Volume 7, Issue 3 p. 331-339
Research Article
Free Access

A framework for detecting natural selection on traits above the species level

Kenneth B. Hoehn

Corresponding Author

Kenneth B. Hoehn

Biology Department, Duke University, Durham, NC, 27708-0338 USA

Department of Zoology, University of Oxford, Oxford, OX1 3PS UK

Correspondence author. E-mail: [email protected]Search for more papers by this author
Paul G. Harnik

Paul G. Harnik

Department of Earth and Environment, Franklin and Marshall College, Lancaster, PA, 17604 USA

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V. Louise Roth

V. Louise Roth

Biology Department, Duke University, Durham, NC, 27708-0338 USA

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First published: 14 August 2015
Citations: 3


  1. To what extent can natural selection act on groupings above the species level? Despite extensive theoretical discussion and growing practical concerns over increased rates of global ecological turnover, the question has largely evaded empirical resolution. A flexible and robust hypothesis-testing framework for detecting the phenomenon could facilitate significant progress in resolving this issue.
  2. We introduce a permutation-based approach, implemented in the R package perspectev, which provides an explicit test of whether empirical patterns of correlation between upper level trait values and survivorship are reducible to correlations manifested at lower levels. The package is applicable to virtually any nested set of upper- and lower level groupings, a wide variety of upper level traits, and both historical and contemporary occurrence data. We apply this approach to five paleontological data sets that represent different magnitudes of extinction and differ in taxonomic breadth, geological timing and geographic extent.
  3. Using simulations, we demonstrate that this method is a robust means of detecting irreducibility in the relationship between upper level traits and survivorship, and outline circumstances in which the method is less effective. We also find evidence consistent with previous findings of selection above the species level for geographic range size in North American K-Pg molluscs and show that this phenomenon was evident for the same molluscan genera globally.
  4. Ultimately, we conclude that at certain points in history, some higher level taxonomic groups have survived differentially with respect to geographic range size in a manner that is not explained by the same trait at the species level, and we show that evidence for this phenomenon varies across taxa and extinction events. We release our method as a flexible and easy-to-use R package that will allow others to help determine the relative frequency of this macroevolutionary phenomenon, both in the fossil record and in estimates of contemporary extinction risk.


The level of organization at which natural selection acts is a fundamental issue in evolutionary biology (Lewontin 1970). The essential question is with what relative frequency, if at all, natural selection occurs at the level of genes (Dawkins 1976), organisms (Darwin 1859; implicitly) or species and higher taxonomic levels. While the frequency of selection acting on taxonomic groups at or above the species level remains a source of contention (Gould 2002; Okasha 2012), previous empirical work has suggested that during mass extinctions natural selection may act at a level as high as genera (Jablonski 1986). Given both this theoretical framework and the rising evidence that present-day ecosystems globally are experiencing greatly elevated extinction rates (Barnosky et al. 2011), whether higher taxa experience natural selection is not only of theoretical interest to macroevolutionary biologists studying the fossil record, but potentially a matter of importance to evolutionary biologists and ecologists studying contemporary taxa.

Despite extensive theoretical discussion of the topic (Dawkins 1976; Brandon 1984; Gould 2002; Jablonski 2007; among many others), the issue of selection at higher taxonomic levels has largely evaded empirical resolution. Most tests have focused on the ‘fecundity’ component of fitness at higher levels – that is, on rates of species diversification (e.g. Simpson 2010; Rabosky & Goldberg 2015), or are limited to traits related to geographic range size (Powell & MacGregor 2011). A flexible hypothesis-testing framework for assessing the reducibility of the relationship between upper level traits and survivorship would facilitate significant progress in addressing this issue empirically.

Here, we develop such a framework and release it as the R package perspectev (permutation of species during turnover events). This package implements a permutation test that determines the significance of a relationship between traits of upper level groupings and their survivorship by comparing observed correlations to a null distribution obtained from randomly assigning lower level units to upper level groups. Perspectev is compatible with virtually any well-defined upper/lower level grouping structure and provides a diverse and customizable library of functions for traits such as geographic range, morphological diversity (i.e. disparity’), and even genetic variation. It may be used not only with paleontological data in which empirical patterns of survivorship are known, but also in contemporary data in which survivorship is given probabilistically (Mooers, Faith & Maddison 2008; Huang 2012).

