A test of founder effect speciation using multiple loci in the auklets (Aethia spp.)

Whether speciation results more frequently from the genetic consequences of founder events or from gradual genetic divergence of large populations is a matter of debate. In this study, multiple analyses were applied to data from three loci (cytochrome b, alpha-enolase intron VIII, and MHC class II B) to test for founder effects associated with speciation in Aethia (Aves: Alcidae), a genus of seabirds thought to have undergone a rapid founder-induced radiation. Effective population sizes (N(e)) were derived from estimators of based on allelic diversity and the coalescent and from data on trans-species polymorphism. Results indicated that N(e) has been on the order of 10(5)-10(6) individuals throughout the evolutionary histories of least and crested auklets (A. pusilla and A. cristatella, respectively) and that N(e) of the ancestral species was at least 16,000 individuals. Computer simulations of MHC evolution indicated that a single-generation bottleneck at speciation could not have involved <85 individuals for each species. More moderate simulation scenarios indicated that population size could not have dropped below 2000 individuals at the time of species founding. Demographic history appears to have been stable for the auklets throughout the past several million years, and a founder effect associated with their speciation is unlikely.     

Model‐based approach to test hard polytomies in the Eulaemus clade of the most diverse South American lizard genus Liolaemus (Liolaemini,Squamata)

Lack of resolution in a phylogenetic tree is usually represented as a polytomy, and often adding more data (loci and taxa) resolves the species tree. These are the ‘soft’ polytomies, but in other cases additional data fail to resolve relationships; these are the ‘hard’ polytomies. This latter case is often interpreted as a simultaneous radiation of lineages in the history of a clade. Although hard polytomies are difficult to address, model‐based approaches provide new tools to test these hypotheses. Here, we used a clade of 144 species of the South American lizard clade Eulaemus to estimate phylogenies using a traditional concatenated matrix and three species tree methods: *BEAST, BEST, and minimizing deep coalescences (MDC). The different species tree methods recovered largely discordant results, but all resolved the same polytomy (e.g. very short internodes amongst lineages and low nodal support in Bayesian methods). We simulated data sets under eight explicit evolutionary models (including hard polytomies), tested these against empirical data (a total of 14 loci), and found support for two polytomies as the most plausible hypothesis for diversification of this clade. We discuss the performance of these methods and their limitations under the challenging scenario of hard polytomies. © 2015 The Linnean Society of London     

Tempo of speciation in a butterfly genus from the Southeast Asian tropics, inferred from mitochondrial and nuclear DNA sequence data

Molecular systematics is frequently beset with phylogenetic results that are not fully resolved. Researchers either state that the absence of resolution is due to character conflict, explosive speciation, or some combination of the two, but seldom do they carefully examine their data to distinguish between these causes. In this study, we exhaustively analyze a set of nuclear and mitochondrial nucleotide data for the Asian tropical butterfly genus Arhopala so as to highlight the causes of polytomies in the phylogenetic trees, and, as a result, to infer important biological events in the history of this genus. We began by using non-parametric statistical methods to determine whether the ambiguously resolved regions in these trees represent hard or soft polytomies. In addition we determined how this correlated to number of inferred changes on branches, using parametric maximum likelihood estimations. Based on congruent patterns in both mitochondrial and nuclear DNA sequences, we concluded that at two stages in the history of Arhopala there have been accelerated instances of speciation. One event, at the base of the phylogeny, generated many of the groups and subgroups currently recognized in this genus, while a later event generated another major clade consisting of both Oriental and Papuan species groups. Based on comparisons of closely related taxa, the ratio of instantaneous rate of evolution between mitochondrial and nuclear DNA evolution is established at approximately 3:1. The earliest radiation is dated between 7 and 11 Ma by a molecular clock analysis, setting the events generating much of the diversity of Arhopala at well before the Pleistocene. Periodical flooding of the Sunda plateau during interglacial periods was, therefore, not responsible for generating the major divisions in the genus Arhopala. Instead, we hypothesize that large-scale climatic changes taking place in the Miocene have induced the early acceleration in speciation.     

PROBLEMS WITH "SOFT" POLYTOMIES

Abstract— The "soft" assumption attributes polytomies to lack of data, not simultaneous cladogenesis (the "hard" assumption). Most systematists prefer the first interpretation, but most parsimony programs implicitly use the second. Results can thus be inconsistent with initial assumptions. Under certain circumstances that seem especially typical for large data sets treating higher taxa, it may be valid to eliminate both compatible and incompatible polytomous trees from consideration. Consistent treatment of soft polytomies can reduce the ambiguity of cladistic solutions and improve the resolution, and testability, of phylogenetic hypotheses.     

