Pulsed evolution shaped modern vertebrate body sizes Michael J. Landisa and Joshua G. Schraiberb,c,1 aDepartment of Ecology and Evolutionary Biology, Yale University, New Haven, CT 06520; bDepartment of Biology, Temple University, Philadelphia, PA 19122; and cInstitute for Genomics and Evolutionary Medicine, Temple University, Philadelphia, PA 19122 Edited by Neil H. Shubin, The University of Chicago, Chicago, IL, and approved October 6, 2017 (received for review June 18, 2017) The relative importance of different modes of evolution in shap- ties of these methods, nor is much known about the prevalence of ing phenotypic diversity remains a hotly debated question. Fos- pulsed change throughout some of Earth’s most intensely stud- sil data suggest that stasis may be a common mode of evolution, ied clades. while modern data suggest some lineages experience very fast Here, we examine evidence for pulsed evolution across ver- rates of evolution. One way to reconcile these observations is to tebrate taxa, using a method for fitting L´evy processes to com- imagine that evolution proceeds in pulses, rather than in incre- parative data. These processes can capture both incremental and ments, on geological timescales. To test this hypothesis, we devel- pulsed modes of evolution in a single, simple framework. We oped a maximum-likelihood framework for fitting Levy´ processes apply this method to analyze 66 vertebrate clades containing to comparative morphological data. This class of stochastic pro- 8,323 extant species for evidence of pulsed evolution by compar- cesses includes both an incremental and a pulsed component. We ing the statistical fit of several varieties of L´evy jump processes found that a plurality of modern vertebrate clades examined are (modeling different types of pulsed evolution) to three models best fitted by pulsed processes over models of incremental change, that emphasize alternative macroevolutionary dynamics. Under stationarity, and adaptive radiation. When we compare our results these models, the adaptive optimum of a lineage may wan- to theoretical expectations of the rate and speed of regime shifts der incrementally and freely (Brownian motion), it may change for models that detail fitness landscape dynamics, we find that our incrementally but remain stationary (Ornstein–Uhlenbeck), or it quantitative results are broadly compatible with both microevolu- may change most rapidly following the initial diversification of a tionary models and observations from the fossil record. clade while decelerating over time, e.g., during an adaptive radi- ation (early burst). Beyond simple model comparison, we show macroevolution j Levy process j pulsed evolution j adaptive landscape that the parameter estimates corresponding to the microevolu- tionary and macroevolutionary mechanisms of the model have key debate in evolutionary biology centers around the seem- biologically meaningful interpretations (2), illuminating previ- Aing contradictions regarding the tempo and mode of evo- ously hidden features of Simpson’s adaptive grid. lution as seen in fossil data compared with ecological data. Results Fossil data often support models of stasis, in which little evo- lutionary change is seen within lineages over long timescales (1, Maximum-Likelihood Method Has Power to Distinguish Pulsed 2), while ecological data show that rapid bursts of evolution are Evolution from Comparative Data. We developed a maximum- not only possible, but potentially common (3, 4). At face value, likelihood method for fitting L´evy processes to phylogenetic these observations seem to contradict one another, an observa- comparative data using restricted maximum-likelihood estima- tion known as the “paradox of stasis” (5). These observations are tion (REML), by analyzing the phylogenetically independent often reconciled through a descriptive model of pulsed evolution, contrasts (16) (Materials and Methods). The L´evy processes we entailing stasis interrupted by pulses of rapid change, as famously apply in this work consist of two components: a Brownian motion articulated by Simpson (6). and a pure jump process. The Brownian motion is characterized On macroevolutionary timescales, pulses of rapid change are expected to look roughly instantaneous. Only recently have sta- Significance tistical methods grown sophisticated enough to model pulsed evolution as a stochastic process, with advances showing that The diversity of forms found among animals on Earth is strik- punctuation is detectable in some fossil time series (7) and ing. Despite decades of study, it has been difficult to reconcile between pairs of living and extinct taxa (8). the patterns of diversity seen between closely related species While these studies establish the