This package is tested using the trait of genus-level geographic range size on the survivorship of multiple taxonomic groups during two mass extinctions (K-Pg and Permian–Triassic) and a series of background extinction intervals in the Cenozoic. Among these examples, North American molluscs during the Cretaceous–Paleogene (K-Pg) mass extinction are an important case study of selection above the species level because Jablonski's (1986) study of K-Pg molluscs of the Atlantic and Gulf Coastal Plains in North America remains one of the few documented examples of differential survival of genera with respect to traits not reducible to lower levels. In this extinction event, molluscan genera showed a significant positive relationship between geographic range size and survivorship, while species within these genera showed no such relationship, and subsequent studies confirmed both these patterns (Jablonski 2007, 2008). However, it is still unclear whether this phenomenon was actually selection for genera per se: Would the same effect be observed with arbitrary groupings of species? Here, we find evidence consistent with selection above the species level in K-Pg molluscs, both globally and in North America, and demonstrate the robustness of the permutation approach more generally.

Material and methods

Calculating test statistic

The goal of the permutation test is to determine the significance of observed correlation between an upper level trait and survivorship. This correlation is tested against the null hypothesis that a value as high as that observed for the given upper level grouping could be produced by random assemblages of lower level units. As in the examples tested here (specified in parentheses), each lower level unit (species) consists of a set of occurrences (sites where specimens were collected). Accompanying each occurrence are trait data (latitude and longitude coordinates) that are used with a specified trait function to calculate trait values (geographic range size) both for the unit (species) and for the grouping (genus) to which it belongs. We apply the term unit to lower level sets of occurrences because once a lower level set is defined, both its trait data and survivorship probability are fixed (though see simulations described below). Trait data and survivorship probabilities for the upper level groupings are calculated from their constituent units, which are permuted among them.

To calculate trait values both for groupings and for units the following must be defined for each occurrence:

  1. lower level units (species)
  2. upper level groupings (genera)
  3. trait data (latitude and longitude coordinates), which are used by a specified
  4. trait function (geographic range: area of a minimum convex polygon encompassing the occurrence data).
Survivorship probability, which may be binary or continuous, must also be given for each distinct lower level unit. Upper level survivorship probability g is calculated for a given grouping as the probability that at least one constituent unit survives, given units survive independently of each other:
where ui is the survivorship probability of constituent unit i in that grouping and m is the number of units in that grouping.

To calculate the permutation-based P value, a null distribution of correlation values is constructed by shuffling units between groupings; recalculating trait values, survivorship, and the correlation between trait value and survivorship at the upper level; and repeating this process. More precisely, where:

  • = number of iterations
  • = {r1..rn} = observed correlation between upper level traits and survivorship
  • = {s1..sn} = correlation between upper level traits and survivorship for groupings of permuted units
  • 1(<statement>) = indicator function: 1 if <statement> is true, 0 if false
rn is the Pearson correlation between grouping trait values and survivorship probability for observed groupings. While for permutation of observed data rn does not vary between iterations, it can vary in simulations (see below).

sn is calculated in the same manner as rn, but uses groupings produced by permutation. At each iteration, units are permuted between groupings and both survivorship probability and trait data accompany units through permutations. For each grouping, the number of constituent units remains constant, though its trait value is re-calculated based on the trait data of its new units, and its survivorship is re-calculated based on eqn 1.

If P is below a pre-specified α value, the null hypothesis is rejected. While α = 0·05 is standard, in simulation analyses we consider a broader range of values.

