Stochastic viability in an island model with partial dispersal: Approximation by a diffusion process in the limit of a large number of islands.

In this paper, we investigate a finite population undergoing evolution through an island model with partial dispersal and without mutation, where generations are discrete and non-overlapping. The population is structured into D demes, each containing N individuals of two possible types, A and B, whose viability coefficients, sA and sB, respectively, vary randomly from one generation to the next. We assume that the means, variances and covariance of the viability coefficients are inversely proportional to the number of demes D, while higher-order moments are negligible in comparison to 1/D. We use a discrete-time Markov chain with two timescales to model the evolutionary process, and we demonstrate that as the number of demes D approaches infinity, the accelerated Markov chain converges to a diffusion process for any deme size N≥2. This diffusion process allows us to evaluate the fixation probability of type A following its introduction as a single mutant in a population that was fixed for type B. We explore the impact of increasing the variability in the viability coefficients on this fixation probability. At least when N is large enough, it is shown that increasing this variability for type B or decreasing it for type A leads to an increase in the fixation probability of a single A. The effect of the population-scaled variances, σA2 and σB2, can even cancel the effects of the population-scaled means, µA and µB. We also show that the fixation probability of a single A increases as the deme-scaled migration rate increases. Moreover, this probability is higher for type A than for type B if the population-scaled geometric mean viability coefficient is higher for type A than for type B, which means that µA-σA2/2>µB-σB2/2.

Genetic evidence for a single founding population of the Lakshadweep Islands.

Lakshadweep is an archipelago of 36 islands located in the Southeastern Arabian Sea. In the absence of a detailed archaeological record, the human settlement timing of this island is vague. Previous genetic studies on haploid DNA makers suggested sex-biased ancestry linked to North and South Indian populations. Maternal ancestry suggested a closer link with the Southern Indian, while paternal ancestry advocated the Northern Indian genetic affinity. Since the haploid markers are more sensitive to genetic drift, which is evident for the Island populations, we have used the biparental high-resolution single-nucleotide polymorphic markers to reconstruct the population history of Lakshadweep Islands.  Using the fine-scaled analyses, we specifically focused on (A) the ancestry components of Lakshadweep Islands populations; (B) their relation with East, West Eurasia and South Asia; (C) the number of founding lineages and (D) the putative migration from Northern India as the paternal ancestry was closer to the North Indian populations. Our analysis of ancestry components confirmed relatively higher North Indian ancestry among the Lakshadweep population. These populations are closely related to the South Asian populations. We identified mainly a single founding population for these Islands, geographically divided into two sub-clusters. By examining the population's genetic composition and analysing the gene flow from different source populations, this study contributes to our understanding of Lakshadweep Island's evolutionary history and population dynamics. These findings shed light on the complex interactions between ethnic groups and their genetic contributions in making the Lakshadweep population.

Rates of convergence in the two-island and isolation-with-migration models.

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds on rates of convergence for parametric estimators in migration models. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible.

Using gridCoal to assess whether standard population genetic theory holds in the presence of spatio-temporal heterogeneity in population size.

Spatially explicit population genetic models have long been developed, yet have rarely been used to test hypotheses about the spatial distribution of genetic diversity or the genetic divergence between populations. Here, we use spatially explicit coalescence simulations to explore the properties of the island and the two-dimensional stepping stone models under a wide range of scenarios with spatio-temporal variation in deme size. We avoid the simulation of genetic data, using the fact that under the studied models, summary statistics of genetic diversity and divergence can be approximated from coalescence times. We perform the simulations using gridCoal, a flexible spatial wrapper for the software msprime (Kelleher et al., 2016, Theoretical Population Biology, 95, 13) developed herein. In gridCoal, deme sizes can change arbitrarily across space and time, as well as migration rates between individual demes. We identify different factors that can cause a deviation from theoretical expectations, such as the simulation time in comparison to the effective deme size and the spatio-temporal autocorrelation across the grid. Our results highlight that FST , a measure of the strength of population structure, principally depends on recent demography, which makes it robust to temporal variation in deme size. In contrast, the amount of genetic diversity is dependent on the distant past when Ne is large, therefore longer run times are needed to estimate Ne than FST . Finally, we illustrate the use of gridCoal on a real-world example, the range expansion of silver fir (Abies alba Mill.) since the last glacial maximum, using different degrees of spatio-temporal variation in deme size.

