The causes and consequences of the evolution of sexual reproduction are a major topic in evolutionary biology. With advances in sequencing technology, it becomes possible to compare sexual chromosomes across species and infer the neutral and selective processes shaping polymorphism at these chromosomes. Most sex and mating-type chromosomes exhibit an absence of recombination in large genomic regions around the animal, plant or fungal sex-determining genes. This suppression of recombination likely occurred in several time steps generating stepwise increasing genomic regions starting around the sex-determining genes. This mechanism generates so-called evolutionary strata of differentiation between sex chromosomes (Nicolas et al., 2004, Bergero and Charlesworth, 2009, Hartmann et al. 2021). The evolution of extended regions of recombination suppression is also documented on mating-type chromosomes in fungi (Hartmann et al., 2021) and around supergenes (Yan et al., 2020, Jay et al., 2021). The exact reason and evolutionary mechanisms for this phenomenon are still, however, debated.

Two hypotheses are proposed: 1) sexual antagonism (Charlesworth et al., 2005), which, nevertheless, does explain the observed occurrence of the evolutionary strata, and 2) the sheltering of deleterious alleles by inversions carrying a lower load than average in the population (Charlesworth and Wall, 1999, Antonovics and Abrams, 2004). In the latter, the mechanism is as follows. A genetic inversion or a suppressor of recombination in cis may exhibit some overdominance behaviour. The inversion exhibiting less recessive deleterious mutations (compared to others at the same locus) may increase in frequency, before at higher frequency occurring at the homozygous state, expressing its genetic load. However, the inversion may never be at the homozygous state if it is genetically linked to a gene in a permanently heterozygous state. The inversion can then be advantageous and may reach fixation at the sex chromosome (Charlesworth and Wall, 1999, Antonovics and Abrams, 2004, Jay et al., 2022). These selective mechanisms promote thus the suppression of recombination around the sex-determining gene, and recessive deleterious mutations are permanently sheltered. This hypothesis is corroborated by the sheltering of deleterious mutations observed around loci under balancing selection (Llaurens et al. 2009, Lenz et al. 2016) and around mating-type genes in fungi and supergenes (Jay et al. 2021, Jay et al., 2022).

In this present theoretical study, Tezenas et al. (2022) analyse how linkage to a necessarily heterozygous fungal mating type locus influences the persistence/extinction time of a new mutation at a second selected locus. This mutation can either be deleterious and recessive, or overdominant. There is arbitrary linkage between the two loci, and sexual reproduction occurs either between 1) gametes of different individuals (outcrossing), or 2) by selfing with gametes originating from the same (intra-tetrad) or different (inter-tetrad) tetrads produced by that individual. Note, here, that the mating-type gene does not prevent selfing. The authors study the initial stochastic dynamics of the mutation using a multi-type branching process (and simulations when analytical results cannot be obtained) to compute the extinction time of the deleterious mutation. The main result is that the presence of a mating-type locus always decreases the purging probability and increases the purging time of the mutations under selfing. Ultimately, deleterious mutations can indeed accumulate near the mating-type locus over evolutionary time scales. In a nutshell, high selfing or high intra-tetrad mating do increase the sheltering effect of the mating-type locus. In effect, the outcome of sheltering of deleterious mutations depends on two opposing mechanisms: 1) a higher selfing rate induces a greater production of homozygotes and an increased effect of the purging of deleterious mutations, while 2) a higher intra-tetrad selfing rate (or linkage with the mating-type locus) generates heterozygotes which have a small genetic load (and are favoured). The authors also show that rare events of extremely long maintenance of deleterious mutations can occur.

The authors conclude by highlighting the manifold effect of selfing which reduces the effective population size and thus impairs the efficiency of selection and increases the mutational load, while also favouring the purge of deleterious homozygous mutations. Furthermore, this study emphasizes the importance of studying the maintenance and accumulation of deleterious mutations in the vicinity of heterozygous loci (e.g. under balancing selection) in selfing species.

