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17 Nov 2017
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ABC random forests for Bayesian parameter inference

Machine learning methods are useful for Approximate Bayesian Computation in evolution and ecology

Recommended by based on reviews by Michael Blum and Dennis Prangle

It is my pleasure to recommend the paper by Raynal et al. [1] about using random forest for parameter inference. There are two reviews about the paper, one review written by Dennis Prangle and another review written by myself. Both reviews were positive and included comments that have been addressed in the current version of the preprint.

The paper nicely shows that modern machine learning approaches are useful for Approximate Bayesian Computation (ABC) and more generally for simulation-driven parameter inference in ecology and evolution.

The authors propose to consider the random forest approach, proposed by Meinshausen [2] to perform quantile regression. The numerical implementation of ABC with random forest, available in the abcrf package, is based on the RANGER R package that provides a fast implementation of random forest for high-dimensional data.

According to my reading of the manuscript, there are 3 main advantages when using random forest (RF) for parameter inference with ABC. The first advantage is that RF can handle many summary statistics and that dimension reduction is not needed when using RF.

The second advantage is very nicely displayed in Figure 5, which shows the main result of the paper. If correct, 95% posterior credibility intervals (C.I.) should contain 95% of the parameter values used in simulations. Figure 5 shows that posterior C.I. obtained with rejection are too large compared to other methods. By contrast, C.I. obtained with regression methods have been shrunken. However, the shrinkage can be excessive for the smallest tolerance rates, with coverage values that can be equal to 85% instead of the expected 95% value. The attractive property of RF is that C.I. have been shrunken but the coverage is of 100% resulting in a conservative decision about parameter values.

The last advantage is that no hyperparameter should be chosen. It is a parameter free approach, which is desirable because of the potential difficulty of choosing an appropriate acceptance rate.

The main drawback of the proposed approach concerns joint parameter inference. There are many settings where the joint parameter distribution is of interest and the proposed RF approach cannot handle that. In population genetics for example, estimation of the severity and of the duration of the bottleneck should be estimated jointly because of identifiability issues. The challenge of performing joint parameter inference with RF might constitute a useful research perspective.


[1] Raynal L, Marin J-M, Pudlo P, Ribatet M, Robert CP, Estoup A. 2017. ABC random forests for Bayesian parameter inference. arXiv 1605.05537v4,
[2] Meinshausen N. 2006. Quantile regression forests. Journal of Machine Learning Research 7: 983-999.

ABC random forests for Bayesian parameter inferenceLouis Raynal, Jean-Michel Marin, Pierre Pudlo, Mathieu Ribatet, Christian P. Robert, Arnaud EstoupThis preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http:// 10.24072/ pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian infer...Bioinformatics & Computational Biology, Evolutionary Applications, Other, Population Genetics / GenomicsMichael Blum2017-07-06 07:42:00 View
13 Dec 2018
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A behavior-manipulating virus relative as a source of adaptive genes for parasitoid wasps

Genetic intimacy of filamentous viruses and endoparasitoid wasps

Recommended by based on reviews by Alejandro Manzano Marín and 1 anonymous reviewer

Viruses establish intimate relationships with the cells they infect. The virocell is a novel entity, different from the original host cell and beyond the mere combination of viral and cellular genetic material. In these close encounters, viral and cellular genomes often hybridise, combine, recombine, merge and excise. Such chemical promiscuity leaves genomics scars that can be passed on to descent, in the form of deletions or duplications and, importantly, insertions and back and forth exchange of genetic material between viruses and their hosts.
In this preprint [1], Di Giovanni and coworkers report the identification of 13 genes present in the extant genomes of members of the Leptopilina wasp genus, bearing sound signatures of having been horizontally acquired from an ancestral virus. Importantly the authors identify Leptopilina boulardi filamentous virus (LbFV) as an extant relative of the ancestral virus that served as donor for the thirteen horizontally transferred genes. While pinpointing genes with a likely possible viral origin in eukaryotic genomes is only relatively rare, identifying an extant viral lineage related to the ancestral virus that continues to infect an extant relative of the ancestral host is remarkable. But the amazing evolutionary history of the Leptopilina hosts and these filamentous viruses goes beyond this shared genes. These wasps are endoparasitoids of Drosophila larvae, the female wasp laying the eggs inside the larvae and simultaneously injecting venom that hinders the immune response. The composition of the venoms is complex, varies between wasp species and also between individuals within a species, but a central component of all these venoms are spiked structures that vary in morphology, symmetry and size, often referred to as virus-like particles (VLPs).
In this preprint, the authors convincingly show that the expression pattern in the Leptopilina wasps of the thirteen genes identified to have been horizontally acquired from the LbFV ancestor coincides with that of the production of VLPs in the female wasp venom gland. Based on this spatio-temporal match, the authors propose that these VLPs have a viral origin. The data presented in this preprint will undoubtedly stimulate further research on the composition, function, origin, evolution and diversity of these VLP structures, which are highly debated (see for instance [2] and [3]).


[1] Di Giovanni, D., Lepetit, D., Boulesteix, M., Ravallec, M., & Varaldi, J. (2018). A behavior-manipulating virus relative as a source of adaptive genes for parasitoid wasps. bioRxiv, 342758, ver. 5 peer-reviewed and recommended by PCI Evol Biol. doi: 10.1101/342758
[2] Poirié, M., Colinet, D., & Gatti, J. L. (2014). Insights into function and evolution of parasitoid wasp venoms. Current Opinion in Insect Science, 6, 52-60. doi: 10.1016/j.cois.2014.10.004
[3] Heavner, M. E., Ramroop, J., Gueguen, G., Ramrattan, G., Dolios, G., Scarpati, M., ... & Govind, S. (2017). Novel organelles with elements of bacterial and eukaryotic secretion systems weaponize parasites of Drosophila. Current Biology, 27(18), 2869-2877. doi: 10.1016/j.cub.2017.08.019

A behavior-manipulating virus relative as a source of adaptive genes for parasitoid waspsD. Di Giovanni, D. Lepetit, M. Boulesteix, M. Ravallec, J. Varaldi<p>To circumvent host immune response, numerous hymenopteran endo-parasitoid species produce virus-like structures in their reproductive apparatus that are injected into the host together with the eggs. These viral-like structures are absolutely n...Adaptation, Behavior & Social Evolution, Genetic conflicts, Genome EvolutionIgnacio Bravo2018-07-18 15:59:14 View
11 Jun 2019
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A bird’s white-eye view on neosex chromosome evolution

Young sex chromosomes discovered in white-eye birds

Recommended by based on reviews by Gabriel Marais, Melissa Wilson and 1 anonymous reviewer

