The ancestral selection graph for a Λ-asymmetric Moran model.

Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanisms, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Λ-reproduction here means that a whole fraction of the population is replaced at a reproductive event. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Provided the measure are ordered stochastically, we can couple them. This allows us to construct the central object of this paper, the Λ-asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinuous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.

Heterogeneous microgeographic genetic structure of the common cockle (Cerastoderma edule) in the Northeast Atlantic Ocean: biogeographic barriers and environmental factors.

Knowledge of genetic structure at the finest level is essential for the conservation of genetic resources. Despite no visible barriers limiting gene flow, significant genetic structure has been shown in marine species. The common cockle (Cerastoderma edule) is a bivalve of great commercial and ecological value inhabiting the Northeast Atlantic Ocean. Previous population genomics studies demonstrated significant structure both across the Northeast Atlantic, but also within small geographic areas, highlighting the need to investigate fine-scale structuring. Here, we analysed two geographic areas that could represent opposite models of structure for the species: (1) the SW British Isles region, highly fragmented due to biogeographic barriers, and (2) Galicia (NW Spain), a putative homogeneous region. A total of 9250 SNPs genotyped by 2b-RAD on 599 individuals from 22 natural beds were used for the analysis. The entire SNP dataset mostly confirmed previous observations related to genetic diversity and differentiation; however, neutral and divergent SNP outlier datasets enabled disentangling physical barriers from abiotic environmental factors structuring both regions. While Galicia showed a homogeneous structure, the SW British Isles region was split into four reliable genetic regions related to oceanographic features and abiotic factors, such as sea surface salinity and temperature. The information gathered supports specific management policies of cockle resources in SW British and Galician regions also considering their particular socio-economic characteristics; further, these new data will be added to those recently reported in the Northeast Atlantic to define sustainable management actions across the whole distribution range of the species.

Regional environmental and climatic concerns on preserving native gene pools of a least concern species: Brown trout lineages in Mediterranean streams.

The European brown trout, Salmo trutta, is a cold-adapted fish reported as a Least Concern species in the IUCN Red List. This species colonized new territories from southern refuges during the last glacial melting, but during the 20th century suffered from anthropic impacts on its habitats. The long-time survival of the species relies on the genetic diversity within and among populations. Brown trout is among the genetically most diverse vertebrate species; however, native populations in Mediterranean rivers have dramatically suffered of introgressive hybridization from extensive releases of evolutionary distant non-native Atlantic stocks. In addition, in Mediterranean rivers climate change will result in unsuitable conditions for the species during the 21st century. Using brown trout populations at the headstreams of a Pyrenean river as a model, this paper revised how hatchery releases have affected the native gene pools and how environmental and climatic variables controlled the amount of local introgression at intra-basin level. Introgressive hybridization was detected in all studied sites. Ten times larger divergence was observed among populations at tributaries than among populations along the main stem. A highly impacted population distributed in a long transect in the main stem suggested that hatchery fish move towards the main stem wherever released. From already highly impacted populations and despite the cessation of hatchery releases, warmer temperatures and lower precipitation expected from climate change will extend the introgressive hybridization along the basin, contributing to the extinction of the native gene pools. Based on available morphological distinction of native, hatchery and hybrid brown trout, we advocate the involvement of regional social groups (e.g. riverside dwellers, anglers, conservationists, hikers) in citizen science programs to detect the spread of non-native phenotypes along the rivers. These are cheap and fast methods to collaborate with fishery managers in the preservation and recovery of the regional native populations.

Segregational instability of multicopy plasmids: A population genetics approach.

Plasmids are extra-chromosomal genetic elements that encode a wide variety of phenotypes and can be maintained in bacterial populations through vertical and horizontal transmission, thus increasing bacterial adaptation to hostile environmental conditions like those imposed by antimicrobial substances. To circumvent the segregational instability resulting from randomly distributing plasmids between daughter cells upon division, nontransmissible plasmids tend to be carried in multiple copies per cell, with the added benefit of exhibiting increased gene dosage and resistance levels. But carrying multiple copies also results in a high metabolic burden to the bacterial host, therefore reducing the overall fitness of the population. This trade-off poses an existential question for plasmids: What is the optimal plasmid copy number? In this manuscript, we address this question by postulating and analyzing a population genetics model to evaluate the interaction between selective pressure, the number of plasmid copies carried by each cell, and the metabolic burden associated with plasmid bearing in the absence of selection for plasmid-encoded traits. Parameter values of the model were estimated experimentally using Escherichia coli K12 carrying a multicopy plasmid encoding for a fluorescent protein and bla TEM-1, a gene conferring resistance to ß-lactam antibiotics. By numerically determining the optimal plasmid copy number for constant and fluctuating selection regimes, we show that plasmid copy number is a highly optimized evolutionary trait that depends on the rate of environmental fluctuation and balances the benefit between increased stability in the absence of selection with the burden associated with carrying multiple copies of the plasmid.