References

Antonovics J, Abrams JY (2004) Intratetrad Mating and the Evolution of Linkage Relationships. Evolution, 58, 702–709. https://doi.org/10.1111/j.0014-3820.2004.tb00403.x

Bergero R, Charlesworth D (2009) The evolution of restricted recombination in sex chromosomes. Trends in Ecology & Evolution, 24, 94–102. https://doi.org/10.1016/j.tree.2008.09.010

Charlesworth D, Morgan MT, Charlesworth B (1990) Inbreeding Depression, Genetic Load, and the Evolution of Outcrossing Rates in a Multilocus System with No Linkage. Evolution, 44, 1469–1489. https://doi.org/10.1111/j.1558-5646.1990.tb03839.x

Charlesworth D, Charlesworth B, Marais G (2005) Steps in the evolution of heteromorphic sex chromosomes. Heredity, 95, 118–128. https://doi.org/10.1038/sj.hdy.6800697

Charlesworth B, Wall JD (1999) Inbreeding, heterozygote advantage and the evolution of neo–X and neo–Y sex chromosomes. Proceedings of the Royal Society of London. Series B: Biological Sciences, 266, 51–56. https://doi.org/10.1098/rspb.1999.0603

Hartmann FE, Duhamel M, Carpentier F, Hood ME, Foulongne-Oriol M, Silar P, Malagnac F, Grognet P, Giraud T (2021) Recombination suppression and evolutionary strata around mating-type loci in fungi: documenting patterns and understanding evolutionary and mechanistic causes. New Phytologist, 229, 2470–2491. https://doi.org/10.1111/nph.17039

Jay P, Chouteau M, Whibley A, Bastide H, Parrinello H, Llaurens V, Joron M (2021) Mutation load at a mimicry supergene sheds new light on the evolution of inversion polymorphisms. Nature Genetics, 53, 288–293. https://doi.org/10.1038/s41588-020-00771-1

Jay P, Tezenas E, Véber A, Giraud T (2022) Sheltering of deleterious mutations explains the stepwise extension of recombination suppression on sex chromosomes and other supergenes. PLOS Biology, 20, e3001698. https://doi.org/10.1371/journal.pbio.3001698

Lenz TL, Spirin V, Jordan DM, Sunyaev SR (2016) Excess of Deleterious Mutations around HLA Genes Reveals Evolutionary Cost of Balancing Selection. Molecular Biology and Evolution, 33, 2555–2564. https://doi.org/10.1093/molbev/msw127

Llaurens V, Gonthier L, Billiard S (2009) The Sheltered Genetic Load Linked to the S Locus in Plants: New Insights From Theoretical and Empirical Approaches in Sporophytic Self-Incompatibility. Genetics, 183, 1105–1118. https://doi.org/10.1534/genetics.109.102707

Nicolas M, Marais G, Hykelova V, Janousek B, Laporte V, Vyskot B, Mouchiroud D, Negrutiu I, Charlesworth D, Monéger F (2004) A Gradual Process of Recombination Restriction in the Evolutionary History of the Sex Chromosomes in Dioecious Plants. PLOS Biology, 3, e4. https://doi.org/10.1371/journal.pbio.0030004

Tezenas E, Giraud T, Véber A, Billiard S (2022) The fate of recessive deleterious or overdominant mutations near mating-type loci under partial selfing. bioRxiv, 2022.10.07.511119, ver. 2 peer-reviewed and recommended by Peer Community in Evolutionary Biology. https://doi.org/10.1101/2022.10.07.511119

Yan Z, Martin SH, Gotzek D, Arsenault SV, Duchen P, Helleu Q, Riba-Grognuz O, Hunt BG, Salamin N, Shoemaker D, Ross KG, Keller L (2020) Evolution of a supergene that regulates a trans-species social polymorphism. Nature Ecology & Evolution, 4, 240–249. https://doi.org/10.1038/s41559-019-1081-1

