Artigos sobre o paradoxo da estase morfológica, feito por evolucionistas, confirmando nossa tese , mas que tentam justificar o modelo convencional antigo desde Darwin 

Muito espaço para mudanças pontuais. Tendências Ecol. Evol. 29: 71-72. Vermeij, GJ e PD Roopnarine. 2013. Reining in the Red Queen: a dinâmica de adaptação e extinção foi reexaminada. Paleobiology 39: 560- 575. Voje, KL, AB Mazzarella, TF Hansen, K. Østbye, T. Klepaker, A. Bass, A. Herland, KM Bærum, F. Gregersen e LA Vøllestad. 2013.

Sobre o problema da estase na evolução organizmal. J. Theor. Biol. 101: 211-224. Walsh, B. e MW Blows. 2009

Tempo does not correlate with mode in the fossil record. (Enviado pelo próprio autor , quem precisar do PDF me contacte que envio +5531975352798 ) 
https://www.ncbi.nlm.nih.gov/pubmed/27748958

ORIGINAL ARTICLE doi:10.1111/evo.13090 Tempo does not correlate with mode in the fossil record Kjetil Lysne Voje1,2 1Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, Oslo, Norway 2E-mail: k.l.voje@ibv.uio.no Received February 8, 2016 Accepted September 22, 2016 The dominating view of evolution based on the fossil record is that established species remain more or less unaltered during their existence. Substantial evolution is on the other hand routinely reported for contemporary populations, and most quantitative traits show high potential for evolution. These contrasting observations on long- and short-time scales are often referred to as the paradox of stasis, which rests on the fundamental assumption that periods of morphological stasis in the fossil record represent minimal evolutionary change. Investigating 450 fossil time series, I demonstrate that the nonaccumulating morphological fluctuations during stasis travel similar distances in morphospace compared to lineages showing directional change. Hence, lineages showing stasis are commonly undergoing considerable amounts of evolution, but this evolution does not accumulate to produce large net evolutionary changes over time. Rates of evolutionary change across modes in the fossil record may be more homogenous than previously assumed and advocated, supporting the claim that substantial evolution is not exclusively or causally linked to the process of speciation. Instead of exemplifying minimal evolution, stasis likely represents information on the dynamics of the adaptive landscape on macroevolutionary time scales, including the persistence of adaptive zones and ecological niches over millions of years. KEY WORDS: Adaptive landscape, evolutionary rates, macroevolution, microevolution, punctuated equilibrium, stasis. We lack of consensus on rates of morphological change across different timescales in evolutionary biology (Gingerich 2009; Hunt 2012). Part of the legacy of the punctuated equilibrium theory (Eldredge and Gould 1972; Gould and Eldredge 1977; Gould 2002) is the realization that established species typically show minimal net evolution over time in the fossil record. Also differences between species in the fossil record have been found to be less than what is expected due to genetic drift alone (e.g., Lande 1976; Lynch 1990; Cheetham et al. 1993). The dominance of slow evolution in the fossil record does not follow directly from what we known from microevolutionary studies: quantitative traits typically harbor substantial genetic variation (Houle 1992, 1998; Hansen et al. 2011), strong selection is commonplace (Hereford et al. 2004), and considerable amounts of evolution is frequently observed on time intervals from years to a few decades (Hendry and Kinnison 1999; Kinnison and Hendry 2001; Hendry et al. 2008, but see Merila et al. 2001). The contrasting observations of evolution- ¨ ary change across long- and short-time scales are known as the “paradox of stasis” (Wake et al. 1983; Hansen and Houle 2004; Futuyma 2010), and makes the long-term history of life seem almost decoupled from the evolutionary process we study on shorter time scales. The claim that directional change was rarely observed in the fossil record and that stasis was the dominating mode in evolutionary lineages (Eldredge and Gould 1972; Gould and Eldredge 1977; Cheetham 1987; Jackson and Cheetham 1999) sparked an intense debate among evolutionary biologists (Gould 1980; Charlesworth et al. 1982), that is still ongoing (e.g., Lieberman and Eldredge 2014; Pennell et al. 2014a,b; Venditti and Pagel 2014). One part of the debate focused on disentangling the relative frequency of different modes in the fossil record, a highly subjective exercise for several decades due to a lack of statistical tools for comparing competing interpretations. In the last decade, building on earlier quantitative approaches (Bookstein 1987; Roopnarine 2001; Sheets and Mitchell 2001), Hunt developed analytical models that allowed fossil time series to be categorized into different modes based on statistical fit (Hunt 2006, 2008). Analyses of several hundred fossil time series using these 1 C 2016 The Author(s). Evolution K. L. VOJE analytical tools have shown that stasis is much more common than directional change in the fossil record (Hunt 2007; Hopkins and Lidgard 2012; Hunt et al. 2015). Thus, given that stasis is interpreted as representing low levels of evolution, a fundamental assumption underlying the paradox of stasis, minimal rates of evolution dominates on long-time scales. However, it has been pointed out that even though traits show almost no net evolution over time, traits sometimes show substantial fluctuations during stasis (e.g., Jablonski 2000; Eldredge et al. 2005; Hunt 2007). To what extent trait fluctuations during periods of stasis in the fossil record generally represent negligible or substantial evolution remains to be rigorously tested. The statistical model that has become standard in characterizing stasis in fossil time series allows for fluctuations in morphology, while predicting no net evolutionary change over time (Hunt 2006, 2007; Hunt and Rabosky 2014). The model therefore portrays stasis well according to how this mode of evolution is generally understood and defined (e.g., Eldredge et al. 2005), with one potential exception: the model puts no constraints on the magnitude of the trait fluctuations (Hunt and Rabosky 2014). Hence, traits that fit this statistical interpretation of stasis may accordingly evolve at any rate as long as the net evolutionary change over time is small. In other words, trait fluctuations during stasis might be due to everything from sampling error of a fixed phenotype (Hunt 2006; Hannisdal 2006) to evolution of a population that is tracking a nonstationary optimum showing bounded movements on the adaptive landscape (Estes and Arnold 2007; Uyeda et al. 2011; Hunt and Rabosky 2014). While it is well-known that mode predicts amounts of net evolutionary change over time, less is known whether mode also predicts the distance traveled in morphospace. In this study, I analyze 450 fossil time series of trait change to investigate whether tempo and mode are correlated in the fossil record. I first categorize the time series into the three canonical evolutionary modes stasis, directional change, and random walk based on statistical fit. I then test whether traits fitting these modes predict differences in net evolution and