A single genomic region involving a putative chromosome rearrangement in flat oyster (Ostrea edulis) is associated with differential host resilience to the parasite Bonamia ostreae.

European flat oyster (Ostrea edulis) is an ecologically and economically important marine bivalve, that has been severely affected by the intracellular parasite Bonamia ostreae. In this study, a flat oyster SNP array (~14,000 SNPs) was used to validate previously reported outlier loci for divergent selection associated with B. ostreae exposure in the Northeast Atlantic Area. A total of 134 wild and hatchery individuals from the North Sea, collected in naïve (NV) and long-term affected (LTA) areas, were analysed. Genetic diversity and differentiation were related to the sampling origin (wild vs. hatchery) when using neutral markers, and to bonamiosis status (NV vs. LTA) when using outlier loci for divergent selection. Two genetic clusters appeared intermingled in all sampling locations when using outlier loci, and their frequency was associated with their bonamiosis status. When both clusters were compared, outlier data sets showed high genetic divergence (F ST > 0.25) unlike neutral loci (F ST not ≠ 0). Moreover, the cluster associated with LTA samples showed much higher genetic diversity and significant heterozygote excess with outlier loci, but not with neutral data. Most outliers mapped on chromosome 8 (OE-C8) of the flat oyster genome, supporting a main genomic region underlying resilience to bonamiosis. Furthermore, differentially expressed genes previously reported between NV and LTA strains showed higher mapping density on OE-C8. A range of relevant immune functions were specifically enriched among genes annotated on OE-C8, providing hypotheses for resilience mechanisms to an intracellular parasite. The results suggest that marker-assisted selection could be applied to breed resilient strains of O. edulis to bonamiosis, if lower parasite load and/or higher viability of the LTA genetic cluster following B. ostreae infection is demonstrated.

The role of connectivity on COVID-19 preventive approaches.

Preventive and modeling approaches to address the COVID-19 pandemic have been primarily based on the age or occupation, and often disregard the importance of heterogeneity in population contact structure and individual connectivity. To address this gap, we developed models based on Erdos-Rényi and a power law degree distribution that first incorporate the role of heterogeneity and connectivity and then can be expanded to make assumptions about demographic characteristics. Results demonstrate that variations in the number of connections of individuals within a population modify the impact of public health interventions such as lockdown or vaccination approaches. We conclude that the most effective strategy will vary depending on the underlying contact structure of individuals within a population and on timing of the interventions.

Genomic Hatchery Introgression in Brown Trout (Salmo trutta L.): Development of a Diagnostic SNP Panel for Monitoring the Impacted Mediterranean Rivers.

Brown trout (Salmo trutta L.) populations have been restocked during recent decades to satisfy angling demand and counterbalance the decline of wild populations. Millions of fertile brown trout individuals were released into Mediterranean and Atlantic rivers from hatcheries with homogeneous central European stocks. Consequently, many native gene pools have become endangered by introgressive hybridization with those hatchery stocks. Different genetic tools have been used to identify and evaluate the degree of introgression starting from pure native and restocking reference populations (e.g., LDH-C* locus, microsatellites). However, due to the high genetic structuring of brown trout, the definition of the "native pool" is hard to achieve. Additionally, although the LDH-C* locus is useful for determining the introgression degree at the population level, its consistency at individual level is far from being accurate, especially after several generations were since releases. Accordingly, the development of a more powerful and cost-effective tool is essential for an appropriate monitoring to recover brown-trout-native gene pools. Here, we used the 2b restriction site-associated DNA sequencing (2b-RADseq) and Stacks 2 with a reference genome to identify single-nucleotide polymorphisms (SNPs) diagnostic for hatchery-native fish discrimination in the Atlantic and Mediterranean drainages of the Iberian Peninsula. A final set of 20 SNPs was validated in a MassARRAY® System genotyping by contrasting data with the whole SNP dataset using samples with different degree of introgression from those previously recorded. Heterogeneous introgression impact was confirmed among and within river basins, and was the highest in the Mediterranean Slope. The SNP tool reported here should be assessed in a broader sample scenario in Southern Europe considering its potential for monitoring recovery plans.

Haldane's formula in Cannings models: the case of moderately strong selection.

For a class of Cannings models we prove Haldane's formula, [Formula: see text], for the fixation probability of a single beneficial mutant in the limit of large population size N and in the regime of moderately strong selection, i.e. for [Formula: see text] and [Formula: see text]. Here, [Formula: see text] is the selective advantage of an individual carrying the beneficial type, and [Formula: see text] is the (asymptotic) offspring variance. Our assumptions on the reproduction mechanism allow for a coupling of the beneficial allele's frequency process with slightly supercritical Galton-Watson processes in the early phase of fixation.