Simulation-based power analysis

To confirm that this test is an informative measure for distinguishing upper- from lower level selective effects, selection for groupings, and then for units, of different degrees of intensity and selectivity, is applied to a given data set, and resulting P values are observed. The number of groupings, numbers of units in the groupings and the trait data of each occurrence are set to match those in the observed data. Perspectev implements a logistic selection model in which each trait value is multiplied by a slope parameter (representing selectivity – the larger the value, the stronger the relationship between trait and survivorship), and added to an intercept parameter (representing intensity – the lower the value, the greater the intensity of extinction). Survivorship probabilities are obtained with an inverse logit function applied to this linear transformation of trait values, for the level under selection. When simulating lower level (unit) selection, once survivorship probabilities are given for each unit, calculation of test statistics proceeds as described in eqns 1 and 2. For upper level selection, survivorship probabilities are assigned for each grouping, and these values are used to calculate the survivorship probabilities of constituent units; adjustments (detailed below) are then also necessary to maintain rates of unit extinction corresponding to those in the observed data set.

To calculate survivorship probability for units when selection is applied to groupings, let k be the number of constituent units with non-zero survivorship probability within a given grouping, and assume survivorship probabilities for these units are equal (u1 = u2 = … uk = u). All other constituent units have survivorship probability of zero. k is determined iteratively, by increasing the number of units within groupings assigned non-zero probability until the expected number of surviving units across all groupings is equal to that in the observed data. The value of u is calculated from the survivorship probability applied to the groupings using a rearrangement of eqn 1:

The process begins with all units' survivorship probability set to zero and proceeds as follows. The target number of surviving units is calculated as the sum of survivorship probabilities across all units in the observed data. In historical data sets, where survivorship is known and binary, this is simply the number of survivors. For each grouping, one constituent unit is picked weighted by its observed survivorship probability, and its new survivorship probability is calculated using eqn 3 with = 1. (If survivorship is binary, this is equivalent to choosing one unit per surviving grouping.) Once this step is completed for all groupings, if the expected number of surviving units equals or exceeds the target number, correlations rn and sn are calculated. Otherwise, a single additional unit, among those in all groupings, is chosen weighted by its observed survivorship probability. This unit's new survivorship probability, and those of all other units with non-zero survivorship in that grouping, is recalculated using eqn 3, with k for that group increased by one. These last two steps are repeated until the expected number of surviving units equals or exceeds the target number, or until no unit remains whose survivorship probability equals zero. Once the target number of surviving units is attained, rn and sn are calculated. The entire process is repeated for N iterations, and the P value is calculated using eqn 2.

To model cases in which survivorship is known (binary), during each iteration survivorship probabilities at the lower level are obtained by drawing from a uniform(0,1) distribution, assigning survivorship probability of one if the draw is less than or equal to the survivorship probability and zero otherwise.

For interpreting results, we suggest the following decision process: if < α, tentatively reject the null hypothesis that upper level groupings are arbitrary with respect to selection. If lower level selection simulations also yield < α, rule the results a potential false positive. If observed P > α and upper level simulations yield > α, rule a potential false negative.

The approach allows simulation of upper- and lower level selection under a variety of extinction selectivities and intensities (slope and intercept parameters, respectively). This means that the sensitivity and specificity of the method can be tested not only under parameters obtained from fitting a logistic regression to the data set being analysed, but also under parameter values obtained for other extinction events. Thus, further simulation can elucidate whether the method could have rejected the null hypothesis had selection operated under different parameters.

The results of these tests can be summarized graphically by calculating rs for each test and simulation, and plotting these values as density functions. On these plots, the P value is the percentage of each distribution to the left of zero; for data sets in which we reject the null hypothesis the bulk of the distribution is to the right (example in File S6). Importantly, however, because rn is a constant value for observed data, but varies in the simulations, simulations are expected to yield a wider distribution of rs and consequently slightly inflated P values. Because of this, we will consider here simulations under both standard (0·05) and relaxed (0·1) α values.

An outline of this analysis pipeline is available in File S1.

