Adaptation and the Parliament of Genes

Fields such as behavioural and evolutionary ecology are built on the assumption that natural selection leads to organisms that behave as if they are trying to maximise their fitness. However, there is considerable evidence for selfish genetic elements that change the behaviour of individuals to increase their own transmission. How can we reconcile these contradictions? We found theoretically that: (1) when selfish genetic elements have a greater impact at the individual level, they are more likely to be suppressed, and suppression spreads more quickly; (2) selection on selfish genetic elements leads to higher levels of distortion, making them more likely to be suppressed. Overall, our results suggest that selfish genetic elements will either have a minor impact at the individual level, or tend to be suppressed, and that selection on selfish genetic elements will often drive their own suppression.


Introduction
stronger of the two distorters is dominant, but found similar results when assuming 206 additivity (Appendix 5). We assume that the similarity in coding sequence and 207 regulatory control means that the original distorter and the mutant are both 208 suppressed by the same suppressor allele, at the same cost (csup) 49 . In Appendix 5, 209 we write the recursions that detail the generational frequency changes in the 210 different possible gametes (y0/+, y0/sup, y1/+, y1/sup, y2/+, y2/sup). 211 We found that stronger mutant distorters (! E >!) will invade from rarity when the 213 marginal increase in offspring they are propagated into exceeds the marginal 214 increase in offspring they are lost from as a result of reduced fitness (Δt(1-215 cdrive(! E ))>Δcdrive, where Δ denotes marginal change (Δt=t(! E )-t(!); Δcdrive=cdrive(! E )-216 cdrive(!))). Consequently, if distortion is initially low, and successive mutant distorters 217 are introduced, each deviating only slightly from the distorters from which they are 218 derived ("δ-weak selection" 42 ), invading distorters will approach a 'target' strength, 219 denoted by !target. The target strength is that at which the marginal benefit of 220 #% F ( (Fig. 2b). If mutations are larger (strong selection), 225 invading distorters may overshoot the target strength of distortion (! E >!target). Weaker 226 mutant distorters (! E <!) are recessive so cannot invade from rarity. 227 As evolution on the distorter increases the level of distortion, it makes it more likely 229 that the distorter reaches the critical level of distortion where suppression will be 230 favoured. When this is the case (csup<cdrive(!target)), the distorter spreads to high 231 frequency, which then causes the suppressor to increase in frequency, reversing the 232 direction of selection on the distorter, towards non-distortion (y0), resulting in zero 233 trait distortion at equilibrium (!*=0) ( Fig. 2a; Appendix 6). Suppression only fails to 234 spread if the individual fitness cost associated with suppression is greater than the 235 individual fitness cost associated with the target trait distortion (csup>cdrive(!target); Fig.  236 2a). Given that the individual fitness cost of pre-translational suppression at a single 237 locus is likely to be low, then any non-negligible distorter is likely to be suppressed. 238

239
Overall, our results suggest that selection on distorters will tend to drive the eventual 240 suppression of those distorters. In Appendix 7 we developed an agent-based 241 simulation, which allowed us to continuously vary the level of both distortion and 242 suppression, and obtained results in close agreement ( Specific Models 246 We then tested the robustness of our above conclusions by developing models for 247 three different biological scenarios: a sex ratio distorter on an X chromosome (X 248 driver); an imprinted gene that is only expressed when maternally inherited; and a 249 gene for the production of a public good by bacteria, which is encoded on a mobile 250 genetic element. We examined these cases because they are different types of 251 distortion, involving different selection pressures, in very different organisms. We 252 obtained qualitatively similar results in all three cases. 253