Inferring the timing and strength of natural selection and gene migration in the evolution of chicken from ancient DNA data.

With the rapid growth of the number of sequenced ancient genomes, there has been increasing interest in using this new information to study past and present adaptation. Such an additional temporal component has the promise of providing improved power for the estimation of natural selection. Over the last decade, statistical approaches for the detection and quantification of natural selection from ancient DNA (aDNA) data have been developed. However, most of the existing methods do not allow us to estimate the timing of natural selection along with its strength, which is key to understanding the evolution and persistence of organismal diversity. Additionally, most methods ignore the fact that natural populations are almost always structured, which can result in an overestimation of the effect of natural selection. To address these issues, we introduce a novel Bayesian framework for the inference of natural selection and gene migration from aDNA data with Markov chain Monte Carlo techniques, co-estimating both timing and strength of natural selection and gene migration. Such an advance enables us to infer drivers of natural selection and gene migration by correlating genetic evolution with potential causes such as the changes in the ecological context in which an organism has evolved. The performance of our procedure is evaluated through extensive simulations, with its utility shown with an application to ancient chicken samples.

Strategies to Assure Optimal Trade-Offs Among Competing Objectives for the Genetic Improvement of Soybean.

Plant breeding is a decision-making discipline based on understanding project objectives. Genetic improvement projects can have two competing objectives: maximize the rate of genetic improvement and minimize the loss of useful genetic variance. For commercial plant breeders, competition in the marketplace forces greater emphasis on maximizing immediate genetic improvements. In contrast, public plant breeders have an opportunity, perhaps an obligation, to place greater emphasis on minimizing the loss of useful genetic variance while realizing genetic improvements. Considerable research indicates that short-term genetic gains from genomic selection are much greater than phenotypic selection, while phenotypic selection provides better long-term genetic gains because it retains useful genetic diversity during the early cycles of selection. With limited resources, must a soybean breeder choose between the two extreme responses provided by genomic selection or phenotypic selection? Or is it possible to develop novel breeding strategies that will provide a desirable compromise between the competing objectives? To address these questions, we decomposed breeding strategies into decisions about selection methods, mating designs, and whether the breeding population should be organized as family islands. For breeding populations organized into islands, decisions about possible migration rules among family islands were included. From among 60 possible strategies, genetic improvement is maximized for the first five to 10 cycles using genomic selection and a hub network mating design, where the hub parents with the largest selection metric make large parental contributions. It also requires that the breeding populations be organized as fully connected family islands, where every island is connected to every other island, and migration rules allow the exchange of two lines among islands every other cycle of selection. If the objectives are to maximize both short-term and long-term gains, then the best compromise strategy is similar except that the mating design could be hub network, chain rule, or a multi-objective optimization method-based mating design. Weighted genomic selection applied to centralized populations also resulted in the realization of the greatest proportion of the genetic potential of the founders but required more cycles than the best compromise strategy.

Separation of timescales for the seed bank diffusion and its jump-diffusion limit.

We investigate scaling limits of the seed bank model when migration (to and from the seed bank) is 'slow' compared to reproduction. This is motivated by models for bacterial dormancy, where periods of dormancy can be orders of magnitude larger than reproductive times. Speeding up time, we encounter a separation of timescales phenomenon which leads to mathematically interesting observations, in particular providing a prototypical example where the scaling limit of a continuous diffusion will be a jump diffusion. For this situation, standard convergence results typically fail. While such a situation could in principle be attacked by the sophisticated analytical scheme of Kurtz (J Funct Anal 12:55-67, 1973), this will require significant technical efforts. Instead, in our situation, we are able to identify and explicitly characterise a well-defined limit via duality in a surprisingly non-technical way. Indeed, we show that moment duality is in a suitable sense stable under passage to the limit and allows a direct and intuitive identification of the limiting semi-group while at the same time providing a probabilistic interpretation of the model. We also obtain a general convergence strategy for continuous-time Markov chains in a separation of timescales regime, which is of independent interest.

Waves Out of the Korean Peninsula and Inter- and Intra-Species Replacements in Freshwater Fishes in Japan.

