Detecting diversiﬁcation rates in relation to preservation ......on common trends (e.g., increasing rock record toward the present) or derived from fossil occurrences ... if preservation

Detecting diversification rates in relation to preservation andtectonic history from simulated fossil records

Tara M. Smiley

Abstract.—For mammals today, mountains are diverse ecosystems globally, yet the strong relationshipbetween species richness and topographic complexity is not a persistent feature of the fossil record.Based on fossil-occurrence data, diversity and diversification rates in the intermontane western NorthAmerica varied through time, increasing significantly during an interval of global warming and regionalintensification of tectonic activity from 18 to 14 Ma. However, our ability to infer originationand extinction rates reliably from the fossil record is affected by variation in preservation history.To investigate the influence of preservation on estimates of diversification rates, I simulated fossil recordsunder four alternative diversification hypotheses and six preservation scenarios. Diversificationhypotheses included tectonically controlled speciation pulses, while preservation scenarios were basedon common trends (e.g., increasing rock record toward the present) or derived from fossil occurrencesand the continental rock record. For each scenario, I estimated origination, extinction, and diversificationrates using three standard methods—per capita, three-timer, and capture–mark–recapture (CMR)metrics—and evaluated the ability of the simulated fossil records to accurately recover the underlyingdiversification dynamics. Despite variable and low preservation probabilities, simulated fossil recordsretained the signal of true rates in several of the scenarios. The three metrics did not exhibit similarbehavior under each preservation scenario: while three-timer and CMRmetrics produced more accuraterate estimates, per capita rates tended to better reproduce true shifts in origination rates. All metricssuffered from spurious peaks in origination and extinction rates when highly volatile preservationimpacted the simulated record. Results from these simulations indicate that elevated diversification ratesin relation to tectonic activity during themiddleMiocene are likely to be evident in the fossil record, evenif preservation in the North American fossil record was variable. Input from the past is necessary toevaluate the ultimate mechanisms underlying speciation and extinction dynamics.

Tara M. Smiley. Department of Integrative Biology, Oregon State University, Corvallis,Oregon 97331 U.S.A. E-mail: [email protected].

Accepted: 3 September 2017Published online: 24 January 2018Data available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.8k56k

Introduction

One of the outstanding questions in biologyremains: How do patterns in species diversityarise and persist over space and time?Explanations for diversity gradients havefrequently emphasized regional or temporaldifferences in diversification rates (e.g.,Jablonski et al. 2006; Weir and Schluter 2007;Mittelbach et al. 2007; Rolland et al. 2014). Onehypothesized mechanism for long-term varia-tion in speciation and extinction rates is theinfluence of tectonic activity and broadscalelandscape changes on species’ geographicranges and diversification dynamics (Cracraft1985; Badgley 2010; Hoorn et al. 2010;Moen and Morlon 2014; Badgley et al. 2017).The generation of topographic complexity andgeographic barriers during tectonic activity

reduces habitat continuity while increasingenvironmental heterogeneity along elevationalgradients (e.g., Mulch 2016). These landscapechanges can isolate populations, therebypromoting population divergence, allopatricspeciation, and high species turnover at theregional scale (e.g., Coblentz and Riitters 2004;Renema et al. 2008; Moen and Morlon 2014).The present-day biogeographic pattern result-ing from these evolutionary, ecological, andhistorical processes has been termed the topo-graphic diversity gradient, or TDG (Badgleyet al. 2017). Examples of the TDG in birds,plants, and mammals have been found on allcontinents where gradients in modern speciesrichness strongly align with gradients intopographic complexity at the regional scale,resulting in elevated species richness in high-relief and often tectonically active regions

Paleobiology, 44(1), 2018, pp. 1–24DOI: 10.1017/pab.2017.28

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(Badgley and Fox 2000; Barthlott et al. 2005;Ruggiero and Hawkins 2008; Badgley 2010).

Approaches for investigating macroevolu-tionary processes governing diversity patternssuch as the TDG have traditionally relied oninference from the fossil record, using occur-rence data to quantify speciation and extinc-tion over time and space (e.g., Stanley 1979;Sepkoski et al. 1981; Foote 2000; Alroy 2009). Inrecent years, phylogenetically based methodshave been developed that use relationshipsamong extant taxa to reconstruct the tempoand mode of diversification through time (e.g.,Ricklefs 2007; Stadler 2011; Rabosky 2014).These approaches have also been employed toquantify regional differences in diversificationrates and explain broadscale diversity gradi-ents (e.g., Weir and Schluter 2007; Rollandet al. 2014). Both phylogenetic and fossiloccurrence–based approaches have theirstrengths and limitations, and a growingnumber of studies demonstrate the advantagesof integrating molecular and fossil data intodiversification analyses (Purvis et al. 2009;Liow et al. 2010; Quental and Marshall 2010;Fritz et al. 2013). Although methods forestimating diversification rates based on eitherphylogenies of extant taxa or the fossil recordrely on model assumptions, an advantage ofthe fossil record is that knowledge of pastdiversity allows rates to be estimated directlyrather than inferred from tree topology (Foote2000; Rabosky 2009). However, preservationand sampling can dampen, accentuate, or evenerase patterns in the fossil record (Raup 1979;Foote and Raup 1996; Smith et al. 2012). Inresponse to these effects, methods have beendeveloped that subsample or standardize fossildata sets (e.g., rarefaction, shareholder quorumsubsampling) or infer sampling probabilities(e.g., Alroy 2014; Liow and Finarelli 2014) toassess the robustness of observed patterns tosampling processes (Raup 1975; Alroy et al.2001; Alroy 2010).

Various diversification analyses and sub-sampling techniques have been applied to theNorth American fossil record to evaluate thehistory of the strong TDG found in mammals(Barnosky and Carrasco 2002; Kohn and Fremd2008; Finarelli and Badgley 2010; Badgley andFinarelli 2013). Today, mammals are twice as

diverse within the topographically complexwestern region compared with the low-reliefGreat Plains (Badgley and Fox 2000; Badgley2010). Multiple lines of evidence suggest thatthe evolution of extant rodent clades wasclosely linked with the Neogene history oftectonic activity in western geological pro-vinces (e.g., Riddle 1996; Hafner et al. 2007;Riddle et al. 2014). In particular, landscaperelief increased significantly during tectonicextension and the development of the Basinand Range Province over the last 30 Myr(Horton and Chamberlain 2006; McQuarrieand Wernicke 2005; Dickinson 2006). The mostintense interval of landscape change occurredduring the middle Miocene from ~18 to 14 Main response to the subduction of the spreadingmargin between the Farallon and Pacifictectonic plates (Atwater and Stock 1998;Sonder and Jones 1999).

Diversification analyses of the mammalianfossil record show a consistent pattern: diver-sity was higher in the tectonically active regionthan in the quiescent region during thisinterval of intense extension and increasedlandscape relief (Barnosky and Carrasco 2002;Kohn and Fremd 2008; Finarelli and Badgley2010). Additionally, the TDG was not persis-tent through time and may have emergedwhen interactions between topographic com-plexity and climate warming (i.e., the middleMiocene Climatic Optimum; Zachos et al.2008) facilitated elevated species richness. Themiddle Miocene peak in mammal diversityoccurred across taxonomic groups, but inparticular among rodents (Fig. 1; Badgley andFinarelli 2013; Badgley et al. 2014). The rodentfossil record is notable for its excellentgeographic coverage, and analysis of diversifi-cation rates for the tectonically active westcompared with the quiescent Great Plains hasrevealed significantly elevated rates of rodentdiversification in the active region during thistime interval as well (Finarelli and Badgley 2010;Badgley and Finarelli 2013). However, largegaps in this record do exist, especially withinthe Basin and Range Province prior to ~18 Ma(Barnosky et al. 2007; Badgley et al. 2015).