Generalized mixture models for molecular phylogenetic estimation

The rapidly growing availability of multigene sequence data during the past decade has enabled phylogeny estimation at phylogenomic scales. However, dealing with evolutionary process heterogeneity across the genome becomes increasingly challenging. Here we develop a mixture model approach that uses reversible jump Markov chain Monte Carlo (MCMC) estimation to permit as many distinct models as the data require. Each additional model considered may be a fully parametrized general time-reversible model or any of its special cases. Furthermore, we expand the usual proposal mechanisms for topology changes to permit hard polytomies (i.e., zero-length internal branches). This new approach is implemented in the Crux software toolkit. We demonstrate the feasibility of using reversible jump MCMC on mixture models by reexamining a well-known 44-taxon mammalian data set comprising 22 concatenated genes. We are able to reproduce the results of the original analysis (with respect to bipartition support) when we make identical assumptions, but when we allow for polytomies and/or use data-driven mixture model estimation, we infer much lower bipartition support values for several key bipartitions.     

Recent Selective Sweeps in North American Drosophila melanogaster Show Signatures of Soft Sweeps

Adaptation from standing genetic variation or recurrent de novo mutation in large populations should commonly generate soft rather than hard selective sweeps. In contrast to a hard selective sweep, in which a single adaptive haplotype rises to high population frequency, in a soft selective sweep multiple adaptive haplotypes sweep through the population simultaneously, producing distinct patterns of genetic variation in the vicinity of the adaptive site. Current statistical methods were expressly designed to detect hard sweeps and most lack power to detect soft sweeps. This is particularly unfortunate for the study of adaptation in species such as Drosophila melanogaster, where all three confirmed cases of recent adaptation resulted in soft selective sweeps and where there is evidence that the effective population size relevant for recent and strong adaptation is large enough to generate soft sweeps even when adaptation requires mutation at a specific single site at a locus. Here, we develop a statistical test based on a measure of haplotype homozygosity (H12) that is capable of detecting both hard and soft sweeps with similar power. We use H12 to identify multiple genomic regions that have undergone recent and strong adaptation in a large population sample of fully sequenced Drosophila melanogaster strains from the Drosophila Genetic Reference Panel (DGRP). Visual inspection of the top 50 candidates reveals that in all cases multiple haplotypes are present at high frequencies, consistent with signatures of soft sweeps. We further develop a second haplotype homozygosity statistic (H2/H1) that, in combination with H12, is capable of differentiating hard from soft sweeps. Surprisingly, we find that the H12 and H2/H1 values for all top 50 peaks are much more easily generated by soft rather than hard sweeps. We discuss the implications of these results for the study of adaptation in Drosophila and in species with large census population sizes.     

Lack of statistical power as a major limitation in understanding MHC‐mediated immunocompetence in wild vertebrate populations

Disentangling the sources of variation in developing an effective immune response against pathogens is of major interest to immunoecology and evolutionary biology. To date, the link between immunocompetence and genetic variation at the major histocompatibility complex (MHC) has received little attention in wild animals, despite the key role of MHC genes in activating the adaptive immune system. Although several studies point to a link between MHC and immunocompetence, negative findings have also been reported. Such disparate findings suggest that limited statistical power might be affecting studies on this topic, owing to insufficient sample sizes and/or a generally small effect of MHC on the immunocompetence of wild vertebrates. To clarify this issue, we investigated the link between MHC variation and seven immunocompetence proxies in a large sample of barn owls and estimated the effect sizes and statistical power of this and published studies on this topic. We found that MHC poorly explained variation in immunocompetence of barn owls, with small‐to‐moderate associations between MHC and immunocompetence in owls (effect size: .1 ≥ r ≤ .3) similar to other vertebrates studied to date. Such small‐to‐moderate effects were largely associated with insufficient power, which was only sufficient (>0.8) to detect moderate‐to‐large effect sizes (r ≥ .3). Thus, studies linking MHC variation with immunocompetence in wild populations are underpowered to detect MHC effects, which are likely to be of generally small magnitude. Larger sample sizes (>200) will be required to achieve sufficient power in future studies aiming to robustly test for a link between MHC variation and immunocompetence.     

