Environmental oscillations favor the evolution of adaptive transgenerational plasticity

Effects of parental environment on offspring traits have been well known for decades. Interest in this transgenerational form of phenotypic plasticity has recently surged due to advances in our understanding of its mechanistic basis. Theoretical research has simultaneously advanced by predicting the environmental conditions that should favor the adaptive evolution of transgenerational plasticity. Yet whether such conditions actually exist in nature remains largely unexplored. Here, using long-term climate data, we modeled optimal levels of transgenerational plasticity for an organism with a one-year life cycle at a spatial resolution of 4km2 across the continental US. Both annual temperature and precipitation levels were often autocorrelated, but the strength and direction of these autocorrelations varied considerably across the continental US and even among nearby sites. When present, such environmental autocorrelations render offspring environments statistically predictable based on the parental environment, a key condition for the adaptive evolution of transgenerational plasticity. Our optimality models confirmed this prediction: high levels of transgenerational plasticity were favored at sites with strong environmental autocorrelations, and little-to-no transgenerational plasticity was favored at sites with weak or non-existent autocorrelations. These results suggest that transgenerational plasticity is highly variable in nature, depending on site-specific patterns of environmental variation. Author Summary Parental environments can alter progeny development, a phenomenon that has received renewed focus as interest in epigenetic inheritance has surged. Mathematical models indicate that these effects can evolve to adaptively match progeny phenotypes and environments when conditions change predictably, but few studies have explored whether such conditions actually exist in nature. This study reveals that patterns of precipitation and temperature variation in many regions of the US should favor the adaptive evolution of parental effects, but the optimal extent of these effects varies widely. Patterns of environmental fluctuations are heterogeneous across the landscape such that not only will there be variation in optimal phenotypes across space, but that there will also be variation for the optimal system of inheritance.


Introduction
6 In our precipitation model, we examine transgenerational effects that persist for up to three 160 generations (Figure 1a), as multiple experimental studies have found that environmentally induced 161 epigenetic and phenotypic effects can persist for at least this long (e.g., 49,50), and in some cases for 162 far longer (51,52). In our temperature model (Figure 1b), we also determine the degree of within-163 generation plasticity that would maximize fitness, in response to both early and late-season 164 temperatures. In both of these models we calculate the fitness of genotypes as a product of the 165 difference between the individual's phenotype value and the environmental optimum for that year. 166 With different genotypes producing their phenotypes based on different weightings of within 167 generation plasticity, transgenerational plasticity, multi-generation epigenetic inheritance, and genetic 168 inheritance, we find that across the US there is extraordinary variation in the optimal ratio of how 169 these various classes of information should inform an individual's phenotype. These findings imply 170 that just as landscape level variation in mean historical conditions selects for locally adapted 171 populations, landscape level variation in the predictability of environmental variation may select for 172 locally adapted patterns of plasticity within and across generations. dataset is long-term consistency making it ideal for our purposes. Individual yearly values were 181 concatenated using the QGIS merge raster function (54), and exported in the .RData format for 182 downstream analysis. For precipitation data, October was chosen to represent the start of the 183 "hydrologic" year in order to more accurately capture water availability patterns during the growing 184 season. For temperature data, mean daily maximum temperature was calculated for March-May as a 185 measure of early growing season temperature for a given year, and July-September mean daily 186 maximum temperature for late growing season temperature. Custom R scripts were used to calculate 187 descriptive statistics for precipitation and temperature separately. Autocorrelations were calculated at 188 lags between 1 and 12 years (i.e., environmental correlations were calculated between year X and to produce the relative fitness of each genotype. This relative fitness was then used as the relative 284 frequency of each genotype for the following year. For each year following the first, the absolute 285 fitness of each genotype was divided by a weighted mean of the fitness of all individuals for that year 286 ) to calculate the relative fitness of each genotype for each 287 generation. This value was then multiplied by the frequency of that genotype in that generation to 288 get the following generation's frequency. The final generation frequency was used for the 289 construction of fitness surface heatmaps. 290 291

Temperature model 292