Given the concurrent, dynamic histories oftectonic activity, mammal diversification, andfossil preservation, the aim of this study was to

2 TARA M. SMILEY

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use simulations of the fossil record to evaluatethe reciprocal impacts of variability acrossthese records. To do so, I first assessedthe origination rates of fossil rodents in theBasin and Range Province using standardrate calculations (per capita, three-timer, andcapture–mark–recapture [CMR]). I then deve-loped theoretically plausible diversificationmodels for the origin of the TDG in relation totectonic history, simulated five fossilizationscenarios based on those models, and usedthese same three methods to quantify diversi-fication dynamics. Finally, I examined to whatdegree different and variable preservationscenarios limit our ability to correctly inferunderlying dynamics.

Diversification and Preservation Models

Within the context of tectonic activity anddevelopment of topographic complexity, fourplausible diversification hypotheses for theorigin and maintenance of high diversitywithin the tectonically active region are asfollows (Fig. 2A). The first model is akin to amountains-as-cradle model, in which time-invariant but elevated speciation rates generatehigh species richness in the region of tectonic

activity. This constant model also represents ascenario in which variation in diversificationrates derived from the fossil record arises onlyfrom stochastic processes or changes in pre-servation probability through time. In contrast,two alternativemodels incorporate variation inspeciation rates through time. The tectonic-pulse model has two shifts in speciation rateover the history of the record, an instantaneousincrease that coincides with the onset ofintensified tectonic extension (18 Ma) and aninstantaneous decrease at the end of thisinterval (14 Ma). The tectonic-constraint modelis a more complex version of the tectonic-pulsemodel and assumes five different rate regimes.In this model, speciation rate through time isdetermined as a function of the area gainedover 6 Myr time intervals during tectonicextension in the southern Basin and RangeProvince (McQuarrie and Wernicke 2005). A50–200% increase in land area in differentregions of western North America resultedfrom the rotation and displacement of fault-bounded blocks during Neogene extensionand increased large-scale basin-and-rangerelief as the landscape broadened (e.g., Snowand Wernicke 2000; Horton and Chamberlain2006). Quantifying relief remains a difficult

Oligocene Miocene

Quiescent

Active

30 25 20 15 10 5

0

20

40

60

80

100

Ma

Spe

cies

ric

hnes

s

FIGURE 1. Rodent species diversity through time for 1 Myr time bins for the active region (west of the Rocky MountainFront Range) in transparent gray and for the quiescent region (Great Plains and east) outlined in black. Peak mammaldiversity for the active region coincided with intense tectonic extension and global warming during the middleMiocene. The quiescent region did not show a corresponding peak during that interval. Both records were dynamicthrough time, and the TDG was only intermittently present. Species diversity was calculated assuming that speciesranged through first and last occurrences within a region and using the methods of Finarelli and Badgley (2010). Fossil-occurrence data were obtained from the MIOMAP database for North American fossil mammals (Carrasco et al. 2007).

DIVERSIFICATION FROM SIMULATED FOSSIL RECORDS 3



problem in the geologic past (Clark 2007; Mulch2016); therefore, I used area gained as a proxy forchange in topographic complexity over theNeogene. For example, the interval of greatestblock faulting was also the interval that experi-enced the largest increase in land area (McQuarrieand Wernicke 2005). Because speciation rates arehigher than extinction rates in each of thesescenarios, species richness increases through timein an exponential or episodic manner.

The final model assumes a different historyof diversity over the Neogene. In the diversity-dependent model, the speciation rate initiallyexceeds the extinction rate, and then changeslinearly as a function of the number of species.While extinction rate remains constant throughtime, the speciation rate slows down until anequilibrium number of species is maintained,and the speciation rate remains constantand equal to the extinction rate. In this

diversification scenario, I focus on the diversi-fication dynamics after species equilibrium hasbeen reached, as the ability of the fossil recordto capture the initial diversity-dependentslowdown in speciation rates has alreadybeen evaluated elsewhere (Liow et al. 2010).Although I do not specify the underlyingmechanism for diversity-dependent diversifi-cation, this model could generate the TDG ifthe species carrying capacity in mountainousregions exceeded that of nearby low-reliefregions, and if diversification declined overtime. Diversification rates may decrease due tofilling up of ecological space or less opportu-nity for allopatric speciation over time inrelation to increasingly finer subdivision ofthe available land area during tectonic activity(Moen and Morlon 2014).

In contrast to varying speciation rates,extinction rate is held constant in each of the

0.0

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0.6R30% IncR PulseR FreqR

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ate

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λμR

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Constant Tectonic-pulse

Tectonic-constraint

λ = μat equilibrium

Diversity-dependent

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30 20 10 030 20 10 030 20 10 030 20 10 0

A

B

FIGURE 2. A, Theoretically plausible diversification models for generating the TDG. The constant model refers to time-invariant but elevated speciation rate, λ, through the Neogene. The tectonic-pulse model simulates a single interval ofelevated speciation rates in relation to intense block-faulting and tectonic activity in the Basin and Range Province from18 to 14 Ma, while the tectonic-constraint model uses area change over 6 Myr intervals in the Basin and Range Provinceto derive a variable speciation rate curve through time. Each of these three models results in exponentially increasingdiversity patterns through time. In contrast, the diversity-dependent model experiences logistic growth through time,and speciation and extinction rates are equal once the species carrying capacity is reached. Diversification analyseswere carrying out during this equilibrium phase, in which species richness does not change (unless due topreservation). B, Each diversification model was preserved as a fossil record under six scenarios of varyingcompleteness. Complete preservation (R100%, not shown), constant, low preservation probability (R30%), increasingpreservation probability (IncR), and pulsed preservation probability related to tectonically driven basin development(PulseR) are hypothetical preservation scenarios. FreqR refers to preservation probability derived from fossil rodentoccurrences, and StratR refers to preservation probability based on the area of the rock record in the active regionextracted from the Macrostrat database (Peters 2008).

