Somatic maintenance alters selection acting on mutation rate

23 The evolution of multi-cellular animals has produced a conspicuous trend toward increased 24 body size. This trend has introduced at least two novel problems: an elevated risk of somatic 25 disorders, such as cancer, and declining evolvability due to reduced population size, lower 26 reproduction rate and extended generation time. Low population size is widely recognized to 27 explain the high mutation rates in animals by limiting the presumably universally negative 28 selection acting on mutation rates. Here, we present evidence from stochastic modeling that the 29 direction and strength of selection acting on mutation rates is highly dependent on the evolution 30 of somatic maintenance, and thus longevity, which modulates the cost of somatic mutations. We 31 propose a theoretical model for how evolvability and germline mutation rates can be under 32 positive selection in sexually reproducing organisms by their co-selection with adaptive alleles 33 that overcomes gene segregation produced by genetic recombination. We argue that this 34 mechanism may have been critical in facilitating animal evolution. 35


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Increasing body size has been one of the major trends in animal evolution across many 39 taxa, as formulated in Cope's rule (Heim et al., 2015, Baker et al., 2015. The evolution of larger 40 bodies introduces some fundamentally new evolutionary challenges. The carrying capacity of 41 ecosystems limits biomass per group/species, so larger body size leads to reduced population 42 size. Furthermore, large animals generally demonstrate lower reproduction rates and longer 43 generation times. In aggregate, such changes weaken selection that can act on a population 44 and thus negatively affect evolvability. This general reduction in evolvability should, however, be 45 at least partially alleviated by diversity facilitated by sexual reproduction. 46 The mutation rate (MR) is another critical evolvability parameter. It is believed that selection 47 generally acts to lower MR (Kimura, 1967, Baer et al., 2007, Dawson, 1999, and the significantly 48 higher MRs observed in animals compared to unicellular organisms have been argued to result 49 from the reduced power of selection imposed by small population sizes (Lynch, 2010, Lynch,  increased cost of sMR should thus exert negative selective pressure on gMR in larger animals. 58 somatic mutation and in aggregate promote lifespan extension by maintaining tissue integrity. 65 We will collectively call these mechanisms -the somatic maintenance program (SMP). 66 We present theoretical evidence from Monte Carlo modeling indicating that somatic 67 maintenance not only improves individuals' survival for large animals by reducing sMR costs, 68 but should have played a crucial role in animal evolution by substantially modifying selection 69 acting on gMR. We show that positive selection for increased body size promotes positive 70 selection for extended longevity by improving SMP. Our results also indicate that positive 71 selection on traits that do not impact somatic risks also promotes selection for an improved SMP. individual has a number of simulated traits: 1) ID, which is 1 (monogenotypic population) or 1 86 mutation rate of 10 -9 AU (explained below); 7) inherited reproduction rate, which is the period 93 with variation between successive reproductions in adult individuals and equals ~600 in the initial 94 population; 8) inherited litter size (initially 1), which is the number of progeny produced per 95 individual per reproduction; 9) inherited parameter of somatic maintenance, which determines 96 the strength of the somatic maintenance program as further explained below; 10) age of first 97 reproduction, which dictates that an individual begins reproducing when its current body mass 98 reaches 0.9693 of its inherited adult body mass (the number is derived so that in the initial 99 population maturity is reached at age ~1000 based on the growth curve).

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Each inherited trait varies in progeny relative to parental. This variation was produced by 101 multiplying the inherited mutation rate by the parameter of inherited variance (inhvar = 102 250,000,000) and the product was used as the standard deviation (STD) of the normally 103 distributed variation in inheritance. This transformation was not necessary, as the inhvar 104 parameter is constant throughout simulation and it simply determines the magnitude of the 105 mutation rate's effects in germline, which is imaginary and in the initial population simply 106 produces 0.000000001 x 25,000,000 = 0.025 that serves as the STD parameter for the normal 107 distribution from which inheritance variation is drawn. However, we kept this two-parametric 108 model for inheritance because mutation rate is also separately used in the equation of the 109 somatic maintenance program (as will be explained later).

