Modifiers of mutation rate: Evolutionary optimum with complete selfing

It often has been assumed that, for infinite random mating populations in a constant environment, natural selection will favor genotypes at a neutral modifier locus that minimize the mutation rate. Mathematical modeling of this process confirms this assertion, independent of the selection regime. The same model under conditions of complete selfing can produce, under certain nondegenerate overdominance conditions, an optimum mutation rate below which increased mutation is favored and above which decreased mutation is favored. This occurs with unidirectional mutation models and a class of reversible mutation models with fitness overdominance. This is the first time that such a modifier optimum has been produced analytically for an infinite population in a constant environment.

Natural selection on inflorescence color polymorphisms in wild Protea populations: The role of pollinators, seed predators, and intertrait correlations

PREMISE OF THE STUDY

The processes maintaining flower color polymorphisms have long been of evolutionary interest. Mechanistic explanations include selection through pollinators, antagonists, local environments, drift, and pleiotropic effects. We examined the maintenance of inflorescence color polymorphisms in the genus Protea (Proteaceae) of South Africa, in which ∼40% of species contain different color morphs. •

METHODS

We studied 10 populations of four bird-pollinated Protea species and compared adult performance, floral and leaf morphology, vegetative pigmentation, germination, and seedling survival between co-occurring pink and white morphs. We also tested for differences in pollination success and pre-dispersal seed predation. •

KEY RESULTS

White morphs produced seeds 10% heavier and 3.5 times more likely to germinate, which all else being equal, should fuel positive selection on white. In one studied population per species, however, white morphs were more susceptible to seed predation by endophagous larvae. Pollinators had no morph-specific effects on female fecundity, as measured by amount or probability of seed set. Differences in stem color indicated that white morphs produced smaller quantities of pigment and associated compounds throughout, possibly explaining their higher seed palatability. •

CONCLUSIONS

Our findings suggest a mechanism for some white protea polymorphisms: deleterious pleiotropic effects on pink morphs are occasionally offset by reduced losses to seed-eating larvae. Because trends were repeated across species, we suggest that similar processes may also occur in other proteas, placing a new emphasis on seed predators for influencing some of South Africa's amazing floral diversity.

Breeding system variation in 10 evening primroses (Oenothera sections Anogra and Kleinia; Onagraceae)

PREMISE OF THE STUDY

We examined two accounts of the relationship between breeding system and life history variation in a clade of evening primroses (Oenothera, Onagraceae): (1) selection for reproductive assurance should generate an association between self-compatibility and monocarpy and (2) phylogenetic conservatism leads to retention of breeding system and life history traits among closely related taxa. •

METHODS

We performed over 4000 hand pollinations under greenhouse conditions to determine the compatibility of 10 Oenothera taxa (sections Anogra [17 taxa] and Kleinia [2 taxa)] for which breeding systems had not previously been reported. We used generalized linear mixed models to evaluate the influence of pollination treatment, parents, and population on fruiting success. •

KEY RESULTS

Among the taxa tested, six were self-incompatible, two were variable in compatibility, and two were self-compatible. We combined these data with published studies in Anogra and Kleinia and mapped breeding system and life history onto a published phylogeny. •

CONCLUSIONS

We found no evidence for phylogenetic conservatism, but detected considerable evolutionary lability in both traits. Additionally, we found no evidence for a consistent relationship between breeding system and life history. Only eight of 19 taxa followed the predicted association between self-incompatibility and polycarpy vs. self-compatibility and monocarpy. Instead, many taxa have retained self-incompatibility, regardless of monocarpy or polycarpy.

Genetics in geographically structured populations: defining, estimating and interpreting F(ST)

Wright's F-statistics, and especially F(ST), provide important insights into the evolutionary processes that influence the structure of genetic variation within and among populations, and they are among the most widely used descriptive statistics in population and evolutionary genetics. Estimates of F(ST) can identify regions of the genome that have been the target of selection, and comparisons of F(ST) from different parts of the genome can provide insights into the demographic history of populations. For these reasons and others, F(ST) has a central role in population and evolutionary genetics and has wide applications in fields that range from disease association mapping to forensic science. This Review clarifies how F(ST) is defined, how it should be estimated, how it is related to similar statistics and how estimates of F(ST) should be interpreted.