4 TARA M. SMILEY



four models. This simplifying assumptionenables the direct assessment of how variablepreservation impacts our ability to identifychanges in speciation rates, without the influ-ence of simultaneous changes in extinctionrates. However, it should be noted thattectonically driven landscape changes likelyalso influenced extinction rates. Therefore,these four scenarios are not the only possiblemodels for generating the TDG, and a fullersuite of models and parameter settings thatincludes variation in extinction rates could betested in the future.Preservation and sampling can affect

estimates of diversity for reasons ranging froma heterogeneous rock record through time tononuniform sampling effort by researchers(Raup 1975; Foote and Raup 1996; Peters andHeim 2010; Smith et al. 2012). For the Neogenemammal record, an unconformity in the rockrecord over most of western North Americarepresents a significant gap in our knowledgefrom ~23 to 18 Ma (e.g., Barnosky et al. 2007;Badgley et al. 2014). For these reasons,I evaluate the fidelity of the simulated diversi-fication records under different preservationscenarios that are either predetermined orempirically derived from the fossil and rockrecords (Fig. 2B). Preservation can distortestimates of diversity and diversification rates,and even diversification metrics that are robustto several different sampling biases remainsensitive to variable preservation rates throughtime (Alroy 1996; Foote 2000; Peters and Foote2001). Comparing fossil records simulatedwith alternative preservation scenarios,I assess how well the observed variation inspeciation and extinction rates reproduces thetrue underlying diversification dynamics andhow much variation should be attributed todifferences in preservation probability (e.g.,Liow et al. 2010). I evaluate diversificationrates using three different metrics—per capitarates (Foote 2000), three-timer rates (Alroy2008), and CMR rates (Nichols and Pollock1983; Connolly and Miller 2001; Liow andFinarelli 2014)—each of which accounts forpreservation in different ways. While it is notthe goal of this paper to reproduce the TDGover time—to do so would require extensiveconsideration of variation in speciation,

extinction, immigration, and preservation ratesthrough time and across space—I aim todemonstrate how variation in one parameter,speciation, could contribute to this distinctivepattern in the fossil record and how inferredrecords of origination rates may be influencedby variation in fossil preservation.

Methods

Evaluating Diversification Rates from theFossil Record

I compiled species-occurrence records fromthe MIOMAP database of North Americanfossil mammals (Carrasco et al. 2007; accessedJuly 2017) to calculate standing diversity inthe tectonically active versus quiescent regionsfor 1 Myr intervals from 35 to 5 Ma (Fig. 1).I then applied three approaches to calculatingdiversification rates for fossil occurrencesfound within the tectonically active Basin andRange Province (Fig. 3).

First, I calculated the instantaneous percapita origination (p̂) and extinction (q̂) ratesaccording to the following equations (Foote2000):

p̂= lnNtNbt

� �=4t; (1)

q̂= lnNbNbt

� �=4t; (2)

where Nt is the number of taxa that cross thetop of the interval only (i.e., first appearancedatum, or FAD), Nb is the number of taxa thatcross the bottom of the interval only (i.e., lastappearance datum, or LAD),Nbt is the numberof taxa that cross both the top and the bottomof the time interval, and the time interval, Δt, is1 Myr for these analyses. Following previousanalyses (e.g., Finarelli and Badgley 2010;Badgley and Finarelli 2013; Badgley et al.2015), I used lineage range-through assump-tions and excluded taxa that occurred in onetime interval only (singleton taxa) from ratecalculations. Singleton taxa can representeither poorly sampled faunas or, if concen-trated in one temporal bin, a disproportio-nately well-sampled interval. They can thusgenerate spurious results that are dominated




by variable preservation rather than accuratechanges in diversification rates (Foote 2000).Diversification rate (d̂) represents the netchange in diversity as extinction rates aresubtracted from speciation rates:

bd= p̂� q̂; or (3)bd= ln Nt

Nb

� �=4t (4)

In addition, I implemented two rate calcula-tions that explicitly incorporate gaps in thefossil record. The first is the three-timerapproach, wherein taxa are not assumed torange through FAD and LAD and internaloccurrences or absences are used to informestimates of diversification rates and sampling(Alroy 2008, 2010). Three-timer origination andextinction rate calculations are based on taxasampled in two consecutive intervals (two-timers), three consecutive intervals (three-timers), or at the start and end of the intervalbut not within it (part-timers). Per 1 Myr-binoccurrence data are also used to estimatesampling probability, which is used as a correc-tion factor to achieve more accurate and lessvolatile rate estimates. Extensive explanation ofthe three-timer method, including rate equa-tions, can be found in Alroy (2008, 2010, 2014).This method was developed and has beenapplied to global data sets of marine inverte-brates (Alroy et al. 2008) and carnivorans (Liowand Finarelli 2014) to limit edge effects, such asthe Signor-Lipps effect (Signor and Lipps 1982)and the Pull of the Recent (Raup 1979).

Finally, I calculated diversification ratesusing CMR methods, which also use informa-tion about the internal occurrences of taxa andhave been shown to perform well underincomplete and variable sampling (ConnollyandMiller 2001). Borrowed from the ecologicalliterature to infer per individual probabilitiesof capture, birth, and death (e.g., Pollock et al.1990), CMR approaches have been adaptedto paleontological data sets by substituting“capture history” with fossil “samplinghistory,” or the time interval in which a taxonwas extant (in between FAD and LAD) andsampled (Nichols and Pollock 1983; Conroyand Nichols 1984). Following the methodology

in Liow and Finarelli (2014), I used thePradel model (1996) to jointly infer per taxonprobabilities of sampling, origination, andextinction per 1 Myr interval from 35 to 5 Ma.The mechanics and assumptions underlyingthe application of CMR methods to paleonto-logical data sets are further outlined inConnolly and Miller (2001, 2002) and Liowand Nichols (2010).

Data input for per capita rate estimates relyonly on FAD and LAD, whereas the three-timerand CMR rates require occurrence data for each1 Myr time bin through a taxon’s duration. Ageuncertainty for some Cenozoic fossil localities(and thus fossil occurrences) can often extendacross multiple 1 Myr time bins; for example,a locality may be dated to within a NorthAmerican Land Mammal Age (NALMA) suchas the Barstovian, extending from 16.3 to 13.6Ma. Traditionally, locality age uncertainty hasbeen incorporated into the lineage duration offossil taxa to calculate per capita rates (e.g.,Finarelli and Badgley 2010). In addition to thisapproach, I calculated three versions of the percapita, three-timer, and CMR origination ratesby assigning fossil occurrence ages based on themaximum age estimate, the minimum ageestimate, and a randomly drawn age withinthe age range of the fossil locality. In this way,taxa are not smeared across multiple intervalsdue to poor temporal resolution and, impor-tantly for the three-timer and CMR analyses,gaps can be retained.

Spatial assignment of fossil localities wasdone in R (R Core Team 2017) using physio-graphic data from the USGS and R packages‘sp’ (Bivand et al. 2013), ‘rgeos’ (Bivand andRundel 2017), and ‘maptools’ (Bivand andLewin-Koh 2017). Diversification rates wereanalyzed in R, following code provided byLiow and Finarelli (2014, 2017) and usingnewly generated functions for the purposes ofthis study. CMR rate analysis also used theprogram MARK (Cooch and White 2006) andthe R package ‘RMark’ (Laake 2013).