Geographic range analyses

The five data sets we examined are listed in Table 1. Our initial focus was on late Cretaceous North American bivalves and gastropods across the K-Pg mass extinction event, for which Jablonski (1986) had found evidence of genus-level selection. As the original raw data set was not available in numerical format, we obtained the list of Maastrichtian (final geological stage of the Cretaceous) molluscan genera from Jablonski (1979) and downloaded North American Maastrichtian and Paleogene (first geological period of the Cenozoic) geographic occurrence data for each of these genera from the Paleobiology data base (hereafter PaleoDB –http://paleobiodb.org) accessed 17th February 2013. This data set is listed in Table 1 as MNAK (Mollusc, North America, K-Pg). We performed a second analysis using the global geographic ranges of the same genera from MNAK, which were also obtained from the PaleoDB accessed 17th February, 2013 (data set MGK – Mollusc, Global, K-Pg). Occurrences in the last geological stage of the Cretaceous (Maastrichtian, coded as minimum age of 65·5 mya in data set) were used to calculate geographic range size for both data sets, and Paleogene occurrences of the same species were taken as indicating survivorship across the mass extinction boundary. For all data sets, we excluded all occurrences with irregular species names (sp., n. sp., form A, etc).

Table 1. Data sets used in analysis
Data Set Taxa Location Time Interval Total Sp. Groups Surviving Sp. Groups Source Notes
MNAK Bivalves and Gastropods North America K-Pg 110 13 (Jablonski 1979); PaleoDB Maastrichtian genera from (Jablonski 1979); geographic occurrence data, and Paleogene occurrence data from PaleoDB
MGK Molluscs Global K-Pg 111 22 PaleoDB Same genera as MNAK, but global in extent
CGK Scleractinian Corals Global K-Pg 39 21 (Kiessling & Baron-Szabo 2004); PaleoDB Chosen to offer comparison between molluscs and other well-skeletonized invertebrate groups during K-Pg mass extinction
IGP Marine Invertebrates Global P-Tr 110 4 (Clapham & Payne 2011); PaleoDB P-Tr genera from (Clapham & Payne 2011), geographic occurrence data from PaleoDB. Chosen to test perspectev using another mass extinction
MNZC Bivalves, Gastropods, and Scaphopods New Zealand Middle Eocene – Present 45–120 36–105 Crampton et al. (2011) Chosen to compare multiple background extinction events in molluscs

We wanted both to assess the broader applicability of this method and to compare our results from K-Pg molluscs to those for other taxa and extinction events. We analysed three additional mass extinction data sets: data set CGK (Corals, Global, K-Pg) – global scleractinian coral genera across the K-Pg event, from lists provided by Kiessling & Baron-Szabo (2004) and occurrence data for the same genera obtained from the PaleoDB, accessed 29th August 2014; data set IGP (Invertebrates, Global, P-Tr) – a diverse sampling of well-skeletonized marine invertebrate taxa globally across the Permo-Triassic mass extinction obtained using genera listed by Clapham & Payne (2011) and occurrence data from PaleoDB, accessed 21st August 2012; and data set MNZC (Molluscs, New Zealand, Cenozoic) – bivalve, gastropod and scaphopod molluscs across several intervals of background extinction during the Cenozoic of New Zealand, obtained by personal communication from Michael Foote as well as from Crampton et al. (2011). We used this last data set to look for evidence consistent with selection above the species level and compare mass extinction and background extinction episodes (Jablonski 1986). For this purpose, we identified in the MNZC data set eight intervals in which the rates of both species and genus extinction were greater than their rates of origination, removed one (0·07 mya) that upon subsequent filtering (see below) showed no victim species and labelled the remaining seven intervals as background extinctions. Data sets for these background extinction events were analysed in the same way as for mass extinctions. In data sets where placement before or after an extinction event was given quantitatively (MNAK, MGK, CGK, and MNZC), age was taken as the minimum listed age of the occurrence. In IGP, occurrences were gathered based on presence in the Changhsingian and listed as survivors based on presence in the Triassic. Only pre-extinction occurrences were used in range calculations. Details regarding the number of taxa included and the intervals over which occurrences were used are summarized in Table S2. Major contributors to the PaleoDB data sets used here are cited in File S8.