average distance traveled in morphospace (Fig. 1). I also present a more detailed investigation of the correlation between tempo and mode in two stickleback traits that evolve toward a new phenotypic optimum according to an Ornstein-Uhlenbeck process. These two traits show directional change as the population ascends the adaptive peak, and fluctuating evolution when the population has reached the optimum (i.e., stasis). Materials and Methods DATA Fossil time series of phenotypic trait change were found by searching the literature. References and data reported in Hunt (2007) and 0 5 10 15 20 0 5 10 15 20 25 Time Trait size 0 5 10 15 20 −5 0 5 10 15 20 Time Accumulated trait change A • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • B • Figure 1. Measures of net evolution and distance traveled in morphospace. Panel A shows two simulated traits fitting the modes directional change (red, crosses) and stasis (black, filled circles). The error bars represent the standard error of the mean trait value for each sample mean. The stasis trait fluctuates around a fixed mean (horizontal line), showing minimal net evolution compared to the trait moving directionally in morphospace. Panel B shows the accumulated distance traveled in morphospace for the two traits in panel A, corrected for sampling (estimation) error in sample means as described in the Methods section. The accumulated distance traveled in morphospace shows how much the trait changes over time, irrespective of the direction of the change (i.e., whether the trait gets larger or smaller). Hopkins and Lidgard (2012) and Hunt et al. (2015) were especially helpful. To enable meaningful comparisons of evolution across different time series, traits had to be either reported on a log-scale or be on a scale where log-transformation is a reasonable scale transformation. For this reason, traits like principal component axes and discriminant functions were not included as part of 2 EVOLUTION 2016 TEMPO AND MODE IN EVOLUTION the data material. Log-transformation makes traits dimensionless, but not dimension-independent, so each sample mean in each time series was divided by the dimensionality of the measurement of the trait (area has a dimension of 2, volume has a dimension of 3 and so on). Likewise, the variances of the trait means in each time series were divided by the square of the dimensionality of the trait. A total of 450 fossil time series were collected. The duration of each time series in millions of years was recorded if that information was available. Traits were categorized into “size” (length or area of parts of the organism), “shape” (ratios of length or area of parts of organisms) or “meristic” to test if these different types of traits have a tendency to evolve according to specific modes. Uncertainty in timing of stratigraphic layers was often not available and accordingly not corrected for. MODES AND RATES OF EVOLUTION Statistical models portraying the evolutionary modes directional change, random walk, and stasis were fit to time series by maximum likelihood using the joint parameterization option in the fit3models function in the paleoTS package (Hunt 2006), using R version 3.1.3. (R Core Team 2016). In these models, time occurs in discrete intervals. For each of the three models, the expected difference between sample means in a time series is represented by a normal distribution, with mean (μ) and variance (σ2). In the random walk model, the mean of the distribution is zero, which means the expected difference between the ancestor and descendant is normally distributed with a zero mean and with a variance equal of tσ2, where t is the number of time steps separating the ancestor and descendent. In the directional change model, the mean of the normal distribution is different from zero (μ 0) and represents the directionality in the evolution of the trait over time, while the σ2 represents the evolutionary fluctuations around the directional trend. In the stasis model, a trait fluctuates around an “optimal”/fixed phenotype. The expected-descendant trait value is normally distributed with a mean equal to this “optimal” trait value (independent of the ancestral value), and with a variance equal to the fluctuations around the optimal phenotype. See Hunt (2006) for a detailed description of the models. The relative fit of each of the three models to each time series was assessed using the bias-corrected Akaike Information Criterion (AICc). I also analyzed a subset of fossil sequences that showed a relatively strong fit to one particular mode of evolution (Akaike weight 0.75) to investigate if the analysis of the total dataset were affected by time series that fitted more than one mode reasonably well. There are numerous ways of estimating rates of evolution (e.g., Haldane 1949; Gingerich 1993), all with their strengths and weaknesses (see Hunt 2012 for a review). For example, estimating evolutionary rates as model parameters is a sound approach when the data fit the assumed model of evolution well (Hunt 2012). Estimating evolutionary rates as model parameters is indeed commonly done in comparative studies (e.g., Adams 2013;Slater 2013, 2015; Voje and Hansen 2013). However, alternative metrics may be preferred when the true nature of evolutionary change deviates from the underlying model (discussed in Hunt 2012), or when there are not enough data to differentiate which model that fits the data best (i.e., when a fossil sequence shows a similar fit to more than one model, see results). In this study, two different measures of evolutionary change were estimated for each fossil time series (Fig. 1): (i) Net evolution was estimated by taking the absolute value of the difference between the first and last sample mean in the sequence. (ii) The average distance traveled in morphospace was calculated by adding all absolute differences between consecutive sample means in a time series, and dividing this total distance by the number of observed samples in the time series minus one. While the net evolutionary rate is a measure of the difference in morphology that has evolved over the interval of the time series, the average distance traveled in morphospace is a measure of how much a trait has changed during the time series, irrespective of whether the changes accumulates over time. Average evolutionary rates in darwins (Haldane 1949) and haldanes (Gingerich 1993) were also estimated when a time series contained time-calibrated stratigraphic layers. One-way ANOVAs were conducted to test for a relationship between mode and the different measures of evolution. Some of the data might be vulnerable to autocorrelations as some traits have been measured on the same evolutionary lineage, and because some studies report data on more than one taxon. I therefore fitted linear-mixed effect models using the lme4 package (Bates et al. 2015) where taxa and study were included as random factors to investigate if these variables had any effect on the estimated relationship between mode and the two metrics for evolutionary change. I used least-squares regression to test for a relationship between the time intervals covered by time series and the average distance traveled in morphospace, both within and across modes of evolution. DETAILED