The general framework of the temperature model is similar, but rather than allowing for the 293 persistence of transgenerational effects across multiple years, it considers early and late season 294 transgenerational effects, as well as within-generation plasticity. We ran the same model on raw data 295 and residuals, calculated as in the precipitation model. Annual plants were used as the motivation for 296 this model, with a growing season from March-September. The growing season was broken down 297 into three parts: early growing season (March, April, May), transitional growing season (June), and 298 late growing season (July, August, September). Within this model there are two bouts of selection, 299 one after the early growing season, and one after the late season. While early season phenotype can 300 only be modified by the previous year's temperature (because organisms are newly born in the spring 301 in this scenario, and therefore cannot respond themselves to temperatures), late growing season 302 phenotype can be modified by the previous year's temperature, and/or the temperature earlier in the 303 growing season. Additionally, this model allows for both early and late season phenotype to be 304 modified by both the previous season's early and late temperatures independently. In other words, 305 early season phenotype can be modified by the previous year's early season temperature, or the 306 previous year's late season temperature; late season phenotype can be modified by these same two 307 factors as well as the current year's early season temperature (i.e., by within-generation plasticity). 308 Thus, this model includes five plasticity parameters, reflecting the effect of 1) the previous of temperature data are not correlated, unlike precipitation data. For this reason, fitness is scaled by 315 a constant 20 rather than the mean temperature of a given site. Results were exceedingly similar 316 when fitness was scaled by constants of 10 and 100; 20 was chosen as it is closer to the mean annual 317 temperature across the US. 318 The geometric mean of genotype fitness was taken over the 119 years for each of the 326 genotypes. For each of the five plasticity (transgenerational and within generational) terms in this 327 model we considered possible values of -0.2 (negative plasticity), 0 (no plasticity), 0.1 (minor 328 plasticity), 0.3 (moderate plasticity), and 0.5 (major plasticity). While this resolution is somewhat 329 coarse, focusing on this subset of values allowed us to consider this model for the full factorial 330 combination of parameter space. In total, fitness was calculated for 3125 genotypes, across each of 331 119 years, at all 481631 locations, for a total of 179 billion measures of fitness. The values of 332 plasticity at which fitness was maximized were recorded from each grid point across the US. Finally, 333 for the same 12 focal sites used in the precipitation model, we calculated the changes in genotype 334 frequency across 119 years using the same methodology as above. All code for these simulations, 335 and other modeling results are available at (github.com/XXXX). 336 337

338
Both mean annual precipitation and growing season temperatures vary immensely across the 339 US (Figure 2 and S1). Mean annual temperature and precipitation are both primary forces driving 340 local adaptation to the diversity of climate regimes across the US, but for the evolution of locally 341 adaptive phenotypic plasticity, it is the patterns of variation that are more relevant. The standard varying from 40mm to 800m, spring temperature IASD from 0.77C to 1.95C, and summer 345 temperature IASD from 0.35C to 1.32C (Figure 2 and S1 and Table S1). The southwest US generally 346 had the highest precipitation IASD relative to its mean precipitation, with IASD being nearly equal 347 to the mean precipitation in some regions (Figure 2). Interestingly, spring temperature IASD was 348 significantly higher than summer temperature IASD across the US. This pattern was largely driven 349 by extremely high spring temperature IASD over the north central US (Figure 2), and consistently 350 low summer temperature IASDs across much of the coastal US. 351 Directional climate change over the past 120 years was prevalent and variable across the US 352 phenomenon has been noted numerous times (55,56) and seems to be largely due to a switch from 358 cropland to natural forest ecosystems across the southeastern US during the past 120 years that has 359 led to greater transpiration cooling. 360 Although a variable environment is necessary for the evolution of adaptive phenotypic 361 plasticity, it is the patterns of this variation that influence which forms of plasticity will be favored. 362 Patterns of climatic oscillation varied substantially across the US over the last 120 years, suggesting 363 the potential for climatically driven variation in locally adaptive plasticity (Figure 2 and S1, Table 1  364 and S1). We examined these patterns by calculating autocorrelations in annual temperature and 365 precipitation between successive years. The climate (temperature or precipitation) of a given year 366 and that of the prior year(s) were often significantly correlated across the US. However, the 367 magnitude and direction of correlations varied depending on the region and climatic parameter. 368 Averaged across all sites, the precipitation autocorrelation (AC) at lag-1 (i.e., the correlation 369 between the precipitation during one year and the next) was slightly positive (mean=0.04, Table 1, 370 Figure S1), and was reduced by half after taking linear changes in precipitation into account 371 (mean=0.02, Table 1, Figure S1). Spatially, we found that the southeastern gulf coast was the largest 372 region with negative lag-1 ACF (dry years tend to be followed by wet years), while the northeastern 373 US was the largest region of substantially positive lag-1 ACF (Figure 2). Somewhat surprisingly, 374 there was higher mean and standard deviation for lag-2 partial ACF than lag-1 ACF ( Figure S1).

