A general model of fitness effects following hybridisation
How does the mode of evolutionary divergence affect reproductive isolation?
Recommendation: posted 19 December 2022, validated 20 December 2022
Hartfield, M. (2022) A general model of fitness effects following hybridisation. Peer Community in Evolutionary Biology, 100543. https://doi.org/10.24072/pci.evolbiol.100543
Studying the effects of speciation, hybridisation, and evolutionary outcomes following reproduction from divergent populations is a major research area in evolutionary genetics . There are two phenomena that have been the focus of contemporary research. First, a classic concept is the formation of ‘Bateson-Dobzhansky-Muller’ incompatibilities (BDMi) [2–4] that negatively affect hybrid fitness. Here, two diverging populations accumulate mutations over time that are unique to that subpopulation. If they subsequently meet, then these mutations might negatively interact, leading to a loss in fitness or even a complete lack of reproduction. BDMi formation can be complex, involving multiple genes and the fitness changes can depend on the direction of introgression . Second, such secondary contact can instead lead to heterosis, where offspring are fitter than their parental progenitors .
Understanding which outcomes are likely to arise require one to know the potential fitness effects of mutations underlying reproductive isolation, to determine whether they are likely to reduce or enhance fitness when hybrids are formed. This is far from an easy task, as it requires one to track mutations at several loci, along with their effects, across a fitness landscape.
The work of De Sanctis et al.  neatly fills in this knowledge gap, by creating a general mathematical framework for describing the consequences of a cross from two divergent populations. The derivations are based on Fisher’s Geometric Model, which is widely used to quantify selection acting on a general fitness landscape that is affected by several biological traits [8,9], and has previously been used in theoretical studies of hybridisation [10–12]. By doing so, they are able to decompose how divergence at multiple loci affects offspring fitness through both additive and dominance effects.
A key result arising from their analyses is demonstrating how offspring fitness can be captured by two main functions. The first one is the ‘net effect of evolutionary change’ that, broadly defined, measures how phenotypically divergent two populations are. The second is the ‘total amount of evolutionary change’, which reflects how many mutations contribute to divergence and the effect sizes captured by each of them. The authors illustrate these measurements using simulations covering different scenarios, demonstrating how different parental states can lead to similar fitness outcomes. They also propose experimental methods to measure the underlying mutational effects.
This study neatly demonstrates how complex genetic phenomena underlying hybridisation can be captured using fairly simple mathematical formulae. This powerful approach will thus open the door for future research to investigate hybridisation in more detail, whether it is by expanding on these theoretical models or using the elegant outcomes to quantify fitness effects in experiments.
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3. Dobzhansky T. Genetics and the Origin of Species. Columbia university press; 1937.
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5. Fraïsse C, Elderfield JAD, Welch JJ. The genetics of speciation: are complex incompatibilities easier to evolve? J Evol Biol. 2014;27: 688-699. https://doi.org/10.1111/jeb.12339
6. Birchler JA, Yao H, Chudalayandi S, Vaiman D, Veitia RA. Heterosis. The Plant Cell. 2010;22: 2105-2112. https://doi.org/10.1105/tpc.110.076133
7. De Sanctis B, Schneemann H, Welch JJ. How does the mode of evolutionary divergence affect reproductive isolation? bioRxiv. 2022. 2022.03.08.483443 version 4. https://doi.org/10.1101/2022.03.08.483443
8. Fisher RA. The genetical theory of natural selection. Oxford: The Clarendon Press; 1930. https://doi.org/10.5962/bhl.title.27468
9. Tenaillon O. The Utility of Fisher's Geometric Model in Evolutionary Genetics. Annu Rev Ecol Evol Syst. 2014;45: 179-201. https://doi.org/10.1146/annurev-ecolsys-120213-091846
10. Barton NH. The role of hybridization in evolution. Molecular Ecology. 2001;10: 551-568. https://doi.org/10.1046/j.1365-294x.2001.01216.x
11. Chevin L-M, Decorzent G, Lenormand T. Niche Dimensionality and The Genetics of Ecological Speciation. Evolution. 2014;68: 1244-1256. https://doi.org/10.1111/evo.12346
12. Fraïsse C, Gunnarsson PA, Roze D, Bierne N, Welch JJ. The genetics of speciation: Insights from Fisher's geometric model. Evolution. 2016;70: 1450-1464. https://doi.org/10.1111/evo.12968
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article. The authors declared that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article.