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Each newborn individual grows, reaches maturity, then reproduces over the rest of its lifetime 111 and eventually dies. The model is asynchronous, so that at every time-point of the simulation 112 the population contains individuals of various ages whose lifecycles develop independently. The 113 model operates with single-parent reproduction model so that each individual descends from 114 one parent. In this regard, technically it is tempting to view it as a model of an asexual population.
115 However, at a higher level of abstraction the fundamental difference between sexual and asexual 116 populations (aside from the issue of purging deleterious mutations) is the amount of variation 117 produced per the same size population per generation. Variance of inheritance in our model (as 118 shown above) is obviously too high to be assumed as being generated by mutations 119 accumulating along a clonal lineage and equals 10% of a trait's value per generation within 95 120 percentile. As the modeled traits are assumed to be multigenic and have a continuous 121 phenotypic range in the population, we did not need to simulate the processes of allelic segregation by recombination in order to reconstruct a sexual population. As such, the model 123 only operates with the net ultimate change of a trait over generations. At this level of abstraction, 124 the effective difference between a sexual and asexual population is reduced to the amount of 125 variation in phenotypically manifested inheritance per population size per generation. We 126 account for population size in this definition by inferring that this variance per se will not depend 127 on population size, but larger populations will have higher chance of generating extreme 128 phenotypes, e.g. those beyond 95 percentile on a per generation basis.

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And finally, three factors of mortality were modelled in the simulations. First, at every timepoint 130 of the simulation, an individual could die of somatic causes with a certain probability. This 131 probability is small at the beginning of life (but still can be caused by some imaginary inherited 132 genetic defects) and increases exponentially with age based on the paradigm of the aging curve, 133 which is primarily determined by an individual's inherited somatic maintenance program (SMP).

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In humans, the aging curve also depends on lifestyle, however we assume in this model that in 135 a wild animal population lifestyle distribution is sufficiently uniform to be neglected. More detailed 136 description of the somatic maintenance paradigm we applied will be explained further below.

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Secondly, the simulated animals had a chance of dying of external hazards, such as predators. 138 We applied the Lotka-Volterra model of predator-prey interactions (Lotka, 1925, Volterra, 1926 139 to implement the dynamics of predator pressure (effectively the chance of dying of an external 140 hazard cause per timeunit). Here we should mention that smaller individuals and juveniles had 141 higher chances of dying of external hazards, which effectively created positive selection for body 142 size and also reflected the typical high mortality rates among juveniles observed in natural 143 populations. And lastly, individuals could die of intra-specific competition. We implemented such 144 competition by setting the upper limit of population's total biomass, which in nature is imposed 145 by the ecosystem's carrying capacity. Therefore, in the simulated population biomass produced 146 over the biomass limit caused additional mortality so that stochastically population total biomass 147 never exceeded the limit. Larger individuals also had lower probability of dying of intra-specific 148 competition, based on the assumption that competition for resources and mates (the failure to 149 reproduce is effectively an evolutionary death) will typically favor larger individuals and this 150 should have been one of the forces that has been driving the macroscopic animal evolutionary 151 trend towards increasing body size. The advantage of size in this mortality model also created additional positive selective pressure for body size. The total age-dependent mortality of all 153 causes in our model did approximate a typical wild animal mortality curve (Supplements: Section 154 3).

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The somatic maintenance program paradigm. In order to replicate natural mortality caused by 156 physiological aging, such as cancer, decreased immune defense and lower ability to avoid 157 predators or to succeed in intra-specific competition, we made use of the aging curve, or somatic with a constant linear fitness advantage will proliferate exponentially. Therefore, we can already 178 assume that mutation rate should have a linear effect on the cancer curve, while time/age adds 179 an exponential component revealed in an exponential growth of a tumor. We can reasonably 180 assume further that a strong SMP will efficiently suppress such a clone, slowing or even 181 preventing its growth. A weaker SMP will allow the clone to proliferate faster. Therefore, SMP 182 . CC-BY-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/181065 doi: bioRxiv preprint first posted online Aug. 25, 2017; strength can modulate the effects of mutations and time on cancer risk. The exact relationship 183 between SMP strength and physiological risk factors is not known. However, we know that their 184 interaction leads to a net exponent in physiological decline and disease risk. We therefore 185 reconstructed the human aging curve by maintaining the general principal relationship between 186 these factors as shown in Eq. 1. As seen from the equation, mutation rate is a linear contributor 187 to aging. Age itself contributes exponentially, and the somatic maintenance composite 188 parameter Som is, in turn, in power relationship to age. The cumulative distribution function of 189 DA (Eq. 1) produces D(A) -the probability of dying of somatic/physiological causes by age A and 190 yields a shape close to the human mortality curve (Fig. 1A,B). We cannot claim that these three Supplements: Section 4, the exact relationship between the Som parameters and each of the 207 other two (mutation rate and age) has no effect on the model, as the model represents SMP and 208 its variation by using area under the mortality curve, therefore the sole purpose of Eq. 1 in the 209 model is to generate an age-dependent curve of physiological mortality whose cumulative 210 function (probability of dying by a certain age) resembles in shape the human mortality/aging 211 curve (see Supplements: Section 4 for detailed explanation and illustration).   Based on the rarity of such events, we can assume that they had the effect of rare early lethal 233 mutations and affected the population at random. Thus we assume these did not affect the