13
ACF >0.2) and significantly negative (5,088 lag-2 PACF <-0.2 vs. 441 lag-1 ACF <-0.2) lag-2 partial 377 autocorrelation (PAC) than lag-1 ACF. These correlations suggest that climatic oscillations 378 impacting annual precipitation tend to operate over more than two years in these regions, and that 379 on a year to year basis, variation is more stochastic (leading to lower absolute lag-1 ACF). The 380 northeastern and northwestern US show substantially positive precipitation lag-2 PACF; in these 381 regions, multi-year climatic oscillations may dictate over 20% of the variation in inter-annual 382 precipitation variation (Figure 2). By contrast, across the southeastern US, negative lag-1 ACF and 383 lag-2 PACF suggest a negative feedback dynamic in which multiple dry years tend to be followed by 384 a wet year, and vice versa (Figure 2). 385 Patterns of temperature autocorrelations extended over larger regions, and were often 386 substantially more extreme, compared to the more complex patterns observed for precipitation 387 autocorrelations ( Figure 2). Lag-1 ACF for spring and summer temperatures varied a great deal, 388 with patterns of summer temperature autocorrelation substantially more positive than those of 389 spring (summer ACF-1 mean: 0.24, spring mean: -0.01, Figure S1). In both cases, however, the 390 western US tended to have more positive autocorrelations than the rest of the country (with the 391 exception of southern Florida; Figure 2). 392 Spring and summer temperatures displayed significant autocorrelations at lags 2 and 3. The 393 mean lag-2 PACF for spring temperature was negative (mean: -0.04, Figure 3) and more variable 394 than lag-1 ACF (sd=0.1 vs. 0.08), with much of the north-central US displaying lag-2 PACF of less 395 than -0.2 ( Figure 2). The mean lag-2 ACF for summer temperatures was positive (mean: 0.09), but 396 substantially lower than the mean lag-1 ACF (mean: 0.24). At a lag of 3, both spring-temperature 397 ACF (mean: 0.05) and summer-temperature ACF (mean: 0.11) were positive (Figure 3), suggesting 398 that long-term climatic trends play a role in temperature variation during the past 120 years. 399 400

Modeling Results 401
Optimal levels of transgenerational plasticity: precipitation 402 As expected, the vast variability of climatic autocorrelations lead to a great deal of variation 403 in the optimal levels of plasticity in the precipitation evolutionary model (Figure 3, Table S1). In the 404 raw variant of the model, optimal parental effect values were positive in 314,118 cases (65%), zero in 405 32,352 (7%), and negative in 135,161 (28%), compared to 55%, 7%, and 38% respectively in the 406 residual variant. The most common "parental effect" value ( ) in the precipitation model was 0.1 parental effect indicates that 90% of phenotypic variance is dictated by the long-term average 409 (genetic effects), and 10% by the difference between the parental environment and the long-term 410 average environment. The second most common optimal value of was 0.2 (19.15% in the raw 411 model, 18.6% in residual model), followed by -0.1 (14.3% in the raw model, 17.2% in the residual, 412 Figure 3a). A value of -0.1 means that 10% of phenotypic variation stems from transgenerational 413 plasticity and 90% from genetic variation, but that the precipitation experienced by parents will 414 influence the progeny in the opposite direction. For example, if the mean annual precipitation at a 415 site is 1000mm (dictating the genetic value), and the previous year's precipitation was 1100mm, then 416 the phenotype of the current generation would be 1010mm (1000*0.9 + (1,100-1000)*0.1) in the 417 case of an allele value of 0.1, and 990mm in the case of an value of -0.1 (assuming there are no 418 multigenerational environmental effects). Optimal values of ranged from -0.6 to 0.9, and were 419 approximately normally distributed, except a dearth of sites for which the optimal allele value was 0 420 due to the lack of multigenerational environmental effects in this situation. 421 The multigenerational persistence ( ) of transgenerational effects was also found to vary 422 greatly across the US with the two most common values being 1 (40.7% raw, 39.5% residual) and 0 423 Additionally, we found that the adaptive value of multigenerational persistence increases as the 435 strength of the transgenerational effect increases, such that little-to-no multigenerational persistence 436 is optimal when the transgenerational effect is close to zero, and strong multigenerational effects are Spatial variation for optimal precipitation plasticity values largely paralleled the spatial 439 distribution of inter-annual precipitation autocorrelation patterns (compare Figure (Table S1). 