Recent advances in next-generation sequencing are allowing us to uncover the evolution of sex chromosomes in non-model organisms. This study [1] represents an example of this application to birds of two Sylvioidea species from the genus Zosterops (commonly known as white-eyes). The study is exemplary in the amount and types of data generated and in the thoroughness of the analysis applied. Both male and female genomes were sequenced to allow the authors to identify sex-chromosome specific scaffolds. These data were augmented by generating the transcriptome (RNA-seq) data set. The findings after the analysis of these extensive data are intriguing: neoZ and neoW chromosome scaffolds and their breakpoints were identified. Novel sex chromosome formation appears to be accompanied by translocation events. The timing of formation of novel sex chromosomes was identified using molecular dating and appears to be relatively recent. Yet first signatures of distinct evolutionary patterns of sex chromosomes vs. autosomes could be already identified. These include the accumulation of transposable elements and changes in GC content. The changes in GC content could be explained by biased gene conversion and altered recombination landscape of the neo sex chromosomes. The authors also study divergence and diversity of genes located on the neo sex chromosomes. Here their findings appear to be surprising and need further exploration. The neoW chromosome already shows unique patterns of divergence and diversity at protein-coding genes as compared with genes on either neoZ or autosomes. In contrast, the genes on the neoZ chromosome do not display divergence or diversity patterns different from those for autosomes. This last observation is puzzling and I believe should be explored in further studies. Overall, this study significantly advances our knowledge of the early stages of sex chromosome evolution in vertebrates, provides an example of how such a study could be conducted in other non-model organisms, and provides several avenues for future work.


[1] Leroy T., Anselmetti A., Tilak M.K., Bérard S., Csukonyi L., Gabrielli M., Scornavacca C., Milá B., Thébaud C. and Nabholz B. (2019). A bird’s white-eye view on neo-sex chromosome evolution. bioRxiv, 505610, ver. 4 peer-reviewed and recommended by PCI Evolutionary Biology. doi: 10.1101/505610

A bird’s white-eye view on neosex chromosome evolutionThibault Leroy, Yoann Anselmetti, Marie-Ka Tilak, Sèverine Bérard, Laura Csukonyi, Maëva Gabrielli, Céline Scornavacca, Borja Milá, Christophe Thébaud, Benoit Nabholz<p>Chromosomal organization is relatively stable among avian species, especially with regards to sex chromosomes. Members of the large Sylvioidea clade however have a pair of neo-sex chromosomes which is unique to this clade and originate from a p...Molecular Evolution, Population Genetics / GenomicsKateryna Makova2019-01-24 14:17:15 View
13 Dec 2016
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Addicted? Reduced host resistance in populations with defensive symbionts

Hooked on Wolbachia

Recommended by and

This very nice paper by Martinez et al. [1] provides further evidence, if further evidence was needed, of the extent to which heritable microorganisms run the evolutionary show.
Wolbachia is an ubiquitous endosymbiont of arthropods who has been recently shown to protect its hosts against viral infections. Here, Martinez et al. are able to show that this multifaceted heritable symbiont weakens selective pressures induced by viruses on host immune genes. In a series of very elegant experiments, Wolbachia-infected and Wolbachia-free populations of D. melanogaster were exposed to Drosophila C virus (a natural, and highly virulent Drosophila pathogen). At the end of a 9-generation artificial selection protocol with DCV, resistance against DCV increased in flies, both in the presence and absence of Wolbachia. Wolbachia-infected flies were still substantially more resistant to DCV viruses than their Wolbachia-free counterparts. Crucially, however, the frequency of the pastrel resistant allele (a key immune gene for DCV resistance) was significantly lower in the Wolbachia-infected lines. As a consequence, when the DCV-evolved lines were treated with antibiotics to cure them from the bacterial infection, the lines who had evolved with Wolbachia tended to be more susceptible to the virus than their uninfected counterparts.
In other words, infection by protective heritable symbionts can affect how selection acts on the host's nuclear-based resistance, effectively rendering it dependent on its symbiont for the fight against pathogens.
But the interest of these results may not be simply academic. The protective qualities of Wolbachia against a range of pathogens have opened up the exciting possibility of transferring these bacteria to mosquito vectors of key human diseases such as dengue or malaria. The long term evolutionary potential for these novel Wolbachia-host interactions has, however, been little explored. Either the Wolbachia, the pathogen or, as shown here, the host, could evolve in more or less predictable ways. There is, for example, evidence showing that in novel hosts Wolbachia evolves rapidly and tends to gradually lose its virulence. If the lost virulence was to result in a decrease in their pathogen defensive qualities, the mosquito, having lost the efficiency of its conventional immune defences, could end up being more vulnerable to infection than before the Wolbachia introduction. Martinez et al.'s paper is a nice example of how investigating the evolutionary potential of such Wolbachia-host-pathogen interactions can be hugely informative as to the long term prospects of these new control methods.


[1] Martinez J, Cogni R, Cao C, Smith S, Illingworth CJR & Jiggins FM. 2016. Addicted? Reduced host resistance in populations with defensive symbionts. Proceedings of the Royal Society of London B 283:20160778. doi: 10.1098/rspb.2016.0778

Addicted? Reduced host resistance in populations with defensive symbiontsMartinez J, Cogni R, Cao C, Smith S, Illingworth CJR & Jiggins FMHeritable symbionts that protect their hosts from pathogens have been described in a wide range of insect species. By reducing the incidence or severity of infection, these symbionts have the potential to reduce the strength of selection on genes ...Adaptation, Evolutionary Applications, Evolutionary Ecology, Experimental Evolution, Life HistoryAna Rivero2016-12-13 20:08:37 View
18 Nov 2020
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A demogenetic agent based model for the evolution of traits and genome architecture under sexual selection