254
In all of our specific models, we assume that the suppressor: is dominant; is only 255 expressed in the presence of the distorter (facultative); completely suppresses the 256 distorter; and may incur a fitness (viability) cost to the individual when it is 257 expressed, independent of distorter strength, denoted by csup (0≤csup≤1) 43,44 . These 258 assumptions fit well to a molecularly characterised suppressor ("nmy") of a sex ratio 259 distorter ("Dox") 39,40 ; and more generally to suppressors that act pre-260 translationally 45,46 . We also relax a simplifying assumption of our illustrative model, 261 by allowing the transmission benefit and individual fitness cost of trait distortion to 262 vary with the population frequency of the distorter. 263 264 Sex Ratio Distortion 265 We examined sex ratio evolution in a diploid species, in a large outbreeding 266 (panmictic) population, with non-overlapping generations, and where males and 267 females are equally costly to produce. Fisher 1 and many others have shown that, in 268 this scenario, individuals would be selected to invest equally in male and female 269 offspring 9,24 . We assumed genetic sex determination, with males as XY and females 270 as XX, and that females mate with λ mates per generation. The distorter (y1) that we 271 considered is an X driving chromosome, which acts in males, killing Y-bearing 272 sperm, and causing the male's mating partners to produce a higher proportion of 273 female (XX) offspring. The proportion is given by (1+!)/2, where ! denotes the 274 proportion of Y-bearing sperm that are killed (0<!≤1). We assumed that the sex ratio individual trait value. Consequently, the extent to which the sex ratio deviates from a 283 50:50 investment will be small or zero 47 (Fig. 3ai). In addition to being more likely to 284 be suppressed, the stronger distortion is, the quicker suppressors spread. Finally, 285 when we allowed the X chromosome driver to evolve, it evolved to high levels of sex 286 ratio distortion (high !target), increasing the likelihood of suppression. 287

288
We only obtained appreciable and detectable levels of sex ratio distortion (>60% 289 females) if the cost of suppression exceeded a 15-35% viability reduction (Fig. S8). 290 This is a much greater cost than what we would expect from natural gene 291 suppression pathways 48 . A suppressor will only fail to spread when the individual 292 cost of sex ratio distortion is less than the cost of suppressing the distorter (Equation 293 S3). Given that the cost of suppression is likely to be low, we would only expect 294 distorters that have relatively little impact at the individual level to evade 295 suppression. We tested the robustness of our population genetic analysis with an 296 agent-based simulation, and a game theory model, and found close agreement ( An imprinted allele has different epigenetic marks, and corresponding expression 315 levels, when maternally and paternally inherited 55 . We examined the evolution of an 316 altruistic helping behaviour in a population capable of genomic imprinting. A 317 behaviour is altruistic if it incurs a cost (c) to perform, by the actor, and provides a 318 benefit (b) to another individual, the recipient. Altruism is favoured if the genetic 319 relatedness (R) between the actor and recipient is sufficiently high, such that Rb>c 3 . 320

321
An individual may be more closely related to their social partners via their maternal 322 or paternal genes 14,15,18 . For example, if a female mates two males, then on average her offspring would be related by Rm=1/2 at maternal genes and Rp=1/4 at paternal 324 genes. If genes can 'gain information' about where they came from, by imprinting, 325 then they could be selected to adjust traits accordingly. Assume that relatedness to 326 social partners is Rp and Rm at paternal and maternal genes respectively. In this 327 case, altruistic helping would be favoured at: maternally imprinted genes when 328 Rmb>c; paternally imprinted genes when Rpb>c; and unimprinted genes when suppression cost is likely to be low, these distorters that evade suppression will have 350 relatively little impact at the individual level. When distortion is strong (high !), then 351 suppression is favoured, and so there is no influence on the individual trait value 58 . 352 Consequently, the extent to which altruistic investment deviates from the individual 353 optimum of zero investment will be small or zero (Fig. 3bi). Finally, when we allowed 354 the imprinted gene to evolve, we found that cooperative distortion increased until it This could help explain both why imprinting appears to be relatively rare within the 368 genome 18,55,60 , and why imprints are removed and re-added every generation in 369 mice, handing control of genomic patterns of imprinting to unimprinted genes 18,59,61 . 370 local population of cells and so can be thought of as public goods 62 . We modelled 374 the evolution of investment in a public good in a large, clonally reproducing 375 population. We assume a public good that costs c to produce, and provides a benefit 376 b to the group. We assume a well-mixed population, meaning genetic relatedness at 377 vertically inherited genes is zero (Rvertical=0), and so public good production is 378 disfavoured at the individual level (Rverticalb=0<c) 3,63 . 379