It is easy to define phenotypic plasticity as a mechanism by which traits change in response to a modification of the environment. Many complex mechanisms are nevertheless involved with plastic responses, their strength, and stability (e.g., reliability of cues, type of exposure, genetic expression, epigenetics). It is rather intuitive to think that environmental cues perceived at different stages of development will logically drive different phenotypic responses (Fawcett and Frankenhuis 2015). However, it has proven challenging to try and explain, or model how and why different effects are caused by similar cues experienced at different developmental or life stages (Walasek et al. 2022). The impact of these ‘sensitive windows’ on the stability of plastic responses within or across generations remains unclear. In their paper entitled “Sensitive windows for within- and trans-generational plasticity of anti-predator defences”, Tariel-Adam (2023) address this question.

In this paper, Tariel et al. acknowledge the current state of the art, i.e., that some traits influenced by the environment at early life stages become fixed later in life (Snell-Rood et al. 2015) and that sensitive windows are therefore more likely to be observed during early stages of development. Constructive exchanges with the reviewers illustrated that Tariel et al. presented a clear picture of the knowledge on sensitive windows from a conceptual and a mechanistic perspective, thereby providing their study with a strong and elegant rationale. Tariel et al. outlined that little is known about the significance of this scenario when it comes to transgenerational plasticity. Theory predicts that exposure late in the life of parents should be more likely to drive transgenerational plasticity because the cue perceived by parents is more likely to be reliable if time between parental exposure and offspring expression is short (McNamara et al. 2016). I would argue that although sensible, this scenario is likely oversimplifying the complexity of evolutionary, ecological, and inheritance mechanisms at play (Danchin et al. 2018). Tariel-Adam et al. (2023) point out in their paper how the absence of experimental results limits our understanding of the evolutionary and adaptive significance of transgenerational plasticity and decided to address this broad question.

Tariel-Adam et al. (2023) used the context of predator-prey interactions, which is a powerful framework to evaluate the temporality of predator cues and prey responses within and across generations (Sentis et al. 2018). They conducted a very elegant experiment whereby two generations of freshwater snails Physa acuta were exposed to crayfish predator cues at different developmental windows. They triggered the within-generation phenotypic plastic response of inducible defences (e.g., shell thickness) and identified sensitive windows as to evaluate their role in within-generation phenotypic plasticity versus transgenerational plasticity. They used different linear models, which lead to constructive exchanges with reviewers, and between reviewers, well trained on these approaches, in particular on effect sizes, that improved the paper by pushing the discussion all the way towards a consensus. 

Tariel-Adam et al. (2023) results showed that the phenotypic plastic response of different traits was associated with different sensitive windows. Although early-life development was confirmed to be a sensitive window, it was far from being the only developmental stage driving within-generation plastic responses of defence traits. This finding contributes to change our views on plasticity because where theoretical models predict early- and late-life sensitive windows, empirical results gathered here present a more continuous opportunity for sensitive windows over the lifetime of freshwater snails. This is likely because multifactorial mechanisms drive the reliability and adaptive significance of predator cues. To me, this paper most original contribution lies probably in the empirical investigation of sensitive windows underlying transgenerational plasticity. Their finding implies mechanistic ties between sensitive windows driving within-generation and transgenerational plasticity for some traits, but they also shed light on the possible independence of these processes. Although one may be disheartened by these findings illustrating the ability of nature to combine complex mechanisms in order to produce somewhat unpredictable scenarios, one can only find that this unlimited range of phenotypic plasticity scenarios is a wonder to investigate because much remains to be understood. As mentioned in the conclusion of the paper, the opportunity for sensitive windows to drive such a range of plastic responses may also be an opportunity for organisms to adapt to a wide range of environmental demands. 

