Sexual antagonism in haplodiploids

Females and males may face different selection pressures, such that alleles conferring a benefit in one sex may be deleterious in the other. Such sexual antagonism has received a great deal of theoretical and empirical attention, almost all of which has focused on diploids. However, a sizeable minority of animals display an alternative haplodiploid mode of inheritance, encompassing both arrhenotoky, whereby males develop from unfertilized eggs, and paternal genome elimination (PGE), whereby males receive but do not transmit a paternal genome. Alongside unusual genetics, haplodiploids often exhibit social ecologies that modulate the relative value of females and males. Here we develop a series of evolutionary-genetic models of sexual antagonism for haplodiploids, incorporating details of their molecular biology and social ecology. We find that: 1) PGE promotes female-beneficial alleles more than arrhenotoky, and to an extent determined by the timing of elimination – and degree of silencing of – the paternal genome; 2) sib-mating relatively promotes female-beneficial alleles, as do other forms of inbreeding, including limited male-dispersal, oedipal-mating, and the pseudo-hermaphroditism of Icerya purchasi; 3) resource competition between related females relatively inhibits female-beneficial alleles; and 4) sexual antagonism foments conflicts between parents and offspring, endosymbionts and hosts, and maternal-origin and paternal-origin genes.

Almost all this research has focused on diploid, "eumendelian" (sensu Normark 2006) 75 organisms. However, a sizeable minority of animals (~15%) display an alternative, 76 haplodiploid mode of inheritance (Normark 2003(Normark , 2006Bachtrog et al. 2014). 77 Haplodiploidy encompasses both arrhenotoky -whereby males develop from 78 unfertilized eggs -and paternal genome elimination (PGE) -whereby males receive but 79 do not transmit a paternal genome -and is employed by a diverse cast of creatures in 80 groups as distinct as mites, nematodes, rotifers, springtails, beetles, wasps and flies. In 81 all of these organisms, males exclusively transmit maternal-origin genes, such that 82 reproduction of females contributes twice as much to the ancestry of future generations 83 as does that of males. Whilst similarities in transmission genetics have drawn 84 comparisons to X-linked genes (Kraaijeveld 2009 affect the balance between female-beneficial versus male-beneficial alleles.

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Moreover, haplodiploids often exhibit characteristic social ecologies, including 98 gregarious broods, chronic inbreeding, and strongly female-biased primary sex ratios 99 (Hamilton 1967). An archetypal example is the date stone beetle (Coccotrypes 100 dactyliperda), whereby a gravid female excavates a tunnel into a date seed and lays a 101 large and heavily female-biased brood, her offspring then mate with each other, and her 102 mated-daughters then leave to search for dates within which to raise their own families 103 (Hamilton 1993;Spennemann 2019). Whilst the particular niche that these species 104 inhabit may vary substantially -from fungal-feeding to sap-or blood-sucking -they 105 often share a similarly viscous population structure, with small, semi-isolated 106 subpopulations, and large amounts of inbreeding (Hamilton 1967(Hamilton , 1978(Hamilton , 1993Normark 107 2006). These unusual mating systems generate peculiar patterns of within-individual 108 and between-individual relatedness, as well as differences in the scales at which the 109 sexes compete and cooperate. Both of these factors are known to modulate the relative 110 genetic value of males and females in the context of sex allocation (Taylor 1981;Frank 111 1986b; Nagelkerke and Sabelis 1996; West 2009), and thus might also be expected to 112 alter the outcome of sexually antagonistic selection.

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Here we develop a series of evolutionary-genetic models of sexual antagonism for 115 haplodiploids, incorporating details of both their molecular biology and social ecology. 116 We first consider how the genetic asymmetries found in haplodiploids are expected to 117 alter the fate of sexually antagonistic alleles, and how this is modified by variation in the 118 timing and expression of the paternal-genome. We then explore how inbreeding alters 119 these conditions, investigating the effects of sib-mating, lower male-dispersal, oedipal-120 mating, and the pseudo-hermaphroditism of Icerya purchasi, as well as the effect of local 121 resource competition amongst females. Finally, we explore how such genetic and 122 ecological asymmetries may foment conflicts over sexual antagonism between parents 123 and offspring, endosymbionts and their hosts, and maternal-origin and paternal-origin 124 genes. 125 126 Genetic asymmetries 127 128 The consequences of asymmetric transmission 129 130 In most sexual organisms, males and females pass on their maternal-origin and 131 paternal-origin genes with equal frequency. In contrast, haplodiploid organisms are 132 united by the fact that they break this fundamental symmetry, with males exclusively 133 passing on maternal-origin genes (Normark 2006 Whilst the different haplodiploid systems are united by their common transmission 187 genetics, they often show distinct somatic genetics (Table 1.). These differences in the 188 number of gene copies carried by males and females, and the particular expression 189 patterns of those genes, may alter the relative magnitude of allelic effects in males and 190 females, and thus shape the dynamics of sexual antagonism.