The location of an occurrence was defined by the paleolatitude and paleolongitude listed for the fossil locality, except in MNZP where only modern latitude and longitude were available. The size of the geographic range at each level was calculated as the area of the Euclidean minimum convex polygon encompassing its occurrences (wild1 package in R, Sargeant 2011). Because an area cannot be defined by fewer than three distinct points, we omitted species that had fewer than three geographically distinct occurrences. This led to substantial reduction in the number of species and genera used (see Table S2; consequences are explored in the Discussion section). Background extinction data went through two rounds of filtering – first, for determining extinction intervals, all species with fewer than three occurrences across the Cenozoic were removed; secondly, species were filtered further to preserve only those with more than three occurrences in the extinction interval being tested. Because the Euclidean minimum convex polygon area assumes a flat plane, the paleocoordinates were transformed using a Mollweide projection provided by the mapproj package (McIlroy et al. 2014; see also Usery & Seong 2014). For all analyses described here, values for geographic range size were log-transformed because geographic range frequency distributions otherwise tended to be right-skewed. Ranges were scaled to a mean of zero and variance of one to allow the relative effects of several potential survivorship predictors to be assessed on a common scale (see next section).

Species were grouped into taxa (genera) according to their classification before the extinction event, as determined by the authors of the respective data sources. These are hereafter referred to as ‘species groups’ rather than genera because several key differences exist between these taxonomic groupings and genera (described more fully in the Discussion section) and to avoid confusion between the properties of these filtered genus-level species groups and those of more complete Linnean taxa.

Measuring effects of species richness and species-group range on survivorship

To determine the effect of permutation on geographic range size, we tracked the median and interquartile geographic ranges for permuted species groups in each data set. If species within real species groups were more spatially co-localized than expected by chance, we expect permuted species groups to have larger interquartile geographic ranges. Alternatively, if species groups are more spatially dispersed than expected by chance, we expect permuted species groups to have smaller interquartile ranges.

Species richness is kept constant during permutation. To examine its role in each data set, we fit multiple logistic regression models in which species richness either was or was not included as a predictor of species-group survival. For these analyses, we scaled species-group range size (after log transformation) and species richness by mean centring each and dividing by their standard deviations. This allowed their relative associations with survival to be considered on a comparable scale.

We additionally performed simulations on data sets with varying intensity, selectivity and species richness, described in File S3.


As we detail below, results suggest that the permutation method developed and implemented in perspectev is a reasonably effective and robust means of detecting evidence consistent with natural selection on higher taxa in fossil data, provided that samples of both surviving and extinct taxa are sufficiently large. In both global and North American K-Pg mollusc data sets, we reject the null hypothesis that differential survival of species groups with respect to geographic range size was reducible to effects of this trait at lower levels. Although we fail to reject this null hypothesis in the other data sets tested, we were able to demonstrate efficacy of the method more generally through simulations. Results are summarized in Table 2, Fig. 1 and Files S3 and S4.

Table 2. Summary of permutation and power analysis results
Data Set Observed P value P values from simulations
Species selection Sp. gr. sel. Species selection Sp. gr. sel.
M = 1·04 M = 3·54 M = 3·54 Observed species param. Observed sp. group param. Observed sp. group param.
B = −3·32 B = −3·73 B = −3·73
Mass Extinction
MNAK 0·005 0·45 0·39 0·021 0·45 0·38 0·023
MGK 0·001 0·30 0·27 9e-04 0·35 0·33 0·002
CGK 0·573 0·40 0·29 0·114 0·47 0·44 0·368
IGP 0·136 0·15 0·01 0·000 0·22 0·02 0·056
MNZC Background Extinction (mya)
10·94 0·921 0·46 0·36 0·075 0·50 0·49 0·687
6·6 0·135 0·47 0·44 0·308 0·49 0·50 0·098
5·17 0·254 0·60 0·67 0·458 0·45 0·42 0·392
2·4 0·146 0·62 0·63 0·002 0·54 0·54 0·367
1·71 0·685 0·52 0·10 5e-04 0·62 0·61 0·581
0·4 0·964 0·45 0·30 0·115 0·51 0·52 0·471
0·225 0·111 0·68 0·52 0·093 0·50 0·54 0·353
  • The first data column gives the P value of observed in the data set. The next three give P values under simulated selection using MNAK parameters (M = slope, B = intercept) at different levels: M = 1·04, B = −3·32 are lower level parameters, while M = 3·54, B = −3·73 are upper level parameters. The remaining three columns give P values from analogous simulations but with parameters observed in each data set individually. Values <0·05 are in bold, and values <0·1 but >0·05 are italicized.
Details are in the caption following the image
Plots of rs for (a) North American K-Pg molluscs (MNAK), (b) global K-Pg molluscs (MGK), (c) global K-Pg scleractinan corals (CGK) and (d) global P-Tr marine invertebrates (IGP), both observed and simulated. O: Observed; S1/2: species selection simulated with MNAK species/species-group level parameters, respectively (Table 2), G: Simulated species-group selection.