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In our simulations, positive selection for body size (Fig. 1C, green) led to a concurrent 272 selection for elevated gMR (Fig. 1D, green) and improved SMP (Fig. 1E, green). Artificially 273 blocking SMP evolution by fixing SMP at the initial value (Fig. 1E, blue) significantly slowed the 274 evolution of body size (Fig. 1C, blue; p << 0.001) and triggered negative selection on gMR (Fig.   275 1D, blue). We implemented the ecosystem carrying capacity by setting a maximum biomass for 276 the population; therefore, increasing body size led to a corresponding decline in population 277 numbers, amplifying the power of drift (Fig. 1F,G). When SMP was allowed to evolve, however, 278 the population entered a "drift zone" when its size decreased to ~4,000 individuals, which shortly 279 thereafter was overcome by selection for even larger body size, visible also by a continuing 280 decline in population numbers (Fig. 1F). When we artificially blocked SMP, however, the drift 281 zone was more profound. It occurred earlier at the population size of ~6,000-7,000 individuals, 282 and the population was not able to escape from it (for ~1,000 generations) and restore its initial 283 rates of evolution (Fig. 1G), indicating an important role of SMP evolution in maintaining 284 evolvability. We further generated a population with two simulated genotypes -Genotype A that 285 could evolve SMP (10% of the population) and Genotype B with SMP fixed at the initial value 286 (90%). We set a maximum population size and removed the maximum biomass limit to rule out 287 body mass effects on population size and selection, and tracked Genotype A and Genotype B 288 frequencies under positive selection for body size (for code see Supplements: Section 1b).

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Despite the initial abundance, Genotype B (with fixed SMP) lost the competition in less than 200 290 generations, reflecting a direct competitive advantage of the capacity to evolve enhanced SMP 291 (Fig. 1H). Hereafter, we will call the setting with positive selection for body size and freely  In the absence of positive selection for increased body mass ( Fig. 2A, blue), both gMR ( Fig.   295 2B, blue) and SMP (Fig. 2C, blue) demonstrate early positive selection, which appeared to have 296 been caused by rapid evolution of reproductive parameters (see Supplement: Section 2).

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Overall, gMR demonstrates a significant general decrease (non-overlapping confidence 298 intervals (CIs) at the beginning relative to the end of the simulation), and SMP undergoes a 299 significantly smaller improvement compared to the standard condition (green; p << 0.001).

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Blocking the evolution of body mass (Fig. 2D, blue) and SMP (Fig. 2F, blue) expectedly led to 301 strong selection for lower gMR (Fig. 2E, blue) compared to the standard condition (p << 0.001), 302 which we interpret as being driven by the sMR costs in the absence of benefits of high gMR. In 303 other words, mutation rate is selected against because of its somatic costs and the absence of 304 benefits of higher gMR in static conditions. In natural populations that are under stabilizing 305 selection, gMR will have costs due to greater phenotypic variance from a well-adapted state that 306 are independent of sMR, but we do not model stabilizing selection in this study.

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To investigate the role of the putative gMR benefit versus sMR cost balance in evolution, 308 we further decoupled gMR and sMR by allowing gMR to evolve but making sMR cost fixed and  As we have seen under blocked selection for body size (Fig. 2B,C, blue), SMP demonstrates 319 an early phase of positive selection (Fig. 2C, blue) that is apparently reflected in a corresponding 320 positive selection for gMR (Fig. 2B, blue). This observation suggests that both SMP and gMR 321 may also respond to selection acting on some other traits, e.g. reproductive parameters 322 . CC-BY-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/181065 doi: bioRxiv preprint first posted online Aug. 25, 2017; (Supplements: Section 2). This raises the question whether SMP and gMR evolution would be 323 sensitive to strong selection for a trait that does not affect somatic risks (greater body size 324 increases the target size for somatic mutations). We simulated a condition that was similar to 325 the standard condition, except positive selection was applied to a trait that did not affect sMR  As anticipated, SMP is positively selected, however in the absence of an increasing sMR cost 334 (associated with larger bodies), SMP's improvement is significantly smaller (Fig. 2L, blue, p << 335 0.001). Notably, even with much less enhanced SMP, gMR is still under positive selection in 336 response to positive selection of the sMR cost unrelated trait (Fig. 2L, blue), consistent with the 337 sMR/gMR cost/benefit ratio being an important factor regulating selection acting on gMR.