462 The most common optimal form of transgenerational plasticity to temperature in both the 463 raw and residual models was the effect of late growing season temperature on the next generation's 464 late growing season phenotype ( , Figure 3f, Table 2a). Effects of late season temperature on the 465 next generation's early season phenotype ( ) were the most variable, with a substantial number of 466 sites having negative transgenerational plasticity values (63,881 raw, 100,267 residual) and many 467 others having moderate (98,524 raw, 66,625 residual) and major (26,967 raw, 10,080 residual) on the next generation's early season phenotype ( ) were slightly more likely to be positive in the 470 raw version of the model (98,089 vs. 89,547), and more likely to be negative in the residual variant 471 (68,441 vs. 132,352). In both cases however, no plasticity was the most common optimal 472 strategy. Finally, the effect of early season temperature on the next generation's late season 473 (+/-0.21) higher in the raw relative to the residual models (although the most common change was 483 0). In the southwestern US, where temperature increased the most over the past 120 years ( Figure  484 2), the difference between the raw and residual model was the greatest (Figure 4g). 485 Variation in different classes of temperature autocorrelations between seasons explains a 486 large portion of the variation in the optimal transgenerational response to temperature at a given 487 site. For example, the autocorrelation between early season growing temperature and the next year's 488 late season growing temperature is the factor that explains the largest amount of variation in optimal 489 levels of (Table 3). We assessed potential tradeoffs between different forms of 490 transgenerational plasticity to temperature by first calculating the residuals of a particular plasticity 491 term after accounting for the effects of environmental autocorrelations, then testing the effect of the 492 other four plasticity terms on these residuals. There was a highly significant negative association 493 between and plasticity, and between and plasticity ( Figure S3a). As higher levels 494 of late-late transgenerational plasticity were favored, the optimal levels of EL plasticity also 495 decreased across all environmental autocorrelation values. These associations suggest that, for a 496 given life history stage in this model, there are tradeoffs between using transgenerational information 497 from the previous generation's early vs. late season temperature (Table S2). For example, there are 498 many sites where no plasticity, plasticity, and plasticity all have higher fitness than 499 individuals exhibiting both and plasticity ( Figure S3b). 500 501

Fitness Landscapes 502
In the previous analyses we used restricted parameter space to identify optimal site-specific 503 combinations of plasticity values across the entire contiguous U.S., but further insight can be gained 504 by comparing fitness landscapes across the full parameter space at individual sites. In the 505 precipitation model we found that, among sites where fitness optima are located near zero 506 transgenerational effects, a vertical fitness ridge formed that was centered near parental effect values 507 of zero. This result is due to transgenerational persistence levels (y-axis) having a minimal impact on 508 phenotype when parental effects are marginal. As absolute optimal parental effect values increased, 509 however, the fitness landscape shifted from a ridge to a peak, with certain values of 510 transgenerational persistence imparting extreme fitness advantages over others (Figure 5 Fitness landscapes for the temperature model are substantially more complex due to the 530 larger number of terms, but do suggest that patterns of environmental variation can favor tradeoffs 531 between multiple forms of plasticity. As the effect of parental early season temperature on offspring late season phenotypes ( ) increased, optimal values decreased ( Figure S4) and vice versa. 533 The same is true for and . At a given stage in the offspring's life cycle there is only so 534 much information value that can be gleaned from the environments of previous generations; this 535 total value ( + ) is one factor that varies across the US in this model. The optimal balance 536 between the two forms of transgenerational plasticity that affect a given life history stage ( : 537 ) is the other parameter that varies, and this balance is what controls the degree to which the 538 early vs. late season parental conditions will modify offspring development at a given stage. favor the genetic evolution of mechanisms that transmit plastic responses from one generation to 553 the next. Absent such correlations, the information provided by the parental environment may not 554 be relevant to offspring, and indeed may prove to be maladaptive (reviewed by 60). 