Polytomies,signal and noise: revisiting the mitochondrial phylogeny and phylogeography of the Eurasian blindsnake species complex (Typhlopidae,Squamata)

Polytomies are multifurcating nodes on a phylogenetic tree that represent unresolved relationships. Contrary to ‘hard’ polytomies that hide simultaneous splitting events, ‘soft’ polytomies can theoretically be resolved with the addition of phylogenetic signal. This is not always successful, especially when a radiation is old and rapid, because adding more signal will inevitably increase the noise. The Xerotyphlops vermicularis species complex is an example of a largely unresolved old and rapid radiation. This mtDNA phylogeny is revisited by analysing samples representative of all lineages and generating a 3700‐bp final data set, after preliminary tests found two of the analysed markers responsible for long‐branch attraction. The new enhanced data set increased phylogenetic resolution, resulting in a robust time‐calibrated phylogeny and phylogeographic conclusions. Jordan/south Syria populations separated during the Middle Miocene, and the Messinian salinity crisis (MSC) appears responsible for the second diversification wave. A third radiation occurred during the Early Pliocene, resulting in four mtDNA groups west, east and south of the Amanos mountains in east Turkey/north Syria. Finally, three hypotheses regarding the number of potential ‘species’ within the complex are made, with the most moderate ‘four species’ hypothesis fitting very well with the diversity patterns and established systematics of east Mediterranean reptiles.     

Properties and power of the Drosophila Synthetic Population Resource for the routine dissection of complex traits

The Drosophila Synthetic Population Resource (DSPR) is a newly developed multifounder advanced intercross panel consisting of >1600 recombinant inbred lines (RILs) designed for the genetic dissection of complex traits. Here, we describe the inference of the underlying mosaic founder structure for the full set of RILs from a dense set of semicodominant restriction-site-associated DNA (RAD) markers and use simulations to explore how variation in marker density and sequencing coverage affects inference. For a given sequencing effort, marker density is more important than sequence coverage per marker in terms of the amount of genetic information we can infer. We also assessed the power of the DSPR by assigning genotypes at a hidden QTL to each RIL on the basis of the inferred founder state and simulating phenotypes for different experimental designs, different genetic architectures, different sample sizes, and QTL of varying effect sizes. We found the DSPR has both high power (e.g., 84% power to detect a 5% QTL) and high mapping resolution (e.g., ～1.5 cM for a 5% QTL).     

Loss and Recovery of Genetic Diversity in Adapting Populations of HIV

The evolution of drug resistance in HIV occurs by the fixation of specific, well-known, drug-resistance mutations, but the underlying population genetic processes are not well understood. By analyzing within-patient longitudinal sequence data, we make four observations that shed a light on the underlying processes and allow us to infer the short-term effective population size of the viral population in a patient. Our first observation is that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time, as opposed to several changes simultaneously. Second, we find that these fixation events are accompanied by a reduction in genetic diversity in the region surrounding the fixed drug-resistance mutation, due to the hitchhiking effect. Third, we observe that the fixation of drug-resistance mutations involves both hard and soft selective sweeps. In a hard sweep, a resistance mutation arises in a single viral particle and drives all linked mutations with it when it spreads in the viral population, which dramatically reduces genetic diversity. On the other hand, in a soft sweep, a resistance mutation occurs multiple times on different genetic backgrounds, and the reduction of diversity is weak. Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be ( confidence interval ). This number is much lower than the actual number of infected cells, but much larger than previous population size estimates based on synonymous diversity. We propose several explanations for the observed discrepancies. Finally, our fourth observation is that genetic diversity at non-synonymous sites recovers to its pre-fixation value within 18 months, whereas diversity at synonymous sites remains depressed after this time period. These results improve our understanding of HIV evolution and have potential implications for treatment strategies.     

Detailed analysis of the relative power of direct and indirect association studies and the implications for their interpretation