Proximity is not a proxy for parentage in an animal-dispersed Neotropical canopy palm

We used parentage analysis to estimate seedling recruitment distances and genetic composition of seedling patches centred around reproductive trees of the animal-dispersed Neotropical canopy palm Iriartea deltoidea in two 0.5 ha plots within second-growth forest and one 0.5 ha plot in adjacent old-growth forest at La Selva Biological Field Station in north-eastern Costa Rica. Seedlings were significantly spatially aggregated in all plots, but this pattern was not due to dispersal limitation. More than 70 per cent of seedlings were dispersed at least 50 m from parent trees. Few seedlings were offspring of the closest reproductive trees. Seedling patches observed beneath reproductive trees originate from dozens of parental trees. Observed patterns of seedling distribution and spatial genetic structure are largely determined by the behaviour of vertebrate seed dispersers rather than by spatial proximity to parental trees.

A Bayesian hierarchical model for analysis of SNP diversity in multilocus, multipopulation samples

The distribution of genetic variation among populations is conveniently measured by Wright's F(ST), which is a scaled variance taking on values in [0,1]. For certain types of genetic markers, and for single-nucleotide polymorphisms (SNPs) in particular, it is reasonable to presume that allelic differences at most loci are selectively neutral. For such loci, the distribution of genetic variation among populations is determined by the size of local populations, the pattern and rate of migration among those populations, and the rate of mutation. Because the demographic parameters (population sizes and migration rates) are common across all autosomal loci, locus-specific estimates of F(ST) will depart from a common distribution only for loci with unusually high or low rates of mutation or for loci that are closely associated with genomic regions having a relationship with fitness. Thus, loci that are statistical outliers showing significantly more among-population differentiation than others may mark genomic regions subject to diversifying selection among the sample populations. Similarly, statistical outliers showing significantly less differentiation among populations than others may mark genomic regions subject to stabilizing selection across the sample populations. We propose several Bayesian hierarchical models to estimate locus-specific effects on F(ST), and we apply these models to single nucleotide polymorphism data from the HapMap project. Because loci that are physically associated with one another are likely to show similar patterns of variation, we introduce conditional autoregressive models to incorporate the local correlation among loci for high-resolution genomic data. We estimate the posterior distributions of model parameters using Markov chain Monte Carlo (MCMC) simulations. Model comparison using several criteria, including DIC and LPML, reveals that a model with locus- and population-specific effects is superior to other models for the data used in the analysis. To detect statistical outliers we propose an approach that measures divergence between the posterior distributions of locus-specific effects and the common F(ST) with the Kullback-Leibler divergence measure. We calibrate this measure by comparing values with those produced from the divergence between a biased and a fair coin. We conduct a simulation study to illustrate the performance of our approach for detecting loci subject to stabilizing/divergent selection, and we apply the proposed models to low- and high-resolution SNP data from the HapMap project. Model comparison using DIC and LPML reveals that CAR models are superior to alternative models for the high resolution data. For both low and high resolution data, we identify statistical outliers that are associated with known genes.

Detecting the influence of ornamental Berberis thunbergii var. atropurpurea in invasive populations of Berberis thunbergii (Berberidaceae) using AFLP1

Japanese barberry (Berberis thunbergii DC.) is a widespread invasive plant that remains an important landscape shrub represented by ornamental, purple-leaved forms of the botanical variety atropurpurea. These forms differ greatly in appearance from feral plants, bringing into question whether they contribute to invasive populations or whether the invasions represent self-sustaining populations derived from the initial introduction of the species in the late 19th century. In this study we used amplified fragment length polymorphism (AFLP) markers to determine whether genetic contributions from B. t. var. atropurpurea are found within naturalized Japanese barberry populations in southern New England. Bayesian clustering of AFLP genotypes and principal coordinate analysis distinguished B. t. var. atropurpurea genotypes from 85 plants representing five invasive populations. While a single feral plant resembled B. t. var. atropurpurea phenotypically and fell within the same genetic cluster, all other naturalized plants sampled were genetically distinct from the purple-leaved genotypes. Seven plants from two different sites possessed morphology consistent with Berberis vulgaris (common barberry) or B. ×ottawensis (B. thunbergii × B. vulgaris). Genetic analysis placed these plants in two clusters separate from B. thunbergii. Although the Bayesian analysis indicated some introgression of B. t. var. atropurpurea and B. vulgaris, these genotypes have had limited influence on extant feral populations of B. thunbergii.