References

Danchin E, A Pocheville, O Rey, B Pujol, and S Blanchet (2019). Epigenetically facilitated mutational assimilation: epigenetics as a hub within the inclusive evolutionary synthesis. Biological Reviews, 94: 259-282. https://doi.org/10.1111/brv.12453

Fawcett TW, and WE Frankenhuis (2015). Adaptive Explanations for Sensitive Windows in Development. Frontiers in Zoology 12, S3. https://doi.org/10.1186/1742-9994-12-S1-S3 

McNamara JM, SRX Dall, P Hammerstein, and O Leimar (2016). Detection vs. Selection: Integration of Genetic, Epigenetic and Environmental Cues in Fluctuating Environments. Ecology Letters 19, 1267–1276. https://doi.org/10.1111/ele.12663

Sentis A, R Bertram, N Dardenne, et al. (2018). Evolution without standing genetic variation: change in transgenerational plastic response under persistent predation pressure. Heredity 121, 266–281. https://doi.org/10.1038/s41437-018-0108-8 

Snell-Rood EC, EM Swanson, and RL Young (2015). Life History as a Constraint on Plasticity: Developmental Timing Is Correlated with Phenotypic Variation in Birds. Heredity 115, 379–388. https://doi.org/10.1038/hdy.2015.47

Tariel-Adam J, E Luquet, and S Plénet (2023). Sensitive windows for within- and trans-generational plasticity of anti-predator defences. OSF preprints, ver. 4 peer-reviewed and recommended by Peer Community in Evolutionary Biology. https://doi.org/10.31219/osf.io/mr8hu

Walasek N, WE Frankenhuis, and K Panchanathan (2022). An Evolutionary Model of Sensitive Periods When the Reliability of Cues Varies across Ontogeny. Behavioral Ecology 33, 101–114. https://doi.org/10.1093/beheco/arab113

Polyploidy, which results in the presence of more than two sets of homologous chromosomes represents a major feature of plant genomes that have undergone successive rounds of duplication followed by more or less rapid diploidization during their evolutionary history. Polyploid complexes containing diploid and derived polyploid taxa are excellent model systems for understanding the short-term consequences of whole genome duplication, and have been particularly well-explored in evolutionary ecology (Ramsey and Ramsey 2014, Rice et al. 2019). Many polyploids (especially when resulting from interspecific hybridization, i.e. allopolyploids) are successful invaders (te Beest et al. 2012) as a result of rapid genome dynamics, functional novelty, and trait evolution. The origin (parental legacy) and modes of formation of polyploids have a critical impact on the subsequent polyploid evolution. Thus, elucidation of the genomic composition of polyploids is fundamental to understanding trait evolution, and such knowledge is still lacking for many invasive species.

Genus Ludwigia is characterized by a complex taxonomy, with an underexplored evolutionary history. Species from section Jussieae form a polyploid complex with diploids, tetraploids, hexaploids, and decaploids that are notorious invaders in freshwater and riparian ecosystems (Thouvenot et al.2013).   Molecular phylogeny of the genus based on nuclear and chloroplast sequences (Liu et al. 2027) suggested some relationships between diploid and polyploid species, without fully resolving the question of the parentage of the polyploids. In their study, Barloy et al. (2023) have used a combination of molecular cytogenetics (Genomic In situ Hybridization), morphology and experimental crosses to elucidate the genomic compositions of the polyploid species, and show that the examined polyploids are of hybrid origin (allopolyploids). The tetraploid L. stolonifera derives from the diploids L. peploides subsp. montevidensis (AA genome) and L. helminthorhiza (BB genome). The tetraploid L. ascendens also share the BB genome combined with an undetermined different genome. The hexaploid L. grandiflora subsp. grandiflora has inherited the diploid AA genome combined with additional unidentified genomes. The decaploid L. grandiflora subsp. hexapetala has inherited the tetraploid L. stolonifera and the hexaploid L. grandiflora subsp. hexapetala genomes. As the authors point out, further work is needed, including additional related diploid (e.g. other subspecies of L. peploides) or tetraploid (L.  hookeri and L. peduncularis)  taxa that remain to be investigated, to address the nature of the undetermined parental genomes mentioned above. 