Determining Model Parameters for FossilRecord Simulations

Three parameters potentially influence thesimulated fossil record: speciation rate (λ),

6 TARA M. SMILEY



extinction rate (μ), and preservation probabil-ity (R) through time (Fig. 2A). The range ofspeciation rates (λ = 0.14–0.30 species/LMA)employed in these simulations is representa-tive of rates yielded by previous fossil andsome molecular analyses. For example,Alroy (2009) found an origination rate of 0.23species/LMA for North American fossilmammals, while Zelditch et al. (2015) usedthe BAMM program (Bayesian Analysis ofMacroevolutionary Mixtures; Rabosky 2014)to infer variation in lineage diversificationrates centered around ~0.20 species/Myr forSciuridae (squirrels) from a consensus treederived from molecular data (Fabre et al.2012). To simplify the diversification modelingprocess, I assumed a constant extinction rate, μ,equal to 0.1 L/Lmyr (lineage per lineagemillion years) throughout the simulated record(e.g., Liow et al. 2010). These values yieldedapproximately the same number of speciespresent in the tectonically active region ofNorth America today (n = ~160; Wilson andReeder 2005).For the constant model, one speciation rate

(λ= 0.2) was applied. For the tectonic-pulsemodel, two speciation rates were applied asI increased the speciation rate for a 4 Myrinterval corresponding with elevated tectonicactivity in the geologic record. For the tectonic-constraint model, variation in speciation ratethrough time was determined as a function ofthe area gained over 6 Myr intervals duringtectonic extension in the southern Basin andRange Province. To estimate area gained overgeologic time, I used the output from thekinematic models of McQuarrie and Wernicke(2005). Specifically, I calculated the area ofthe tectonic reconstructions (bounded by thegeographic distribution of fossil localities) andassessed changes in total area for successivetime intervals. Thus, area gained served as aproxy for tectonic activity and the develop-ment of topographic complexity and wasdirectly correlated with speciation rates inthis simulation. For the diversity-dependentmodel, the speciation rate was initially similarto that of the constant model, but decreasedover time as a function of the number ofspecies in the clade. In this logistic-growthmodel, speciation and extinction rates varied

stochastically around a single value (λ= μ) toyield the equilibrium number of species. Thewindow of analysis was restricted to thisequilibrium period of diversification.

I imposed five preservation scenarios(Fig. 2B) to remove species randomly from thesimulated fossil record under each diversifica-tion model (removal process described in“Simulating Diversification and PreservationScenarios”). The preservation probability (R)refers to the remaining proportion of occur-rences (taxa present and preserved per unittime) and is not dependent on additionalfactors, such as taxon abundance in the fossilrecord. Two of the preservation scenariosrepresent general patterns in the fossil androck records. In the first scenario, I applied alow, constant preservation probability of 30%throughout the record (R30%). This preserva-tion probability is consistent with previousestimates for Cenozoic mammal species, whichrange from 25% to 37% (e.g., Foote 1997; Footeet al. 1999). In the second scenario, fossilpreservation improved linearly from 10% to50%within progressively younger rocks (Raup1979; Kidwell and Holland 2002), resulting inincreasing preservation probability throughtime (IncR). This trend reflects a secular changein the rock record, where older rock formationshave potentially undergone increased erosionand/or physical and chemical alternation thatincreasingly limits the preservation of fossils.This trend need not be a linear increase, andalternative increasing preservation scenarioscould be tested. The third preservationscenario was based on the idea that relief, andtherefore sediment accumulation and preser-vation probability, was highest during theinterval of intense faulting and extension anddeclined subsequently (PulseR). Two addi-tional scenarios were derived from gap ana-lysis of fossil-rodent occurrence data (Footeand Raup 1996; Foote 2000) and from thenumber and duration of rock-unit packages inwestern North America (Peters 2008). Gapanalysis refers to an approach for estimatingvariation in preservation probability based onthe temporal distribution of fossil occurrencescompared with lineage durations, assumingthat species range through their first and lastoccurrences in the fossil record (e.g., Foote and




Raup 1996). The ratio of species-level occur-rences to tallied diversity per interval in theNorth American rodent record provided afrequency-based approach to estimating pre-servation probability (FreqR). It is also possibleto derive an independent estimate of preserva-tion potential based on the geographic andtemporal distribution of the rock record (e.g.,Smith et al. 2012). For the fifth scenario, I usedthe Macrostrat database (Version 0.3; accessedApril 2016) to assess the maximum possibleextent of nonmarine rock units for 1 Myrintervals over the Neogene (StratR). Thegeospatial analysis was restricted to the tecto-nically active region only, and the proportionalarea of rock of a given age was used to estimatepreservation probability through the Neogene.This estimate served as a coarse first approx-imation, however, and more precise filteringof the rock record (e.g., fluvial, fossiliferoussediments) may produce a different preserva-tion curve. I compared results from these fivepreservation scenarios with a sixth preserva-tion scenario with complete fossil preservationor no loss of fossil occurrences throughtime (R100%).

Simulating Diversification and PreservationScenarios

Using a stochastic birth–death process deve-loped by Silvestro et al. (2014b), I simulated 1000fossil records per diversificationmodel. Each runwas initiated with 10 taxa to limit the effect ofhaving too few taxa from which to infer ratesearly in the clade history, speciation rates couldvary through time, and extinction rate wasconstant in all simulations. The fossil simulatorproduced a lineage duration for each taxon (i.e., 1Myr interval of first appearance and last appear-ance). In these simulations, first appearanceswere treated as speciation events and not asimmigration events; however, in a regional-scaleanalysis of the fossil record, a first appearance, ororigination event, could be interpreted as eitherwithout additional biogeographic information.Time was divided into discrete, 1 Myr intervalsto match previous analyses of the North Amer-ican fossil mammal record over the Cenozoic(e.g., Finarelli and Badgley 2010). Simulationswere run for 40 Myr, but results of downstream

analyses were retained for the middle 30 Myrto avoid significant edge effects (Foote 2000) andto correspond temporally with the intervalof tectonic extension in western North America(30 Ma to present; McQuarrie and Wernicke2005). The diversity-dependent model wasevaluated for longer than 40 Myr to ensure thatthe model would reach equilibrium (constantdiversity through time within each 1 Myr timebin). The initial period of decreasing speciationrates was removed prior to diversificationanalyses, as were 5 Myr intervals on either endof the analysis window to avoid edge effectsand match the methods implemented in theprior three models. In comparison to completepreservation (R100%), I imposed the five differ-ent preservation scenarios described earlier(Fig. 2B) on the simulated fossil records. Taxapresent within a 1 Myr window were randomlysampled according to the corresponding pre-servation probability, R, for that interval. In thisway, lineage first (FAD) or last (LAD) appear-ance data or any of the intervening 1 Myrintervals could be lost from the record.Simulated fossil records were generated usinga Python script developed by Silvestro et al.(2014b), while preservation scenarios wereexecuted in R (R Core Team 2017). See Supple-mentary Material for links to the available codefor all diversification and preservation simula-tions and rate calculations.

Evaluating Fidelity of the Fossil RecordFor each simulated record, I applied

the three approaches described earlier (see“Evaluating Diversification Rates from the FossilRecord”) to calculate origination (p̂), extinction(q̂), and diversification (d̂) rates in comparison totrue speciation (λ) and extinction (μ) valuesfrom the underlying diversification model(Fig. 2A). For per capita rate calculations, range-through assumptions were applied (Foote 2000);therefore, if an occurrence of a lineage was lostbetween the FAD and LAD, it was still con-sidered present through sampling gaps andthereby contributed to the diversity count anddiversification rate analysis of those interveningintervals. Additionally, singleton taxa wereremoved from rate calculations. In contrast,internal gaps in the fossil record and singleton

8 TARA M. SMILEY



taxa were retained for rate calculations using thethree-timer and CMR methods.Beyond visual inspection of rate variation

through time, I also examined how well thesimulated fossil record retained the originaldiversification pattern under each preservationscenario using two primary tests. First, Ievaluated the accuracy of the rate estimatesunder the constant diversification model.Because diversification rates were uniformthrough time, the average estimated origina-tion rate should reflect the true λ value;deviation from this value could be the resultof preservation or assumptions of the approachused for calculating rates. I used the nonpara-metric Wilcoxon rank-sum test to evaluatethe null hypothesis: the mean value of theestimated origination rates under each preser-vation scenario are equivalent to the trueλ value. Even if rates calculated using the percapita, three-timer, or CMR approaches did notreproduce the accurate estimates (e.g., esti-mated rates were systematically higher orlower than the true λ), variation in λ andestimated p̂ rates should still be correlated. Toinvestigate whether the simulated fossil recordprovided a reliable signal of temporal variationin underlying diversification rates, I appliedSpearman’s rank correlation analysis to test forsignificant, positive correlations between true λand calculated mean origination rates for thesimulated and preserved records.