ANALYSIS OF STICKLEBACK DATASETS Two fossil stickleback time series have been shown to fit an Ornstein–Uhlenbeck (OU) model on an proportional scale (Hunt et al. 2008). An OU model portrays evolution toward a new phenotypic optimum, meaning the trait shows directional change in the beginning of the time series as the population ascends the adaptive peak, and fluctuating evolution around the optimal value (i.e., stasis) when the trait has reached the optimum. Sample means in both time series come from 250-year intervals, hence the time available to evolve is equal between consecutive sample means. To evaluate if evolution increase or decrease as the traits approaches their optimum, I fitted a power function using the nls function in R to the accumulated distance traveled in morphospace per elapsed sample. A slope of 1 would indicate a constant rate of evolution, while EVOLUTION 2016 3 K. L. VOJE slopes larger and smaller than 1 would indicate accelerating and decelerating rates of evolution per elapsed sample, respectively. CORRECTING FOR ESTIMATION ERROR The accuracy of sample means decrease with lower sample sizes. Such error in estimating sample means can be analytically equivalent to stasis (Hannisdal 2006; Hunt 2006); a lineage with a fixed trait mean over time will show fluctuations around this true (fixed) mean due to sampling (estimation) error in trait means in the time series. Sampling error in trait means will accordingly create an upward bias in the estimated distance traveled in morphospace, not only for lineages fitting stasis, but independent of mode of evolution. Sampling error was controlled for in each fossil time series using a bootstrap approach: 10,000 pseudoreplicated time series were created for each fossil time series. Each individual sample mean in a pseudoreplicated time series was estimated using the sample size (N) and the sample variance of the observed sample mean in the true (observed) time series. For each pseudoreplicated time series, the distance traveled in morphospace between consecutive sample means was subtracted from the equivalent distance traveled in morphospace in the observed fossil time series, creating 10,000 time series where evolution due to sampling (estimation) error had been subtracted. The average (± standard error) distance traveled between sample means in these 10,000 time series represent the distance traveled controlled for sampling error for a particular time series. Evolution in pseudoreplicated time series can show larger amounts of change between consecutive sample means if the sample means in the observed time series are very similar to each other, or have large sample variances. Such cases result in average negative evolution between sample means after correcting for sampling error and were set to zero. An R function calculating the measures of evolution used in this study, including an option of correcting for sampling error as described above, is included in the supplementary material. Results FREQUENCIES OF EVOLUTIONARY MODES The relative frequency of fossil time series that fitted the models of stasis, random walk, and directional change overlaps with what previous studies have found (Hopkins and Lidgard 2012; Hunt et al. 2015), a result that was not given as this study is the first large-scale study of traits analyzed on a logarithmic scale (Table 1): 118 (28.5%) fitted the stasis model, 53 (12.8%) fitted the directional change model and 243 (58.7%) fitted the random walk model based on their AICc score. Thirty-six time series had an identical AICc weight to the precision of three decimals for the stasis and random walk model. All-time series traveling a zero distance in morphospace after accounting for estimation error (eight in total) were among these 36 time series. It can be argued that time series traveling only very small or zero distances in morphospace fit the concept of morphological stasis, even though these time series did not fit the stasis model better than the random walk model. I therefore analyzed a dataset where I excluded the 36 time series and another one where I classified all the 36 indeterminate time series as stasis. Of the 414 time series that fitted a particular model best, 254 were size traits, 97 were shape traits and 63 were meristic traits. There was no tendency for different types of traits to be unevenly distributed among the three modes (Table 2). The dataset consisting of fossil sequences that showed a relatively strong fit to one particular model of evolution (Akaike weight 0.75) contained 177 sequences, which means more than 60% of the 450 time series showed a similar fit to at least two models. Lack of strong fit to one of the models was not related to the length of the time series; the mean and median length of all 450 time series were 19.4 and 14.5, while the corresponding numbers for the 177 time series showing a relatively strong fit to one particular model were 18.2 and 14.0. In the reduced data set, 74 time series fitted stasis (41.8%), 78 time series fitted the random walk (44.1%) and 25 time series fitted directional change (14.1%). Detailed results for all-time series analyzed are reported in Table S1. EVOLUTIONARY MODE AND NET EVOLUTION Traits fitting the directional change model showed much larger net evolution compared to traits fitting the stasis and random walk models (Table 1, Fig. 2A); one-way ANOVA: directional = 0.375 (±0.040 SE); random walk = 0.282 (±0.044 SE); stasis = 0.140 (±0.048 SE), P = 5.79 × 10−7, R2 = 0.07. The dataset where the 36 indeterminate time series were classified as stasis gave qualitatively identical results (Table 1), as did the linearmixed effect model that included taxa and study as random effects to control for possible autocorrelation in the data (Table S2). The reduced dataset containing time series that fitted one model particularly well also showed qualitatively very similar results (Table 1, Fig. 3A); one-way ANOVA: directional = 0.400 (± 0.050 SE); random walk = 0.266 (±0.058 SE); stasis = 0.166 (±0.058 SE), P = 2.87 × 10−3, R2 = 0.08. EVOLUTIONARY MODE AND DISTANCE TRAVELED IN MORPHOSPACE Traits that best fitted the stasis or the random walk model traveled on average larger distances in morphospace compared to traits fitting the model for directional change (Table 1, one-way ANOVA: P = 0.04, R2 = 0.01), an effect that was also present when controlling for study and taxa (Table S2). However, mode was not found to significantly predict average distances traveled in morphospace when analyzing the data set where the 36 4 EVOLUTION 2016 TEMPO AND MODE IN EVOLUTION Tab le 1 . Evolutionary mode and morphological change in fossil time series. Mode N (%) Net evolution (SE) Average distance traveled (SE) Time series that fit a particular model best (N = 414) Stasis 118 (28.5) 0.140 (±0.048) 0.056 (±0.009) Random walk 243 (58.7) 0.282 (±0.044) 0.050 (±0.008) Directional change 53 (12.8) 0.375 (±0.040) 0.033 (±0.008) P = 5.79 × 10−7, R2 = 0.07. P = 0.04, R2 = 0.01 Full dataset (indeterminate mode set as stasis (N = 450) Stasis 155 (34.2) 0.120 (±0.045) 0.045 (±0.009) Random walk 243 (54.0) 0.282 (±0.043) 0.050 (±0.008) Directional change 53 (11.8) 0.375 (±0.039) 0.034 (±0.009) P = 3.11 × 10−10, R2 = 0.09. P = 0.13, R2 = 0.01. Reduced dataset (AICc weight 0.75 for one of the models, N = 177) Stasis 74 (41.8) 0.166 (±0.058) 0.070 (±0.015) Random walk 78 (44.1) 0.266 (±0.058) 0.070 (±0.015) Directional change 25 (14.1) 0.400 (±0.050) 0.043 (±0.013) P = 2.87 × 10−3, R2 = 0.08 P = 0.16, R2 = 0.01 One-way ANOVAs testing whether mode predicts differences in net evolution and average distance traveled in morphospace in three different datasets. Net evolution and average distance traveled are reported in log units. N = number of time series, SE = standard error. R2 = coefficient of determination. Tab le 2 . Relationship between mode and trait type. Trait type N = 450 AICc weight 0.75 for stasis AICc weight 0.75 for directional AICc weight 0.75 for random walk Size 281 (62.4%) 45 (60.8%) 17 (68.0%) 51 (65.4%) Shape 97 (23.3%) 17 (23.0%) 4 (16.0%) 13 (16.7%) Meristic 64 (14.2%) 12 (16.2%) 4 (16.0%) 14 (17.9%) First column lists trait categories and second column shows how many fossil time series that group within the different trait categories in the full dataset. Third to fifth column list the number of time series in each trait category that have an AICc weight 0.75 for a particular model of evolution. indeterminate time series had been classified as stasis (Table 1, one-way ANOVA: P = 0.13, R2 = 0.01) or in the analysis of the reduced dataset (Table 1, one-way ANOVA: P = 0.16, R2 = 0.01). Also, darwins and haldanes did not differ across modes (Table S2). All tests returned very low R2 values (Table 1), which indicate large variation in the average distances traveled in morphospace for fossil sequences classified as following the same mode. No relationship between average distances traveled in morphospace and the duration of time series was detected, neither across nor within evolutionary modes; Least-square regression of average distance traveled in morphospace as a function of duration of time series in millions of years for sequences fitting stasis: slope = 0.000 (±0.002 SE, P-value = 0.92, adjusted R2 = 0.00, N = 90, Fig. S1A), directional change; slope = 0.002 (±0.002 SE, P-value = 0.41, adjusted R2 = 0.00, N = 43, Fig. S1B), random walk; slope = –0.001 (±0.001 SE, P-value = 0.31, adjusted R2 = 0.00, N = 195, Fig. S1C), and across modes; slope = –0.001 (±0.001 SE, P-value = 0.33, adjusted R2 = 0.00, N = 328, Fig. S1D). Interval length (in million years) differs on average among modes: One-way ANOVA: directional = 4.88 (±0.62 SE); random walk = 3.44 (±0.68 SE); stasis = 2.96 (±0.75 SE), P = 0.04, but mode is a weak predictor of interval length (R2 = 0.01). The median percent trait change that is not realized as net phenotypic change for traits showing directional change in the total dataset was 43.7% (mean = 49.7%, SD = 25.3%), while it was 83.7% (mean = 77.8%, SD = 19.4%) for traits evolving according to the stasis model and 64.0% (mean = 60.9%, SD = 25.6%) for traits fitting the random walk model, respectively. Figure 4 shows three datasets that exemplify the variation in distances traveled in morphospace among traits fitting different modes; The Stricklandia dataset: five fossil time series of shape EVOLUTION 2016 5 K. L. VOJE 0.1 0.2 0.3 0.4 0.5 Net trait change Directional Random w. Stasis A B N = 53 N = 243 N = 118 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Average trait change Directional Random w. Stasis N = 53 N = 243 N = 118 • • • • • • Figure 2. Mode as predictor of net evolution and average distance traveled in morphospace (N = 414). (A) Large differences in net evolution (absolute difference of first and last sample mean in time series) for traits fitting different evolutionary modes. (B) Small (albeit statistically significant) differences in average distances traveled in morphospace across evolutionary modes (Table 1). Bars indicate 95% confidence intervals.0.0 0.1 0.2 0.3 0.4 0.5 0.6 Net trait change Directional Random w. Stasis A B N = 25 N = 78 N = 74 0.00 0.02 0.04 0.06 0.08 Average trait change Directional Random w. Stasis N = 25 N = 78 N = 74 • • • • • • Figure 3. Mode as predictor of net evolution and average distance traveled in morphospace (reduced dataset N = 177). (A) Mode predicts differences in net evolution for traits fitting one mode particularly well (Akaike weight 0.75), but (B) predicts no difference in average distance traveled in morphospace (Table 1). Bars indicate 95% confidence intervals. traits from the brachiopod lineage Stricklandia lens–laevi (Baarli 1986); The Cantius dataset: three fossil time series of primate tooth evolution in the chronospecies Cantius torresi–ralstone– mckennai–triginodus–abditus (Clyde and Gingerich 1994); The Striatojaponocapsa dataset: nine fossil time series from the radiolarian Striatojaponocapsa plicarium–synconexa (Hatakeda et al. 2007). The time series within each of the datasets in Figure 4 are of exact same length and the sample means have been estimated from the same stratigraphic layers, hence the time available to evolve has been the same among time series within each dataset. The fit of the three different modes to time series within each dataset usually differs by several AICc units (Table S3). Changes in traits fitting stasis and directional change show weak to moderate correlations within each dataset (Table S4). STICKLEBACK TIME SERIES In the two stickleback time series fitting an Ornstein–Uhlenbeck model (Table S5), both changes in number of dorsal spines and in the number of pterygiophores showed an overall faster evolution as the population ascends the adaptive peak compared to the phase when the traits have reached the optimum and fluctuates around the optimal value (i.e., stasis): The slope of the fitted power function to the curve showing accumulated evolution was b = 0.660 (±0.037 SE) for dorsal spines and b = 0.758 (±0.031 6 EVOLUTION 2016 TEMPO AND MODE IN EVOLUTION 0 50 100 150 200 250 0.0 0.5 1.0 1.5 Stratigraphic level (m) − Base of Silurian Accumulated (log) change in trait 5 1 2 3 4 0 200 400 600 800 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Thickness of strata (m) − Early Eocene (1.34Ma) Accumulated (log) change in trait 1 2 3 0 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Thickness of strata (m) − Middle to Late Jurassic Accumulated (log) change in trait 5 6 7 8 9 1 2 3 4 A B C Figure 4. Tempo and mode in time series sampled from identical stratigraphic sequences. Accumulated distance traveled in morphospace for (A) five fossil time series of shape traits from the brachiopod Stricklandia lens–laevi (Baarli 1986), (B) three fossil time series of primate tooth evolution in the chronospecies Cantius torresi–ralstone–mckennai–triginodus–abditus (Clyde and Gingerich 1994), and (C) nine fossil time series from the radiolarian Striatojaponocapsa plicarium–synconexa (Hatakeda et al. 2007). Color indicates evolutionary mode: Red (crosses) = directional change, black (filled circles) = stasis, gray (open circles) = random walk. Error bars represent the standard errors of each accumulated change (see Methods). Numbers refer to the traits in Table S3. SE) for pteryigophores. However, both the directional phase and the stasis phase contain time periods where both traits undergo close to zero evolution (strict stasis). Discussion A tight link between tempo and mode in evolution has long been assumed