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Under arrhenotoky, females carry two genes at each locus, whilst males carry only one.

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This is conceptually similar to the X chromosomes in an XO system (or an XY system 194 insofar as there is no homologue on the Y) and, as with X chromosomes, it is not 195 necessarily straightforward to compare relative fitness effects across ploidy levels. If an 196 allele's effect is of similar magnitude in a homozygous and a hemizygous setting, then 197 this will mean that alleles will typically have larger effects on average when expressed 198 in males than in females (Charlesworth et al. 1987 as invasion conditions for female-beneficial alleles are less stringent, and those male-256 beneficial alleles are more stringent (see Figure 2).

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Ecological asymmetries 259 260 Sib-mating and ecological asymmetries between the sexes 261 262 The above results apply to outbreeding populations with no social interactions between 263 relatives, and therefore it is only the direct fitness effects of alleles that required 264 consideration. But many haplodiploid species diverge from this, with mating schemes 265 and life-cycles that result in chronic inbreeding (Hamilton 1967(Hamilton , 1978(Hamilton , 1993. These 266 population structures may alter the relatedness within and between individuals, as well 267 as the intensity with which males and females compete with relatives, potentially 268 generating indirect fitness effects of sexually antagonistic alleles upon social partners. 269 Such factors have long been recognised in sex allocation research to alter the relative 270 value of sons and daughters (Taylor 1981;Frank 1986b; Nagelkerke and Sabelis 1996; 271 West 2009), and thus may be expected to play a similar role with regards to sexual 272 antagonism.

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We investigate how inbreeding may modulate sexual antagonism by modelling a 275 population of monogamous females, in which a proportion of females in the brood 276 mate with their sibs, whilst a proportion 1 − mate with males from the population at 277 large ( Figure 3). Introducing sib-mating has multiple distinct effects upon sexual 278 antagonism. The first is that sib-mating inflates the consanguinity of an individual to 279 themselves, i.e. their inbredness (sensu Frank 1986a), which has a feminisation 280 promoting effect under arrhenotoky -as a gene copy will have indirect fitness effects 281 upon the other identical by descent gene copy in females, but not in males, which are 282 haploid (Tazzyman and Abbott 2015; Hitchcock and Gardner 2020) -but not for PGE or 283 diploidy, where gene copies in both males and females experience these within 284 individual indirect fitness effects. Secondly, sib-mating increases the probability that 285 males will compete with brothers for mates, discounting the inclusive-fitness benefits of 286 male-beneficial alleles to their male carriers, and mollifying the inclusive-fitness costs of 287 male-deleterious alleles. Thirdly, the direct fitness effects of alleles upon their female 288 carriers will have indirect fitness effects upon their carriers' mates. If females sib-mate, 289 then female-beneficial alleles will generate indirect benefits for their brothers, and 290 female-deleterious alleles will impose indirect costs. All three of these effects have 291 parallels in sex allocation, with increased sib-mating increasing the relatedness of a 292 female to her daughters but not her sons under arrhenotoky, increased competition 293 between brothers decreasing the genetic returns on males (i.e. local mate competition; 294 Hamilton 1967), and increased sib-mating meaning that increased investment into 295 daughters will increase the fitness of sons, either through extra mating opportunities, or 296 through higher quality mates (Taylor 1981;Frank 1986b;West 2009). 297 298 Collecting these effects, we may write the condition for a female beneficial to invade in 299 the form of a potential for feminisation , with a female beneficial allele invading 300 provided < / . If > 1, then feminisation is expected, whilst if < 1 then 301 masculination is expected. Assuming additivity and weak selection, we find that under 302 arrhenotoky and diploidy = 1/(1 − ), and under male PGE = (4 − s)/(2 (1 − s)) 303 (results for dominance and stronger selection can be found in the Supplementary 304 Material). Thus, we find that, across all these genetic systems, increased sib-mating 305 promotes feminisation, with the effect being strongest under PGE (see Figure 3). 306 307 So far, we have assumed that females compete globally, however, many haplodiploid 308 species have more generally viscous populations in which females may also disperse 309 short distances -if at all. For instance, in the date stone beetle, females may start their 310 own families within the seed in which they were born (Spennemann 2019). Similarly, in 311 many mealybugs, females crawl relatively small distances away from their natal patch 312 (Varndell and Godfray 1996; Ross et al. 2010a). In these species females may compete 313 with sisters for breeding spots, just as their brothers competed with each other for 314 mates, i.e. local resource competition (Clark 1978). Incorporating these factors yields 315 two further consequences for sexual antagonism. Firstly, with limited female dispersal, 316 direct fitness benefits to females incur indirect fitness costs to their sisters by depriving 317 them of breeding spots, just as obtained for local mate competition in males. Secondly, 318 whilst a fit female confers indirect fitness benefits upon brothers with whom she mates, 319 she may also incur indirect fitness costs by competing with her brothers' mates, and 320 thereby indirectly depriving her brothers of reproductive success. With increasing local 321 resource competition, the invasion condition becomes less stringent for male-beneficial 322 alleles and more stringent for female-beneficial alleles. The dual effects of sib-mating 323 and limited female dispersal can be seen in Figure 3, with full analytical results given in 324 the Supplementary Material.