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Regardless, the results demonstrate that both gMR and SMP are responsive to selection for 339 somatic risk unrelated traits, which indicates that high mutation rate is beneficial in positively 340 selective conditions.

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As we have seen in Fig. 2D-F, in the absence of strong positive selection for body size and 342 SMP efficiency, selection acts to lower gMR. Fig. 3 shows, however, that this selection is 343 significantly modified by the efficiency of SMP. Stronger SMPs (lower Som value) relax selection 344 for lower gMR when directional selection is weak (non-overlapping CIs between the standard 345 (red) and either of the improved SMPs). As will be explained further below, this observation may negatively impact individual fitness and therefore be under negative selection. To investigate 351 this question, we mixed two simulated genotypes, one "wild-type" (50%) and one "mutator" 352 (50%) in a population of stable size and under positive selection for a sMR cost unrelated trait. 353 We then observed the genotypes' frequencies in the population using varying strength of 354 mutators. Fig. 4A demonstrates that while the mutator's fitness initially is lower compared to wild-355 type, eventually the mutator outcompetes its wild-type counterpart. Interestingly, with increased 356 mutation rate, the magnitude of the mutator's initial decline increases, but so does the speed at  Our study demonstrates that positive selection for body size triggers a concurrent selection 373 for improved somatic maintenance to mitigate the increased somatic risks of larger bodies.

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Improved somatic maintenance, in turn, promotes selection for higher germline mutation rates 375 by reducing the cost of somatic mutations and thus altering the sMR/gMR cost/benefit ratio.

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Conditions of strong positive selection for other than SMP traits, as our model shows, can also 377 . CC-BY-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . alter this balance by elevating the benefits of higher gMR. Under stable conditions, alternatively, 378 the sMR/gMR cost/benefit balance is altered by the existing cost of somatic mutations and by 379 the increased cost and absent/reduced benefits of gMR itself (as shown in Fig. 5A), which 380 ultimately favors lower mutations rates. Under stasis, gMR exerts a cost independent of somatic 381 risks by increasing deviation of progeny phenotypes from population mean/median and thus 382 reducing their fitness. Our study thus demonstrates that the evolution of mutation rate is not 383 exclusively limited by negative selection and population size, but is highly tunable and governed  on other evidence that the efficiency of such segregation in sexual populations is limited (Draghi 406 & Wagner, 2008). Here, we argue that given the polygenic nature of mutation rate, such 407 segregation should be much less efficient in small populations that are under positive selection, 408 and should be substantially impeded by selection for extreme phenotypes (as shown in Fig. 5).

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The polygenic nature of mutation rate should also impede segregation of mutator phenotypes 410 from adaptive phenotypes, as most genes contributing to the overall mutation rate will

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Yet robust experimental corroboration of such a possibility appears to be lacking.

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In conclusion, our results raise the question of whether the evolution of large body size in 463 animals would be possible without such a complex pattern of selection acting on mutation rate, 464 and whether such a complex relationship is necessary to explain the evolution of large animals.

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The evolution of large bodies has entailed the cost of losing the ability to evolve via all major 466 parameters that define this ability, such as population size, reproduction rate and generation 467 time, except mutation rate (which increased). Therefore, one scenario could have been that this 468 cost has been so prohibitive for many species that positive selection for mutation rate was 469 necessary to allow evolution of large animals. Alternatively, mutation rate could have been high 470 enough to maintain evolvability at the negative selection/drift barrier point where negative 471 selection was no longer able to reduce it further (Lynch, 2010). Understanding which of these 472 scenarios prevails in the evolution of large animals requires more research.   parameter was fixed at 0.34 (red), 0.24 (green; enhanced 10X) and 0.2 (blue; enhanced 40X); a linear decrease in 576 the Som value results in a substantially improved SMP, so that the green SMP is ~10X more efficient compared to 577 red, and the blue is a ~4X more efficient SMP than the green. The standard (red) SMP leads to a significantly 578 stronger selection for lower gMR (non-overlapping 95% CIs); however, the absence of difference between the 10X 579 (green) and 40X (blue) improved SMPs indicates that overly improved SMPs might not provide any further 580 difference for how selection acts on gMR.