Results

In this section, I first discuss estimatedorigination rates from the North American(specifically, from the Basin and Range Pro-vince) fossil record of rodents. I then describethe empirical preservation probabilities thatwere used in the modeling framework. Finally,I present results from four diversificationmodels under six preservation scenarios toassess the fidelity of the simulated fossilrecords.

North American Rodent RecordOrigination rates of fossil rodents from the

Basin and Range Province, which has experi-enced a high degree of landscape change (areagain and increased relief) due to tectonic

extension during the Neogene, were estimatedbased on three alternative metrics (Fig. 3,Supplementary Figs. 1–3). Excluding intervalswithout sufficient data for rate calculations,the mean per capita origination rate from 35 to5 Ma is 0.51± 0.57 (±1 SD), the mean three-timer origination rate is 0.27 ± 0.55, and themean CMR origination probability is 0.48±0.58 species per 1 Myr interval. The per capita(Fig. 3A,B) and CMR (Fig. 3D) metricsdemonstrate significantly elevated (95% con-fidence interval> 0) origination rates slightlypreceding and during intense Basin andRange tectonism from 18 to 14 Ma, while thethree-timer (Fig. 3C) metric does not haveenough data to calculate rates throughoutthe whole interval. Maximum, minimum, andrandom ages for fossil occurrences usingthe per capita approach are significantlycorrelated; in contrast, the three-timer andCMR approaches appear quite differentthrough time. While rate estimates under eachage assumption are not correlated, the timingof major peaks and dips in the CMR recordroughly correspond.

Empirical Preservation ProbabilitiesTo simulate the impact of preserva-

tion on diversification models, I employedboth hypothetical preservation probabilities(R100%, R30%, IncR, and PulseR) and empiri-cally derived preservation curves (FreqR andMacroR). Empirical estimates of preservationprobabilities, R, through time were derivedfrom gap analysis of the actual fossil recordand from rock area extracted from theMacrostrat database (Version 0.3; Peters2008). Fossil-based preservation probability(FreqR) was highly variable through time(Fig. 2B). A weak but significant relationshipwas found between diversity and FreqRpreservation probability (Spearman’s r= 0.45,p= 0.02), suggesting that variability in preserva-tion may be contributing to the volatile patternof Neogene rodent diversity in western NorthAmerica. These findings contrast with previousstudies assessing the North American rodentdiversity record, which did not find significantsampling biases based on the correlationbetween the number of fossil localities anddiversity or through shareholder quorum




subsampling (Alroy 2010; Finarelli and Badgley2010; Badgley et al. 2014). The areal extent of therock record may be an independent measure ofpreservation probability (e.g., Smith et al. 2012),and data fromMacrostrat reflected the commontrend of increasing rock area toward the present(Fig. 2B). Somewhat surprisingly, this rockrecord did not signal a pulse of sedimentaccumulation associated with tectonic activityand basin development in western North

America during the middle Miocene. Thisfinding may be a result of the coarse geographicand lithological resolution of this analysis.

Simulated DiversificationThe six preservation scenarios had different

effects on diversification dynamics inferredfrom simulated fossil records. Similarly, thethree approaches for calculating rates haddistinct strengths and weaknesses under dif-ferent preservation scenarios. Two aspects ofthese approaches to estimating diversificationrate from the fossil record were assessed: theaccuracy of the estimated origination rates andthe ability of each metric to reliably estimateconstant or variable origination rates throughtime under different preservation histories.Mean estimates—per capita, three-timer, andCMR—for origination, extinction, and diversi-fication rates from 1000 simulated records arepresented for each diversification model(Figs. 4–7), with each row representing adifferent preservation scenario.

As these figures demonstrate, true ratevalues and temporal variation in rates (or lackthereof) were reproduced by simulated fossilrecords with perfect preservation (R100%).Edge effects on diversification rate calculationsat the beginning and end of the simulatedfossil record were mostly avoided by runningthe simulations over 40 Myr (or longer toreach equilibrium for the diversity-dependentmodel) and then removing the initial and final

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FIGURE 3. Origination dynamics from the fossil record ofrodents in the Basin and Range Province from 35 to 5 Ma.The light gray bar indicates the timing of intense tectonicextension and land area gain in the province from 18 to 14Ma (e.g., McQuarrie and Wernicke 2005). A, Per capitarates (Foote 2000), with 95% confidence intervals in darkgray, assuming taxa range through first and last occurrencedata. B, Per capita rates using three age assumptions due touncertainty in fossil locality age data: the age of fossiloccurrences are equivalent to the maximum (Max; solidblack line) or minimum (Min; dashed black line) age of thefossil locality or a randomly selected age (Rand; gray solidline) within the locality age range. C, Three-timer rates(Alroy 2008), and D, CMR rates (e.g., Connolly and Miller2001; Liow and Finarelli 2014), using the same three ageassumptions as in B. The 95% confidence intervals for eachminimum, maximum, and random age assumption areshown in Supplementary Figs. 1–3. These estimates arebased on fossil occurrence and locality data from theMIOMAP database for North American fossil mammals(Carrasco et al. 2007).

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5 Myr of results. However, for diversificationscenarios with increasing diversity throughtime, one common feature of these simulationsis that the 95% confidence intervals around rateestimates narrow toward the present, indicat-ing that lower diversity at the start of thesimulated histories (ninitial= 10 taxa) leads tomore variable rate estimates (see results from1000 simulated records per diversificationmodel for each preservation scenario anddiversification metric presented in Supplemen-tary Figs. 4–15). Low diversity at the start of thesimulated fossil record in combination with lowpreservation rates (e.g., R = 10%) had thegreatest impact on CMR rate estimates, leadingto unrealistically high estimates of originationand extinction rates (Figs. 4–6, IncR and PulseR).With constant, high diversity through time, thediversity-dependent model does not exhibitthis behavior, suggesting that the number ofspecies present within a given time bin mayinfluence simulated diversification dynamicsand model uncertainty. Under perfect preserva-tion (R100%), the convergence of rate estimateson the true rates with time (and increasednumber of taxa) supports the notion that speciesrichness affects rate accuracy. To compare theaccuracy of each method for estimating ratesusing fossil taxa, I evaluated origination ratesunder the constant diversification model(Table 1). Across the different preservationscenarios, the CMR and three-timer approachesyielded accurate rate estimates more often thanthe per capita approach. Per capita rate estimateswere systematically higher than model para-meter values, while three-timer origination andextinction estimates tended to be lower andmore variable than the true rates.