555 Our modeling results revealed that the vast majority of sites in the contiguous US 556 experienced autocorrelations in precipitation and temperature that should favor the evolution of 557 adaptive transgenerational plasticity. As predicted by other models, the predictability of an 558 environmental variable based on its autocorrelation or its association with other environmental 559 variables is a major factor driving the optimal level of plasticity (e.g., 12,18,21,61). Furthermore, we 560 find that the strength and direction of autocorrelations in precipitation and temperature varied 561 substantially across the U.S., and consequently, the optimal levels of plasticity were also highly 562 variable. Although both precipitation and temperature interact to shape the moisture availability and including some values near zero. In turn, the optimal direction and strength of transgenerational 589 effects of precipitation also varied. Positive parental effects, wherein individuals are developmentally 590 predisposed to perform better in environments that match their parents' environment, were optimal 591 across more than twice as many regions (65% of sites) as negative transgenerational effects (28% of 592 sites), wherein individuals perform better in a different environment compared to that of their 593 parents. Relatively strong parental effect values of 0.3 or higher were optimal in nearly 30% of sites, Intriguingly, multigenerational persistence values of 0 (18.7% of sites) and 1 (40.7% of sites) 596 were the most common, representing strategies in which transgenerational effects lasted only a 597 single generation or persisted fully through to the third generation, respectively. The remaining 598 persistence values were somewhat evenly distributed between 0 and 1 and represent strategies in 599 which environmental information gets passed through three generations, but the environment of 600 more recent years is weighted more heavily. By contrast, complete absence of parental effects was 601 favored in only 7% of sites. 602 The optimal level of transgenerational effects varied on multiple scales. On the largest scale, 603 we found that the western and northern US experience conditions that select for the highest levels 604 of transgenerational plasticity (Figure 4a). There was a striking contrast between the northeast, 605 where positive transgenerational plasticity was generally optimal, and the southeast, where negative 606 transgenerational plasticity predominated. These large-scale differences in plasticity levels stemmed 607 from substantial differences in precipitation autocorrelations between these regions. There was also 608 considerable variation in optimal levels of transgenerational plasticity on much finer scales. In some 609 cases, optimal levels of transgenerational plasticity were highly divergent between adjacent sites (e.g., 610 in central Texas and Minnesota). Furthermore, some sites had bimodal fitness landscapes, in which 611 genotypes that express either positive or negative transgenerational effects were favored over 612 genotypes that do not express plasticity (Figure 5b). For example, after a wetter-than-average year 613 but two drier than average years prior to that, a genotype that prepares its offspring for another 614 wetter-than-average year (i.e., a positive transgenerational effect), or one that prepares its offspring 615 for a drier-than-average year (i.e., a negative transgenerational effect), will have higher fitness than a 616 genotype that does not express transgenerational plasticity. To our knowledge, this represents the 617 first demonstration that patterns of environmental variation can favor both positive and negative 618 transgenerational effects in the same site. Our modeling results suggest that genetic variation for 619 transgenerational precipitation effects may stem in part from fine-scale spatial variation in 620 precipitation autocorrelations. We predict that such variation in precipitation autocorrelations 621 translates into variable selection for transgenerationally plastic responses to precipitation, resulting in 622 the maintenance of genetic variation for transgenerational plasticity within species.  (12,49,66,67). In order for these responses to adaptively match phenotypes 636 with natural environments, there must be substantial correlations in temperature within and between 637 growing seasons. 638 We found significant autocorrelations in temperature, both within and between years. Within 639 a single growing season, temperatures early and late in the growing season tended to be positively 640 correlated across the U.S. Furthermore, we found that the temperatures of the late growing season 641 months (July, August, September) were generally strongly autocorrelated between successive years. 642 Interannual correlations between the temperatures of the early growing season months (February, 643 March, April) were often much lower. Surprisingly, early growing season temperatures were 644 generally more predictive of the following late seasons temperature than they were of the following 645 early seasons temperature. These results suggest that early spring temperatures may be a harbinger of 646 temperatures to come later in the same growing season and the latter half of the following growing 647 season but provide little information regarding the following year's early season temperature. 