Mass extinction of North American and global K-Pg molluscs

For North American molluscs (MNAK), our permutation analysis returned a P value of 0·005, indicating that the correlation observed between range and survivorship from genus-level species groups is not likely to be found for arbitrary groupings of species. We then compared this value to those produced by simulation of species-group (upper level) and species (lower level) selection under different parameters on the same data set. Fitting a logistic regression to species survivorship and geographic range gave an intercept of −3·32 and a slope of 1·04. Simulating species selection under these same parameters gave a P value of 0·45. Fitting a logistic regression to species-group survivorship and geographic range gave an intercept of −3·73 and a slope of 3·54. Simulating species selection under these parameters gave a P value of 0·39, and simulating selection on species groups under these parameters gave a P value of 0·021. The results of these simulations compared with the observed P values are plotted in Fig. 1a. Note the substantial overlap between the rs distribution for species-group selection and the observed data.

Our global mollusc data set for the end Cretaceous (MGK) returned a lower P value of 0·001. For simulation analyses of this data set (as well as all subsequent data sets), we modelled selection using parameters fitted both from MNAK and from the data set being analysed. This allowed us to test the efficacy of the permutation approach in each data set using both a standardized set of mass extinction parameters and the set of parameters observed in the data under examination. These results are also summarized in Table 2. Importantly, for the global molluscan data set, all simulations of species-level selection returned P values much higher than 0·05. These results – plotted in Fig. 1b – lead us to reject the hypothesis that the significance of our upper level species groups during the K-Pg mass extinction was limited to North American molluscs and was rather a global phenomenon for these taxa.

Effectiveness of the permutation approach

Results of applying this technique to the other mass extinction and background extinction events are summarized in Table 2 and plotted in File S7. The null hypothesis is rejected when < α (0·05 here). Among these, true positives are indicated when simulations of selection on species groups using MNAK species-group parameters also yield values of P < α (fourth column of numbers in Table 2). True negatives are indicated when species selection simulations using either species- or species-group level parameters yield P ≥ α value (second and third column in Table 2). In discussing the performance of the simulation approach generally, our comments here will focus on results using one set of parameters – those for species and species groups from MNAK – with all data sets. Where the focus instead is on the results from a particular set of data, parameters observed for that data set should be used. As noted earlier, whereas r in observed data sets is constant between iterations, r varies in tests using simulations of selection, so greater variation is expected for rs and P values will be comparatively inflated. Results passing α thresholds of both 0·05 and 0·1 are therefore highlighted for simulation tests. Errors that were observed were almost always indicative of low sensitivity, not low specificity, which is important when testing for events expected to be rare. Overall, the method showed reasonable sensitivity by rejecting the null hypothesis under upper level selection (< 0·05: 5/11, < 0·1: 7/11) and high specificity by failing to reject the null hypothesis under lower level selection (P > 0·05: 21/22, > 0·1: 21/22). Simulations performed in File S4 describe sensitivity and specificity of this analysis on the mass extinction data sets under a wider variety of slope and intercept parameters. Simulation analyses detailed in File S3 further demonstrated the method's robustness for application to taxonomic groupings of varying richness and under a variety of selective scenarios.

Interpreting results from the two other mass extinction data sets is less straightforward. The P value for CGK is too large to reject the null hypothesis and simulation analyses suggest that even if upper level selection did occur on the corals during the K-Pg mass extinction, its signature was not strong enough to be recognized with confidence, and this example would yield a false negative (Table 2, Fig. 1c). With only 39 species groups prior to extinction, CGK was by far the smallest mass extinction data set considered, and the high P values obtained for simulations on this data set indicate that if selection for the defined species groups had occurred at the intensity and strength experienced by molluscs during the same extinction event, our method would be unable to detect it.