existence of pulsed evolution, with those observed when studying single species on eco- it is still unknown whether the evolutionary mode is common or logical timescales. We propose a set of models, called Levy´ rare. How many clades in the Tree of Life were shaped by abrupt processes, to attempt to reconcile rapid evolution between pulses of rapid evolution? If these evolutionary pulses are com- species with the relatively stable distributions of phenotypes mon, then that should inform our expectations about how traits seen within species. These models, which have been success- evolved for clades that left no fossils and the potential for vulner- fully used to model stock market data, allow for long peri- able species to adapt rapidly to climate change (9). To this end, ods of stasis followed by bursts of rapid change. We find that phylogenetic models—models of trait evolution that account for many vertebrate groups are well fitted by Levy´ models com- the shared ancestry of species—have played a vital role in mea- pared with models for which traits evolve toward a stationary suring the relative support of competing Simpsonian modes of optimum or evolve in an incremental and wandering manner. evolution. A pioneering meta-analysis (10) fitted a collection of phyloge- Author contributions: M.J.L. and J.G.S. designed research, performed research, analyzed netic models to 49 animal clades, finding preference for modes of data, and wrote the paper. incremental, but not explosive, evolutionary change. That work The authors declare no conflict of interest. predated the advent of phylogenetic models of pulsed evolution This article is a PNAS Direct Submission. (11, 12), so its frequency could not have been measured. More- This open access article is distributed under Creative Commons Attribution- over, there remains a concern that models of incremental and NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). pulsed change leave similar patterns of trait variation in neonto- See Commentary on page 13068. logical data (13, 14). While recent methodological developments 1To whom correspondence should be addressed. Email: [email protected]. show that there is power in comparative data to identify pulsed This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. evolution (11, 12, 15), little is known about the statistical proper- 1073/pnas.1710920114/-/DCSupplemental. 13224–13229 j PNAS j December 12, 2017 j vol. 114 j no. 50 www.pnas.org/cgi/doi/10.1073/pnas.1710920114 Downloaded by guest on September 24, 2021 by a rate parameter, σ2, and the pure jump process is character- lutionary mode is enriched in any of the five vertebrate groups ized by a L´evy measure, ν(·), where ν(dx)dt can be thought of (χ2 test, P ≈ 0:10). L´evy jump models and Brownian models SEE COMMENTARY as the probability of a jump with a size in the interval (x; x + dx) fitted to any given clade yield nearly identical estimates of pro- occurring in the short time dt. Note that this model does not cou- cess variance (SI Appendix), indicating that the tempo and mode ple pulses of evolution to cladogenesis, as in the classical theory of evolution leave distinct patterns in comparative data. of punctuated equilibrium (17). Instead, pulses may occur at any We speculated that clades would favor models that produced time, sometimes known as “punctuated anagenesis” (18). similar patterns in comparative data. To characterize this, we Both L´evy processes with jumps and pure Brownian motion applied a principal components analysis to the vectors of wAICc accumulate variance proportionally to time (SI Appendix), lead- scores of Fig. 1 and then clustered wAICc profiles using k-means ing to speculation that it is impossible to distinguish between (k = 4). The first three principal components explain 85.6% pulsed and certain incremental models from comparative data of the variance. Fig. 2 shows that four clusters form around (13, 14). For simulations with moderately sized clades (>100 clades that select models of incremental evolution (BM and taxa), we had sufficient power to differentiate pulsed evolution OU), explosive evolution (EB), and the two models represent- from other Simpsonian modes of evolution. This is due to the ing pulsed evolution (JN and NIG). Interestingly, the third com- impact of rare, large jumps resulting in a heavy-tailed distribu- ponent separates clades that favored the two different kinds of tion of trait change (SI Appendix). Moreover, we saw low false jump models we explored, with the most pulsed process (JN) run- positive rates for identifying pulsed evolution, even in the pres- ning opposite to the infinitely active processes (NIG). This sug- ence of phylogenetic error (4% for clades with ∼100 taxa, 7% for gests that with more power