Information Theory Broadens the Spectrum of Molecular Ecology and Evolution.

Information or entropy analysis of diversity is used extensively in community ecology, and has recently been exploited for prediction and analysis in molecular ecology and evolution. Information measures belong to a spectrum (or q profile) of measures whose contrasting properties provide a rich summary of diversity, including allelic richness (q=0), Shannon information (q=1), and heterozygosity (q=2). We present the merits of information measures for describing and forecasting molecular variation within and among groups, comparing forecasts with data, and evaluating underlying processes such as dispersal. Importantly, information measures directly link causal processes and divergence outcomes, have straightforward relationship to allele frequency differences (including monotonicity that q=2 lacks), and show additivity across hierarchical layers such as ecology, behaviour, cellular processes, and nongenetic inheritance.

Comparing the van Oosterhout and Chybicki-Burczyk methods of estimating null allele frequencies for inbred populations.

In spite of the usefulness of codominant markers in population genetics, the existence of null alleles raises challenging estimation issues in natural populations that are characterized by positive inbreeding coefficients (F > 0). Disregarding the possibility of F > 0 in a population will generally lead to overestimates of null allele frequencies. Conversely, estimates of inbreeding coefficients (F) may be strongly biased upwards (excess homozygotes), in the presence of nontrivial frequencies of null alleles. An algorithm has been presented for the estimation of null allele frequencies in inbred populations (van Oosterhout method), using external estimates of the F-statistics. The goal of this study is to introduce a modification of this method and to provide a formal comparison with an alternative likelihood-based method (Chybicki-Burczyk). Using simulated data, we illustrate the strengths and limitations of these competing methods. Under most circumstances, the likelihood method is preferable, but for highly inbred organisms, a modified van Oosterhout method offers some advantages.

PSA: software for parental structure analysis of seed or seedling patches.

Parental structure analysis (PSA) is a computer program to analyse separate contributions of paternal and maternal parents to postdispersal plant offspring. The program provides joint estimates of maternal, paternal and cross-parental correlations within and among a set of predefined groups of seeds or seedlings, as well as derivative estimates of effective parental numbers. PSA utilizes data sets that distinguish between maternal and paternal contributions to the genotype of each offspring in the sample, but does not require parental samples per se. The approach requires assay of codominant diploid markers from both seed coat (maternally inherited) and seedling/embryo (biparentally inherited) tissues for each offspring. A simulation analysis of PSA's performance shows that it provides fairly accurate parental correlation estimates from affordable sampling effort. PSA should be of interest to plant biologists studying the interplay between dispersal, demography and genetics, as well as plant-animal interactions.

Climatic niche and neutral genetic diversity of the six Iberian pine species: a retrospective and prospective view.

Quaternary climatic fluctuations have left contrasting historical footprints on the neutral genetic diversity patterns of existing populations of different tree species. We should expect the demography, and consequently the neutral genetic structure, of taxa less tolerant to particular climatic extremes to be more sensitive to long-term climate fluctuations. We explore this hypothesis here by sampling all six pine species found in the Iberian Peninsula (2464 individuals, 105 populations), using a common set of chloroplast microsatellite markers, and by looking at the association between neutral genetic diversity and species-specific climatic requirements. We found large variation in neutral genetic diversity and structure among Iberian pines, with cold-enduring mountain species (Pinus uncinata, P. sylvestris and P. nigra) showing substantially greater diversity than thermophilous taxa (P. pinea and P. halepensis). Within species, we observed a significant positive correlation between population genetic diversity and summer precipitation for some of the mountain pines. The observed pattern is consistent with the hypotheses that: (i) more thermophilous species have been subjected to stronger demographic fluctuations in the past, as a consequence of their maladaptation to recurrent glacial cold stages; and (ii) altitudinal migrations have allowed the maintenance of large effective population sizes and genetic variation in cold-tolerant species, especially in more humid regions. In the light of these results and hypotheses, we discuss some potential genetic consequences of impending climate change.

Restricted pollen flow of Dieffenbachia seguine populations in fragmented and continuous tropical forest.