I describe the patterns observed for eachdiversification model in the following para-graphs; correlation results between true andestimated rates and between estimated ratesand preservation probability are provided inSupplementary Tables 1 and 2, respectively.Under the constant diversification model, bothmean speciation and mean extinction rateswere time-invariant throughout the Neogene,a pattern that remained consistent in three ofthe five incomplete preservation scenarios(Fig. 4). Surprisingly, variable preservationrates (e.g., IncR, StratR) alone were not respon-sible for notable deviations from the truediversification dynamics. Only large jumps inpreservation rate, such as those imposed by thePulseR and FreqR scenarios, seriously compro-mised the fidelity of the simulated fossil record.Highly variable preservation probabilities hada greater impact on per capita and three-timerrates than on CMR rates. However, as men-tioned earlier, CMR rate estimates sufferedfrom low species richness and low preserva-tion probability during the first ~10 Myr of theIncR and PulseR preservation scenarios; thisis true of the following two diversificationscenarios (tectonic-pulse and tectonic-constraint)as well. The effects of preservation impactedall diversification metrics; however, the netdiversification rate, d̂, exhibited less variabilitythrough time.

In the tectonic-pulse diversification model,increased speciation rates over a 4 Myrinterval can be detected under all preserva-tion scenarios, although to varying degreesdepending on the method used to calculatediversification rates (Fig. 5). With perfectpreservation (R100%), the mean origination

TABLE 1. Results from Wilcoxon rank-sum test of estimated origination rates compared with thetrue origination rate (λ = 0.2) under the constant diversification model. A nonsignificant p-value(in bold) indicates higher accuracy for each method of rate calculation under different preservation(R) scenarios. Values in square brackets for CMR (IncR, PulseR, and StratR) are the p-valuesafter excluding the interval from 30 to 20 Ma of the simulation, during which rate estimates arespuriously high due to low species richness and low preservation probability.

Preservation probability Per capita Three-timer CMR

R100%

estimates, p̂, for each metric were positivelycorrelated with the true origination rate,λ (Spearman’s rank correlation, p< 0.05; seeSupplementary Table 1). Using the per capitarate approach, the origination pulse was pre-sent, albeit dampened (R30%, IncR, StratR) oraccentuated (PulseR, FreqR), depending on thepreservation dynamics. In all scenarios exceptfor FreqR, a significant, positive correlationbetween λ andmean per capita p̂was found (viaSpearman’s rank correlation coefficient, p<0.01), indicating that underlying diversificationdynamics could be recovered despite moderatevariation in preservation probability. Resultsfrom three-timer and CMR approaches did notalways reflect the origination pulse; however,these metrics were less impacted by large jumpsin preservation probability (e.g., see diversifica-tion estimates under the PulseR preservationscenario in Fig. 5 and correlation results inSupplementary Table 2). In the FreqR preserva-tion scenario, spurious origination and extinc-tion rate peaks also arose for all three metrics,with the three-timer and the CMR estimatesbeing the most and less variable, respectively.

The tectonic-constraint model—based onarea change during Neogene extension inwestern North America as a proxy for tectonicactivity and corresponding temporal variationin λ—had more complex behavior under thedifferent diversification scenarios (Fig. 6)than the previous two diversification models.Variation in per capita origination rates wasobserved and significantly, positively corre-lated with λ (Spearman’s rank correlation,p< 0.01; see Supplementary Table 1) in all thepreservation scenarios; however, rates weredistorted under the PulseR and FreqRscenarios. If the first 10 intervals with unreli-able, inflated CMR origination rates areremoved from the IncR, PulseR, and StratRpreservation scenarios, the CMR approach alsoreflects the true underlying diversificationdynamics (Spearman’s rank correlation,p< 0.05; see Supplementary Table 1). Overall,the three-timer rate calculations do not per-form well in capturing the true rates, suggest-ing that diversification histories with severalrate shifts may be difficult to detect in the fossilrecord using this method, regardless of pre-servation probabilities through time. Rate

estimates under all diversification scenariosimproved during younger intervals (Supple-mentary Figs. 4–15), again suggesting a biastoward false rates during older intervals whendiversity is low. The similarity of these findingsacross all three models may reflect an artifact ofthemodeling process but should prompt cautionwhen applyingmetrics to data setswith very lowspecies richness. Early in the simulated histories,diversification dynamics are more volatile, andthe addition or loss of species appears to have agreater proportional impact, even on per capitarates or three-timer and CMR rates that explicitlyaccount for sampling probabilities.

Finally, the diversity-dependent modelexhibited behavior distinct from the previousthree models, in part due to a different under-lying diversity pattern (Fig. 7). Because thetotal number of species in sequential 1 Myrtime bins remained roughly constant and high,the diversity-dependent model represented anequilibrium diversification scenario, with λ =μ, and a net diversification rate of approxi-mately zero. When preservation probabilitywas constant through time (e.g., R30%),equilibrium diversity was reduced but pre-served. Not surprisingly, simulated diversitydynamics under variable preservationscenarios closely matched preservation prob-ability through the Neogene, with false peaksin species richness occurring during intervalsof elevated preservation. Despite this, simu-lated origination and extinction rates remainedroughly constant and equal under all but twoof the preservation scenarios, PulseR andFreqR (Fig. 7). Similar to the previous threediversification models, under the variablePulseR and FreqR preservation scenarios, thefossil record inaccurately reflected the trueunderlying rates and could lead to the mis-identification of significant changes in specia-tion and extinction rates through time.However, preservation effects on speciationand extinction rates tended to cancel out,and diversification rates under all scenariosremained tightly clustered around zero, asexpected during the maintenance of equili-brium diversity (Fig. 7). The three-timer rateestimates were the most variable under eachincomplete preservation scenario, while theper capita rate estimates exhibited the most

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prominent impact of preservation on the netdiversification rates (e.g., see diversificationestimates under the PulseR and FreqR pre-servation scenarios in Fig. 7 and correlationresults in Supplementary Table 2).

Discussion

North American Rodent Record in Relation toTectonic HistoryThe fossil record provides a crucial picture of

diversification dynamics in the past and lead-ing to present-day diversity gradients. Theorigin of the topographic diversity gradient,or TDG, is explored here, with a focus onthe exceptional rodent record of western NorthAmerica. In particular, I examined howchanges in tectonic activity during basinextension may have promoted speciationevents and thus contributed to variability indiversification rates throughout the evolution-ary history of mammalian faunas in this region(e.g., Badgley 2010; Badgley et al. 2017).Increased diversity in the tectonically active,western North America compared with thetectonically quiescent Great Plains (Fig. 1) andelevated origination rates (for some, but notall metrics) in the Basin and Range Province(Fig. 3) are a feature of the rodent fossil recordduring the middle Miocene from 18 to 14 Ma.These results agree with findings from similarstudies of rodents (Finarelli and Badgley 2010;Badgley and Finarelli 2013; Badgley et al.2014), rodents and lagomorphs (Samuels andHopkins 2017), predominantly large mammals(Barnoksy and Carrasco 2002), and ungulatesand carnivores (Kohn and Fremd 2008) withintectonically active regions of western NorthAmerica during the Neogene. The strength ofthe origination peak depends both on theapproach used to estimate rates and theassumed age for fossil localities. Per capitarates (Fig. 3A,B) are highest immediatelypreceding the 18–14 Ma interval, possibly dueto a backward “smearing” effect found usingthis approach to calculate rates (e.g., Alroy2014), and remain significantly elevated duringthe Miocene Climatic Optimum. CMR rates arealso high during and just before this interval;however, age assumptions lead to different