and advocated (Simpson 1944; Eldredge and Gould 1972; Jackson and Cheetham 1999) and is a central backdrop of long-lasting debates in biology (Gould 1980; Gingerich 1984; Venditti and Pagel 2014; Pennell et al. 2014a). The analyses in this article confirm that mode predicts differences in net evolution over time, but also show that mode is a poor predictor of the amount of evolution that occurs in a lineage. On average, traits changing in a directional manner in morphospace do not evolve more compared to traits fitting the models of stasis and a random walk. If anything, lineages fitting the stasis and random walk models tend to move slightly larger distances in morphospace compared to lineages showing a directional trend, but the predictive power of mode on average distance traveled in morphospace is almost nonexistent. This seems to be true independent of whether the trait is related to the size or shape of the evolving lineage. The main difference between lineages evolving according to the modes stasis, directional change, and random walk in the fossil record is accordingly the amount of evolution that accumulates to produce net evolutionary change. Hence, assuming minimal evolution in a lineage showing stasis in the fossil record will often be incorrect. That periods of phenotypic stasis in fossil lineages represent minimal rates of evolution is a core assumption of the paradox of stasis (Wake et al. 1983; Hansen and Houle 2004; Futuyma 2010). The paradox comes from observations of large potential for evolution and frequent observations of substantial evolutionary change on microevolutionary time scales, while phenotypic changes in the fossil record are found to be generally small. That trait fluctuations during stasis often represent substantial evolution makes the paradox seems less paradoxical, but only alters what needs to be explained: Why do lineages so often show bounded evolution instead of accumulating phenotypic change over time? Suggested causes of stasis, like stabilizing selection (Charlesworth et al. 1982; Haller and Hendry 2014), homogenizing gene flow (Futuyma 1987; Williams 1992; Lieberman et al. 1995), and variational constraints (Hansen and Houle 2004; Blows and Hoffmann 2005; Walsh and Blows 2009; Hine et al. 2014) are known to constrain evolution, some of them limiting evolution to particular directions in morphospace (e.g., Schluter 1996; Voje et al. 2013, 2014). These constraining factors are probably important explanations of stasis in some long-term studies of contemporary populations (Merila et al. 2001; Kruuk et al. 2002), but their ¨ relevance on million-year time scales is less known. Macroevolutionary changes must be associated with changes in the adaptive EVOLUTION 2016 7 K. L. VOJE landscape itself (Simpson 1944; Arnold et al. 2001; Hansen 2012), but while we have rigorous models and theory for microevolutionary change (e.g., Lynch and Walsh 1998), models for long-term dynamics of the adaptive landscape are less developed. Assuming populations have the ability to track optima on the adaptive landscape with an insignificant time-lag on million-year time scales, the different modes in the fossil record can be interpreted as general patterns of how the adaptive landscape itself changes over time (Hunt 2007; Hunt and Rabosky 2014). The results presented here suggest that optima showing bounded fluctuations (stasis) move as much as optima that move randomly (random walk) or unidirectionally (directional change) on the adaptive landscape. In other words, given the resolution of the analyzed fossil time series, it is not the pace (tempo) but the manner (mode) these optima move on the adaptive landscape that causes the differences in observed net evolution across lineages in the fossil record. Of all the fossil time series analyzed, 88% fitted the random walk or stasis model best, which both show little net evolution compared to traits showing directional change. That most traits show little net evolution but still undergo substantial change is consistent with the hypothesis that lineages mostly evolve within rather narrow adaptive zones, as envisioned by Simpson (1944, 1953) and as observed by Uyeda and colleges in the blunderbusspattern of body size evolution (Uyeda et al. 2011). Rapid and substantial phenotypic changes are well documented on macroevolutionary time scales (Hunt 2008; Uyeda et al. 2011), and may represent shifts in optima across adaptive zones (Arnold 2014), sensu Simpson’s concept of quantum evolution (Simpson 1944; 1953). However, such large shifts seem much rarer compared to fluctuating or random wanderings of optima on the adaptive landscape on a million-year time scale (Uyeda et al. 2011). According to the theory of punctuated equilibrium, species are assumed to remain more or less unaltered during their existence, with evolutionary change mainly happening during relatively rapid speciation events where phenotypes change directionally in morphospace (Eldredge and Gould 1972; Gould and Eldredge 1977). Periods of directional change in the fossil record are therefore predicted to happen during shorter time intervals compared to times of stasis, but the opposite pattern is found for the lineages analyzed in this study. However, the time series analyzed here do not represent line-splitting events, but are rather examples of anagenesis. It can therefore be argued that the analyzed fossil time series are not expected to follow the pattern predicted from the theory of punctuated equilibrium. Whether it is due to anagenesis or a line-splitting event, speciation is necessarily associated with some sort of directional phenotypic divergence, but whether speciation causally drives phenotypic diversification is debated (e.g., Rabosky 2012; Pennell et al. 2014a,b; Venditti and Pagel 2014). From a population genetic perspective, processes not necessarily connected to speciation can cause rates of evolution to vary, like fluctuating changes in the strength and direction of selection (e.g., Siepielski et al. 2009). This study shows that similar average amounts of evolution happen independent of whether lineages move directionally, or show bounded or random movements on the adaptive landscape on thousand to million-year time scales. Substantial evolution independent of speciation therefore seems to be common in the fossil record, as exemplified by the stickleback time series (Fig. 5) showing rapid anagenetic divergence toward a new adaptive peak. The observed fluctuations in morphology during stasis can also be of a magnitude that can explain phenotypic divergence between species. For example, two traits (height and number of whorls) in a fossil lineage of the gastropod Bellamya in lake Malawi (Van Bocxlaer and Hunt 2013) show a strong fit to the stasis model (Akaike weigths 0.99, Table S1). The phenotypic distances traveled by the two traits during the 5280 years the fossil lineage has been sampled are among the top 10 largest distances traveled in the whole dataset (average distance between 21 sample means; height = 0.30 log units, number of whorls = 0.45 log units, Table S1). Four extant Bellamya species found in lake Malawi are assumed to be descendants of the fossil lineage (Van Bocxlaer and Hunt 2013). Given a literal reading of the