The Japanese archipelago is located at the periphery of the continent of Asia. Rivers in the Japanese archipelago, separated from the continent of Asia by about 17 Ma, have experienced an intermittent exchange of freshwater fish taxa through a narrow land bridge generated by lowered sea level. As the Korean Peninsula and Japanese archipelago were not covered by an ice sheet during glacial periods, phylogeographical analyses in this region can trace the history of biota that were, for a long time, beyond the last glacial maximum. In this study, we analyzed the phylogeography of four freshwater fish taxa, Hemibarbus longirostris, dark chub Nipponocypris temminckii, Tanakia ssp. and Carassius ssp., whose distributions include both the Korean Peninsula and Western Japan. We found for each taxon that a small component of diverse Korean clades of freshwater fishes migrated in waves into the Japanese archipelago to form the current phylogeographic structure of biota. The replacements of indigenous populations by succeeding migrants may have also influenced the phylogeography.

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal, with an application to socially synergistic traits.

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance-covariances between traits that experience frequency-dependent selection. Assuming a multivariate-normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within-individuals depends on the fitness effects of such associations between-individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within-individuals is costly but synergistically beneficial between-individuals. As dispersal becomes limited and relatedness increases, associations between-traits between-individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.

Structural properties of the seed bank and the two island diffusion.

We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank in conjunction with and contrast to the two-island model analysed e.g. in Kermany et al. (Theor Popul Biol 74(3):226-232, 2008) and Nath and Griffiths (J Math Biol 31(8):841-851, 1993), including moments, stationary distribution and reversibility, for which our main tool is duality. Further, we show that the Wright-Fisher diffusion with seed bank can be reformulated as a one-dimensional stochastic delay differential equation, providing an elegant interpretation of the age structure in the seed bank also forward in time in the spirit of Kaj et al. (J Appl Probab 38(2):285-300, 2001). We also provide a complete boundary classification for this two-dimensional SDE using martingale-based reasoning known as McKean's argument.

Using Hadoop MapReduce for Parallel Genetic Algorithms: A Comparison of the Global, Grid and Island Models.

The need to improve the scalability of Genetic Algorithms (GAs) has motivated the research on Parallel Genetic Algorithms (PGAs), and different technologies and approaches have been used. Hadoop MapReduce represents one of the most mature technologies to develop parallel algorithms. Based on the fact that parallel algorithms introduce communication overhead, the aim of the present work is to understand if, and possibly when, the parallel GAs solutions using Hadoop MapReduce show better performance than sequential versions in terms of execution time. Moreover, we are interested in understanding which PGA model can be most effective among the global, grid, and island models. We empirically assessed the performance of these three parallel models with respect to a sequential GA on a software engineering problem, evaluating the execution time and the achieved speedup. We also analysed the behaviour of the parallel models in relation to the overhead produced by the use of Hadoop MapReduce and the GAs' computational effort, which gives a more machine-independent measure of these algorithms. We exploited three problem instances to differentiate the computation load and three cluster configurations based on 2, 4, and 8 parallel nodes. Moreover, we estimated the costs of the execution of the experimentation on a potential cloud infrastructure, based on the pricing of the major commercial cloud providers. The empirical study revealed that the use of PGA based on the island model outperforms the other parallel models and the sequential GA for all the considered instances and clusters. Using 2, 4, and 8 nodes, the island model achieves an average speedup over the three datasets of 1.8, 3.4, and 7.0 times, respectively. Hadoop MapReduce has a set of different constraints that need to be considered during the design and the implementation of parallel algorithms. The overhead of data store (i.e., HDFS) accesses, communication, and latency requires solutions that reduce data store operations. For this reason, the island model is more suitable for PGAs than the global and grid model, also in terms of costs when executed on a commercial cloud provider.

Constraints on the FST-Heterozygosity Outlier Approach.

