Inversions Can Accumulate Balanced Sexual Antagonism: Evidence from Simulations and Drosophila Experiments

Reviewer #1 (Public Review):

The idea is that inversions capture genetic variants that have antagonistic effects on male sexual success (via some display traits) and survival of females (or both sexes) until reproduction. A series of simulations are presented and show that the scenario works at least under some conditions. While a polymorphism at a single locus with large antagonistic effects can be maintained for a certain range of parameters, a second such variant with somewhat smaller effects tends to be lost unless closely linked. It becomes much more likely for genomically distant variants that add to the antagonism to spread if they get trapped in an inversion; the model predicts this should drive the accumulation of sexually antagonistic variants on the inversion versus standard haplotype, leading to the evolution of haplotypes with very strong cumulative antagonistic pleiotropic effects. This idea has some analogies with one of the predominant hypotheses for the evolution of sex chromosomes, and the authors discuss these similarities. To provide empirical support for this idea, the authors study the dynamics of inversions in population cages over one generation, tracking their frequencies through amplicon sequencing, from the parental generation through embryos to aged adults of either sex. Out of four inversions included in the experiment, two show patterns consistent with antagonistic effects on male sexual success (competitive paternity) and the survival of offspring, especially females, until old age, which the authors interpret as consistent with their theory.

This is an interesting idea, and the authors should be praised for combining a model with experimental data. However, in addition to the potential for improvement of presentation (details below), the study has some substantial weaknesses that could be addressed with additional simulations and additional experiments.

(1) The authors claim that the negative frequency dependence that maintains polymorphism in their model results from a non-linear relationship between the display trait and sexual success. I am not convinced about that. It seems to me that the "best of n" female choice implemented in the model (l. 741ff and Figure 2) does not lead to negative frequency dependence. Let p be the frequency of the competitively inferior male genotype. Assuming no noise in the male display, a female will mate with an inferior male only if all males among the n males sampled by the female are of the inferior genotype, which will be the fraction p^n, the remaining 1-p^n matings will go to the superior males. Thus, per capita, the inferior males will achieve (p^n)/p or p^(n-1) matings while the per-capita matings per superior male will be (1-p^n)/(1-p). Thus, the ratio of the mating success of the inferior to the superior males will be (1-p) p^(n-1) / (1- p^n). For the range of p from 0 to 1, this is an increasing function of p. E.g., with n = 2, the sexual fitness of the inferior genotype relative to that of the superior phenotype is p/(1+p). Thus, at least in the absence of noise in the mate choice, this generates positive rather than negative frequency dependence. Maybe I missed something, but the authors do not provide support for their claim about the negative frequency-dependence of sexual selection in their simulations. To do so they could (1) extract the relationship between the relative mating success of the two male types from the simulations and (2) demonstrate that polymorphism is not maintained if the relationship between male display trait and mating success is linear.

(2) The authors only explore versions of the model where the survival costs are paid by females or by both sexes. We do not know if polymorphism would be maintained or not if the survival cost only affected males, and thus if sexual antagonism is crucial.

(3) The authors assume no cost to aneuploidy, with no justification. Biologically, investment in aneuploid eggs would not be recoverable by Drosophila females and thus would potentially act against inversions when they are rare.

(4) The authors appear to define balanced polymorphism as a situation in which the average allele frequency from multiple simulation runs is intermediate between zero and one (e.g., Figure 3). However, a situation where 50% of simulation runs end up with the fixation of allele A and the rest with the fixation of allele B (average frequency of 0.5) is not a balanced polymorphism. The conditions for balanced polymorphism require that selection favors either variant when it is rare.

(5) Possibly the most striking result of the experiment is the fact that for 14 out of 16 combinations of inversion x maternal background, the changes in allele frequencies between embryo and adult appear greater in magnitude in females than in males irrespective of the direction of change, being the same in the remaining two combinations. The authors interpret this as consistent with sexually antagonistic pleiotropy in the case of In(3L)Ok and In(3R)K. The frequencies of adult inversion frequencies were, however, measured at the age of 2 months, at which point 80% of flies had died. For all we know, this may have been 90% of females and 70% of males that died at this point. If so, it might well be that the effects of inversion on longevity do not systematically differ between the ages and the difference in Figure 9B results from the fact that the sample includes 30% longest-lived males and 10% longest-lived females.