fossil record constraining all four extant species to have diverged from the fossil lineage during the last 5500 years, and assuming an equal ability to evolve during the radiation as observed in the fossil time series, seven out of eight trait states in the four extant taxa are easily reachable from the fossil trait states within the 5500 years that separates the fossil lineage and the extant taxa: All four extant taxa are less than 4.5 log units different in number of whorls compared to the mean in the fossil lineage, while three out of four extant taxa are less than 2.0 log units different in height compared to the mean in the fossil lineage (see Fig. 2 in Van Bocxlaer and Hunt 2013). Speciation seems unlikely to be a necessary driver of high rates of evolutionary change. Drivers of macroevolutionary patterns are a frequent debate within paleobiology (e.g., Jablonski 2008; Benton 2009; Voje et al. 2015) and stasis has been argued to be incompatible with continuous evolution due to biotic interactions on longer time scales (Stenseth and Maynard-Smith 1984; Vermeij and Roopnarine 2013), a central idea in the Red Queen hypothesis (Van Valen 1973; Liow et al. 2011). The Red Queen hypothesis proposes evolution does not depend on changes in the abiotic environment as biotic interactions will constantly change the selection pressures operating on other species and thereby keep evolution going (Van Valen 1973). The hypothesis that biotic interactions often will lead to evolution is not supported if stasis equals almost no change, but may still hold if stasis represent substantial lineage evolution, as indicated by this study. Furthermore, that lineages rarely show signs of not undergoing evolution, and that random walk is the most common mode in the fossil record, lend some 8 EVOLUTION 2016 TEMPO AND MODE IN EVOLUTION 0 5000 10000 15000 0.6 0.8 1.0 1.2 1.4 Time (years) Log trait mean A 0 5000 10000 15000 0.0 0.2 0.4 0.6 0.8 Time (years) Accumulated (log) change in trait C 0 5000 10000 15000 0.6 0.8 1.0 1.2 1.4 Time (years) Log trait mean B 0 5000 10000 15000 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time (years) Accumulated (log) change in trait D Figure 5. Tempo and mode when ascending an adaptive peak. The evolutionary trajectory toward a new optimal phenotype in (A) log number of dorsal spines and (B) log number of touching pteryigophores in a stickleback population over 14,750 years. The lines represent the expected trait trajectory according to the Ornstein–Uhlenbeck model that best fitted the data (Hunt et al. 2008, Table S5). Gray area represents 95% probability envelope. Plot C and D show the accumulated log trait change across time for number of dorsal spines (C) and pteryigophores (D), respectively. The slope parameter (b) of the power function (y = axb) is b = 0.660 (±0.037 SE) for dorsal spines and b = 0.758 (±0.031 SE) for the pteryigophores, indicating an overall faster evolution during the ascent of the adaptive peak (directional change) in both traits. Note, however, that both traits show periods of almost no change (strict stasis) during the ascent of the adaptive peak. plausibility to the Brownian motion model of trait evolution, an essential component in most phylogenetic comparative methods (e.g., Felsenstein 1985; Hansen et al. 2008; Harmon et al. 2010; Adams 2013). The results of this study should not be read as a critique of the model framework developed by Hunt (2006, 2008). Hunt’s statistical models were developed to distinguish different modes of evolution in the fossil record, and have indeed been useful in documenting the rarity of directional trends in fossil time series (Hunt 2007; Hopkins and Lidgard 2012; Hunt et al. 2015). The current study does not challenge this result, but finds evidence that evolutionary modes are poor predictors of the distances traveled in morphospace by lineages in the fossil record. A seemingly contradictory result was reported by Hunt and Rabosky (2014), who found that traits having an Akaike weight larger than 0.8 for the stasis model showed substantially less evolutionary change compared to traits that showed a poor fit to the stasis model (Akaike weigth < 0.2). Their analysis was based on 182 time series that partly overlap with the data analyzed in the current study (Gene Hunt, pers. comm.), and their measure of evolutionary change was the estimated omega parameter in the stasis model from Hunt (2006). However, there is no contradiction between the result presented in the current study and the result reported in Hunt and Rabosky (2014), as the distance traveled in morphospace is EVOLUTION 2016 9 K. L. VOJE 5 10 15 20 0 5 10 15 20 Time Trait mean Stasis Net evolution = 1 Average distance = 1 Omega squared = 0.50 5 10 15 20 0 5 10 15 20 Time Trait mean Directional trend Net evolution = 19 Average distance = 1 Omega squared = 5.77 Figure 6. The omega parameter and average distance traveled in morphospace. An example illustrating the different aspects of trait evolution measured by the omega parameter in Hunt’s (2006) model of stasis and the average distance traveled in morphospace. The omega parameter in Hunt’s (2006) stasis model represents the magnitude of fluctuations around the fixed mean/optimal phenotype. Traits showing directional change will therefore tend to have a larger omega parameter compared to traits following stasis, and this can happen independent of the average distance traveled in morphospace. The distance traveled between consecutive sample means in the time series showing stasis (left plot) and the directional trend (right plot) is both 1, while the net evolution (absolute difference between first and last sample mean in time series) differs dramatically between the two lineages. In this example, the estimated square root of the omega parameters (estimated using the opt.joint.Stasis function in the R package PaleoTS (Hunt 2006; 2008)) differ by an order of magnitude. measuring something different than the omega parameter (Fig. 6). This is especially true when the omega is used to estimate evolutionary change in lineages following other modes than stasis. The omega parameter represents the magnitude of fluctuations around the fixed mean/“optimal” phenotype in the stasis model (Hunt 2006). The omega will accordingly be positively correlated with the width of the distribution of sample means in a time series, and lineages evolving larger net evolution over time will tend to have wider distributions of sample means compared to traits fitting stasis. Two lineages travelling identical distances between sample means may therefore be described by very different omega parameters if they over time evolve different amounts of net evolution (Fig. 6). At the same time as fossil data represents opportunities to study morphological evolution covering time spans not accessible in studies of contemporary populations, fossil sequences only provide snap shots of evolutionary trajectories. Rapid shifts in adaptive optima are probably too brief to be manifested in most fossil sequences (Hunt 2007), although the stickleback time series (Fig. 5) show that detailed evolutionary dynamics are possible to observe in the fossil record. These two traits show a pattern where the directional phase on average involve