BDS and HS acknowledge support from the Wellcome Trust program in Mathematical Genomics and Medicine (WT220023 and RG92770)
Evaluation round #2
DOI or URL of the preprint: https://www.biorxiv.org/content/10.1101/2022.03.08.483443v3
Version of the preprint: 3
Author's Reply, 07 Dec 2022
Decision by Matthew Hartfield, posted 02 Dec 2022, validated 02 Dec 2022
Many thanks for your substantial revisions of this preprint. Both reviewers and myself find this new version more comprehensive than before, and appreciate the effort made into improving the clarity of these complex analyses. That said, given the large amount of changes that have been made (to me it felt a bit like reading a whole new paper), there are still several suggestions that were made for improving the manuscript and its clarity. I hence feel it is worth further revising the manuscript before it can be recommended by PCI, but I foresee that it would not be sent out for further reviews after the next submission.
I have a few additional comments to add:
- I feel the two functions m, M could be defined earlier, when Figure 1 is introduced. I found it difficult to fully understand Figure 1 on a first read, as it makes references to these functions but they were not yet defined in the text. I think it would be sufficient to simply define the mathematical functions here, and leave the interpretation section in the same location.
- Line 178: missing full stop (or other punctuation mark) at the end of this sentence.
- Figure 2: It's not clear to me what the big and little arrows represent in the 'Divergence scenarios' box. Furthermore I do not understand why there is a big arrow coming from P1 if only P2 moves in this case?
Reviewed by Luis-Miguel Chevin, 17 Nov 2022
Reviewed by Juan Li, 31 Oct 2022
Evaluation round #1
DOI or URL of the preprint: https://doi.org/10.1101/2022.03.08.483443
Author's Reply, 11 Oct 2022
Decision by Matthew Hartfield, posted 30 May 2022
Your manuscript has been assessed by two reviewers. Both find this a good and insightful investigation into how the form form of divergence influences reproduction isolation, and I agree. This manuscript has potential to be recommended by PCI Evolutionary Biology, but the reviewers have made several suggestions for revisions. I have made a few myself that I list below, but note that most suggestions revolve around improving the clarity of the manuscript rather than substantial methodological changes.
My additional comments below:
- I would like a bit more information on the model assumptions regarding how the two parental individuals diverge in the first place, and how they relate to the MRCA. I presume that, sometime in the past, there was an ancestral individual in a well-mixed population (the MRCA individual), whose offspring started diverging genetically, leading to the two parental individuals P1 and P2. Hence, the fixed genetic differences (of which there are D of them) are given relative to this ancestral individual. Is that the case? I also assume that the MRCA can be located anywhere in fitness space (as suggested in Figure 1), and not necessarily at the optimum (as is mostly simulated in Figure 2)? Clarifying these starting assumptions will help the reader better understand the biological process that are being modelled.
- It would be easier to understand Figure 2 if the different scenarios were explained first, before the figure is discussed in depth on pages 6-8. These scenarios are eventualy explained over the subsequent few pages, but on first reading it is unclear what is being investigated and hence how they affect the quantities being studied.
- Eq. 26: Could you clarify what is meant by the notation 'if lnwP1 = 0 or lnwP2 = 0'? If applied literally then this equation would reduce to the absolute value of the non-zero term and does not need to be spelt out in full.
- Line 312: Unclear what is meant by "heterozygosity has little impact on the results" as it does not appear that heterozygosity has been investigated in Figure 3.
- In the simulations, it is unclear what is meant when selection and dominance effects have 'vanishing' parameters (on lines 455 and 458). Perhaps it would be better to write out the distributions in full?