Sexual selection goes dynamic

Recommended by based on reviews by Frédéric Guillaume and 1 anonymous reviewer

150 years after Darwin published ‘Descent of man and selection in relation to sex’ (Darwin, 1871), the evolutionary mechanism that he laid out in his treatise continues to fascinate us. Sexual selection is responsible for some of the most spectacular traits among animals, and plants, and it appeals to our interest in all things reproductive and sexual (Bell, 1982). In addition, sexual selection poses some of the more intractable problems in evolutionary biology: Its realm encompasses traits that are subject to markedly different selection pressures, particularly when distinct, yet associated, traits tend to be associated with males, e.g. courtship signals, and with females, e.g. preferences (cf. Ah-King & Ahnesjo, 2013). While separate, such traits cannot evolve independently of each other (Arnqvist & Rowe, 2005), and complex feedback loops and correlations between them are predicted (Greenfield et al., 2014). Traditionally, sexual selection has been modelled under simplifying assumptions, and quantitative genetic approaches that avoided evolutionary dynamics have prevailed. New computing methods may be able to free the field from these constraints, and a trio of theoreticians (Chevalier, De Coligny & Labonne 2020) describe here a novel application of a ‘demo-genetic agent (or individual) based model’, a mouthful hereafter termed DG-ABM, for arriving at a holistic picture of the sexual selection trajectory. The application is built on the premise that traits, e.g. courtship, preference, gamete investment, competitiveness for mates, can influence the genetic architecture, e.g. correlations, of those traits. In turn, the genetic architecture can influence the expression and evolvability of the traits. Much of this influence occurs via demographic features, i.e. social environment, generated by behavioral interactions during sexual advertisement, courtship, mate guarding, parental care, post-mating dispersal, etc.
The authors provide a lengthy verbal description of their model, specifying the genomic and behavioral parameters that can be set and how a ‘run’ may be initialized. There is a link to an internet site where users can then enter their own parameter values and begin exploring hypotheses. Back in the article several simulations illustrate simple tests; e.g. how gamete investment and preference jointly evolve given certain survival costs. One obvious test would have been the preference – courtship genetic correlation that represents the core of Fisherian runaway selection, and it is regrettable that it was not examined under a range of demographic parameters. As presented the author’s DG-ABM appears particularly geared toward mating systems in ‘higher’ vertebrates, where couples form during a discrete mating season and are responsible for most reproduction. It is not clear how applicable the model could be to a full range of mating systems and nuances, including those in arthropods and other invertebrates as well as plants.
What is the likely value of the DG-ABM for sexual selection researchers? We will not be able to evaluate its potential impact until readers with specialized understanding of a question and taxon begin exploring and comparing their results with prior expectations. Of course, lack of congruence with earlier predictions would not invalidate the model. Hopefully, some of these specialists will have opportunities for comparing results with pertinent empirical data.


Ah-King, M. and Ahnesjo, I. 2013. The ‘sex role’ concept: An overview and evaluation Evolutionary Biology, 40, 461-470. doi:
Arnqvist, G. and Rowe, L. 2005. Sexual Conflict. Princeton University Press, Princeton. doi:
Bell, G. 1982. The Masterpiece of Nature: The Evolution and Genetics of Sexuality. University of California Press, Berkeley.
Chevalier, L., De Coligny, F. and Labonne, J. (2020) A demogenetic individual based model for the evolution of traits and genome architecture under sexual selection. bioRxiv, 2020.04.01.014514, ver. 4 peer-reviewed and recommended by PCI Evol Biol. doi:
Darwin, C. 1871. The Descent of Man and Selection in Relation to Sex. J. Murray, London.
Greenfield, M.D., Alem, S., Limousin, D. and Bailey, N.W. 2014. The dilemma of Fisherian sexual selection: Mate choice for indirect benefits despite rarity and overall weakness of trait-preference genetic correlation. Evolution, 68, 3524-3536. doi:

A demogenetic agent based model for the evolution of traits and genome architecture under sexual selectionLouise Chevalier, François de Coligny, Jacques Labonne<p>Sexual selection has long been known to favor the evolution of mating behaviors such as mate preference and competitiveness, and to affect their genetic architecture, for instance by favoring genetic correlation between some traits. Reciprocall...Adaptation, Behavior & Social Evolution, Evolutionary Dynamics, Evolutionary Theory, Life History, Population Genetics / Genomics, Sexual SelectionMichael D Greenfield2020-04-02 14:44:25 View
05 Nov 2020
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A genomic amplification affecting a carboxylesterase gene cluster confers organophosphate resistance in the mosquito Aedes aegypti: from genomic characterization to high-throughput field detection

Identification of a gene cluster amplification associated with organophosphate insecticide resistance: from the diversity of the resistance allele complex to an efficient field detection assay

Recommended by based on reviews by Diego Ayala and 2 anonymous reviewers

The emergence and spread of insecticide resistance compromises the efficiency of insecticides as prevention tool against the transmission of insect-transmitted diseases (Moyes et al. 2017). In this context, the understanding of the genetic mechanisms of resistance and the way resistant alleles spread in insect populations is necessary and important to envision resistance management policies. A common and important mechanism of insecticide resistance is gene amplification and in particular amplification of insecticide detoxification genes, which leads to the overexpression of these genes (Bass & Field, 2011). Cattel and coauthors (2020) adopt a combination of experimental approaches to study the role of gene amplification in resistance to organophosphate insecticides in the mosquito Aedes aegypti and its occurrence in populations of South East Asia and to develop a molecular test to track resistance alleles.
Their first approach consists in performing an artificial selection on laboratory Ae. Aegypti populations started with individuals collected in Laos. In the selected population, an initial 90% mortality by adult exposure to the organophosphate insecticide malathion is imposed. This population shows a steep increase in resistance to malathion and other organophosphate insecticides, which is absent in the paired control population. The transcriptomic patterns of the control and the evolved populations as well as of a reference sensitive population reveals, among other differences, the over-expression of five carboxy/choline esterase (CCE) genes in the insecticide selected population. These five genes happen to be clustered in the Ae. aegypti genome and whole genome sequencing of a highly resistant population combined to qPCR test on genomic DNA showed that the overexpression of these genes is due to gene amplification. Although it would have been more elegant to have replicate selected and control populations and to perform the transcriptomic and the genomic analyses directly on the experimental populations, the authors gather a set of experimental evidence which combined to previous knowledge on the function of the amplified and over-expressed genes and on their implication in organophosphate insecticide resistance in other species allow to discard the possibility that this gene amplification spread by drift in the selected population.
In a second part of the paper, copy number variation for CCE genes is checked in field sample populations. This test reveals the presence of resistance alleles in half of the fourteen South East Asia populations sampled. Very interestingly, it also reveals a high level of complexity and diversity among the resistance alleles: it shows first the existence, both in the experimental and the field populations, of at least two amplified alleles (differing by the number of genes amplified) and second a high variation in the copy number of amplified genes. This indicates that gene amplification as a molecular resistance mechanism has actually lead to a high diversity of resistance alleles. These alleles are likely to differ both by the level of resistance conferred and the fitness cost imposed in the absence of the insecticide and these two values are affecting the evolution of their frequency in the field and ultimately the spread of resistance.
The last part of the paper is devoted to the development of a high-throughput Taqman assay which allows to determine rapidly the copy number of one of the esterase genes amplified in the resistance alleles described earlier. This assay is nicely validated and will definitely be a useful tool to determine the occurrence of these resistance alleles in field population. The fact that it gives access to the copy number will also allow to follow its copy number across time and get insight into the complexity of resistance evolution by gene amplification.
To sum up, this paper studies the implication of carboxy/choline esterase genes amplification in organophosphate resistance evolution in Ae. aegypti, reveals the diversity among individuals and populations of this resistance mechanism, because of variation both in the identity of the genes amplified and in their copy number and sets up a fast and efficient tool to detect and follow the spread of these resistant alleles in the field. Additionally, the different experimental approaches adopted have generated genomic and transcriptomic data, of which only the part related to CCE gene amplification has been exploited. These data are very likely to reveal other genomic and expression determinants of resistance that will give access to an extra degree of complexity in organophosphate insecticide resistance determinism and evolution.