faster evolution (longer distances traveled in morphospace) compared to the stasis phase, but both phases show time intervals where no evolutionary change can be documented (strict stasis, Hunt et al. 2015). Evolutionary theory does not predict evolution to happen at a constant rate, and it is likely that tempo and mode might be found to correlate stronger in microevolutionary studies where detailed evolutionary dynamics can more easily be studied. However, the present study indicates that the rates of peak movements across thousand to million-year time scales are not predicted by the directionality of the movements of the peaks. Rates of evolutionary change based on data from the fossil record may accordingly be more homogenous than previously assumed and advocated. Instead of indicating minimal evolution, the appearance of bounded evolution in the fossil record may hold information on the stability of adaptive zones and ecological niches on the adaptive landscape over macroevolutionary timescales (Williams 1992; Arnold 2014). ACKNOWLEDGMENTS I thank all those who generated the fossil time series data and especially G. Hunt, M. J. Hopkins, and S. Lidgard for making much of the data easily accessible via their publications. Suggestions and recommendations from Associate Editor Miriam Zelditch, Gene Hunt and Graham J. Slater greatly improved the manuscript, and I am indebted to Gene Hunt for advice when exploring the relationship between the omega parameter in his stasis model and estimates of distance traveled in morphospace. I also thank F. Eroukhmanoff, T. F. Hansen, M. Grabowski, L. H. Liow, A. Runemark, and J. Starrfelt for fruitful discussions and valuable comments on earlier versions of this manuscript. All data analyzed are available in the literature (Table S1), and have been deposited in the Dryad 1 0 EVOLUTION 2016 TEMPO AND MODE IN EVOLUTION Digital Repository DOI: 10.5061/dryad.71mn5. A grant from the Research Council of Norway funded the work (grant # 227860). DATA ARCHIVING The doi for our data is 10.5061/dryad.71mn5. LITERATURE CITED Adams, D. C. 2013. Comparing evolutionary rates for different phenotypic traits on a phylogeny using likelihood. Syst. Biol. 62:181–192. Arnold, S. J. 2014. Phenotypic evolution: the ongoing synthesis. Am. Nat. 183:729–746. Arnold, S. J., M. E. Pfrender, and A. G. Jones. 2001. The adaptive landscape as a conceptual bridge between micro- and macroevolution. Genetica 112–113:9–32. Bates, D., M. Maechler, B. Bolker, and S. Walker 2015. Fitting Linear MixedEffects Models Using lme4. Journal of Statistical Software 67:1–48. Baarli, B. G. 1986. A biometric re-evaluation of the Silurian brachiopod lineage Stricklandia lens/S. laevis. Palaeontology 29:187–205. Benton, M. J. 2009. The Red Queen and the Court Jester: species diversity and the role of biotic and abiotic factors through time. Science 323:728–732. Blows, M. W., and A. A. Hoffmann. 2005. A reassessment of genetic limits to evolutionary change. Ecology 86:1371–1384. Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446–464. Charlesworth, B., R. Lande, and M. Slatkin. 1982. A neo-Darwinian commentary on macroevolution. Evolution 36:474–498. Cheetham, A. H. 1987. Tempo of evolution in a Neogene bryozoan: are trends in single morphologic characters misleading? Paleobiology 13:286–296. Cheetham, A. H., Jackson, J. B. C., and Hayek, L.-A. C. 1993. Quantitative genetics of bryozoan phenotypic evolution. I. Rate tests for random change versus selection in differentiation of living species. Evolution 47:1526–1538. Clyde, W. C., and P. D. Gingerich. 1994. Rates of evolution in the dentition of early Eocene Cantius: comparison of size and shape. Paleobiology 20:506–522. Eldredge, N., and S. J. Gould. 1972. Punctuated equilibria: an alternative to phyletic gradualism. Pp. 82–115 in T. Schopf, ed. Models in paleobiology. Models in paleobiology, San Francisco. Eldredge, N., J. N. Thompson, P. M. Brakefield, S. Gavrilets, D. Jablonski, J. B. C. Jackson, R. E. Lenski, B. S. Lieberman, M. A. McPeek, and III. William Miller. 2005. The dynamics of evolutionary stasis. Paleobiology 31:133–145. Estes, S., and S. J. Arnold. 2007. Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales. Am. Nat. 169:227–244. Felsenstein, J. 1985. Phylogenies and the comparative method. Am. Nat. 125:1–15. Futuyma, D. J. 1987. On the role of species in anagenesis. Am. Nat. 130:465– 473. Futuyma, D. J. 2010. Evolutionary constraint and ecological consequences. Evolution 64:1865–1884. Gingerich, P. D. 1984. Punctuated equilibria—where is the evidence? Syst. Zool. 33:335–338. ———. 1993. Quantification and comparison of evolutionary rates. Am. J. Sci. 293-A:453–478. ———. 2009. Rates of evolution. Annu. Rev. Ecol. Evol. Syst. 40:657–675. Gould, S. J. 1980. Is a new and general theory of evolution emerging? Paleobiology 6:119–130. ———. 2002. The structure of evolutionary theory. Harvard Univ. Press, Cambridge. Gould, S. J., and N. Eldredge. 1977. Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology 3:115–151. Haldane, J. B. S. 1949. Suggestions as to quantitative measurement of rates of evolution. Evolution 3:51–56. Haller, B. C., and A. P. Hendry. 2014. Solving the paradox of stasis: squashed stabilizing selection and the limits of detection. Evolution 68:483–500. Hannisdal, B. 2006. Phenotypic evolution in the fossil record: numerical experiments. J. Geol. 114:133–153. Hansen, T. F. 2012. Adaptive landscapes and macroevoutionary macroevolutionary dynamics. Pp. 205–226 in E. I. Svensson and R. Calsbeek, eds. The adaptive landscape in evolutionary biology. Oxford Univ. Press, Oxford. Hansen, T. F., and D. Houle. 2004. Evolvability, stabilizing selection, and the problem of stasis. Pp. 130–150 in M. Pigliucci and K. Preston, eds. Phenotypic integration. Oxford Univ. Press, Oxford. Hansen, T. F., C. Pelabon, and D. Houle. 2011. Heritability is not evolvability. ´ Evol. Biol. 38:258–277. Hansen, T. F., J. Pienaar, and S. H. Orzack. 2008. A comparative method for studying adaptation to a randomly evolving environment. Evolution 62:1965–1977. Harmon, L. J., J. B. Losos, T. J. Davies, R. G. Gillespie, J. L. Gittleman, W. B. Jennings, K. H. Kozak, M. A. McPeek, F. Moreno-Roark, T. J. Near, et al. 2010. Early bursts of body size and shape evolution are rare in comparative data. Evolution 64:2385–2396. Hatakeda, K., N. Suzuki, and A. Matsuoka. 2007. Quantitative morphological analyses and evolutionary history of the Middle Jurassic polycystine radiolarian genus Striatojaponocapsa Kozur. Mar. Micropaleontol. 63:39–56. Hendry, A. P., and M. T. Kinnison. 1999. Perspective: the pace of modern life: measuring rates of contemporary microevolution. Evolution 53:1637– 1653. Hendry, A. P., T. J. Farrugia, and M. T. Kinnison. 2008. Human influences on rates of phenotypic change in wild animal populations. Mol. Ecol. 17:20–29. Hereford, J., T. F. Hansen, and D. Houle. 2004. Comparing strengths of directional selection: how strong is strong? Evolution 58:2133–2143. Hine, E., K. McGuigan, and M. W. Blows. 2014. Evolutionary constraints in high-dimensional trait sets. Am. Nat. 184:119–131. Hopkins, M. J., and S. Lidgard. 2012. Evolutionary mode routinely varies among morphological traits within fossil species lineages. PNAS 109:20520–20525. Houle, D. 1992. Comparing evolvability and variability of quantitative traits. Genetics 130:195–204. ———. 