The presented work (Barloy et al.  2023) provides significant knowledge of this poorly investigated group with regard to genomic information and polyploid origin, and opens perspectives for future studies. The authors also detect additional diagnostic morphological traits of interest for in-situ discrimination of the taxa when monitoring invasive populations.  

References

Barloy D., Portillo-Lemus L., Krueger-Hadfield S.A., Huteau V., Coriton O. (2024). Genomic relationships among diploid and polyploid species of the genus Ludwigia L. section Jussiaea using a combination of molecular cytogenetic, morphological, and crossing investigations. BioRxiv, ver. 4 peer-reviewed and recommended  by Peer Community in Evolutionary Biology https://doi.org/10.1101/2023.01.02.522458

te Beest M., Le Roux J.J., Richardson D.M., Brysting A.K., Suda J., Kubešová M., Pyšek P. (2012). The more the better? The role of polyploidy in facilitating plant invasions. Annals of Botany, Volume 109, Issue 1 Pages 19–45, https://doi.org/10.1093/aob/mcr277

Ramsey J. and Ramsey T. S. (2014). Ecological studies of polyploidy in the 100 years following its discovery Phil. Trans. R. Soc. B369 1–20  https://doi.org/10.1098/rstb.2013.0352  

Rice, A., Šmarda, P., Novosolov, M. et al. (2019). The global biogeography of polyploid plants. Nat Ecol Evol 3, 265–273. https://doi.org/10.1038/s41559-018-0787-9

Thouvenot L, Haury J, Thiebaut G. (2013). A success story: Water primroses, aquatic plant pests. Aquat. Conserv. Mar. Freshw. Ecosyst. 23:790–803  https://doi.org/10.1002/aqc.2387  

Growth, development and reproduction in animals are all limited by dietary nutrients. Expansion of an organism’s diet to sources not accessible to closely related species reduces food competition, and eases the constraints of nutrient-limited diets. Adult butterflies are herbivorous insects known to feed primarily on nectar from flowers, which is rich in sugars but poor in amino acids.  Only certain species in the genus Heliconius are known to also feed on pollen, which is especially rich in amino acids, and is known to prolong their lives by several months. The ability to digest pollen in Heliconius has been linked to specialized feeding behaviors (Krenn et al. 2009) and extra-oral digestion using enzymes, possibly including duplicated copies of cocoonase (Harpel et al. 2016; Smith et al. 2016 and 2018), a protease used by some moths to digest silk upon eclosion from their cocoons. In this reprint, Pinheiro de Castro and colleagues investigated the impact of artificial and natural diets on egg-laying ability, body weight, and cyanogenic glucoside abundance in adult Heliconius erato butterflies of both sexes. 

Previous studies (Dunlap-Pianka et al. 1981) in H. charithonia demonstrated that access to dietary pollen led to extended egg-laying ability among adult female butterflies compared to females deprived of pollen, and compared to Dryas iulia females which feed only on nectar. In the current study, Pinheiro de Castro et al. (2023) examine the impact of diet on both young and old H. erato, over a longer period of time than the earlier work, highlighting the importance of extending the time period over which effects are evaluated. In addition to extending egg-laying ability in older females, the authors found that pollen in the diet appeared to maintain older female body weight, presumably because the pollen contained nutrients depleted during egg-laying.

The authors then investigated the effects of nutrition on the production of cyanogenic glycoside defenses. Heliconius are aposematic butterflies that sequester cyanide-forming defense chemicals from food plants as larvae or synthesize these compounds de novo. The authors found the abundance of cyanogenic glycosides to be significantly greater in butterflies with access to pollen, but again only in older females.