inferences about the exact timing and magni-tude of the origination peak (Fig. 3D). Becausethe three-timer approach calculates ratesaccording to the presence of species acrossmultiple time bins, there is insufficient databefore and at the start of this interval tocalculate origination rates during the onset ofintense, regional tectonic extension in the Basinand Range Province (Fig. 3C). These results inrelation to the middle Miocene species richnesspeak and prominent TDG highlight two mainfindings. First, using the same underlyingfossil occurrence data, these metrics can pro-duce strikingly different inferred diversifica-tion histories; therefore, metric selectionshould be carefully considered. Simulations,such as those presented herein, help to betterunderstand the impact of preservation oneach metric separately (e.g., Holland andPatzkowsky 1999; Holland 2000). Second,three-timer and CMR rate calculations, whichretain and use internal gaps, present uniquechallenges when the age uncertainty for someor all fossil localities exceeds the per bininterval length of the analysis or when occur-rence data are lacking for time bins adjacent tothe interval of interest (e.g., the gap in the fossilrecord just prior to 18–14 Ma). Therefore, atrade-off exists between the potential benefitsof using range-through assumptions to calculateper capita rates and the benefits of jointlyestimating and correcting for sampling probabil-ities under the three-timer and CMR approaches.

While the fossil record provides evidence ofpast diversity beyond what we would be ableto retrieve from molecular phylogenies alone(e.g., Quental and Marshall 2010), diversifica-tion dynamics, such as the strengthening andweakening of the TDG, can be distorted bypreservation (e.g., Foote 2000). Qualitativeinspection of the empirically derived preserva-tion scenarios through time (Fig. 2B) indicatesthat the Neogene mammal diversity curve inNorth America (Fig. 1) is not a direct productof frequency-based fossil occurrences or thetemporal distribution of the rock record. Like-wise, the middle Miocene diversity peak is notcorrelated with the number of localities in thefossil record or lost when subsampled (Badgleyet al. 2014). Therefore, the elevated speciesrichness west of the Rocky Mountains during




this interval remains a pattern demandingexplanation. The fact that we do not find acorresponding peak in the adjacent, but tecto-nically quiescent Great Plains region wouldsuggest that tectonic activity and the genera-tion of topographic complexity throughgeographical isolation of populations andincreased speciation rates (e.g., tectonic-pulseand tectonic-constraint scenarios) play a role inpromoting species diversity (Cracraft 1985;Renema et al. 2008; Badgley 2010; Badgleyet al. 2017). Concurrent global warming duringthe Miocene Climatic Optimum may havefacilitated range shifts into intermontaneregions, further contributing to the peak indiversity during this time.

Simulating the Fossil RecordFindings from these simulations emphasize

the insight that can be gained from investigat-ing not only diversity patterns through time,but also teasing apart the mechanisms drivingthose patterns. In particular, I explore howpreservation probabilities, especially nonuni-form preservation through time, impact infer-ence about diversification dynamics. Severalexcellent examples from the marine record offossil invertebrates demonstrate how assessingthe quality of the record (e.g., taphonomicfilters and stratigraphic setting) and account-ing for variable preservation through timeproduce better estimates of diversificationdynamics (e.g., Kidwell and Holland 2002;Peters 2008; Smith et al. 2012; Holland 2016).In comparison, such work within terrestrialsettings is currently underdeveloped. There-fore, to simulate the impact of preservation ondiversification models, I employed both idea-lized preservation probabilities and empiri-cally derived preservation curves. In thesesimulations, the parameter values used areplausible if basic.

Under most preservation scenarios, thesimulated fossil records reflected the temporalvariation in the true underlying diversificationdynamics. Stability in speciation and extinctionrates was recovered for the constant anddiversity-dependent diversification models,while variation in speciation rates was evidentfor the tectonic-pulse and tectonic-constraint

models, despite low constant (R30%) andvariable, but increasing (IncR, StratR) preser-vation probabilities (Figs. 4–7). However,preservation scenarios with large jumps inpreservation probability from one temporalbin to the next (PulseR, FreqR) generated falsepeaks in speciation and extinction rates. Ingeneral, deviations from the original modelwere limited to the intervals of pronouncedpreservation change; however, the degree ofrate variability elsewhere in the recorddepended on the metric used for calculatingdiversification rates. Importantly, thesemetrics—per capita, three-timer, and CMR—did not respond in similar fashion in responseto different preservation histories. While percapita rates tended to best reproduce theunderlying origination dynamics (Supplemen-tary Table 1), these rates suffered themost fromlarge jumps in preservation rates (e.g., PulseRand FreqR; Supplementary Table 2). This effectwas additionally observed in the per capita netdiversification rates, whereas the two othermetrics dampened this preservation “noise.”Three-timer and CMR rates were more accu-rate than per capita rates (Table 1); however,the behavior of these metrics, especially whenspecies richness and preservation probabilitywas low, was sometimes erratic and unreliable.These results indicate that all three metricsprovide useful information but are not guar-anteed to correspond even with similar under-lying fossil occurrence data and preservationhistory. Finally, as demonstrated for NorthAmerican rodents (Fig. 3), some metrics maynot produce results during certain time inter-vals due to a lack of sufficient data or may havecertain limitations depending on the ageresolution of fossil localities. It is thereforeadvisable to assess at least three primaryfactors regarding the quality of the fossil recordof interest when determining which approachto use: total species richness and uniformityacross the record, age uncertainty of fossillocalities in relation to the temporal-bin lengthof analysis, and whether the preservationhistory is expected to be highly variablethrough time.

Preservation probability varies not only overtime, but also over space, physical environments,and across clades. These preservation issues

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were avoided in the record simulated here; forinstance, small-mammal teeth have similartaphonomic properties (Hibbard 1941), and withthe exception of Quaternary cave deposits (e.g.,Terry 2010), small-mammal fossils are typicallyfound by screen-washing retrieval methods thatare frequently applied to alluvial sediments (e.g.,Lindsay 1972; Badgley et al. 1998). How toreconcile variability in diversification rates withheterogeneous preservation remains a challen-ging but important problem in paleoecology andmacroevolution (e.g., Foote 2000), especiallygiven that preservation rates are often treatedas time-invariant or assumed to follow a com-mon trajectory with respect to lineage durationacross the history of a clade (e.g., Liow et al. 2010;Silvestro et al. 2014b). Some of this simplificationoccurs so as to avoid over-parameterizationof complex models (Silvestro et al. 2014a).However, if preservation parameters thatare independent from lineage history (e.g., basedon rock-record estimates from Macrostrat) areapplied, some of these simplifying assumptionscan be reconciled, thus enhancing our capabilityto recover the actual dynamics underpinningdiversity patterns over time (e.g., Holland andPatzkowsky 1999; Smith et al. 2012).