Bass C, Field LM (2011) Gene amplification and insecticide resistance. Pest Management Science, 67, 886–890.
Cattel J, Haberkorn C, Laporte F, Gaude T, Cumer T, Renaud J, Sutherland IW, Hertz JC, Bonneville J-M, Arnaud V, Nous C, Fustec B, Boyer S, Marcombe S, David J-P (2020) A genomic amplification affecting a carboxylesterase gene cluster confers organophosphate resistance in the mosquito Aedes aegypti: from genomic characterization to high-throughput field detection. bioRxiv, 2020.06.08.139741, ver. 4 peer-reviewed and recommended by PCI Evolutionary Biology.
Moyes CL, Vontas J, Martins AJ, Ng LC, Koou SY, Dusfour I, Raghavendra K, Pinto J, Corbel V, David J-P, Weetman D (2017) Contemporary status of insecticide resistance in the major Aedes vectors of arboviruses infecting humans. PLOS Neglected Tropical Diseases, 11, e0005625.

A genomic amplification affecting a carboxylesterase gene cluster confers organophosphate resistance in the mosquito Aedes aegypti: from genomic characterization to high-throughput field detectionJulien Cattel, Chloé Haberkorn, Fréderic Laporte, Thierry Gaude, Tristan Cumer, Julien Renaud, Ian W. Sutherland, Jeffrey C. Hertz, Jean-Marc Bonneville, Victor Arnaud, Camille Noûs, Bénédicte Fustec, Sébastien Boyer, Sébastien Marcombe, Jean-Phil...<p>By altering gene expression and creating paralogs, genomic amplifications represent a key component of short-term adaptive processes. In insects, the use of insecticides can select gene amplifications causing an increased expression of detoxifi...Adaptation, Evolutionary Applications, Experimental Evolution, Genome Evolution, Molecular EvolutionStephanie Bedhomme2020-06-09 13:27:18 View
04 Jul 2022
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A genomic assessment of the marine-speciation paradox within the toothed whale superfamily Delphinoidea

Reticulated evolution marks the rapid diversification of the Delphinoidae

Recommended by based on reviews by Christelle Fraïsse, Simon Henry Martin, Andrew Foote and 2 anonymous reviewers

Historically neglected or considered a rare aberration in animals under the biological species concept, interspecific hybridisation has by now been recognised to be taxonomically widespread, particularly in rapidly diversifying groups (Dagilis et al. 2021; Edelman & Mallet 2021; Mallet et al. 2016; Seehausen 2004). Yet the prevalence of introgressive hybridizations, its evolutionary significance, and its impact on species diversification remain a hot topic of research in evolutionary biology. The rapid increase in genomic resources now available for non-model species has significantly contributed to the detection of introgressive hybridization across taxa showing that reticulated evolution is far more common in the animal kingdom than historically considered. Yet, detecting it, quantifying its magnitude, and assessing its evolutionary significance remains a challenging endeavour with constantly evolving methodologies to better explore and exploit genomic data (Blair & Ané 2020; Degnan & Rosenberg 2009; Edelman & Mallet 2021; Hibbins & Hahn 2022).

In the marine realm, the dearth of geographic barriers and the large dispersal abilities of pelagic species like cetaceans have raised the questions of how populations and species can diverge and adapt to distinct ecological conditions in face of potentially large gene-flow, the so-called marine speciation paradox (Bierne et al. 2003). Contemporaneous hybridization among cetacean species has been widely documented in nature despite large phenotypic differences (Crossman et al. 2016). The historical prevalence of reticulated evolution, its evolutionary significance, and how it might have impacted the evolutionary history and diversification of the cetaceans have however remained elusive so far. Recent phylogenomic studies suggested that introgression has been prevalent in cetacean evolutionary history with instances reported among baleen whales (mysticetes) (Árnason et al. 2018) and among toothed whales (odontocetes), especially in the rapidly diversifying dolphins family of the Delphininae (Guo et al. 2021; Moura et al. 2020).

Analysing publicly available whole-genome data from nine cetacean species across three families of Delphinoidae – dolphins, porpoises, and monondontidae – using phylogenomics and demo-genetics approaches, Westbury and colleagues (2022) take a step further in documenting that evolution among these species has been far from a simple bifurcating tree. Instead, their study describes widespread occurrences of introgression among Delphinoidae, drawing a complex picture of reticulated evolutionary history. After describing major topology discordance in phylogenetic gene trees along the genome, the authors use a panel of approaches to disentangle introgression from incomplete lineage sorting (ILS), the two most common causes of tree topology discordances (Hibbins & Hahn 2022). Applying popular tests that separate introgression from ILS, such as the Patterson’s D (a.k.a. ABBA-BABA) test (Durand et al. 2011; Green et al. 2010), QuIBL (Edelman et al. 2019), and D-FOIL (Pease & Hahn 2015), the authors report that signals of introgression are present in the genomes of most (if not all) the cetacean species included in their study. However, this picture needs to be nuanced. Most introgression signals seem to echo old introgression events that occurred primarily among ancestors. This is suggested by the differential signals of topology discordance along the genome when considering sliding windows along the genome of varying sizes (50kb, 100kb, and 1Mb), and by patterns of excess derived allele sharing along branches of the species tree, as captured by the f-branch test (Malinsky et al. 2021; Malinsky et al. 2018). The authors further investigated the dynamic of cessation of gene flow (and/or ILS) between species using the F1 hybrid PSMC (or hPSMC) approach (Cahill et al. 2016). By estimating the cross-coalescent rates (CRR) between species pairs with time in light of previously estimated species divergence times (McGowen et al. 2020), the authors report that gene flow (and/or ILS) most likely has stopped by now among most species, but it may have lasted for more than half of the time since the species split from each other. According to the author, this result may reflect the slow process by which reproductive isolation would have evolved between cetacean lineages, and that species isolation was marked by significant introgression events.