Multigenerational genetic analysis of tropical secondary regeneration in a canopy palm

Iriartea deltoidea (Arecaceae) is an abundant canopy palm with a wide geographic distribution in Neotropical wet forests. We analyzed the genetic profile across three generations of Iriartea within a 43-ha area encompassing two areas of second-growth and adjoining old-growth forest at La Selva Biological Field Station in northeastern Costa Rica. A total of 311 reproductively mature trees, 99 large saplings, 207 small saplings, and 601 seedlings were genotyped using 141 AFLP loci. Parentage analysis revealed high dispersal distances, both for seed (over 2.3 km) and pollen (over 3.8 km), indicating a large genetic neighborhood within La Selva Biological Station. In a 20-ha area of second growth, the founding palm population was dominated by a small number of parental trees located in the adjacent old-growth forest; two old-growth trees contributed 48% of the second-growth genes. The genetic diversity of reproductively mature trees in this second-growth forest was significantly reduced compared to adjacent old-growth forest. Within 400 m of the border with old-growth forest, we observed a similar reduction of genetic diversity in saplings, and an even greater loss of genetic diversity in the second generation of seedlings. Nearly half of these seedlings were offspring of local parents. In contrast, in the distant portion of second-growth forest (400-800 m from the old-growth border), parentage analysis showed that 40% of seedlings originated from outside the study area and only 10% were offspring of local parents. These high levels of gene flow maintained genetic diversity in saplings and seedlings similar to levels observed in old-growth forest. Our findings highlight the importance of gene flow from diverse seed and pollen sources for sustaining levels of genetic diversity of tree populations in second-growth forests.

Model fitting and inference under Latent Equilibrium Processes

This paper presents a methodology for model fitting and inference in the context of Bayesian models of the type f(Y | X, theta)f(X | theta)f(theta), where Y is the (set of) observed data, theta is a set of model parameters and X is an unobserved (latent) stationary stochastic process induced by the first order transition model f(X((t+1)) | X((t)), theta), where X((t)) denotes the state of the process at time (or generation) t. The crucial feature of the above type of model is that, given theta, the transition model f(X((t+1)) | X((t)), theta) is known but the distribution of the stochastic process in equilibrium, that is f(X | theta), is, except in very special cases, intractable, hence unknown. A further point to note is that the data Y has been assumed to be observed when the underlying process is in equilibrium. In other words, the data is not collected dynamically over time.We refer to such specification as a latent equilibrium process (LEP) model. It is motivated by problems in population genetics (though other applications are discussed), where it is of interest to learn about parameters such as mutation and migration rates and population sizes, given a sample of allele frequencies at one or more loci. In such problems it is natural to assume that the distribution of the observed allele frequencies depends on the true (unobserved) population allele frequencies, whereas the distribution of the true allele frequencies is only indirectly specified through a transition model.As a hierarchical specification, it is natural to fit the LEP within a Bayesian framework. Fitting such models is usually done via Markov chain Monte Carlo (MCMC). However, we demonstrate that, in the case of LEP models, implementation of MCMC is far from straightforward. The main contribution of this paper is to provide a methodology to implement MCMC for LEP models. We demonstrate our approach in population genetics problems with both simulated and real data sets. The resultant model fitting is computationally intensive and thus, we also discuss parallel implementation of the procedure in special cases.

Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.

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.