The FST-heterozygosity outlier approach has been a popular method for identifying loci under balancing and positive selection since Beaumont and Nichols first proposed it in 1996 and recommended its use for studies sampling a large number of independent populations (at least 10). Since then, their program FDIST2 and a user-friendly program optimized for large datasets, LOSITAN, have been used widely in the population genetics literature, often without the requisite number of samples. We observed empirical datasets whose distributions could not be reconciled with the confidence intervals generated by the null coalescent island model. Here, we use forward-in-time simulations to investigate circumstances under which the FST-heterozygosity outlier approach performs poorly for next-generation single nucleotide polymorphism (SNP) datasets. Our results show that samples involving few independent populations, particularly when migration rates are low, result in distributions of the FST-heterozygosity relationship that are not described by the null model implemented in LOSITAN. In addition, even under favorable conditions LOSITAN rarely provides confidence intervals that precisely fit SNP data, making the associated P-values only roughly valid at best. We present an alternative method, implemented in a new R package named fsthet, which uses the raw empirical data to generate smoothed outlier plots for the FST-heterozygosity relationship.

Reconsidering connectivity in the sub-Antarctic.

Extreme and remote environments provide useful settings to test ideas about the ecological and evolutionary drivers of biological diversity. In the sub-Antarctic, isolation by geographic, geological and glaciological processes has long been thought to underpin patterns in the region's terrestrial and marine diversity. Molecular studies using increasingly high-resolution data are, however, challenging this perspective, demonstrating that many taxa disperse among distant sub-Antarctic landmasses. Here, we reconsider connectivity in the sub-Antarctic region, identifying which taxa are relatively isolated, which are well connected, and the scales across which this connectivity occurs in both terrestrial and marine systems. Although many organisms show evidence of occasional long-distance, trans-oceanic dispersal, these events are often insufficient to maintain gene flow across the region. Species that do show evidence of connectivity across large distances include both active dispersers and more sedentary species. Overall, connectivity patterns in the sub-Antarctic at intra- and inter-island scales are highly complex, influenced by life-history traits and local dynamics such as relative dispersal capacity and propagule pressure, natal philopatry, feeding associations, the extent of human exploitation, past climate cycles, contemporary climate, and physical barriers to movement. An increasing use of molecular data - particularly genomic data sets that can reveal fine-scale patterns - and more effective international collaboration and communication that facilitates integration of data from across the sub-Antarctic, are providing fresh insights into the processes driving patterns of diversity in the region. These insights offer a platform for assessing the ways in which changing dispersal mechanisms, such as through increasing human activity and changes to wind and ocean circulation, may alter sub-Antarctic biodiversity patterns in the future.

Restarting and recentering genetic algorithm variations for DNA fragment assembly: The necessity of a multi-strategy approach.

DNA Fragment assembly - an NP-Hard problem - is one of the major steps in of DNA sequencing. Multiple strategies have been used for this problem, including greedy graph-based algorithms, deBruijn graphs, and the overlap-layout-consensus approach. This study focuses on the overlap-layout-consensus approach. Heuristics and computational intelligence methods are combined to exploit their respective benefits. These algorithm combinations were able to produce high quality results surpassing the best results obtained by a number of competitive algorithms specially designed and tuned for this problem on thirteen of sixteen popular benchmarks. This work also reinforces the necessity of using multiple search strategies as it is clearly observed that algorithm performance is dependent on problem instance; without a deeper look into many searches, top solutions could be missed entirely.

Evolutionary Stability of Jointly Evolving Traits in Subdivided Populations.

The evolutionary stability of quantitative traits depends on whether a population can resist invasion by any mutant. While uninvadability is well understood in well-mixed populations, it is much less so in subdivided populations when multiple traits evolve jointly. Here, we investigate whether a spatially subdivided population at a monomorphic equilibrium for multiple traits can withstand invasion by any mutant or is subject to diversifying selection. Our model also explores the correlations among traits arising from diversifying selection and how they depend on relatedness due to limited dispersal. We find that selection tends to favor a positive (negative) correlation between two traits when the selective effects of one trait on relatedness is positively (negatively) correlated to the indirect fitness effects of the other trait. We study the evolution of traits for which this matters: dispersal that decreases relatedness and helping that has positive indirect fitness effects. We find that when dispersal cost is low and the benefits of helping accelerate faster than its costs, selection leads to the coexistence of mobile defectors and sessile helpers. Otherwise, the population evolves to a monomorphic state with intermediate helping and dispersal. Overall, our results highlight the effects of population subdivision for evolutionary stability and correlations among traits.

Geography, assortative mating, and the effects of sexual selection on speciation with gene flow.