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Alternative life-cycles and modes of inbreeding 327 328 Above we considered one particular inbreeding scenario, in which a fixed proportion of 329 matings are reserved for siblings. However, the specific mechanism by which 330 inbreeding occurs may also modulate sexual antagonism, as different mating schemes 331 and life-cycles will differ in how relatedness builds up, and how intensely males and 332 females compete with relatives. To investigate this, we contrast the above model with 333 an alternative involving a patch structured population in which the degree of 334 inbreeding is modulated by the extent of dispersal (Wright 1931), whereby males 335 remain on their natal patch with probability , and females with probability . We 336 consider two variants, the first in which mating occurs before female dispersal (male 337 dispersal → mating → female dispersal, DMD), and a second in which mating occurs  offspring (Figure 4a). This parallels a previous effect found in relation to sex allocation, 396 whereby offspring typically favour less extreme sex ratio deviations than their parents 397 (Trivers 1974 for arrhenotoky, the situation is similar to diploidy, with mothers and offspring in 402 agreement under random mating, but with mothers favouring a greater female bias 403 when there is sib-mating (Figure 4c). For PGE, however, when there is no sib-mating 404 then offspring favour more female bias than their mothers, as females are twice as 405 valuable as males from the perspective of the offspring, whilst sons and daughters are 406 equally valuable from their mothers' perspective. However, this situation reverses as 407 sib-mating increases, with mothers once again favouring more female-biased trait 408 values than their offspring (Figure 4b).

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Considering instead a sexually antagonistic allele that acts through fathers, we find that to their daughters in the brood, similarly to how fathers favour an exclusively female 416 brood under outbreeding (Hamilton 1967). Nonetheless, with increased sib-mating they 417 are increasingly related to their mates' sons, and thus place value on their fitness too, 418 but with further sib-mating this is counteracted by the effects of increased local mate 419 competition, once again favouring feminisation (Fig 4c). PGE yields a qualitatively 420 similar outcome; however, as a male's paternal-origin genome is passed to neither sons 421 nor daughters directly, then fathers are not as highly related to their daughters as 422 compared with arrhenotoky, and they therefore favour slightly less feminisation (Fig  423  3b) For those endosymbionts and chromosomes that are strictly matrilineally inherited, 441 they will place no direct value upon the fitness of males, bringing them into conflict with 442 the rest of the genome (Wade 2014; Hurst and Frost 2015). These elements may also 443 therefore provide a rich source of evidence for the "Mother's Curse" hypothesis, i.e. that 444 mitochondria accumulate mutations which are deleterious for males (Gemmell et al. 445 2004). Under full outbreeding this conflict is at its most intense, but with increasing 446 amounts of sib-mating the autosomes becomes increasingly female biased too, aligning 447 the interests of these two sets of genes, and thus reducing the extent of the conflict. This 448 also applies to patrilineally-inherited symbionts, which although much rarer than 449 matrilineally inherited counterparts have been documented in a variety of species Finally, a further intragenomic conflict that may emerge over sexual antagonism is that 460 between maternal-origin and paternal-origin genes (Haig 2002). The asymmetric 461 transmission genetics that defines haplodiploidy may subsequently generate 462 differences between maternal-origin and paternal-origin genes in how they value males 463 and females, and also their relatedness to the males and females with whom they 464 interact (Haig 1992 from the paternal-origin copy, and a proportion 1 − to come from the maternal-origin 478 copy, we find that the potential for feminisation is = 1/(1 − ). Thus, when maternal-479 origin genes control the trait in males ( = 0), then = 1, equivalent to the 480 arrhenotokous case, whist when expression is exclusively from the paternal-origin copy 481 ( = 1), then = ∞, i.e. female beneficial alleles will always invade, regardless of the 482 cost they impose upon males, analogous to how paternal-origin genes may favour male 483 suicide when there is competition between male and female siblings (Ross et al. 2011b).