380
We consider a distorter (y1) of public goods production that is on a mobile gene, 381 such as a plasmid. Mobile genes can spread within groups, increasing genetic 382 relatedness at the mobile locus (Rhorizontal>0), potentially favouring public goods 383 production 64,65 . We assume that the distorter increases public goods investment by 384 some amount (!), at a fitness cost to the individual (0≤cHGT(!)≤1) and benefit shared 385 within the group (bHGT(!)>cHGT(!)), that are both monotonically increasing functions 386 of investment " #{H NIO ,) NIO } #% ≥ 0(. We also assume a potential suppressor (sup) that is 387 immobile 46,66,67 . Each generation, individuals randomly aggregate into groups, and 388 one allele at the mobile locus (y0,y1,y2) spreads horizontally within each group, each 389 with equal likelihood, increasing relatedness at the mobile locus. Public goods may 390 then be produced and shared within groups, before individuals reproduce and die 391 (non-overlapping generations). 392

393
In Supplementary Information 6, we show with a population genetic analysis that our 394 plasmid model produces similar results to our illustrative model. When distortion is impact at the individual level (Fig. 3ci). When distortion is strong (high !), then 397 suppression is favoured, and so there is no influence on the individual trait value 67 . 398 Consequently, the extent to which public goods investment deviates from the 399 individual optimum of zero investment will be relatively small or zero (Fig. 3ci). 400 Finally, when we allowed the mobile distorter to evolve, we found that higher levels 401 of public goods investment (high !target) are favoured, leading to selection for 402 suppression (Fig. 3cii). We lack empirical data that would allow us to test our model 403 of mobile public goods genes. 404 405 Discussion 406 We have found that the individual level consequences of selfish genetic elements 407 ('distorters') will be either small or non-existent. If distorters lead to only small 408 distortions of traits, then they will not be suppressed, but they will only have small 409 effects on traits (Figs. 1 & 3). Specifically, distorters will only remain unsuppressed if 410 trait distortion compromises individual fitness less than suppression of the trait 411 distorter does (cdrive(!)<csup). Given that the individual fitness cost of pre-translational 412 suppression at a single locus is likely to be low, we can say that trait distortion 413 conferred by unsuppressed distorters is likely to be relatively negligible. 414 415 However, if distorters lead to large distortions of traits then this selects for their 416 suppression, and so they will have no net effect on traits at the individual level (Figs. 417 distorters will often drive their own demise (Figs. 2 & 4). These results suggest that 421 even if there is substantial potential for genetic conflict, distorters will have relatively 422 little influence at the individual level, in support of Leigh common, they will tend to be either weak and negligible, or suppressed. This 452 suggests that even if there is the potential for appreciable genetic conflict, individual 453 level fitness maximisation will still often be a reasonable assumption. This allows us 454 to explain why certain traits, especially the sex ratio, have been able to provide such 455 clear support for both individual level fitness maximisation and genetic conflict. 456 (y1) can spread to fixation if the p*=1 equilibrium is stable, which requires that the 468 differential of p' with respect to p, at p*=1, is less than one. This requirement always 469 holds true, demonstrating that there is no negative frequency dependence on the 470 distorter, and that it will always spread to fixation after its initial invasion. 471 472