648 In our framework, temperature plays two roles related to fitness at both the early and late 649 growing season time points. First, temperature acts as a selective agent, by which fitness is reduced 650 according to the deviation between the actual temperature and a genotype's phenotypic temperature 651 optimum. Second, temperature is a source of information that a plant can use to alter its phenotype 652 later in the growing season, and to alter the phenotype of its offspring in the following year. As a 653 result, five classes of plasticity are available to plants in this model in order to best prepare 654 themselves and their progeny for the most likely temperature conditions in the future. These 655 plasticity classes include within-generation plasticity and four classes of transgenerational plasticity 656 representing all permutations of early and late season temperature effects across the parent and 657 offspring generations. 658 As expected, we find that, at a given site, the strength of the correlation between the average 659 temperature during the season in which information is gathered and the average temperature during 660 the season when selection occurs is highly predictive of both the type and degree of plasticity that 661 will be favored. For example, warmer than average springs were very often followed by hotter than 662 average summers, and this information yielded benefits via within-generation responses to 663 temperature in many sites. The optimal strategy in more than 99% of sites across the U.S. contained 664 some form of transgenerational plasticity, suggesting that environmental oscillations generally 665 provide valuable information that allows transgenerational plasticity to improve the match between 666 phenotypes and temperature regimes. Although we identified general patterns in temperature autocorrelations, a key finding was 685 that these autocorrelations varied considerably across the U.S., leading to vastly different optimal 686 levels of within-and transgenerational plasticity among sites. The west coast of the US and southern 687 Florida experienced the highest optimal transgenerational plasticity values. Because these regions are 688 due east of large bodies of water, their climates are heavily influenced by maritime airflow including heat capacity than either rock or soil, the location of these land masses downstream of maritime air 691 may predispose them to temperature autocorrelations between years. Additionally, we found highly 692 variable correlations between late growing season temperature and the following generation's early 693 growing season temperature. This result is intriguing because the temperature experienced during 694 seed maturation interacts with the post-dispersal temperature to strongly influence the dormancy 695 and germination behavior of seeds, with cascading effects throughout the life cycles of annual plants 696 (31,70). Consequently, site-specific correlations between maternal late-season temperature and the 697 early-season temperature in the next generation may select for divergent, site-specific effects of 698 maternal temperature on germination for species that set seed in late summer. Intriguingly, parental 699 effects of temperature on germination and flowering time are highly genetically variable in 700 Arabidopsis thaliana (12,70,71). In Plantago lanceolata, such genotype-by-maternal temperature effects 701 persist throughout the offspring life cycle to generate variation in offspring reproduction in the field 702 (72). Our results suggest that such genetic variation for maternal effects may derive in part from 703 variable selection imposed by differences among sites in intergenerational temperature correlations 704 (see also 12). 705 706

Common Themes and Future Directions 707
Although our precipitation and temperature models yielded distinct insights into the 708 dynamics of each of these factors, common themes emerged in both sets of analyses. For example, 709 we found higher levels of inter-annual autocorrelation, and therefore more prominent 710 transgenerational effects, at northern latitudes and along coastal regions within both models. Studies 711 that compare patterns of transgenerational plasticity across such large geographic regions will be 712 necessary to determine whether underlying differences in environmental patterns do in fact drive 713 differences in transgenerational plasticity. Another common finding of both the raw temperature 714 and precipitation models is that transgenerational effects are expected to provide greater benefits in 715 changing climates relative to purely oscillating climates, in which linear climate change has been 716 removed (i.e., the residual models). We also found that populations in regions undergoing the most 717 severe climate change are expected to benefit most by increasing transgenerational plasticity. 