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As the rate of sib-mating increases, the intragenomic conflicts become more complex.

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We now explore the effects of parent-of-origin specific gene expression in both males 487 and females. Allow for a proportion of a locus's expression in males to come from 488 their paternal-origin copy and a proportion 1 − from their maternal-origin copy, and 489 allowing a proportion of that locus's gene expression in females to come from their 490 maternal-origin copy, and proportion 1 − from their paternal-origin copy. Then we 491 find the degree of feminisation under PGE becomes: 492 493 With the results for arrhenotoky generated by setting = 0. We can see that assigning i.e the degree of feminisation always increases with increasing s. In contrast, if we 499 assign full control to the paternal-origin genes ( = 0, = 1), then = [3 + (1 − ) 2 ]/ 500 [(1 − ) ]. When = 0, then the paternal-origin copy is unrelated to the other gene 501 copy in a male, and thus places no value on male fitness. As increases then the value 502 that a paternal-origin gene places on males increases too, as that gene copy is related to 503 the other gene copy it resides in a male with. However, with further increases in , this 504 is countered both by the increasing competition between related males, and also the 505 indirect effects from related females. 506 507 Previously, intragenomic conflict between maternal-origin and paternal-origin genes 508 has been suggested to drive the evolution of genomic imprinting at such loci, i.e. the 509 expression of one parental copy, and the silencing of the other parental copy. This 510 results from an escalating conflict over joint expression levels, which ultimately results 511 in the gene copy that favours lower expression levels becoming silenced, whilst the one 512 that favours higher expression levels is expressed at its optimum level, a process 513 termed the "loudest voice prevails" principle (Haig 1996). If we apply the logic of this 514 principle to conflicts over sexually antagonistic traits then, under PGE, we may expect 515 paternal-origin genes to be expressed for female-beneficial trait promoters and male-516 beneficial trait inhibitors, whilst we would expect maternal-origin genes to be 517 expressed for male-beneficial trait promoters, and female-beneficial trait inhibitors. 518 These predictions are distinct from those made under other theories of sexually 519 antagonistic genomic imprinting (Day and Bonduriansky 2004), whereby we would 520 expect paternal-origin genes to be expressed in males, and maternal-origin genes to be 521 expressed in females.  Table 1, Figure 5). Our analyses here have shown how some of 528 the unusual genetic and ecological asymmetries that define these groups are expected 529 to modulate the outcome of sexual antagonism. We find that PGE systems are broadly 530 more favourable to the invasion of female-beneficial alleles (and less favourable to their 531 male-beneficial counterparts) as compared to arrhenotoky and diploidy, that the 532 chronic inbreeding associated with many of these species promotes feminisation, and 533 that both of these factors may foment conflicts between different parties over sexually 534 antagonistic traits. We have also considered how some of the diversity of genetics and 535 life-history exhibited by haplodiploids may further modify these results, generating 536 variation in the fate of sexually antagonistic alleles across loci, tissues, and species. 