Appendix 2: Suppressor invasion condition 473
We ask when the suppressor (sup) can spread from rarity in a population in which 474 the distorter (y1) and non-suppressor (+) are fixed at equilibrium. We derive the 475 Jacobian stability matrix for this equilibrium, which is a matrix of each genotype 476 frequency (x1', x2', x3', x4') differentiated by each genotype frequency in the prior 477 generation (x1, x2, x3, x4), at the equilibrium position given by x1*=0, x2*=0, x3*=1, 478 The suppressor can invade when the equilibrium is unstable, which occurs when the 483 leading eigenvalue is greater than one. The leading eigenvalue is (1-csup)/(1-cdrive), 484 meaning the suppressor invasion criterion is cdrive>csup. 485 non-equilibrium maintenance of the distorter in the population, but this effect is 512 diluted as the cost of trait distortion (cdrive) is increased relative to suppression (csup) 513 ( Supplementary Information 2, Fig. S1). Stronger distorters (with higher !, leading to 514 higher cdrive and t) are therefore generally suppressed and purged more rapidly than 515 weaker distorters (Fig. 1b). Exceptions are distorters that reduce individual fitness 516 relatively negligibly after the point (!) at which suppression is favoured, such that 517 which occurs when the leading eigenvalue of the Jacobian stability matrix for this 545 equilibrium is greater than one. Testing for stability in this way, we find that, if the 546 mutant distorter is weaker than the resident, it can never invade. If the mutant 547 distorter is stronger than the resident, it invades from rarity when Δt(1-548 The implication is that, if trait distortion is initially low, and mutant distorters are 551 successively introduced, each deviating only very slightly from the resident distorter 552 from which they are derived, such that ! E =!±δ, where δ is very small ("δ-weak 553 selection" 42 ), then distorters will approach a 'target' strength at which #% . In the absence of suppression, this target (!target) is the equilibrium 555 level of distortion (!*=!target). However, if mutant distorters (y2) are allowed to deviate 556 appreciably from residents (y1) (strong selection), then distorters may invade even if 557 they overshoot the target (! E >!target). In the absence of suppression, !target is then not the equilibrium level of distortion, but rather, the minimum equilibrium level of 559 distortion (!*>!target) ( Supplementary Information 3, Fig. S2b). 560

561
We could alternatively have assumed that an individual's trait is distorted according 562 to the average strength of its alleles (additive gene interactions), rather than 563 according to the stronger (higher-k) allele (dominance). Such an assumption leads to 564 a single invasion criterion for a mutant distorter, regardless of whether the mutant 565 distorter is stronger or weaker than the resident distorter, given by: 566 Δt(2-cdrive(!)-cdrive(! E ))>Δcdrive. In the absence of suppression, this leads to an 567 equilibrium level of distortion (!*), that holds even under strong selection, that 568 We ask what equilibrium state will arise after the invasion of a mutant distorter. We 573 assume that the mutant distorter (y2) is introduced from rarity when the resident 574 distorter (y1) has reached the population frequency given by q. We numerically 575 iterate Equations (A2), over successive generations, until equilibrium has been 576 reached. At equilibrium, for all parameter combinations (q, t(!), t(! E ), csup, cdrive(!), 577 cdrive(! E )), the resident distorter (y1) is lost from the population (x3,x4=0), with either 578 the mutant distorter (y2) and non-suppressor (+) at fixation (x5*=1), or the non-579 distorter at fixation alongside the suppressor at an internal equilibrium (x1*+x2*=1). 580 The latter scenario arises if the mutant distorter triggers suppressor invasion suppressor (sup) a selective advantage, leading to high suppressor frequency, which 583 in turn reverses the selective advantage of distortion, leading to distorter (y1,y2) loss 584 and suppressor equilibration. 585 We construct an agent-based simulation to ask what level of trait distortion evolves 588 when continuous variation is permitted at distorter and suppressor loci. We model a 589 population of N=2000 individuals and track evolution at two autosomal loci: a 590 distorter locus (L1) and a suppressor locus (L2). Each individual has two alleles at 591 the distorter locus, with strengths denoted by ka and kb, and two alleles at the 592 suppressor locus, with strengths denoted by ma and mb (diploid). Strengths can take 593 any continuous value between zero and one. We assume that, for both loci, the 594 meaning the parental allele of strength ka is inherited, rather than the allele of 607 strength kb, with the probability (1+(t(ka)-t(kb))(1-max(ma,mb)))/2. The transmission 608 bias function, t, is given an explicit form in simulations (Supplementary Information 3, 609    The trait distorter (y 1 ) and its suppressor (sup) are introduced from rarity. In part (a), 791