OBJECTIVES: Genetic association studies are usually based upon restricted sets of 'tag' markers selected to represent the total sequence variation. Tag selection is often determined by some threshold for the r(2) coefficients of linkage disequilibrium (LD) between tag and untyped markers, it being widely assumed that power to detect an effect at the untyped sites is retained by typing the tag marker in a sample scaled by the inverse of the selected threshold (1/r(2)). However, unless only a single causal variant occurs at a locus, it has been shown [Eur J Hum Genet 2006;14:426-437] that significant power loss can occur if this principle is applied. We sought to investigate whether unexpected loss of power might be an exceptional case or more general concern. In the absence of detailed knowledge about the genetic architecture at complex disease loci, we developed a mathematical approach to test all possible situations. METHODS: We derived mathematical formulae allowing the calculation of all possible odds ratios (OR) at a tag marker locus given the effect size that would be observed by typing a second locus and the r(2) between the two loci. For a range of allele frequencies, r(2) between loci, and strengths of association at the causal locus (OR from 0.5 to 2) that we consider realistic for complex disease loci, we next determined the sample sizes that would be necessary to give equivalent power to detect association by genotyping tag and causal loci and compared these with the sample sizes predicted by applying 1/r(2). RESULTS: Under most of the hypothetical scenarios we examined, the calculated sample sizes required to maintain power by typing markers that tag the causal locus at even moderately high r(2) (0.8) were greater than that calculated by applying 1/r(2). Even in populations with apparently similar measurements of allele frequency, LD structure, and effect size at the susceptibility allele, the required sample size to detect association with a tag marker can vary substantially. We also show that in apparently similar populations, associations to either allele at the tag site are possible. CONCLUSIONS: Indirect tests of association are less powered than sizes predicted by applying 1/r(2) in the majority of hypothetical scenarios we examined. Our findings pertain even for what we consider likely to be larger than average effect sizes in complex diseases (OR = 1.5-2) and even for moderately high r(2) values between the markers. Until a substantial number of disease genes have been identified through methods that are not based on tagging, and therefore biased towards those situations most favourable to tagging, it is impossible to know how the true scenarios are distributed across the range of possible scenarios. Nevertheless, while association designs based upon tag marker selection by necessity are the tool of choice for de novo gene discovery, our data suggest power to initially detect association may often be less than assumed. Moreover, our data suggest that to avoid genuine findings being subsequently discarded by unpredictable losses of power, follow up studies in other samples should be based upon more detailed analyses of the gene rather than simply on the tag SNPs showing association in the discovery study.     

Estimates of Genetic Differentiation Measured by F(ST) Do Not Necessarily Require Large Sample Sizes When Using Many SNP Markers

Population genetic studies provide insights into the evolutionary processes that influence the distribution of sequence variants within and among wild populations. F_ST is among the most widely used measures for genetic differentiation and plays a central role in ecological and evolutionary genetic studies. It is commonly thought that large sample sizes are required in order to precisely infer F_ST and that small sample sizes lead to overestimation of genetic differentiation. Until recently, studies in ecological model organisms incorporated a limited number of genetic markers, but since the emergence of next generation sequencing, the panel size of genetic markers available even in non-reference organisms has rapidly increased. In this study we examine whether a large number of genetic markers can substitute for small sample sizes when estimating F_ST. We tested the behavior of three different estimators that infer F_ST and that are commonly used in population genetic studies. By simulating populations, we assessed the effects of sample size and the number of markers on the various estimates of genetic differentiation. Furthermore, we tested the effect of ascertainment bias on these estimates. We show that the population sample size can be significantly reduced (as small as n = 4–6) when using an appropriate estimator and a large number of bi-allelic genetic markers (k>1,000). Therefore, conservation genetic studies can now obtain almost the same statistical power as studies performed on model organisms using markers developed with next-generation sequencing.     

Global phylogeography of a cryptic copepod species complex and reproductive isolation between genetically proximate "populations"

The copepod Eurytemora affinis has a broad geographic range within the Northern Hemisphere, inhabiting coastal regions of North America, Asia, and Europe. A phylogenetic approach was used to determine levels of genetic differentiation among populations of this species, and interpopulation crosses were performed to determine reproductive compatibility. DNA sequences from two mitochondrial genes, large subunit (16S) rRNA (450 bp) and cytochrome oxidase I (COI, 652 bp), were obtained from 38 populations spanning most of the species range and from two congeneric species, E. americana and E. herdmani. Phylogenetic analysis revealed a polytomy of highly divergent clades with maximum sequence divergences of 10% in 16S rRNA and 19% in COI. A power test (difference of a proportion) revealed that amount of sequence data collected was sufficient for resolving speciation events occurring at intervals greater than 300,000 years, but insufficient for determining whether speciation events were approximately simultaneous. Geographic and genetic distances were not correlated (Mantel's test; r = 0.023, P = 0.25), suggesting that populations had not differentiated through gradual isolation by distance. At finer spatial scales, there was almost no sharing of mtDNA haplotypes among proximate populations, indicating little genetic exchange even between nearby sites. Interpopulation crosses demonstrated reproductive incompatibility among genetically distinct populations, including those that were sympatric. Most notably, two geographically distant (4000 km) but genetically proximate (0.96% 16S, 0.15% COI) populations exhibited asymmetric reproductive isolation at the F2 generation. Large genetic divergences and reproductive isolation indicate that the morphologically conservative E. affinis constitutes a sibling species complex. Reproductive isolation between genetically proximate populations underscores the importance of using multiple measures to examine patterns of speciation.     