537 538 Whilst our analysis indicates that these groups may provide a particularly rich set of 539 comparative tests for how ecology and genetics modulate sexual antagonism, relatively 540 little work has been carried out to investigate this (although see Table 2 for a 541 summary). One of the reasons for this is that the within-genome comparisons often 542 used to study sexual antagonism have been considered impossible for the many 543 haplodiploid species that lack sex chromosomes. However, this overlooks the 544 exceptions that provide excellent opportunities for testing theory. For instance, sciarid 545 flies not only have male PGE, but also an XO sex chromosome system (Metz 1938;Rieffel 546 and Crouse 1966), thus allowing a within-organism comparison of these inheritance 547 systems in relation to sexual antagonism. This is also true of some other groups with 548 germline PGE such as gall midges and globular springtails (Gallun and Hatchett 1969;549 White 1977; Dallai 2000; Anderson et al. 2020). In these groups we may expect female-550 beneficial variants to be enriched on the autosomes, whilst male-beneficial ones would 551 be expected to be overrepresented on the sex chromosomes, regardless of assumptions 552 about dominance, making this a more straightforward prediction than between 553 autosomes and sex chromosomes in conventional eumendelian systems (Rice 1984;554 Patten 2019). In addition to X autosome comparisons, some of these groups contain 555 further genomic elements such as germline-restricted chromosomes that are Similarly, whilst it has been suggested that the X chromosome should be relatively 561 enriched for sexually antagonistic polymorphisms in eumendelian systems as compared 562 to the autosomes (Rice 1984), again this depends on assumptions about dominance 563 (Fry 2010; Ruzicka and Connallon 2020). We find here that the same is true of 564 comparisons between PGE and X chromosomes/arrhenotoky, with arrhenotokous 565 organisms ones having a higher potential for polymorphism under parallel dominance, 566 but a smaller space for polymorphisms under dominance reversals (see Supplementary  567 Material). Additionally, such sexually antagonistic polymorphisms may be easier to 568 detect in some haplodiploid species as compared to eumendelian ones, because the 569 asymmetric transmission genetics means that allele frequency differences that build up 570 between the sexes in one generation, will carry over to the next (Crow and Kimura 571 1970; Ruzicka and Connallon 2020). 572 573 Additionally, we find that the chronic inbreeding exhibited by many haplodiploids less intensely with relatives. Here we recover that same pattern, but also find that other 581 mating schemes that characterise haplodiploid groups can involve an additional 582 feminising effect, as females may confer fitness benefits upon their mates. Alongside dispersal regimes in order to investigate the evolution of sex allocation; those 587 demographies predicted to lead to greater female bias in the sex ratio would also be 588 expected to promote female bias in relation to sexual antagonism. Thus, under these 589 conditions, we may expect to see either increased fixation of female-beneficial sexually 590 antagonistic alleles and/or phenotypes moving toward the female optimum. 591 Reinvestigation of these evolved lines or new experiments with similar design would 592 enable testing of predictions emerging from our analysis. 593 594 Furthermore, we have shown how population structure and transmission asymmetries 595 may foment conflicts between different genetic parties over sexually antagonistic traits. 596 In particular, we identify potential for conflict between parents and offspring. Whilst 597 there has been similar work considering the differing interests between parents and 598 offspring with regards to sex allocation (Trivers 1974 sperm-derived versus egg-derived products, and between those to genes expressed 606 after the maternal-to-zygotic transition, may help reveal such conflicts over 607 development. A further, particularly interesting case to investigate the logic of such 608 conflicts is with the bacteriome of the armoured scale insects. These are pentaploid 609 tissues containing two complete copies of the mother's genome and a copy of the 610 paternal-origin genome (Normark 2004b). Thus whilst not identical to the parents 611 interests, the bacteriome nonetheless might be expected to have more similar genetic 612 interests to the mother than the offspring it resides within, and thus the interface 613 between them provides a within-individual arena for this parent-offspring conflict.