1998. How should we explain variation in the genetic variance of traits? Genetica 102–103:241–253. Hunt, G. 2006. Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 32:578–601. ———. 2007. The relative importance of directional change, random walks, and stasis in the evolution of fossil lineages. PNAS 104:18404–18408. ———. 2008. Gradual or pulsed evolution: when should punctuational explanations be preferred? Paleobiology 34:360–377. ———. 2012. Measuring rates of phenotypic evolution and the inseparability of tempo and mode. Paleobiology 38:351–373. Hunt, G., M. A. Bell, and M. P. Travis. 2008. Evoution towards a new adaptive optimum: phenotypic evolution in a fossil stickleback lineage. Evolution 62:700–710. Hunt, G., and D. L. Rabosky. 2014. Phenotypic evolution in fossil species: pattern and process. Annu. Rev. Earth Planet. Sci. 42:421–441. Hunt, G., M. J. Hopkins, and S. Lidgard. 2015. Simple versus complex models of trait evolution and stasis as a response to environmental change. PNAS 112:4885–4890. EVOLUTION 2016 1 1 K. L. VOJE Jablonski, D. 2000. Micro- and macroevolution: scale and hierarchy in evolutionary biology and paleobiology. Paleobiology 26:15–52. Jablonski, D. 2008. Biotic interactions and macroevolution: extensions and mismatches across scales and levels. Evolution 62:715–739. Jackson, J. B. C., and A. H. Cheetham. 1999. Tempo and mode of speciation in the sea. Trends Ecol. Evol. 14:72–77. Kinnison, M. T., and A. P. Hendry. 2001. The pace of modern life II: from rates of contemporary microevolution to pattern and process. Genetica 112–113:145–164. Kruuk, L. E. B., J. Slate, J. M. Pemberton, S. Brotherstone, F. Guinness, and T. Clutton-Brock. 2002. Antler size in red deer: heritability and selection but no evolution. Evolution 56:1683–1695. Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334. Lieberman, B. S., and Eldredge, N. 2014. What is punctuated equilibrium? What is macroevolution? A response to Pennell et al. TREE 29:185–186. Lieberman, B. S., C. E. Brett, and N. Eldredge. 1995. Patterns and processes of stasis in two species lineages of brachiopods from the middle Devonian of New York state. Paleobiology 21:15–27. Liow, L. H., L. Van Valen, and N. C. Stenseth. 2011. Red Queen: from populations to taxa and communities. Trends Ecol. Evol. 26:349–358. Lynch, M. 1990. The rate of morphological evolution in mammals from the standpoint of the neutral expectation. Am. Nat. 136:727–741. Lynch, M., and B. Walsh. 1998. Genetics and analysis of quantitative traits. Sunderland, Sinauer, Sunderland, MA. Merila, J., B. C. Sheldon, and L. E. B. Kruuk. 2001. Explaining stasis: mi- ¨ croevolutionary studies in natural populations. Genetica 112–113:199– 222. Pennell, M. W., L. J. Harmon, and J. C. Uyeda. 2014a. Is there room for punctuated equilibrium in macroevolution? Trends Ecol. Evol. 29:23– 32. ———. 2014b. Speciation is unlikely to drive divergence rates. Trends Ecol. Evol. 29:72–73. Rabosky, D. L. 2012. Positive correlation between diversification rates and phenotypic evolvability can mimic punctuated equilibrium on molecular phylogenies. Evolution 66:2622–2627. R Core Team. 2016. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at https://www.R-project.org/ Roopnarine, P. D. 2001. The description and classification of evolutionary mode: a computational approach. Paleobiology 27:446–465. Schluter, D. 1996. Adaptive radiation along genetic lines of least resistance. Evolution 50:1766–1774. Sheets, H. D., and C. E. Mitchell. 2001. Why the null matters: statistical tests, random walks and evolution. Genetica 8:105–125. Siepielski, A. M., J. D. DiBattista, and S. M. Carlson. 2009. It’s about time: the temporal dynamics of phenotypic selection in the wild. Ecol. Lett. 12:1261–1276. Simpson, G. G. 1944. Tempo and mode in evolution. Columbia Univ. Press, New York. ———. 1953. The major features of evolution. Columbia Univ. Press, New York. Slater, G. J. 2013. Phylogenetic evidence for a shift in the mode of mammalian body size evolution at the Cretaceous-Palaeogene boundary. Methods Ecol. Evol. 4:734–744. ———. 2015. Iterative adaptive radiations of fossil canids show no evidence for diversity-dependent trait evolution. PNAS, 112:4897– 4902. Stenseth, N. C., and J. Maynard-Smith. 1984. Coevolution in ecosystems: Red Queen evolution or stasis. Evolution 38:870–880. Uyeda, J. C., T. F. Hansen, S. J. Arnold, and J. Pienaar. 2011. The million-year wait for macroevolutionary bursts. PNAS 108:15908–15913. Van Valen, L. 1973. A new evolutionary law. Evol. Theory 1:1–30. Van Bocxlaer, B., and G. Hunt. 2013. Morphological stasis in an ongoing gastropod radiation from Lake Malawi. PNAS 110:13892–13897. Venditti, C., and M. Pagel. 2014. Plenty of room for punctuational change. Trends Ecol. Evol. 29:71–72. Vermeij, G. J., and P. D. Roopnarine. 2013. Reining in the Red Queen: the dynamics of adaptation and extinction reexamined. Paleobiology 39:560– 575. Voje, K. L., A. B. Mazzarella, T. F. Hansen, K. Østbye, T. Klepaker, A. Bass, A. Herland, K. M. Bærum, F. Gregersen, and L. A. Vøllestad. 2013. Adaptation and constraint in a stickleback radiation. J. Evol. Biol. 26:2396–2414. Voje, K. L., and T. F. Hansen. 2013. Evolution of static allometries: adaptive change in allometric slopes of eye span in stalk-eyed flies. Evolution 67:453–467. Voje, K. L., T. F. Hansen, C. K. Egset, G. H. Bolstad, and C. Pelabon. 2014. ´ Allometric constraints and the evolution of allometry. Evolution 68:866– 885. Voje, K. L., Ø. H. Holen, L. H. Liow, and N. C. Stenseth. 2015. The role of biotic forces in driving macroevolution: beyond the Red Queen. Proc. R. Soc. Lond. B 282:20150186–20150186. Wake, D. B., G. Roth, and M. H. Wake. 1983. On the problem of stasis in organismal evolution. J. Theor. Biol. 101:211–224. Walsh, B., and M. W. Blows. 2009. Abundant genetic variation + strong selection = multivariate genetic constraints: a geometric view of adaptation. Annu. Rev. Ecol. Evol. Syst. 40:41–59 Williams, G. C. 1992. Natural selection: domains, levels and challenges Oxford University Press. Oxford Univ. Press, New York. Associate Editor: M. Zelditch Handling Editor: P. Tiffin Supporting Information Additional Supporting Information may be found in the online version of this article at the publisher’s website: Fig S1A: Length of time interval does not predict average distance traveled in phenotype space for linages showing stasis. Fig S1B: Length of time interval does not predict average distance traveled in phenotype space for linages showing directional change. Fig S1C: Length of time interval does not predict average distance traveled in phenotype space for linages showing random walk. Fig S1D: Length of time interval does not predict average distance traveled in phenotype space (corrected for the number of samples in each time series) across modes. Table S3: Three data sets of fossil time series (figure 4 in main text). Table S4: Correlation (above diagonal) and R2 (below diagonal) of trait changes across time series within each of the three data sets shown in figure 4. Table S5: Parameter estimates of the Ornstein-Uhlenbeck model fitted to the two stickleback traits. 1 2 EVOLUTION 2016