Habitat fragmentation can change the ecological context of populations, rupturing genetic connectivity among them, changing genetic structure, and increasing the loss of genetic diversity. We analyzed mating system and pollen structure in two population fragments and two continuous forest populations of Dieffenbachia seguine (Araceae), an insect-pollinated understory herb in the tropical rain forest of Los Tuxtlas, México, using nine allozyme loci. Mating system analysis indicated almost complete outcrossing but some inbreeding among the adults. Pollen structure analysis indicated highly restricted pollen flow, both within and among populations. We showed that the effective pollination neighborhood was small in all populations, and slightly (though not significantly) smaller in fragments, partially as a consequence of an increase in density of reproductive individuals in those fragments. Using assignment analysis, we showed that all populations were strongly structured, suggesting that pollen and seed flow across the Los Tuxtlas landscape has been spatially restricted, though sufficient to maintain connectedness. Forest fragmentation at Los Tuxtlas has (so far) had limited impact on pollen dynamics, despite the changing ecological context, with reduced pollinator abundance being partially offset by increased flowering density in fragments. Continued outcrossing and limited pollen immigration, coupled with more extensive seed migration, should maintain genetic connectedness in D. seguine, if fragmentation is not further exacerbated by additional deforestation.

Estimating anisotropic pollen dispersal: a case study in Quercus lobata.

The pollen dispersal distribution is an important element of the neighbourhood size of plant populations. Most methods aimed at estimating the dispersal curve assume that pollen dispersal is isotropic, but evidence indicates that this assumption does not hold for many plant species, particularly wind-pollinated species subject to prevailing winds during the pollination season. We propose here a method of detecting anisotropy of pollen dispersal and of gauging its intensity, based on the estimation of the differentiation of maternal pollen clouds (TWOGENER extraction), assuming that pollen dispersal is bivariate and normally distributed. We applied the new method to a case study in Quercus lobata, detecting only a modest level of anisotropy in pollen dispersal in a direction roughly similar to the prevailing wind direction. Finally, we conducted a simulation to explore the conditions under which anisotropy can be detected with this method, and we show that while anisotropy is detectable, in principle, it requires a large volume of data.

Pollen-mediated gene dispersal within continuous and fragmented populations of a forest understorey species, Trillium cuneatum.

Pollen movement plays a critical role in the distribution of genetic variation within and among plant populations. Direct measures of pollen movement in the large, continuous populations that characterize many herbaceous plant species are often technically difficult and biologically unreliable. Here, we studied contemporary pollen movement in four large populations of Trillium cuneatum. Three populations, located in the Georgia Piedmont, are exposed to strong anthropogenic disturbances, while the fourth population, located in the Southern Appalachian Mountains, is relatively undisturbed. Using the recently developed TwoGener analysis, we extracted estimates of the effective number of pollen donors (N(ep)), effective mating neighbourhood size (A(ep)) and the average distance of pollen movement (delta) for each population. We extended the TwoGener method by developing inference on the paternal gametic contribution to the embryo in situations where offspring genotypes are inferred from seeds and elaiosomes of species with bisporic megagametogenesis. Our estimates indicate that maternal plants do not sample pollen randomly from a global pool; rather, pollen movement in all four populations is highly restricted. Although the effective number of pollen donors per maternal plant is low (1.22-1.66) and pollen movement is highly localized in all populations, N(ep) in the disturbed Piedmont populations is higher and there is more pollen movement than in the mountains. The distance pollen moves is greater in disturbed sites and fragmented populations, possibly due to edge effects in Trillium habitats.

Measuring the genetic structure of the pollen pool as the probability of paternal identity.

Contemporary pollen flow in forest plant species is measured by the probability of paternal identity (PPI) for two randomly sampled offspring, drawn from a single female, and contrasting that with PPI for two random offspring, drawn from different females. Two different estimation strategies have emerged: (a) an indirect approach, using the 'genetic structure' of the pollen received by different mothers and (b) a direct approach, based on parentage analysis. The indirect strategy is somewhat limited by the assumptions, but is widely useful. The direct approach is most appropriate where a large majority of the true fathers can be identified exactly, which is sometimes possible with high-resolution SSR markers. Using the parentage approach, we develop estimates of PPI, showing that the obvious estimates are severely biased, and providing an unbiased alternative. We then illustrate the methods with SSR data from a 36-tree isolated population of Pinus sylvestris from the Meseta region of Spain, for which categorical paternity assignment was available for over 95% of offspring. For all the females combined, we estimate that PPI=0.0425, indicating uneven male reproductive contributions. Different (but overlapping) arrays of males pollinate different females, and for the average female, PPI=0.317, indicating substantial 'pollen structure' for the population. We also relate the direct measures of PPI to those available from indirect approaches, and show that they are generally comparable.

Two-generation analysis of pollen flow across a landscape V: a stepwise approach for extracting factors contributing to pollen structure.