Now, while the present study provides a good overview of how complex is the reticulated evolutionary history of the Delphinoidae, getting a complete picture will require overcoming a few important limitations. The first ones are methodological and related to the phylogenomic analyses. Given the sampling design with one diploid genome per species, the authors could not phase the data into the parental haplotypes, but instead relied on a majority consensus creating mosaic haploidized genomes representing a mixture between the two parental copies. Moreover, by using large genomic windows (≥50kb) that likely span multiple independent loci, phylogenetic analyses in windows encompassed distinct phylogenetic signals, potentially leading to bias and inaccuracy in the inferences. Thawornwattana et al (2018) previously showed that this “concatenation approach”  could significantly impact phylogenetic inferences. They proposed instead to use loci small enough to minimise the risk of intra-locus recombination and to consider them in blocks of non-recombining loci along the genome in order to conduct phylogenetic analysed, ideally under the multi-species coalescent (MSC) that can account for ILS (e.g. BPP; Flouri et al. 2018; Jiao et al. 2020; Yang 2015). Such an approach applied to the diversification of the Delphinidae may reveal substantial changes compared to the currently admitted species tree.

Inaccuracy in the species tree estimation may have a major impact on the introgression analyses conducted in this study since the species tree and branching order must be supplied in the introgression analyses to properly disentangle introgression from ILS. Here, the authors rely on the tree topology that was previously estimated in McGowen et al. (2020), which they also recovered using their consensus estimation from ASTRAL-III (Zhang et al. 2018). While the methodologies accounted to a certain extent for ILS, albeit with potential bias induced by the concatenation approach, they ignore the presumably large amount of introgression among species during the diversification process. Estimating species branching order while ignoring introgression can lead to major bias in the phylogenetic inference and can lead to incorrect topologies. Even if these MSC-based methods account for ILS, inferences can become very inaccurate or even break down as gene flow increases (see for ex. Jiao et al. 2020; Müller et al. in press; Solís-Lemus et al. 2016). Dedicated approaches have been developed to model explicitly introgression together with ILS to estimate phylogenetic networks (Blair & Ané 2020; Rabier et al. 2021) or in isolation-with-migration model (Müller et al. in press; Wang et al. 2020). Future studies revisiting the reticulated evolutionary history of the Delphinoidae with such approaches may not only precise the species branching order, but also deliver a finer view of the magnitude and prevalence of introgression during the evolutionary history of these species.

A final part of Westbury et al. (2022)'s study set out to test whether historical periods of low abundance could have facilitated hybridization among Delphinoidae species. During these periods of low abundance, species may encounter only a limited number of conspecifics and may consider individuals from other species as suitable mating partners, leading to hybridisation (Crossman et al. 2016; Edwards et al. 2011; Westbury et al. 2019). The authors tested this hypothesis by considering genome-wide genetic diversity (or heterozygosity) as a proxy of historical effective population size (Ne), itself as a proxy of the evolution of census size with time. They also try to link historical Ne variation (from PSMC, Li & Durbin 2011) with their estimated time to cessation of gene flow or ILS (from the CRR of hPSMC). However, no straightforward relationship was found between the genetic diversity and the propensity of species to hybridize, nor was there any clear link between Ne variation through time and the cessation of gene flow or ILS. Such a lack of relationship may not come as a surprise, since the determinants of genome-wide genetic diversity and its variation through evolutionary time-scale are far more diverse and complex than just a direct link with hybridization, introgression, or even with the census population size. In fact, genetic diversity results from the balance between all the evolutionary processes at play in the species' evolutionary history (see the review of Ellegren & Galtier 2016). Other important factors can strongly impact genetic diversity, including demography and structure, but also linked selection (Boitard et al. 2022; Buffalo 2021; Ellegren & Galtier 2016). 

All in all, Westbury and coll. (2022) present here an interesting study providing an additional step towards resolving and understanding the complex evolutionary history of the Delphinoidae, and shedding light on the importance of introgression during the diversification of these cetacean species. Prospective work improving upon the taxonomic sampling, with additional genomic data for each species, considered with dedicated approaches tailored at estimating species tree or network while accounting for ILS and introgression will be key for refining the picture depicted in this study. Down the road, altogether these studies will contribute to assessing the evolutionary significance of introgression on the diversification of Delphinoides, and more generally on the diversification of cetacean species, which still remain an open and exciting perspective. 


Árnason Ú, Lammers F, Kumar V, Nilsson MA, Janke A (2018) Whole-genome sequencing of the blue whale and other rorquals finds signatures for introgressive gene flow. Science Advances 4, eaap9873.

Bierne N, Bonhomme F, David P (2003) Habitat preference and the marine-speciation paradox. Proceedings of the Royal Society of London. Series B: Biological Sciences 270, 1399-1406.

Blair C, Ané C (2020) Phylogenetic Trees and Networks Can Serve as Powerful and Complementary Approaches for Analysis of Genomic Data. Systematic Biology 69, 593-601.

Boitard S, Arredondo A, Chikhi L, Mazet O (2022) Heterogeneity in effective size across the genome: effects on the inverse instantaneous coalescence rate (IICR) and implications for demographic inference under linked selection. Genetics 220, iyac008.

Buffalo V (2021) Quantifying the relationship between genetic diversity and population size suggests natural selection cannot explain Lewontin's Paradox. e-Life 10, e67509.

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A genomic assessment of the marine-speciation paradox within the toothed whale superfamily DelphinoideaMichael V Westbury, Andrea A Cabrera, Alba Rey-Iglesia, Binia De Cahsan, David A. Duchêne, Stefanie Hartmann, Eline D Lorenzen<p>The importance of post-divergence gene flow in speciation has been documented across a range of taxa in recent years, and may have been especially widespread in highly mobile, wide-ranging marine species, such as cetaceans. Here, we studied ind...Evolutionary Dynamics, Hybridization / Introgression, Molecular Evolution, Phylogenetics / Phylogenomics, SpeciationMichael C. Fontaine2020-10-25 08:55:50 View
25 Feb 2021
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Alteration of gut microbiota with a broad-spectrum antibiotic does not impair maternal care in the European earwig

Assessing the role of host-symbiont interactions in maternal care behaviour

Recommended by based on reviews by Nadia Aubin-Horth, Gabrielle Davidson and 1 anonymous reviewer