(6) Irrespective of the above problem, survival until the age of 2 months is arguably irrelevant from the viewpoint of fitness consequences and thus maintenance of inversion polymorphism in nature. It would seem that trade-offs in egg-to-adult survival (as assumed in the model), female fecundity, and possibly traits such as females resistance to male harm would be much more relevant to the maintenance of inversion polymorphisms.

(7) The experiment is rather minimalistic in size, with four cages in total; given that each cage contains a different female strain, it essentially means N=1. The lack of replication makes statements like " In(2L)t and In(2R)NS each showed elevated survival with all maternal strains except ZI418N" (l. 493) unsubstantiated because the claimed special effect of ZI418N is based on a single cage subject to genetic drift and sampling error. The same applies to statements on inversion x female background interaction (e.g., l. 550), as this is inseparable from residual variation. It is fortunate that the most interesting effects appear largely consistent across the cages/female backgrounds. Still, I am wondering why more replicates had not been included.

Reviewer #2 (Public Review):

Summary:

In their manuscript, the authors address the question of whether the inversion polymorphism in D. melanogaster can be explained by sexually antagonistic selection. They designed a new simulation tool to perform computer simulations, which confirmed their hypothesis. They also show a tradeoff between male reproduction and survival. Furthermore, some inversions display sex-specific survival.

Strengths:
It is an interesting idea on how chromosomal inversions may be maintained

Weaknesses:
General points:
The manuscript lacks clarity of writing. It is impossible to fully grasp what the authors did in this study and how they reached their conclusions. Therefore, I will highlight some cases that I found problematic.
Although this is an interesting idea, it clearly cannot explain the apparent influence of seasonal and clinal variation on inversion frequencies.

Specific points:
The simulations are highly specific and make very strong assumptions, which are not well-justified.

Reviewer #3 (Public Review):

Summary:
In this study, McAllester and Pool develop a new simulation model to explain the maintenance of balanced inversion polymorphism, based on (sexually) antagonistic alleles and a trade-off between male reproduction and survival (in females or both sexes). In support of the plausibility of this model, the authors use laboratory experiments on four naturally occurring inversion polymorphisms in Drosophila melanogaster, finding evidence for the existence of the above-mentioned trade-off in two out of the four cases.

Strengths:
1. The study develops and analyzes a new (Drosophila melanogaster-inspired) model for the maintenance of balanced inversion polymorphism, combining elements of (sexually) antagonistically (pleiotropic) alleles, negative frequency-dependent selection, and synergistic epistasis. To this end, the authors developed and used a new simulator (although it was not 100% clear as to why SLiM could not have been used as SLiM has been used to study inversions).

2. The above-mentioned model assumes, as a specific example, a trade-off between male reproductive display and survival; in the second part of their study, the authors perform laboratory experiments on four common D. melanogaster inversions to study whether these polymorphisms may be subject to such a trade-off. The authors find that two of the four inversions show suggestive evidence that is consistent with a trade-off between male reproduction and survival. The new amplicon sequencing approach to track inversion frequencies used by the authors seems promising in terms of studying fitness effects/trade-offs associated with polymorphic inversions and how such effects play out dynamically.