Patterns of pollen dispersal are central to both the ecology and evolution of plant populations. However, the mechanisms controlling either the dispersal process itself or our estimation of that process may be influenced by site-specific factors such as local forest structure and nonuniform adult genetic structure. Here, we present an extension of the AMOVA model applied to the recently developed TWOGENER analysis of pollen pool structure. This model, dubbed the Stepwise AMOVA (StAMOVA), focuses on determining to what extent ecological, demographic, and/or environmental factors influence the observed genetic variation in spatially separated pollen pools. The analysis is verified for efficacy, using an extensive battery of simulations, illustrating: (1) how nonuniform adult genetic structure influences the differentiation of spatially separated pollen pools, and (2) how effectively the Stepwise analysis performs in carrying out the appropriate corrections. Finally, the model is applied to a Quercus alba data set, from which we have prior evidence that the adult genetic structure is nonuniformly distributed across the sampling landscape. From this data set, we show how the Stepwise model can be applied to remove the effects of spatial adult genetic structure on pollen pool differentiation and contrast these results with those derived from the original TWOGENER analysis.

A multiyear estimate of the effective pollen donor pool for Albizia julibrissin.

Studies of pollen movement in plant populations are often limited to a single reproductive event, despite concerns about the adequacy of single-year measures for perennial organisms. In this study, we estimate the effective number of pollen donors per tree from a multiyear study of Albizia julibrissin Durazz (mimosa, Fabaceae), an outcrossing, insect-pollinated tree. We determined 40 seedling genotypes for each of 15 seed trees during 4 successive years. A molecular analysis of variance of the pollen gametes fertilizing the sampled seeds was used to partition variation in pollen pools among seed trees, among years, and within single tree-year collections. Using these variance components, we demonstrate significant male gametic variability among years for individual trees. However, results indicate that yearly variation in the 'global pollen pool', averaged over all 15 seed trees for these 4 years, is effectively zero. We estimate the effective number of pollen donors for a single mimosa tree (N(ep)) to be 2.87. Single season analyses yield N(ep) approximately 2.05, which is 40% less than the value of N(ep) estimated from 4 years of data. We discuss optimal sampling for future studies designed to estimate N(ep). Studies should include more trees, each sampled over at least a few years, with fewer seeds per tree per year than are needed for a traditional parentage study.

Pollen movement in declining populations of California Valley oak, Quercus lobata: where have all the fathers gone?

The fragmented populations and reduced population densities that result from human disturbance are issues of growing importance in evolutionary and conservation biology. A key issue is whether remnant individuals become reproductively isolated. California Valley oak (Quercus lobata) is a widely distributed, endemic species in California, increasingly jeopardized by anthropogenic changes in biota and land use. We studied pollen movement in a savannah population of Valley oak at Sedgwick Reserve, Santa Barbara County, to estimate effective number of pollen donors (Nep) and average distance of effective pollen movement (delta). Using twogener, our recently developed hybrid model of paternity and genetic structure treatments that analyses maternal and progeny multilocus genotypes, we found that current Nep = 3.68 individuals. Based on an average adult density of d= 1.19 stems/ha, we assumed a bivariate normal distribution to model current average pollen dispersal distance (delta) and estimated delta= 64.8 m. We then deployed our parameter estimates in spatially explicit models of the Sedgwick population to evaluate the extent to which Nep may have changed, as a consequence of progressive stand thinning between 1944 and 1999. Assuming that pollen dispersal distance has not changed, we estimate Nep was 4.57 individuals in 1944, when stand density was 1.48. Both estimates indicate fewer effective fathers than one might expect for wind-pollinated species and fewer than observed elsewhere. The results presented here provide a basis for further refinements on modelling pollen movement. If the trends continue, then ongoing demographic attrition could further reduce neighbourhood size in Valley oak resulting in increased risk of reproductive failure and genetic isolation.

Two-generation analysis of pollen flow across a landscape. I. Male gamete heterogeneity among females.

Gene flow is a key factor in the spatial genetic structure in spatially distributed species. Evolutionary biologists interested in microevolutionary processess and conservation biologists interested in the impact of landscape change require a method that measures the real time process of gene movement. We present a novel two-generation (parent-offspring) approach to the study of genetic structure (TwoGener) that allows us to quantify heterogeneity among the male gamete pools sampled by maternal trees scattered across the landscape and to estimate mean pollination distance and effective neighborhood size. First, we describe the model's elements: genetic distance matrices to estimate intergametic distances, molecular analysis of variance to determine whether pollen profiles differ among mothers, and optimal sampling considerations. Second, we evaluate the model's effectiveness by simulating spatially distributed populations. Spatial heterogeneity in male gametes can be estimated by phiFT, a male gametic analogue of Wright's F(ST) and an inverse function of mean pollination distance. We illustrate TwoGener in cases where the male gamete can be categorically or ambiguously determined. This approach does not require the high level of genetic resolution needed by parentage analysis, but the ambiguous case is vulnerable to bias in the absence of adequate genetic resolution. Finally, we apply TwoGener to an empirical study of Quercus alba in Missouri Ozark forests. We find that phiFT = 0.06, translating into about eight effective pollen donors per female and an effective pollination neighborhood as a circle of radius about 17 m. Effective pollen movement in Q. alba is more restricted than previously realized, even though pollen is capable of moving large distances. This case study illustrates that, with a modest investment in field survey and laboratory analysis, the TwoGener approach permits inferences about landscape-level gene movements.