The role of microbial symbionts in governing social traits of their hosts is an exciting and developing research area. Just like symbionts influence host reproductive behaviour and can cause mating incompatibilities to promote symbiont transmission through host populations (Engelstadter and Hurst 2009; Correa and Ballard 2016; Johnson and Foster 2018) (see also discussion on conflict resolution in Johnsen and Foster 2018), microbial symbionts could enhance transmission by promoting the social behaviour of their hosts (Ezenwa et al. 2012; Lewin-Epstein et al. 2017; Gurevich et al. 2020). Here I apply the term ‘symbiosis’ in the broad sense, following De Bary 1879 as “the living together of two differently named organisms“ independent of effects on the organisms involved (De Bary 1879), i.e. the biological interaction between the host and its symbionts may include mutualism, parasitism and commensalism.
So far, we have relative few studies that explore the role of symbionts in promoting social behaviours such as parental care. Clearly, disentangling cause and effect when assessing the functional significance of symbiotic relationships in general is extremely challenging, and perhaps even more caution is needed when assessing the role of symbionts in the evolution of parental care, given the high fitness benefits to the offspring of receiving care. An interesting study on the symbiotic relationship between termites and their eukaryotic gut symbionts proposes a role of gut flagellates in the origin of subsocial behaviour (extended offspring care) in the termites through proctodeal trophallaxis (i.e. anus-to-mouth feeding), driven by mutualistic beneficial interactions (Nalepa 2020). Van Meyel et al. (2021) hypothesized a role of gut symbionts in promoting maternal care behaviour in the European earwig, and set out to test this idea in a carefully executed experimental study. They used a broad-spectrum antibiotic treatment to alter gut microbiota in mothers and examined its effect on maternal care provisioning. While the antibiotic treatment altered the gut microbiome, no effect on pre- or post-hatching maternal care was detected. The authors also investigated a broad range of physiological and reproductive traits measured over a major part of a female’s lifetime, and detected no effect of microbiome alteration on these traits. The study therefore does not provide evidence for a direct role of the gut microbiome in shaping offspring care in this population of European earwigs.
Within populations, earwigs show inter-individual variation in the expression of maternal care (Meunier et al. 2012; Ratz et al. 2016), and there is evidence that genetic and environmental factors contribute to this this variation (Meunier and Kolliker 2012; Kramer et al. 2017). The study by Van Meyel et al. (2021) is the first to analyse microbiome composition of the European earwig, and they study host-symbiont associations in a single population. A next step could be to explore among population variation in the gut microbiome, to achieve a better understanding on host-microbiome variation and dynamics in wild populations. Depending on the nature of host-symbiont associations across populations, new perspectives on their functional significance may arise (Hird 2017; Johnson and Foster 2018). It is therefore too early to conclusively confirm or reject the role of microbial symbionts in the expression of parental care in this system.


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Meunier, J., Wong, J. W., Gómez, Y., Kuttler, S., Röllin, L., Stucki, D., and Kölliker, M. (2012). One clutch or two clutches? Fitness correlates of coexisting alternative female life-histories in the European earwig. Evolutionary Ecology, 26(3), 669-682. doi:

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Van Meyel, S., Devers, S., Dupont, S., Dedeine, F. and Meunier, J. (2021) Alteration of gut microbiota with a broad-spectrum antibiotic does not impair maternal care in the European earwig. bioRxiv, 2020.10.08.331363. ver. 5 peer-reviewed and recommended by PCI Evol Biol.

Alteration of gut microbiota with a broad-spectrum antibiotic does not impair maternal care in the European earwigSophie Van Meyel, Séverine Devers, Simon Dupont, Franck Dedeine and Joël Meunier<p>The microbes residing within the gut of an animal host often increase their own fitness by modifying their host’s physiological, reproductive, and behavioural functions. Whereas recent studies suggest that they may also shape host sociality and...Behavior & Social Evolution, Evolutionary Ecology, Experimental Evolution, Life History, Species interactionsTrine Bilde2020-10-09 14:07:47 View
28 Mar 2019
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Ancient tropical extinctions contributed to the latitudinal diversity gradient

One (more) step towards a dynamic view of the Latitudinal Diversity Gradient

Recommended by and based on reviews by Juan Arroyo, Joaquín Hortal, Arne Mooers, Joaquin Calatayud and 2 anonymous reviewers

The Latitudinal Diversity Gradient (LDG) has fascinated natural historians, ecologists and evolutionary biologists ever since [1] described it about 200 years ago [2]. Despite such interest, agreement on the origin and nature of this gradient has been elusive. Several tens of hypotheses and models have been put forward as explanations for the LDG [2-3], that can be grouped in ecological, evolutionary and historical explanations [4] (see also [5]). These explanations can be reduced to no less than 26 hypotheses, which account for variations in ecological limits for the establishment of progressively larger assemblages, diversification rates, and time for species accumulation [5]. Besides that, although in general the tropics hold more species, different taxa show different shapes and rates of spatial variation [6], and a considerable number of groups show reverse patterns, with richer assemblages in cold temperate regions (see e.g. [7-9]).
Understanding such complexity needs integrating ecological and evolutionary research into the wide temporal and spatial perspectives provided by the burgeoning field of biogeography. This integrative discipline ¬–that traces back to Humboldt himself (e.g. [10])– seeks to put together historical and functional explanations to explain the complex dynamics of Earth’s biodiversity. Different to quantum physicists, biogeographers cannot pursue the ultimate principle behind the patterns we observe in nature due to the interplay of causes and effects, which in fact tell us that there is not such a single principle. Rather, they need to identify an array of basic principles coming from different perspectives, to then integrate them into models that provide realistic –but never simple– explanations to biodiversity gradients such as LDG (see, e.g., [5; 11]). That is, rather than searching for a sole explanation, research on the LDG must aim to identify as many signals hidden in the pattern as possible, and provide hypotheses or models that account for these signals. To later integrate them and, whenever possible, to validate them with empirical data on the organisms’ distribution, ecology and traits, phylogenies, fossils, etc.
Within this context, Meseguer & Condamine [12] provide a novel perspective to LDG research using phylogenetic and fossil evidence on the origin and extinction of taxa within the turtle, crocodile and lizard (i.e. squamate) lineages. By digging into deep time down to the Triassic (about 250 Myr ago) they are able to identify several episodes of flattening and steepening of the LDG for these three clades. Strikingly, their results show similar diversification rates in the northern hemisphere and in the equator during the over 100 Myr long global greenhouse period that extends from the late Jurassic to the Cretaceous and early Neogene. During this period, the LDG for these three groups would have appeared quite even across a mainly tropical Globe, although the equatorial regions were apparently much more evolutionarily dynamic. The equator shows much higher rates of origination and extinction of branches throughout the Cretaceous, but they counteract each other so net diversification is similar to that of the northern hemisphere in all three groups. The transition to a progressively colder Earth in the Paleogene (starting around 50 Myr ago) provokes a mass extinction in the three clades, which is compensated in the equator by the dispersal of many taxa from the areas that currently pertain to the Holarctic biogeographical realm. Finally, during the coldhouse Earth’s climatic conditions of the Neogene only squamates show significant positive diversification rates in extratropical areas, while the diversity of testudines remains, and crocodiles continue declining progressively towards oblivion in the whole world.
Meseguer & Condamine [12] attribute these temporal patterns to the so-called asymmetric gradient of extinction and dispersal (AGED) framework. Here, the dynamics of extinction-at and dispersal-from high latitudes during colder periods increase the steepness of the LDG. Whereas the gradient flattens when Earth warms up as a result of dispersal from the equator followed by increased diversification in extratropical regions. This idea in itself is not new, for the influence of climatic oscillations on diversification rates is well known, at least for the Pleistocene Ice Ages [13], as is the effect of niche conservatism on the LDG [14]. Nevertheless, Meseguer & Condamine’s AGED provides a synthetic verbal model that could allow integrating the three main types of processes behind the LDG into a single framework. To do this it would be necessary to combine AGED’s cycles of dispersal and diversification with realistic models of: (1) the ecological limits to host rich assemblages in the colder and less productive temperate climatic domains; (2) the variations in diversification rates with shifts in temperature and/or energy regimes; and (3) the geographical patterns of climatic oscillation through time that determine the time for species accumulation in each region.
Integrating these models may allow transposing Meseguer & Condamine’s [12] framework into the more mechanistic macroecological models advocated by Pontarp et al. [5]. This type of mechanistic models has been already used to understand the development of biodiversity gradients through the climatic oscillations of the Pleistocene and the Quaternary (e.g. [11]). So the challenge in this case would be to generate a realistic scenario of geographical dynamics that accounts for plate tectonics and long-term climatic oscillations. This is still a major gap and we would benefit from the integrated work by historical geologists and climatologists here. For instance, there is little doubt about the progressive cooling through the Cenozoic based in isotope recording in sea floor sediments [15]. Meseguer & Condamine [12] use this evidence for separating greenhouse, transition and coldhouse world scenarios, which should not be a problem for these rough classes. However, a detailed study of the evolutionary correlation of true climate variables across the tree of life is still pending, as temperature is inferred only for sea water in an ice-free ocean, say earlier half of the Cenozoic [15]. Precipitation regime is even less known. Such scenario would provide a scaffold upon which the temporal dynamics of several aspects of the generation and loss of biodiversity can be modelled. Additionally, one of the great advantages of selecting key clades to study the LDG would be to determine the functional basis of diversification. There are species traits that are well known to affect speciation and extinction probabilities, such as reproductive strategies or life histories (e.g. [16]). Whereas these traits might also be a somewhat redundant effect of climatic causes, they might foster (i.e. “extended reinforcement”, [17]) or slow diversification. Even so, it is unlikely that such a model would account for all the latitudinal variation in species richness. But it will at least provide a baseline for the main latitudinal variations in the diversity of the regional communities (sensu [18]) worldwide. Within this context the effects of recent ecological, evolutionary and historical processes, such as environmental heterogeneity, current diversification rates or glacial cycles, will only modify the general LDG pattern resulting from the main processes contained in Meseguer & Condamine’s AGED, thereby providing a more comprehensive understanding of the geographical gradients of diversity.