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We have focused here on cases where there are only two classes of individual: males 616 and females. However, many of the better known haplodiploid species -most notably 617 the eusocial Hymentoptera -exhibit not just sex-structure, but also caste-structure. For 618 instance, in the eusocial bees, wasps, and ants, in addition to reproductive females 619 (queens) and reproductive males (drones), there is also an additional female neuter 620 class (workers) who are morphologically, physiologically, and behaviourally distinct 621 from the queen. Whilst the addition of caste structure on its own is not expected to 622 modulate sexual antagonism per se, i.e. trade-offs between queens and reproductive 623 males, if the trade-off occurs through female workers and reproductive males then 624 results would be expected to diverge, as phenotypic effects that manifest in females 625 would only have indirect effects through their effects on the reproductive females. 626 Moreover, with more than two castes there is the possibility for more complex trade-627 offs operating across multiple classes, such as between workers and queens, workers 628 and males, and three-way trade-offs; such trade-offs have previously been referred to in 629 terms of 'intralocus caste antagonism' (Holman 2014;Pennell et al. 2018). A similar 630 complexity occurs when males exhibit polyphenisms, for instance in fig wasps between  631 winged and non-winged male forms (Hamilton 1979;Cook et al. 1997). Such male 632 dimorphism can be extreme, not only concerning the presence/absence of wings, but 633 also with respect to other aspects of morphology and behaviour. If a sexually 634 antagonistic allele affects these morphs differently, then outcomes will be more 635 complex than those emerging from our analysis, depending on the relative fraction of 636 male dispersers. Similarly to caste structure, this may lead to trade-offs amongst these 637 male morphs, previously termed 'intralocus tactical evolution' (Morris et al. 2013).

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Our predictions have been derived under the assumption of non-overlapping 640 generations, yet age-structure may also have an important modulating effect on sexual 641 antagonism ( Finally, we have considered mating to be the only social interaction between males and 660 females. Yet invasion conditions for sexually antagonistic alleles are liable to be 661 modulated by more extensive and complex intersexual interactions. For instance, 662 intrabrood competition may result in male-beneficial alleles decreasing the fitness of 663 females both through the direct effect of those alleles being expressed by females, but 664 also through those females being outcompeted by their brothers (and vice versa, for 665 female-beneficial alleles). The extent of such competition will vary with ecological 666 context. For instance, bark beetles are understood to experience intense sib-667 competition, whilst phloem feeders are less likely to do so (Normark 2004a(Normark , 2006.

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Intense intrabrood competition is also an ecology well-suited to the evolution of 669 cytoplasmic male killing (Hurst 1991;Hamilton 1993;Normark 2004a pinworms (Adamson 1989). 681 682 In conclusion, we have explored how genetic and ecological asymmetries that 683 characterise haplodiploid groups are expected to modulate sexual antagonism, and how 684 these may in turn foment conflicts both between and within individuals over such traits.

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Exploring the consequences of these unusual genetic systems and life-cycles has 686 previously offered rich insights into sex allocation (Charnov 1982;West 2009), and thus 687 leveraging the natural diversity within these groups may also deepen our 688 understanding of sexual antagonism and the evolution of sexual dimorphism. Gene 689 expression studies increasingly look for sex biased gene expression in such non-model 690 and non-eumendelian species, and our predictions will facilitate interpretation of these 691 data, as well as identifying where future research effort may be most fruitfully focused. 692 Finally, many of the species that reproduce through arrhenotoky or PGE are pests and 693 parasites of humans, livestock, and crops, e.g the coffee borer beetle, hessian fly, head 694 lice, and the citrus mealybug. Improved understanding of the evolutionary 695 consequences of these unusual lifecycles and genetics therefore also has practical 696 relevance in guiding our use of chemical, biological, and genetic controls.     , is plotted as a function of either the amount of male and female philopatry, or the amount of female philopatry and the proportion of sib-mating, under three inheritance systems (diploidy, germline PGE, and arrhenotoky), and for three mating ecologies (sib-mating (a-c), viscous population with mating pre-female dispersal (d-f), and viscous population with mating post-female dispersal (g-i)).When /(1 + ) > 0.5, then feminisation is expected, and when /(1 + ) < 0.5 masculinsation is expected. 709 710 711 Figure 4: Conflicts within and between individuals over sexually antagonistic traits, across different genetic systems. The optimal level of a sexually antagonistic trait z under diploidy, germline PGE, and arrhenotoky when control of that trait is assigned to: offspring, mothers, and fathers (a-c); autosomal genes, matrilineal cytoplasmic genes, and patrilineal cytoplasmic genes (d-f); ignorant genes, maternal-origin genes, and paternal-origin genes (g-i).
In these examples, fitness is a gaussian distributed trait with an optimum of 1 for females and -1 for males, with equal variance.