Weaknesses:
1. Mechanisms of balancing selection maintaining balanced inversion polymorphism. In Section 1.1 a better and more accurate overview of the different selective mechanisms that might contribute to the maintenance of balanced inversion polymorphisms should be given (for a recent review see Berdan et al. 2023). For example, negative frequency-dependent selection (NFDS), spatially and temporally varying selection are not mentioned here and are brought up only later, which is not really ideal. While I agree that in most cases our understanding of balanced inversion polymorphism is very limited, there are many empirical examples of these and other mechanisms of balancing selection being at play (e.g., NFDS: Wright & Dobzhansky 1946; Nassar et al. 1973; Álvarez-Castro and Álvarez 2005; Jay et al. 2021; and many examples of evidence for other mechanisms as well). Thus, while the prevalence of inversion polymorphisms is indeed in many cases "enigmatic", the reader should not be given the impression that we do not have yet any empirical evidence for specific mechanisms in particular cases. Similarly, the authors mention the classical (essentially Dobzhansky's) scenario of epistatically interacting loci only in passing, even though this coadaptation scenario may be simpler than the local adaptation mechanism of Kirkpatrick & Barton (2016): in its simplest form, epistatic coadaptation does not require any migration load or locally adaptive alleles à la Kirkpatrick & Barton, but just the capture of 2 overdominant loci, with inversion protecting this fittest double heterozygote from recombination load (Charlesworth 1974; also see Charlesworth & Charlesworth 1974; Charlesworth & Flatt 2021; also see discussion in Charlesworth and Barton 2018). On the other hand, the plausibility of the mutational load/associative overdominance (AOD) mechanism (Sturtevant & Mather 1938; Nei et al. 1967; Ohta 1971) seems to be given too much weight: new work by Charlesworth (2023; https://www.biorxiv.org/content/10.1101/2023.10.16.562579v1) suggests that load likely contributes only very modestly to heterokaryotypic advantage of inversions at intermediate frequencies, and that is very unlikely to provide a sufficient selective (heterotic) advantage to new autosomal inversions in order to explain their establishment (also see Nei et al. 1967; Connallon and Olito 2021; Jay et al. 2022).

2. The general reduction principle and inversion polymorphism. In Section 1.2., the authors state that "there has not been a proposed mechanism whereby alleles at multiple linked loci would directly benefit from linkage and thereby maintain an associated inversion polymorphism under indirect selection." Perhaps I am misunderstanding something, but in my reading, this statement is factually incorrect. In fact, the simplest version of Dobzhansky's epistatic coadaptation model (see Charlesworth 1974; also see Charlesworth and Charlesworth 1973 and discussion in Charlesworth & Flatt 2021; Berdan et al. 2023) seems to be an example of exactly what the authors seem to have in mind here: two loci experiencing overdominance, with the double heterozygote possessing the highest fitness (i.,e., 2 loci under epistatic selection, inducing some degree of LD between these loci), with subsequent capture by an inversion; in such a situation, a new inversion might capture a haplotype that is present in excess of random expectation (and which is thus fitter than average). The selective benefits of recombination suppression in the inversion heterokaryotype will then confer a heterozygote advantage to the inversion and prevent it from going to fixation (see Charlesworth 1974). This is probably the simplest (or one of the simplest) models of multilocus balancing selection that can act on inversions. Incidentally, this model represents a prime example of the "reduction principle", which the authors mention on two occasions in their paper: generally, any multi-locus polymorphism held at equilibrium by any type of balancing selection involving fitness epistasis will cause selection for reduced recombination (e.g., Feldman & Liberman, 1986; Zhivotovsky et al., 1994); notably, the example of inversion polymorphism is explicitly discussed in Altenberg's and Feldman's (1987) paper on the reduction principle. It is also noteworthy in this context that the 2-locus epistatic model of Charlesworth (1974) assumes constant fitness values/selection coefficients but actually leads to what one could call "apparent" frequency-dependent selection with different equilibria.