[1] Humboldt, A. v. (1808). Ansichten der Natur, mit wissenschaftlichen Erläuterungen. J. G. Cotta, Tübingen.
[2] Hawkins, B. A. (2001). Ecology's oldest pattern? Trends in Ecology & Evolution, 16, 470. doi: 10.1016/S0169-5347(01)02197-8
[3] Lomolino, M. V., Riddle, B. R. & Whittaker, R. J. (2017). Biogeography. Fifth Edition. Sinauer Associates, Inc., Sunderland, Massachussets.
[4] Mittelbach, G. G., Schemske, D. W., Cornell, H. V., Allen, A. P., Brown, J. M., Bush, M. B., Harrison, S. P., Hurlbert, A. H., Knowlton, N., Lessios, H. A., McCain, C. M., McCune, A. R., McDade, L. A., McPeek, M. A., Near, T. J., Price, T. D., Ricklefs, R. E., Roy, K., Sax, D. F., Schluter, D., Sobel, J. M. & Turelli, M. (2007). Evolution and the latitudinal diversity gradient: speciation, extinction and biogeography. Ecology Letters, 10, 315-331. doi: 10.1111/j.1461-0248.2007.01020.x
[5] Pontarp, M., Bunnefeld L., Cabral, J. S., Etienne, R. S., Fritz, S. A., Gillespie, R. Graham, C. H., Hagen, O., Hartig, F., Huang, S., Jansson, R., Maliet, O., Münkemüller, T., Pellissier, L., Rangel, T. F., Storch, D., Wiegand, T. & Hurlbert, A. H. (2019). The latitudinal diversity gradient: novel understanding through mechanistic eco-evolutionary models. Trends in ecology & evolution, 34, 211-223. doi: 10.1016/j.tree.2018.11.009
[6] Hillebrand, H. (2004). On the generality of the latitudinal diversity gradient. The American Naturalist, 163, 192-211. doi: 10.1086/381004
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[8] Morinière, J., Van Dam, M. H., Hawlitschek, O., Bergsten, J., Michat, M. C., Hendrich, L., Ribera, I., Toussaint, E. F. A. & Balke, M. (2016). Phylogenetic niche conservatism explains an inverse latitudinal diversity gradient in freshwater arthropods. Scientific Reports, 6, 26340. doi: 10.1038/srep26340
[9] Weiser, M. D., Swenson, N. G., Enquist, B. J., Michaletz, S. T., Waide, R. B., Zhou, J. & Kaspari, M. (2018). Taxonomic decomposition of the latitudinal gradient in species diversity of North American floras. Journal of Biogeography, 45, 418-428. doi: 10.1111/jbi.13131
[10] Humboldt, A. v. (1805). Essai sur la geographie des plantes; accompagné d'un tableau physique des régions equinoxiales. Levrault, Paris.
[11] Rangel, T. F., Edwards, N. R., Holden, P. B., Diniz-Filho, J. A. F., Gosling, W. D., Coelho, M. T. P., Cassemiro, F. A. S., Rahbek, C. & Colwell, R. K. (2018). Modeling the ecology and evolution of biodiversity: Biogeographical cradles, museums, and graves. Science, 361, eaar5452. doi: 10.1126/science.aar5452
[12] Meseguer, A. S. & Condamine, F. L. (2019). Ancient tropical extinctions contributed to the latitudinal diversity gradient. bioRxiv, 236646, ver. 4 peer-reviewed and recommended by PCI Evol Biol. doi: 10.1101/236646
[13] Jansson, R., & Dynesius, M. (2002). The fate of clades in a world of recurrent climatic change: Milankovitch oscillations and evolution. Annual review of ecology and systematics, 33(1), 741-777. doi: 10.1146/annurev.ecolsys.33.010802.150520
[14] Wiens, J. J., & Donoghue, M. J. (2004). Historical biogeography, ecology and species richness. Trends in ecology & evolution, 19, 639-644. doi: 10.1016/j.tree.2004.09.011
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Ancient tropical extinctions contributed to the latitudinal diversity gradientAndrea S. Meseguer, Fabien Condamine<p>Biodiversity currently peaks at the equator, decreasing toward the poles. Growing fossil evidence suggest that this hump-shaped latitudinal diversity gradient (LDG) has not been persistent through time, with similar species diversity across lat...Evolutionary Dynamics, Evolutionary Ecology, Macroevolution, Paleontology, Phylogenetics / Phylogenomics, Phylogeography & BiogeographyJoaquín Hortal2017-12-20 14:58:01 View
16 May 2023
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A new and almost perfectly accurate approximation of the eigenvalue effective population size of a dioecious population: comparisons with other estimates and detailed proofs