Theoretical and empirical research on the evolution of reproductive isolation have both indicated that the effects of sexual selection on speciation with gene flow are quite complex. As part of this special issue on the contributions of women to basic and applied evolutionary biology, I discuss my work on this question in the context of a broader assessment of the patterns of sexual selection that lead to, versus inhibit, the speciation process, as derived from theoretical research. In particular, I focus on how two factors, the geographic context of speciation and the mechanism leading to assortative mating, interact to alter the effect that sexual selection through mate choice has on speciation. I concentrate on two geographic contexts: sympatry and secondary contact between two geographically separated populations that are exchanging migrants and two mechanisms of assortative mating: phenotype matching and separate preferences and traits. I show that both of these factors must be considered for the effects of sexual selection on speciation to be inferred.

Statistical mechanics of protein structural transitions: Insights from the island model.

The so-called island model of protein structural transition holds that hydrophobic interactions are the key to both the folding and function of proteins. Herein, the genesis and statistical mechanical basis of the island model of transitions are reviewed, by presenting the results of simulations of such transitions. Elucidating the physicochemical mechanism of protein structural formation is the foundation for understanding the hierarchical structure of life at the microscopic level. Based on the results obtained to date using the island model, remaining problems and future work in the field of protein structures are discussed, referencing Professor Saitô's views on the hierarchic structure of science.

The effects of sexual selection on trait divergence in a peripheral population with gene flow.

The unique aspects of speciation and divergence in peripheral populations have long sparked much research. Unidirectional migration, received by some peripheral populations, can hinder the evolution of distinct differences from their founding populations. Here, we explore the effects that sexual selection, long hypothesized to drive the divergence of distinct traits used in mate choice, can play in the evolution of such traits in a partially isolated peripheral population. Using population genetic continent-island models, we show that with phenotype matching, sexual selection increases the frequency of an island-specific mating trait only when female preferences are of intermediate strength. We identify regions of preference strength for which sexual selection can instead cause an island-specific trait to be lost, even when it would have otherwise been maintained at migration-selection balance. When there are instead separate preference and trait loci, we find that sexual selection can lead to low trait frequencies or trait loss when female preferences are weak to intermediate, but that sexual selection can increase trait frequencies when preferences are strong. We also show that novel preference strengths almost universally cannot increase, under either mating mechanism, precluding the evolution of premating isolation in peripheral populations at the early stages of species divergence.

Demographic inference using genetic data from a single individual: Separating population size variation from population structure.

The rapid development of sequencing technologies represents new opportunities for population genetics research. It is expected that genomic data will increase our ability to reconstruct the history of populations. While this increase in genetic information will likely help biologists and anthropologists to reconstruct the demographic history of populations, it also represents new challenges. Recent work has shown that structured populations generate signals of population size change. As a consequence it is often difficult to determine whether demographic events such as expansions or contractions (bottlenecks) inferred from genetic data are real or due to the fact that populations are structured in nature. Given that few inferential methods allow us to account for that structure, and that genomic data will necessarily increase the precision of parameter estimates, it is important to develop new approaches. In the present study we analyze two demographic models. The first is a model of instantaneous population size change whereas the second is the classical symmetric island model. We (i) re-derive the distribution of coalescence times under the two models for a sample of size two, (ii) use a maximum likelihood approach to estimate the parameters of these models (iii) validate this estimation procedure under a wide array of parameter combinations, (iv) implement and validate a model rejection procedure by using a Kolmogorov-Smirnov test, and a model choice procedure based on the AIC, and (v) derive the explicit distribution for the number of differences between two non-recombining sequences. Altogether we show that it is possible to estimate parameters under several models and perform efficient model choice using genetic data from a single diploid individual.

Design and Analysis of Schemes for Adapting Migration Intervals in Parallel Evolutionary Algorithms.

The migration interval is one of the fundamental parameters governing the dynamic behaviour of island models. Yet, there is little understanding on how this parameter affects performance, and how to optimally set it given a problem in hand. We propose schemes for adapting the migration interval according to whether fitness improvements have been found. As long as no improvement is found, the migration interval is increased to minimise communication. Once the best fitness has improved, the migration interval is decreased to spread new best solutions more quickly. We provide a method for obtaining upper bounds on the expected running time and the communication effort, defined as the expected number of migrants sent. Example applications of this method to common example functions show that our adaptive schemes are able to compete with, or even outperform, the optimal fixed choice of the migration interval, with regard to running time and communication effort.