3. Trade-offs and antagonistic pleiotropy involved in maintaining inversions. Throughout the manuscript, previous work implicating trade-offs and/or antagonistic pleiotropy (AP) in the maintenance of inversion polymorphisms should be more adequately acknowledged and discussed - from the text as it currently stands one gains the impression that barely anything is known about the connection between inversions and pleiotropy/AP/trade-offs (e.g., Betrán et al. 1998; Mérot et al. 2020, which is cited but not really in the context of AP/trade-offs; Pei et al. 2023, etc.). The paper by Pei and colleagues is particularly relevant in the context of the present study: the authors find that the inverted allele has beneficial effects on male siring success and female fecundity but negative effects on survival. Generally, numerous studies have found that inversion polymorphisms have "pleiotropic" (albeit not always antagonistically pleiotropic) effects upon multiple fitness components (e.g., Etges 1989; Betrán et al. 1998; Küpper et al. 2016; Durmaz et al. 2018; Mérot et al. 2020). More broadly, the general role of AP in maintaining (life-history) polymorphisms should be mentioned by referring to previous theories (e.g., Rose 1982, 1985; Curtsinger et al. 1994; Charlesworth & Hughes 2000 chapter in Lewontin Festschrift; Conallon & Chenoweth 2019 - this latter paper is particularly relevant in terms of AP effects in the context of sexual antagonism).

4. Sexually antagonistic selection and inversion polymorphism. The authors' model of sexual antagonism being involved in maintaining an inversion polymorphism is novel and interesting, but again I felt that the authors' ideas could be better connected to what has been done before. First, several papers have made connections between sexual antagonism and inversion polymorphisms: for example, an important study that deserves discussion in this context is the paper by Natri and colleagues (2019) where the authors study sexual antagonism as a source of balancing selection that maintains an inversion polymorphism in the ruff. Similarly, another relevant study in this context is Hearn et al. 2022 on Littorina saxatilis snails. Also see Giraldo-Deck et al. (2022). A very interesting paper that may be worth discussing is Connallon & Chenoweth (2019) about dominance reversals of antagonistically selected alleles (even though C&C do not discuss inversions): AP alleles (with dominance reversals) affecting two or more life-history traits provide one example of such antagonistically selected alleles (also see Rose 1982, 1985; Curtsinger et al. 1994) and sexually antagonistically selected alleles provide another. The two are of course not necessarily mutually exclusive, thus making a conceptual connection to what the authors model here.

5. The model. In general, the description of the model and of the simulation results was somewhat hard to follow and vague. There are several aspects that could be improved: (1) it would help the reader if the terminology and distinction of inverted vs. standard arrangements and of the three karyotypes would be used throughout, wherever appropriate. (2) The mention of haploid populations/situations and haploid loci (e.g., legend to Figure 1) is somewhat confusing: the mechanism modelled here, of course, requires suppressed recombination in the inversion/standard heterokaryotype; and thus, while it may make sense to speak of haplotypes, we're dealing with an inherently diploid situation. (3) The authors have a situation in mind where the 2 karyotypes (INV vs. STD) in the heterokaryotype carry distinct sets of loci in LD with each other, with one karyotype/haplotype carrying antagonistic variants favoring high male display success and with the other karyotype/haplotype carrying non-antagonistic alternative alleles at these loci and which favor survival. Thus, at each of the linked loci, we have antagonistic alleles and non-antagonistic alleles - however, the authors don't mention or discuss the degree of dominance of these alleles. The degree of dominance of the alleles could be an important consideration, and I found it curious that this was not mentioned (or, for that matter, examined). (4) In many cases, the authors do not provide sufficient detail (in the main text and the main figures) about which parameter values they used for simulations; the same is true for the Materials & Methods section that describes the simulations. Conversely, when the text does mention specific values (e.g., 20N generations, 0.22-0.25M, etc.), little or no clear context or justification is being provided. (5) The authors sometimes refer to "inversion mutation(s)" - the meaning of this terminology is rather ambiguous.

6. Throughout the manuscript, especially in the description and the discussion of the model and simulations, a clearer conceptual distinction between initial "capture" and subsequent accumulation / "gain" of variants by an inversion should be made. This distinction is important in terms of understanding the initial establishment of an inversion polymorphism and its subsequent short- as well as long-term fate. For example, it is clear from the model/simulations that an inversion accumulates (sexually) antagonistic variants over time - but barely anything is said about the initial capture of such loci by a new inversion.