Two-generation analysis of pollen flow across a landscape. II. Relation between phi(ft), pollen dispersal and interfemale distance.

We study the behavior of Phi(ft), a recently introduced estimator of instantaneous pollen flow, which is basically the intraclass correlation of inferred pollen cloud genetic frequencies among a sample of females drawn from a single population. Using standard theories of identity by descent and spatial processes, we show that Phi(ft) depends on the average distance of pollen dispersal (delta) and on the average distance between sampled mothers (x(1)). Provided that mothers are sampled far enough apart (x(1) > 5delta), Phi(ft) becomes independent of x(1) and is then inversely proportional to the square of delta. Provided that this condition is fulfilled, delta is directly estimable from Phi(ft). Even when x(1) < 5delta, estimation can easily be achieved via numerical evaluation. We show that the relation between Phi(ft) and delta is only modestly affected by the shape of the distribution function, a result of importance, since this shape is generally unknown. We also study the impact of adult density within the population on Phi(ft), showing that to achieve the correct inference of delta from Phi(ft) it must be taken into account, but that it has no effect on the distance at which mothers must be sampled.

Two-generation analysis of pollen flow across a landscape. III. Impact of adult population structure.

The rate and distance of instantaneous pollen flow in a population are parameters of considerable current interest for plant population geneticists and conservation biologists. We have recently developed an estimator (phi ft) of differentiation between the inferred pollen clouds that fertilize several females, sampled within a single population. We have shown that there is a simple relation between phi ft and the average pollen dispersal distance (delta) for the case of a population with no geographic structure. Though forest trees usually show considerable pollen flow, assuming an absence of spatially distributed genetic structure is not always wise. Here, we develop analytical theory for the relation between phi ft and delta, for the case where the probability of Identity by Descent (IBD) for two individuals decreases with the physical distance between them. This analytical theory allows us to provide an effective method for estimating pollen dispersal distance in a population with adult genetic structure. Using real examples, we show that estimation errors can be large if genetic structure is not taken into account, so it is wise to evaluate adult genetic structure simultaneously with estimation of phi ft for the pollen clouds. We show that the results are only moderately affected by changes in the decay function, a result of some importance since no completely established theory is available for this function.

Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure.

Population genetic theory predicts that plant populations will exhibit internal spatial autocorrelation when propagule flow is restricted, but as an empirical reality, spatial structure is rarely consistent across loci or sites, and is generally weak. A lack of sensitivity in the statistical procedures may explain the discrepancy. Most work to date, based on allozymes, has involved pattern analysis for individual alleles, but new PCR-based genetic markers are coming into vogue, with vastly increased numbers of alleles. The field is badly in need of an explicitly multivariate approach to autocorrelation analysis, and our purpose here is to introduce a new approach that is applicable to multiallelic codominant, multilocus arrays. The procedure treats the genetic data set as a whole, strengthening the spatial signal and reducing the stochastic (allele-to-allele, and locus-to-locus) noise. We (i) develop a very general multivariate method, based on genetic distance methods, (ii) illustrate it for multiallelic codominant loci, and (iii) provide nonparametric permutational testing procedures for the full correlogram. We illustrate the new method with an example data set from the orchid Caladenia tentaculata, for which we show (iv) how the multivariate treatment compares with the single-allele treatment, (v) that intermediate frequency alleles from highly polymorphic loci perform well and rare alleles poorly, (vi) that a multilocus treatment provides clearer answers than separate single-locus treatments, and (vii) that weighting alleles differentially improves our resolution minimally. The results, though specific to Caladenia, offer encouragement for wider application.

Analytical aspects of population-specific DNA fingerprinting for individuals.