All you ever wanted to know about Ne in one handy place

Recommended by based on reviews by Jesse ("Jay") Taylor and 1 anonymous reviewer

​Of the four evolutionary forces, three can be straightforwardly summarized both conceptually and mathematically in the context of an allele at a genomic locus.  Mutation (the mutation rate, μ) is simply captured by the per-site, per-generation probability that an allele mutates into a different allele. Recombination (the recombination rate, r) is captured as the probability of recombination between two sites, wherein alleles that are in different genomes in one generation come together in the same genome in the next generation.  Natural selection (the selection coefficient, s) is captured by the probability that an allele is present in the next generation, relative to some reference.  

Random genetic drift – the random fluctuation in allele frequency due to sampling in a finite population - is not so straightforwardly summarized.  The first, and most common way of characterizing evolutionary dynamics in a finite population is the Wright-Fisher model, in which the only deviation from the assumptions of Hardy-Weinberg conditions is finite population size.  Importantly, in a W-F population, mating between diploid individuals is random, which implies self-fertile monoecy, and generations are non-overlapping.  In an ideal W-F population, the probability that a gene copy leaves i descendants in the next generation is the result of binomial sampling of uniting gametes (if the locus is biallelic).  The – and the next word is meaningful – magnitude/strength/rate/power/amount of genetic drift is proportional to 1/2N, where N is the size of the population.  All of the following are affected by genetic drift: (1) the probability that a neutral allele ultimately reaches fixation, (2) the rate of loss of genetic variation within a population, (3) the rate of increase of genetic variance among populations, (4) the amount of genetic variation segregating in a population, (5) the probability of fixation/loss of a weakly selected variant.    

Presumably no real population adheres to ideal W-F conditions, which leads to the notion of "effective population size", Ne (Wright 1931), loosely defined as "the size of an ideal W-F population that experiences an equivalent strength of genetic drift".  Almost always, Ne<N, and any violation of W-F assumptions can affect Ne.  Importantly, Ne can be defined in different ways, and the specific formulation of Ne can have different implications for evolution.  Ne was initially defined in terms of the rate of decrease of heterozygosity (inbreeding effective size) and increase in variance among populations (variance effective size).  Ewens (1979) defined the Eigenvalue effective size (equivalent to the "random extinction" effective size) and elaborated on the conditions under which the various formulations of Ne differ (Ewens 1982).  Nordborg and Krone (2002) defined the effective size in terms of the coalescent, and they identified conditions in which genetic drift cannot be described in terms of a W-F model (Sjodin et al. 2005); also see Karasov et al. (2010); Neher and Shraiman (2011).

Distinct from the issue of defining Ne is the issue of calculating Ne from data, which is the focus of this paper by De Meeus and Noûs (2023).  Pudovkin et al. (1996) showed that the Eigenvalue effective size in a dioecious population can be formulated in terms of excess heterozygosity, which the current authors note is equivalent to formulating Ne in terms of Wright's FIS statistic.  As emphasized by the title, the marquee contribution of this paper is to provide a better approximation of the Eigenvalue effective size in a dioecious population.  Science marches onward, although the empirical utility of this advance is obviously limited, given the tremendous inherent sources of uncertainty in real-world estimates of Ne.  Perhaps more valuable, however, is the extensive set of appendixes, in which detailed derivations are provided for the various formulations of effective size.  By way of analogy, the material presented here can be thought of as an extension of the material presented in section 7.6 of Crow and Kimura (1970), in which the Inbreeding and Variance effective population sizes are derived and compared.  The appendixes should serve as a handy go-to source of detailed theoretical information with respect to the different formulations of effective population size.


Crow, J. F. and M. Kimura. 1970. An Introduction to Population Genetics Theory. The Blackburn Press, Caldwell, NJ.

De Meeûs, T. and Noûs, C. 2023. A new and almost perfectly accurate approximation of the eigenvalue effective population size of a dioecious population: comparisons with other estimates and detailed proofs. Zenodo, ver. 6 peer-reviewed and recommended by Peer Community in Evolutionary Biology.

Ewens, W. J. 1979. Mathematical Population Genetics. Springer-Verlag, Berlin.

Ewens, W. J. 1982. On the concept of the effective population size. Theoretical Population Biology 21:373-378.

Karasov, T., P. W. Messer, and D. A. Petrov. 2010. Evidence that adaptation in Drosophila Is not limited by mutation at single sites. Plos Genetics 6.

Neher, R. A. and B. I. Shraiman. 2011. Genetic Draft and Quasi-Neutrality in Large Facultatively Sexual Populations. Genetics 188:975-U370.

Nordborg, M. and S. M. Krone. 2002. Separation of time scales and convergence to the coalescent in structured populations. Pp. 194–232 in M. Slatkin, and M. Veuille, eds. Modern Developments in Theoretical Population Genetics: The Legacy of Gustave Malécot. Oxford University Press, Oxford.

Pudovkin, A. I., D. V. Zaykin, and D. Hedgecock. 1996. On the potential for estimating the effective number of breeders from heterozygote-excess in progeny. Genetics 144:383-387.

Sjodin, P., I. Kaj, S. Krone, M. Lascoux, and M. Nordborg. 2005. On the meaning and existence of an effective population size. Genetics 169:1061-1070.

Wright, S. 1931. Evolution in Mendelian populations. Genetics 16:0097-0159.

A new and almost perfectly accurate approximation of the eigenvalue effective population size of a dioecious population: comparisons with other estimates and detailed proofsThierry de Meeûs and Camille Noûs<p>The effective population size is an important concept in population genetics. It corresponds to a measure of the speed at which genetic drift affects a given population. Moreover, this is most of the time the only kind of population size that e...Bioinformatics & Computational Biology, Evolutionary Ecology, Evolutionary Theory, Population Genetics / Genomics, Reproduction and SexCharles Baer2023-02-22 16:53:49 View