Genetic Consequences of Tropical Second-Growth Forest Regeneration

Secondary forests are more extensive than old-growth forests in many tropical regions, yet the genetic composition of colonizing populations is poorly understood. We analyzed the parentage of a founder population of 130 individuals of the canopy palm Iriartea deltoidea in a 24-year-old second-growth forest in lowland Costa Rica. Among 66 trees in adjacent old-growth forest, only two individuals contributed 56% of the genes in founders. Second-growth trees had lower genetic diversity and larger patches of similar genotypes than old-growth trees. Recovery of genetic diversity of populations in tropical second-growth forests may take many generations and will require continued dispersal from genetically diverse source populations.

Bayesian models for the analysis of genetic structure when populations are correlated

MOTIVATION

Population allele frequencies are correlated when populations have a shared history or when they exchange genes. Unfortunately, most models for allele frequency and inference about population structure ignore this correlation. Recent analytical results show that among populations, correlations can be very high, which could affect estimates of population genetic structure. In this study, we propose a mixture beta model to characterize the allele frequency distribution among populations. This formulation incorporates the correlation among populations as well as extending the model to data with different clusters of populations.

RESULTS

Using simulated data, we show that in general, the mixture model provides a good approximation of the among-population allele frequency distribution and a good estimate of correlation among populations. Results from fitting the mixture model to a dataset of genotypes at 377 autosomal microsatellite loci from human populations indicate high correlation among populations, which may not be appropriate to neglect. Traditional measures of population structure tend to overestimate the amount of genetic differentiation when correlation is neglected. Inference is performed in a Bayesian framework.

CONTACT

fur@ohsu.edu.

Natural selection on light response curve parameters in the herbaceous annual, Impatiens capensis

We tested for genetic variation in light response curves and their acclimation to sun versus shade in recombinant inbred lines (RILs) of the annual species Impatiens capensis derived from a cross between sun and shade populations. We exposed replicates of 49 RILs to experimentally manipulated light levels (open versus shade) in a greenhouse and measured photosynthetic light response curves, height, biomass, and reproduction. Plants were taller in the shade treatment, but we were unable to detect differences between light treatments (i.e., acclimation) in the maximal rate of photosynthesis, the light compensation point, or the quantum efficiency of photosynthesis. Genotypic selection analyses indicated that higher maximal rates of carbon assimilation and higher light compensation points (typical of sun-acclimated light curves) were favored by natural selection in both light treatments. Thus, it appears that the pattern of selection on photosynthetic parameters may not depend on light environment in this species.

Bayesian approaches for the analysis of population genetic structure: an example from Platanthera leucophaea (Orchidaceae)

We describe four extensions to existing Bayesian methods for the analysis of genetic structure in populations: (i) use of beta distributions to approximate the posterior distribution of f and theta(B); (ii) use of an entropy statistic to describe the amount of information about a parameter derived from the data; (iii) use of the Deviance Information Criterion (DIC) as a model choice criterion for determining whether there is evidence for inbreeding within populations or genetic differentiation among populations; and (iv) use of samples from the posterior distributions for f and theta(B) derived from different data sets to determine whether the estimates are consistent with one another. We illustrate each of these extensions by applying them to data derived from previous allozyme and random amplified polymorphic DNA surveys of an endangered orchid, Platanthera leucophaea, and we conclude that differences in theta(B) from the two data sets may represent differences in the underlying mutational processes.

Local differentiation and plasticity in size and sex expression in jack-in-the-pulpit, Arisaema triphyllum (Araceae)

The size advantage hypothesis suggests that natural selection will favor size-dependent sex expression when one sex gains more than the other by being large. But members of a minority sex will also have a higher reproductive value, on average. Thus, an individual's reproductive success depends on the reproductive decisions made by neighboring individuals. As a result, the optimal relationship between size and sex may differ among populations. In Arisaema triphyllum, the probability for an individual to be female increases with size, regardless of the character measured. A reciprocal transplant experiment showed the relationship between size and sexual expression is environmentally plastic. Plants originating from our two study sites became female at a larger average size when grown at one site than when grown at the other. In addition to environmental influence on sex expression, the experiment demonstrated genetic differences in the relationship between size and sex. Plants collected from one site became female at a larger size than those from the other, regardless of where they were grown. Thus, while the environment in which an individual was grown had a substantial influence on its sex expression, populations only a few kilometers apart have genetically different relationships between size and sex.