Curiously, field studies of male and female H. charithonia butterflies found that females in the wild collected more pollen than males (Mendoza-Cuenca and Macías-Ordóñez 2005). Taken together, these new findings raise the intriguing possibility that females collect more pollen than males, in part, because pollen has a bigger impact on female survival and reproduction. A small limitation of the study is the use of wing length, rather than body weight, at the zero time point. But the trend is clear in both males and females, and it adds supporting detail to the efficacy of pollen feeding as an unusual strategy for increasing fertility and survival in Heliconius butterflies.

References
 
Dunlap-Pianka, Helen, Carol L. Boggs, Lawrence E. Gilbert. (1977) Ovarian dynamics in heliconiine butterflies: Programmed senescence versus eternal youth. Science, 197: 487-490, https://doi.org/10.1126/Science.197.4302.487
 
Pinheiro de Castro, Erika C., Josie McPherson, Glennis Julian, Anniina L. K. Mattila, Søren Bak, Stephen H. Montgomery, Chris Jiggins. (2023) Pollen-feeding delays reproductive senescence and maintains toxicity of Heliconius erato. bioRxiv, 2023.01.13.523799, ver. 4 peer-reviewed and recommended by Peer Community in Evolutionary Biology. https://doi.org/10.1101/2023.01.13.523799
 
Krenn, Harald W., Monika J. B. Eberhard, Stefan H. Eberhard, Anna-Laetitia Hikl, Werner Huber, Lawrence E. Gilbert (2009). Mechanical damage to pollen aids nutrient acquisition in Heliconius butterflies (Nymphalidae).  Arthropod-Plant Interactions, 3: 203–208. https://doi.org/10.1007/s11829-009-9074-7
 
Harpel, Desiree, Darron A. Cullen, Swidbert R. Ott, Chris D. Jiggins, James R. Walters (2015) Pollen feeding proteomics: Salivary proteins of the passion flower butterfly, Heliconius melpomene. Insect Biochemistry and Molecular Biology, 63: 7-13, https://doi.org/10.1016/j.ibmb.2015.04.004
 
Mendoza-Cuenca, Luis, Rogelio Macías-Ordóñez (2005) Foraging polymorphism in Heliconius charitonia (Lepidoptera: Nymphalidae): morphological constraints and behavioral compensation. Journal of Tropical Ecology, 21: 407-415. https://doi.org/10.1017/S0266467405002385
 
Smith, Gilbert, Aide Macias-Muñoz, John Kelly, Carter Butts, Rachel Martin, Adriana D. Briscoe (2018) Evolutionary and structural analyses uncover a role for solvent interactions in the diversification of cocoonases in butterflies. Proceedings of the Royal Society B, 285: 20172037. https://doi.org/10.1098/rspb.2017.2037 
 
Smith, Gilbert, Aide Macias-Muñoz, Adriana D. Briscoe (2016) Gene duplication and gene expression changes play a role in the evolution of candidate pollen-feeding genes in Heliconius butterflies. Genome Biology and Evolution, 8: 2581-2596. https://doi.org/10.1093/gbe/evw180

​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.

REFERENCES

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. https://doi.org/10.5281/zenodo.7927968

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Ewens, W. J. 1982. On the concept of the effective population size. Theoretical Population Biology 21:373-378. https://doi.org/10.1016/0040-5809(82)90024-7

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. https://doi.org/10.1371/journal.pgen.1000924

Neher, R. A. and B. I. Shraiman. 2011. Genetic Draft and Quasi-Neutrality in Large Facultatively Sexual Populations. Genetics 188:975-U370. https://doi.org/10.1534/genetics.111.128876

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. https://www.webpages.uidaho.edu/~krone/malecot.pdf

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. https://doi.org/10.1093/genetics/144.1.383

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. https://doi.org/10.1534/genetics.104.026799

Wright, S. 1931. Evolution in Mendelian populations. Genetics 16:0097-0159. https://doi.org/10.1093/genetics/16.2.97