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.

Low impact of different SNP panels from two building-loci pipelines on RAD-Seq population genomic metrics: case study on five diverse aquatic species.

BACKGROUND: The irruption of Next-generation sequencing (NGS) and restriction site-associated DNA sequencing (RAD-seq) in the last decade has led to the identification of thousands of molecular markers and their genotyping for refined genomic screening. This approach has been especially useful for non-model organisms with limited genomic resources. Many building-loci pipelines have been developed to obtain robust single nucleotide polymorphism (SNPs) genotyping datasets using a de novo RAD-seq approach, i.e. without reference genomes. Here, the performances of two building-loci pipelines, STACKS 2 and Meyer's 2b-RAD v2.1 pipeline, were compared using a diverse set of aquatic species representing different genomic and/or population structure scenarios. Two bivalve species (Manila clam and common edible cockle) and three fish species (brown trout, silver catfish and small-spotted catshark) were studied. Four SNP panels were evaluated in each species to test both different building-loci pipelines and criteria for SNP selection. Furthermore, for Manila clam and brown trout, a reference genome approach was used as control. RESULTS: Despite different outcomes were observed between pipelines and species with the diverse SNP calling and filtering steps tested, no remarkable differences were found on genetic diversity and differentiation within species with the SNP panels obtained with a de novo approach. The main differences were found in brown trout between the de novo and reference genome approaches. Genotyped vs missing data mismatches were the main genotyping difference detected between the two building-loci pipelines or between the de novo and reference genome comparisons. CONCLUSIONS: Tested building-loci pipelines for selection of SNP panels seem to have low influence on population genetics inference across the diverse case-study scenarios here studied. However, preliminary trials with different bioinformatic pipelines are suggested to evaluate their influence on population parameters according with the specific goals of each study.

Genomic Signatures After Five Generations of Intensive Selective Breeding: Runs of Homozygosity and Genetic Diversity in Representative Domestic and Wild Populations of Turbot (Scophthalmus maximus).

Massive genotyping of single nucleotide polymorphisms (SNP) has opened opportunities for analyzing the way in which selection shapes genomes. Artificial or natural selection usually leaves genomic signatures associated with selective sweeps around the responsible locus. Strong selective sweeps are most often identified either by lower genetic diversity than the genomic average and/or islands of runs of homozygosity (ROHi). Here, we conducted an analysis of selective sweeps in turbot (Scophthalmus maximus) using two SNP datasets from a Northeastern Atlantic population (36 individuals) and a domestic broodstock (46 individuals). Twenty-six families (∼ 40 offspring per family) from this broodstock and three SNP datasets applying differing filtering criteria were used to adjust ROH calling parameters. The best-fitted genomic inbreeding estimate (FROH) was obtained by the sum of ROH longer than 1 Mb, called using a 21,615 SNP panel, a sliding window of 37 SNPs and one heterozygous SNP per window allowed. These parameters were used to obtain the ROHi distribution in the domestic and wild populations (49 and 0 ROHi, respectively). Regions with higher and lower genetic diversity within each population were obtained using sliding windows of 37 SNPs. Furthermore, those regions were mapped in the turbot genome against previously reported genetic markers associated with QTL (Quantitative Trait Loci) and outlier loci for domestic or natural selection to identify putative selective sweeps. Out of the 319 and 278 windows surpassing the suggestive pooled heterozygosity thresholds (ZHp) in the wild and domestic population, respectively, 78 and 54 were retained under more restrictive ZHp criteria. A total of 116 suggestive windows (representing 19 genomic regions) were linked to either QTL for production traits, or outliers for divergent or balancing selection. Twenty-four of them (representing 3 genomic regions) were retained under stricter ZHp thresholds. Eleven QTL/outlier markers were exclusively found in suggestive regions of the domestic broodstock, 7 in the wild population and one in both populations; one (broodstock) and two (wild) of those were found in significant regions retained under more restrictive ZHp criteria in the broodstock and the wild population, respectively. Genome mining and functional enrichment within regions associated with selective sweeps disclosed relevant genes and pathways related to aquaculture target traits, including growth and immune-related pathways, metabolism and response to hypoxia, which showcases how this genome atlas of genetic diversity can be a valuable resource to look for candidate genes related to natural or artificial selection in turbot populations.

The Wright-Fisher model with efficiency.