Microsatellite measures of inbreeding: a meta-analysis

Abstract Meta-analyses of published and unpublished correlations between phenotypic variation and two measures of genetic variation at microsatellite loci, multilocus heterozygosity (MLH) and mean d², revealed that the strength of these associations are generally weak (mean r < 0.10). Effects on life-history trait variation were significantly greater than zero for both measures over all reported effect sizes ( r = 0. 0856 and 0.0479 for MLH and mean d ², respectively), whereas effects on morphometric traits were not ( r = 0.0052 and r = 0.0038), which is consistent with the prediction that life-history traits exhibit greater inbreeding depression than morphometric traits. Effect sizes reported using mean d ² were smaller and more variable than those reported using MLH, suggesting that MLH may be a better metric for capturing inbreeding depression most of the time. However, analyses of paired effect sizes reported using both measures from the same data did not differ significantly. Several lines of evidence suggest that published effects sizes are upwardly biased. First, effect sizes from published studies were significantly higher than those reported in unpublished studies. Second, fail-safe numbers for reported effect sizes were generally quite low, with the exception of correlations between MLH and life-history traits. Finally, the slope of the regression of effect size on sample size was negative for most sets of traits. Taken together, these results suggest that studies designed to detect inbreeding depression on a life-history trait using microsatellites will need to sample in excess of 600 individuals to detect an average effect size ( r = 0.10) with reasonable statistical power (0.80). Very few published studies have used samples sizes approaching this value.     

Intrinsic Variability in Shell and Soft Tissue Growth of the Freshwater Mussel Lampsilis siliquoidea

Freshwater mussels are ecologically and economically important members of many aquatic ecosystems, but are globally among the most imperiled taxa. Propagation techniques for mussels have been developed and used to boost declining and restore extirpated populations. Here we use a cohort of propagated mussels to estimate the intrinsic variability in size and growth rate of Lampsilis siliquoidea (a commonly propagated species). Understanding the magnitude and pattern of variation in data is critical to determining whether effects observed in nature or experimental treatments are likely to be important. The coefficient of variation (CV) of L. siliquoidea soft tissues (6.0%) was less than the CV of linear shell dimensions (25.1–66.9%). Size-weight relationships were best when mussel width (the maximum left-right dimension with both valves appressed) was used as a predictor, but 95% credible intervals on these predictions for soft tissues were ∼145 mg wide (about 50% of the mean soft tissue mass). Mussels in this study were treated identically, raised from a single cohort and yet variation in soft tissue mass at a particular size class (as determined by shell dimensions) was still high. High variability in mussel size is often acknowledged, but seldom discussed in the context of mussel conservation. High variability will influence the survival of stocked juvenile cohorts, may affect the ability to experimentally detect sublethal stressors and may lead to incongruities between the effects that mussels have on structure (via hard shells) and biogeochemical cycles (via soft tissue metabolism). Given their imperiled status and longevity, there is often reluctance to destructively sample unionid mussel soft tissues even in metabolic studies (e.g., studies of nutrient cycling). High intrinsic variability suggests that using shell dimensions (particularly shell length) as a response variable in studies of sublethal stressors or metabolic processes will make confident identifications of smaller effect sizes difficult.     

Power analysis to determine sample size for monitoring vegetation change in salt marsh habitats

