear habitat is explored. The analysis is restricted to a single locus in the absence of selection, and every mutant is assumed to be new to the population. An explicit formula is derived for the probability that two homologous genes separated by a given distance at any time t are the same allele. The ultimate rate of approach to equilibrium is shown to be t(-3/2)e(-2ut), where u is the mutation rate. An approximation is given for the stationary probability of allelism in an infinite two-dimensional population, which, unlike previous expressions, is finite everywhere. For a finite habitat of arbitrary shape and any number of dimensions, it is proved that if the population density is very high, then asymptotically the transient part of the probability of allelism is spatially uniform and decays at the rate e(-[2u+1/(2N)]t), where N is the total population size. Thus, in this respect the population behaves as if it were panmictic. The dependence of the amount of local gene frequency differentiation on population density and habitat size and dimensionality is discussed.