718 These results suggest that transgenerational effects may have an important role in adaptation 719 to human-induced climate change, and that rapid climate change should select for more could lead to genetic adaptation to changing conditions. The potential for transgenerational plasticity 723 to either promote or hinder genetic adaptation has been explored (73), but our models do not 724 address this issue. Instead, we set the baseline phenotype of an organism as the optimal phenotype 725 for the average conditions over the 120 years for which we have data, and then compared the fitness 726 of genotypes that vary in their expression of plasticity. In the absence of genetic evolution, it follows 727 that if there is a linear trend towards hotter or drier years in addition to climatic oscillations (as in the 728 raw model variants), then there is more transgenerational information relative to a situation in which 729 only climatic oscillations are occurring (residual model variants). Theory indicates that these 730 dynamics become much more complex when local genetic adaptation to changing conditions is 731 allowed to occur along with transgenerational plasticity (12). For instance, in some scenarios 732 transgenerational effects can increase fitness in the short term, while reducing it in the long term 733 (74). In future studies, it will be critical to investigate the influence of standing genetic variation for 734 transgenerational plasticity on evolutionary trajectories, and to examine the availability of novel 735 mutations that alter the dynamics of transgenerational effects. Answering both of these questions in 736 the same system will be necessary to determine the likelihood that selection on transgenerational 737 plasticity is a viable route to adaptation in the face of changing conditions. 738 Temperature and precipitation autocorrelations and optimal plasticity values likely stem in 739 part from the same broad-scale climatic oscillations, such as the El Niño Southern Oscillation (75), 740 the Quasi-biennial oscillation (76), and the Pacific Decadal Oscillation (77,78). Aside from these 741 climatic oscillations, autocorrelations will arise due simply to "red" or "pink" noise in which rare, 742 large events and common, small events have equal power in explaining variation (79). It has been 743 demonstrated that even without clear underlying phenomena explaining variation, pink-noise is 744 often the model that best explains patterns of ecological and abiotic time-series variation (80). These 745 oscillations and general patterns of red noise will interact with each other to varying degrees across 746 different regions of the US, leading to variable levels of autocorrelation at all lags for both 747 precipitation and temperature. 748 Furthermore, because temperature and precipitation interact to alter moisture availability, it 749 is likely that organisms do not process temperature and precipitation information independently, but 750 rather use them in tandem along with other sources of information to fine tune phenotypes for the 751 most likely future environment. For instance, temperature influences water availability by influencing 752 rates of evaporation and transpiration. Interactions between temperature and water availability also Understanding how these environmental factors jointly influence the expression of transgenerational 755 plasticity is an important goal for future research. Another critical goal of future research is to better 756 understand how within-and transgenerational plasticity interact to influence phenotypic expression. 757 A key element of this research direction is to study environmental (auto)correlations at fine scales in 758 the context of dispersal distances. It is possible that transgenerational plasticity may be a more In summary, we demonstrate that patterns of climatic variation in nature may favor the 767 adaptive evolution of transgenerational plasticity in organisms with approximately annual generation 768 times, such as annual plants. Our models indicate that differing patterns of climatic oscillations 769 across the US lead to strikingly different optimal patterns of within-and transgenerational plasticity. 770 Thus, for a given species, one may expect that environmental variation across its range not only 771 selects for different locally adapted mean trait values, but also different classes and magnitudes of 772 plasticity. Perhaps the most meaningful result of this study is that the climatic patterns across 773 relatively small geographic regions vary so dramatically that the optimal value of transgenerational 774 plasticity ranges from extremely high to non-existent. It should therefore be expected that although 775 many species, environmental variables, or phenotypes of interest may show no evidence of 776 transgenerational plasticity, such results may be due to their specific situation rather than a 777 fundamental biological limitation. This applies equally strongly to the other side of the coin: because 778 a single population or species expresses strong transgenerational plasticity does not mean that this 779 process is a key driver of evolutionary processes. Rather, variation in transgenerational plasticity 780 should be expected, just as genetic variation is ubiquitous in natural populations. Transgenerational 781 plasticity is best considered in the specific ecological and evolutionary context of the study organism, 782 and broad generalizations about the role of these effects in evolution should be avoided until 783 considerably more field data are in hand. The results described here provide a source of testable 784 predictions for geographical variation in this mode of adaptation.              Figure S4