Numerous initiatives are underway throughout New England and elsewhere to quantify salt marsh vegetation change, mostly in response to habitat restoration, sea level rise, and nutrient enrichment. To detect temporal changes in vegetation at a marsh or to compare vegetation among different marshes with a degree of statistical certainty an adequate sample size is required. Based on sampling 1 m² vegetation plots from 11 New England salt marsh data sets, we conducted a power analysis to determine the minimum number of samples that were necessary to detect change between vegetation communities. Statistical power was determined for sample sizes of 5, 10, 15, and 20 vegetation plots at an alpha level of 0.05. Detection of subtle differences between vegetation data sets (e.g., comparing vegetation in the same marsh over two consecutive years) can be accomplished using a sample size of 20 plots with a reasonable probability of detecting a difference when one truly exists. With a lower sample size, and thus lower power, there is an increased probability of not detecting a difference when one exists (e.g., Type II error). However, if investigators expect to detect major changes in vegetation (e.g., such as those between an un-impacted and a highly impacted marsh) then a sample size of 5, 10, or 15 plots may be appropriate while still maintaining adequate power. Due to the relative ease of collecting vegetation data, we suggest a minimum sample size of 20 randomly located 1 m² plots when developing monitoring designs to detect vegetation community change of salt marshes. The sample size of 20 plots per New England salt marsh is appropriate regardless of marsh size or permanency (permanent or non-permanent) of the plots.     

A simple algorithm to infer gene duplication and speciation events on a gene tree

MOTIVATION: When analyzing protein sequences using sequence similarity searches, orthologous sequences (that diverged by speciation) are more reliable predictors of a new protein's function than paralogous sequences (that diverged by gene duplication), because duplication enables functional diversification. The utility of phylogenetic information in high-throughput genome annotation ('phylogenomics') is widely recognized, but existing approaches are either manual or indirect (e.g. not based on phylogenetic trees). Our goal is to automate phylogenomics using explicit phylogenetic inference. A necessary component is an algorithm to infer speciation and duplication events in a given gene tree. RESULTS: We give an algorithm to infer speciation and duplication events on a gene tree by comparison to a trusted species tree. This algorithm has a worst-case running time of O(n(2)) which is inferior to two previous algorithms that are approximately O(n) for a gene tree of sequences. However, our algorithm is extremely simple, and its asymptotic worst case behavior is only realized on pathological data sets. We show empirically, using 1750 gene trees constructed from the Pfam protein family database, that it appears to be a practical (and often superior) algorithm for analyzing real gene trees. AVAILABILITY: http://www.genetics.wustl.edu/eddy/forester.     

Inferring Demographic History from a Spectrum of Shared Haplotype Lengths

There has been much recent excitement about the use of genetics to elucidate ancestral history and demography. Whole genome data from humans and other species are revealing complex stories of divergence and admixture that were left undiscovered by previous smaller data sets. A central challenge is to estimate the timing of past admixture and divergence events, for example the time at which Neanderthals exchanged genetic material with humans and the time at which modern humans left Africa. Here, we present a method for using sequence data to jointly estimate the timing and magnitude of past admixture events, along with population divergence times and changes in effective population size. We infer demography from a collection of pairwise sequence alignments by summarizing their length distribution of tracts of identity by state (IBS) and maximizing an analytic composite likelihood derived from a Markovian coalescent approximation. Recent gene flow between populations leaves behind long tracts of identity by descent (IBD), and these tracts give our method power by influencing the distribution of shared IBS tracts. In simulated data, we accurately infer the timing and strength of admixture events, population size changes, and divergence times over a variety of ancient and recent time scales. Using the same technique, we analyze deeply sequenced trio parents from the 1000 Genomes project. The data show evidence of extensive gene flow between Africa and Europe after the time of divergence as well as substructure and gene flow among ancestral hominids. In particular, we infer that recent African-European gene flow and ancient ghost admixture into Europe are both necessary to explain the spectrum of IBS sharing in the trios, rejecting simpler models that contain less population structure.     

Genetic Diversity in Introduced Populations with an Allee Effect

A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the demographic Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame either a strong Allee effect, in which populations smaller than a certain critical size are expected to decline, or a weak Allee effect, in which the population growth rate is reduced at small sizes but not negative. Our results indicate that compared to successful populations without an Allee effect, successful populations with a strong Allee effect tend to (1) derive from larger founder population sizes and thus have a higher initial amount of genetic variation, (2) spend fewer generations at small population sizes where genetic drift is particularly strong, and (3) spend more time around the critical population size and thus experience more genetic drift there. In the case of multiple introduction events, there is an additional increase in diversity because Allee-effect populations tend to derive from a larger number of introduction events than other populations. Altogether, a strong Allee effect can either increase or decrease genetic diversity, depending on the average founder population size. By contrast, a weak Allee effect tends to decrease genetic diversity across the entire range of founder population sizes. Finally, we show that it is possible in principle to infer critical population sizes from genetic data, although this would require information from many independently introduced populations.     

Polytomies and Bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short branch lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.