An emerging problem of some interest is whether we can determine the population membership of a single individual, using a population-specific "genetic fingerprint." The levels of accuracy and precision required are beyond the reach of allozyme analysis, and attention has shifted to DNA polymorphisms. There are different types of DNA markers available for population surveys: RFLPs, mini- and micro-satellites, and RAPDs, and each type has its own strengths and weaknesses. We present a generic analysis that relates gene pool separation to our ability to assign individuals, an analysis that does not depend on the type of marker. We then review strengths and weaknesses of different DNA markers, in the context of DNA fingerprinting. Codominant loci are best. It is possible to gain more information per marker with multiallelic loci, but diminishing returns set in rapidly, and it is better to add loci. A modest number of independent loci is best, each locus with a modest number of alleles and with each allele in modest frequency.

Genetic analysis of male reproductive contributions in Chamaelirium luteum (L.) gray (Liliaceae).

Genealogical analysis is a powerful tool for analysis of reproductive performance in both natural and captive populations, but assignment of paternity has always been a stumbling block for this sort of work. Statistical methods for determining paternity have undergone several phases of development, ranging from straightforward genetic exclusion to assignment of paternity based on genetic likelihood criteria. In the present study, we present a genetic likelihood-based iterative procedure for fractional allocation of paternity within a progeny pool and apply this method to a population of Chamaelirium luteum, a dioecious member of the Liliaceae. Results from this analysis clearly demonstrate that different males make unequal contributions to the overall progeny pool, with many males contributing essentially nothing to the next generation. Furthermore, the distribution of paternal success among males shows a highly significant departure from (Poisson) randomness. The results from the present analysis were compared with earlier results obtained from the same data set, using likelihood-based categorical paternity assignments. The general biological pattern revealed by the two analyses is the same, but the estimates of reproductive success are only modestly (though significantly) correlated. The iterative procedure makes more complete use of the data and generates a more sharply resolved distribution of male reproductive success.

Using allele frequencies and geographic subdivision to reconstruct gene trees within a species: molecular variance parsimony.

We formalize the use of allele frequency and geographic information for the construction of gene trees at the intraspecific level and extend the concept of evolutionary parsimony to molecular variance parsimony. The central principle is to consider a particular gene tree as a variable to be optimized in the estimation of a given population statistic. We propose three population statistics that are related to variance components and that are explicit functions of phylogenetic information. The methodology is applied in the context of minimum spanning trees (MSTs) and human mitochondrial DNA restriction data, but could be extended to accommodate other tree-making procedures, as well as other data types. We pursue optimal trees by heuristic optimization over a search space of more than 1.29 billion MSTs. This very large number of equally parsimonious trees underlines the lack of resolution of conventional parsimony procedures. This lack of resolution is highlighted by the observation that equally parsimonious trees yield very different estimates of population genetic diversity and genetic structure, as shown by null distributions of the population statistics, obtained by evaluation of 10,000 random MSTs. We propose a non-parametric test for the similarity between any two trees, based on the distribution of a weighted coevolutionary correlation. The ability to test for tree relatedness leads to the definition of a class of solutions instead of a single solution. Members of the class share virtually all of the critical internal structure of the tree but differ in the placement of singleton branch tips.

Multivariate fluctuating asymmetry in Israeli adults.

Fluctuating asymmetry serves as an indicator of developmental homeostasis; any genetic or environmental factor that destroys homeostasis disturbs bilateral symmetry. Many studies have attempted to correlate increased fluctuating asymmetry with measures of developmental homeostasis or of adaptation, but collective results have been equivocal. We still have much to learn about fluctuating asymmetry itself. We develop a multivariate treatment of bilateral asymmetry that allows us to measure and adjust for the effects of both directional (right versus left) asymmetry and antisymmetry (handedness) and for the effects of size and sex. We examine 29 morphometric traits (13 size and shape, 8 pairs of bilateral traits) on 400 Israeli adults. We show that, even if metric traits are logarithmically transformed at the outset so that nonlinear allometric relations among them are properly accounted for and if the resulting measures are adjusted for sex by subtracting the means and dividing by the standard deviations, the correlation matrices among traits are strongly heterogeneous across sexes. Although the bilateral traits as a set are modestly correlated with the size and shape traits, neither size nor shape is correlated with asymmetry. Moreover, asymmetry traits are virtually uncorrelated inter se. We also examine the often touted connection between asymmetry and departures from morphometric modality and show that asymmetry is not correlated with deviations from either average size or average shape. If properly measured, fluctuating asymmetry becomes a measure of the noise in development; in our study it correlates with nothing. We discuss these results in light of empirical results and in terms of developmental theory suggesting that fluctuating asymmetry should be correlated with measures of maladaptation. Some of the effects reported in the literature need to be reexamined with more refined morphometric and statistical techniques.