In this article, we propose a Wright-Fisher model with two types of individuals: the inefficient individuals, those who need more resources to reproduce and can have a higher growth rate, and the efficient individuals. In this model, the total amount of resource N is fixed, and the population size varies randomly depending on the number of efficient individuals. We show that, as N increases, the frequency process of efficient individuals converges to a diffusion which is a generalization of the Wright-Fisher diffusion with selection. The genealogy of this model is given by a branching-coalescing process that we call the Ancestral Selection/Efficiency Graph, and that is an extension of the Ancestral Selection Graph (Krone and Neuhauser, 1997a,b). The main contribution of this paper is that, in evolving populations, inefficiency can arise as a promoter of selective advantage and not necessarily as a trade-off.

Population Genomics in Rhamdia quelen (Heptapteridae, Siluriformes) Reveals Deep Divergence and Adaptation in the Neotropical Region.

Rhamdia quelen, a Neotropical fish with hybridization between highly divergent mitochondrial DNA (mtDNA) lineages, represents an interesting evolutionary model. Previous studies suggested that there might be demographic differences between coastal lagoons and riverine environments, as well as divergent populations that could be reproductively isolated. Here, we investigated the genetic diversity pattern of this taxon in the Southern Neotropical Basin system that includes the La Plata Basin, Patos-Merin lagoon basin and the coastal lagoons draining to the SW Atlantic Ocean, through a population genomics approach using 2b-RAD-sequencing-derived single nucleotide polymorphisms (SNPs). The genomic scan identified selection footprints associated with divergence and suggested local adaptation environmental drivers. Two major genomic clusters latitudinally distributed in the Northern and Southern basins were identified, along with consistent signatures of divergent selection between them. Population structure based on the whole set of loci and on the presumptive neutral vs. adaptive loci showed deep genomic divergence between the two major clusters. Annotation of the most consistent SNPs under divergent selection revealed some interesting candidate genes for further functional studies. Moreover, signals of adaptation to a coastal lagoon environment mediated by purifying selection were found. These new insights provide a better understanding of the complex evolutionary history of R. quelen in the southernmost basin of the Neotropical region.

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.

Modelling and simulating Lenski's long-term evolution experiment.

We revisit the model by Wiser et al. (2013), which describes how the mean fitness increases over time due to beneficial mutations in Lenski's long-term evolution experiment. We develop the model further both conceptually and mathematically. Conceptually, we describe the experiment with the help of a Cannings model with mutation and selection, where the latter includes diminishing returns epistasis. The analysis sheds light on the growth dynamics within every single day and reveals a runtime effect, that is, the shortening of the daily growth period with increasing fitness; and it allows to clarify the contribution of epistasis to the mean fitness curve. Mathematically, we explain rigorous results in terms of a law of large numbers (in the limit of infinite population size and for a certain asymptotic parameter regime), and present approximations based on heuristics and supported by simulations for finite populations.

Genetic Variability Under the Seedbank Coalescent.

We analyze patterns of genetic variability of populations in the presence of a large seedbank with the help of a new coalescent structure called the seedbank coalescent. This ancestral process appears naturally as a scaling limit of the genealogy of large populations that sustain seedbanks, if the seedbank size and individual dormancy times are of the same order as those of the active population. Mutations appear as Poisson processes on the active lineages and potentially at reduced rate also on the dormant lineages. The presence of "dormant" lineages leads to qualitatively altered times to the most recent common ancestor and nonclassical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with a seedbank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seedbank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seedbank, are compared. The effect of a seedbank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seedbank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect from genetic data the presence of a large seedbank in natural populations.

Strong seed-bank effects in bacterial evolution.

Bacterial genomes are mosaics with fragments showing distinct phylogenetic origins or even being unrelated to any other genetic information (ORFan genes). Thus the analysis of bacterial population genetics is in large part a collection of explanations for anomalies in relation to classical population genetic models such as the Wright-Fisher model and the Kingman coalescent that do not adequately describe bacterial population genetics, genomics or evolution. The concept of "species" as an evolutionary coherent biological group that is genetically isolated and shares genetic information through recombination among its members cannot be applied to any bacterial group. Recently, a simple probabilistic model considering the role of strong seed-bank effects in population genetics has been proposed by Blath et al. This model suggests the existence of a genetic pool with high diversity that is not subject to classical selection and extinction. We reason that certain bacterial population genetics anomalies could be explained by the prevalence of strong seed-bank effects among bacteria. To address this possibility we analyzed the genome of the bacterium Azotobacter vinelandii and show that genes that code for functions that are essential for the bacterium biology do not have a relation of ancestry with closely related bacteria, or are ORFan genes. The existence of essential genes that are not inherited from the most recent ancestor cannot be explained by classical population genetics models and is irreconcilable with the current view of genes acquired by horizontal transfer as being accessory or adaptive.