Alternative Diversification Models andApproachesThe modeling framework presented here is

simplified to distinguish the impacts of varia-tion in two model parameters. Several otherdiversification processes are not only plausible,but also necessary to produce the diversitypatterns we observe through time. For small-mammal species richness to rise and fall overthe Neogene within the two regions of NorthAmerica (Fig. 1) requires that extinction ratesvary and even exceed origination rates at times(Alroy 2009; Finarelli and Badgley 2010;Badgley et al. 2014). Alternatively, under adiversity-dependentmodel, once an equilibriumnumber of species has been reached, large-scalevariation in preservation alone could produce ahighly variable species richness pattern throughthe Cenozoic. Evidence for exponential speciesincrease, as modeled in the constant, tectonic-pulse, and tectonic-constraint diversificationscenarios, is not typically recovered from the

fossil record (e.g., Alroy et al. 2000). Fossil andmolecular records alike support the concept ofdiversification slowdowns over time (Alroy2009; Rabosky 2013). The mechanisms for theseslowdowns, or diversity-dependent diversifica-tion as modeled here, are often debated;however, factors related to both biotic inter-actions and changes in the geographic templateare likely to play an important role in limitingthe total number of species that a region can bothgenerate and support (Moen and Morlon 2014;Rabosky and Hurlbert 2015). Importantly,Neogene tectonic activity in western NorthAmerica led to increased topographic complexityregionally and substantial gains in land area,both of which could have promoted elevatedspecies richness (Cracraft 1985; Rosenzweig1995).

Diversity-dependent diversification can be acompelling mechanism for explaining diver-sity patterns over space and time; however,the volatile record of North American rodentdiversity is not necessarily consistent withthis process. Depending on the spatial andtemporal scale of the analysis, the NorthAmerican mammal record has been used toinfer both diversity-dependent dynamics (e.g.,driven by biotic interactions) and landscape-driven dynamics (Alroy et al. 2000; Barnosky2001). In the second case, various analyseshave coupled variation in diversity and diver-sification rates with changes in tectonic activity(e.g., extension), climate (e.g., the MioceneClimatic Optimum), and vegetation hetero-geneity (e.g., Vrba 1992; Barnosky andCarrasco 2002; Kohn and Fremd 2008; Finarelliand Badgley 2010; Eronen et al. 2015). Thesedifferent mechanisms are not mutuallyexclusive, and the changing nature of speciesecology, geographic distributions, and com-munity assembly over a topographically andenvironmentally complex and dynamiclandscape is likely to be a product of theinteractions between biotic and abiotic factors(Badgley 2010; Blois and Hadly 2009; Hoornet al. 2010). For example, diversificationdynamics in mountainous regions may followa diversity-dependent pattern during thedevelopment of topographic complexity as(1) species diversify to fill up ecological spacealong elevational gradients, and (2) geographic




opportunities for vicariance decline throughtime in response to finer subdivision of theavailable landscape (Moen and Morlon 2014).Therefore, even under a diversity-dependentscenario, one might expect dynamic speciesrichness and nonequilibrium diversity fromthe fossil record during an interval of intensetectonic activity. In addition to evidence fromthe fossil record, quantifying rate variationfrom comparative phylogenetic methods mayilluminate underlying diversification mechani-sms (e.g., Stadler 2011; Zelditch et al. 2015).For example, approaches such as BAMM(Rabosky 2014) could be implemented forNorth American rodents and may yield inter-esting differences in speciation and extinctionrates between clades found predominantly inthe tectonically active or quiescent regions.Ideally, fossil data can be integrated as tip taxaor direct ancestors (e.g., via BioGeoBEARS;Matzke 2013) into such comparative methods(Liow et al. 2010; Quental and Marshall 2010).

A vital biogeographic process governingspecies distributions and diversity patterns isabsent from the modeling framework of thisstudy. In addition to in situ speciation, immi-gration and geographic-range expansions aremajor processes that add new species to aregion (Jablonski et al. 2006; Martin et al.2008; Riddle et al. 2014). Examples of specia-tion, extinction, and immigration feature pro-minently in the North American recordthroughout the Neogene, influencing regionaldiversification, faunal composition, and turn-over (e.g., Davis 2005; Alroy 2009; DeSantiset al. 2012; Badgley and Finarelli 2013; Badgleyet al. 2015). At regional spatial scales, theorigination metric, p̂, includes both speciationand immigration (Finarelli and Badgley 2010),but distinguishing these two processes in thefossil record is challenging. However, anincrease in faunal similarity across spatialscales in the active region from 17 to 14 Masuggests that range shifts were contributing tospecies richness patterns (Badgley et al. 2015).Spatially explicit modeling approaches (e.g.,Pires et al. 2015; Silvestro et al. 2016) that canincorporate species exchange between thetectonically active and quiescent regions—forinstance, due to climate warming and rangeshifts to higher elevations—may elucidate the

biogeographic processes contributing to thestrengthening and weakening of the TDGgradient over geologic time. Given high-resolution temporal and spatial coverage offossil occurrences, it is possible to track thegeographic distribution of lineages throughouttheir history to identify immigration eventsand range shifts over regional scales (Jablonskiet al. 2006; Stigall and Lieberman 2006;Maguire and Stigall 2008; Terry et al. 2011).

Given the modeling framework providedhere, it would be useful to consider whatcombination of model parameter values couldpotentially produce the diversification recordobserved in North American rodents. Tectonicactivity may underpin variation in origination,extinction, immigration, and preservation (i.e.,by enhancing sediment accumulation), leadingto positive correlations among all three factors(e.g., Peters 2008). Results from this studysuggest that, although the nature of thesecorrelations may differ across time periodsand geographic regions, underlying diversifi-cation dynamics for the most part can becorrectly inferred. In the future, Bayesianmodeling approaches in which differenthypotheses for diversification in relation totectonic regimes are tested against fossil-occurrence data or the timing of majordivergences inferred from molecular or full-evidence phylogenies may prove particularlyilluminating (e.g., Rabosky 2014; Silvestro et al.2014b, 2015). Likewise, explicit considerationof both the temporal and geographic distribu-tion of the sedimentary record in relation tofossil localities is critical to better understandthe influence of preservation on our readingof diversity patterns from the fossil record(Holland 2016). Although different factors maydrive the TDG diversity gradient at differenttimes, topographic and climate interactions arelikely to remain an important influence ondiversification dynamics.

Conclusions

The fossil record can be used to robustlyinfer shifts in diversification rates when pre-servation and sampling are explicitly modeled.Rate estimates from simulated fossil recordsreliably reflected the underlying origination

20 TARA M. SMILEY



pulse under a variety of preservation scenarios.However, caution should be applied whenestimating diversification rates during periodswhen preservation probability is considered tobe highly variable between sequential timebins. Increased origination rates in relation totectonic extension are hypothesized to havecontributed to elevated mammal richness inwestern North America during the middleMiocene. While new species can be added tothe region by speciation and immigration,basic models such as those explored hereincan help constrain the processes that influencediversity patterns over geologic time. Ulti-mately, integration of data from fossil andmolecular records combined with approachesthat consider diversification (i.e., speciationand extinction) and biogeographic (i.e., immi-gration and geographic-range shifts) processesjointly will be necessary to understand themechanistic underpinnings of diversity gradi-ents such as the TDG.

Acknowledgments

This work was supported by the Universityof Michigan Rackham Predoctoral Fellowship.I thank Jonathan Mitchell, Tomasz Baumiller,and Dan Rabosky for valuable discussion ofthe concepts in this article and CatherineBadgley for thoughtful editing of this paper.I benefited greatly from helpful commentsprovided by Steve Holland, Michael Foote, andan anonymous reviewer. Finally, I am especiallygrateful to Pascal Title and Daniele Silvestro forproviding guidance with R and Python codeused for simulations and analyses.

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Detecting diversiﬁcation rates in relation to preservation ......on common trends (e.g., increasing rock record toward the present) or derived from fossil occurrences ... if preservation