IGP, on the other hand, was a large data set but contained only 4 surviving species groups and 7 surviving species. This produced the unusual results of < 0·05 for species and species groups when selection was simulated at either level with species-group level parameters from the MNAK data set, a pattern similar to that produced in simulations using IGP species-group parameters (Table 2, Fig. 1d). This result demonstrates the importance of supplementing observed results with simulations to clarify whether imposing selection at different levels in a particular data set in fact yields different patterns of correlation between trait and survivorship. Because of the limitations in the data sets CGK and IGP, namely small data set size and small numbers of surviving species groups or species, these data perhaps serve best as test cases for the effects of small sample size on the method, rather than as formal tests that the correlation between species-group range and survival is reducible to the species level in these taxa.

None of the seven background extinction intervals produced a P value <0·05 for observed data or for simulations at either level using observed parameters. However, for upper level selection simulated with MNAK parameters, two intervals showed < 0·05 and two showed < 0·1. This indicates that the method could have detected species-group selection in these intervals were selection acting at mass extinction, but not at observed, strength and intensity. The other three intervals showed high P values for all simulations tested, but each of these included fewer than 70 species groups. Importantly, no background interval returned a P value less than 0·1 for species selection under either parameter set. This indicates that while sensitivity in some data sets was fairly low (true positive rate was 2/7 or 4/7, depending on α value), the method showed high specificity in all background intervals tested (14/14).

Logistic regression results

We performed two logistic regressions for upper level survivorship: (i) on species-group geographic range alone and (ii) on species-group geographic range and species richness. These results are summarized in Table 3. Comparing the parameter estimates from these regression models indicates the relative effects of range size and species richness in predicting species-group survivorship. In the cases producing < 0·05, MNAK and MGK, the geographic range parameter was by far the strongest determining factor in species-group survivorship and, consistent with Jablonski (2008), was relatively unchanged with the inclusion of species richness. For all other data sets, the inclusion of richness as a factor resulted in a parameter estimate for geographic range that was either reduced or consistently small (a value of ~1 or less) and usually the less predictive of the two parameters for species-group survivorship. In fact, we found that in multiple background extinction intervals all victim species groups had species richness less than or equal to all surviving species groups (perfect linear separation).

Table 3. Logistic regression results
Data set Survivorship vs. range Survivorship vs. range + richness
Intercept Range Intercept Range Richness
Mass extinction
MNAK −3·73 3·54 −3·65 3·32 0·12
MGK −2·80 2·90 −2·74 2·68 0·21
CGK 0·15 0·71 0·27 0·51 0·84
IGP −5·66 2·93 −4·66 0·85 0·98
MNZC background extinction (mya)
10·94 1·89 0·24 2·03 0·08 0·73
6·6 2·17 1·02 Perfect linear separation
5·17 1·48 0·59 Perfect linear separation
2·4 2·66 0·79 Perfect linear separation
1·71 3·37 0·88 3·37 0·87 0·01
0·4 4·29 0·39 Failed to converge
0·225 4·56 0·97 Perfect linear separation
  • Regression parameters obtained from logistic regression models of species-group survivorship on species-group range (first two columns) and species-group range + species richness (last three columns). Parameters could not be obtained in cases of perfect linear separation, in which all surviving species groups had richness greater than or equal to the richness of all victim species groups, or of failed model convergence.

Changes in permuted interquartile ranges

If species groups (as a proxy for genera) are more spatially localized than random assemblages of species, we expect permuted species groups to have, on average, larger geographic ranges. This was observed for all mass extinction data sets we considered, but not frequently in background extinction events, perhaps because our background extinction data were restricted to New Zealand whereas taxa from the mass extinctions were more widespread. The results for all of these analyses are summarized in File S5.


Here, we present a generalizable framework for testing the reducibility of the relationship between differential survival of upper level groupings and traits defined at that level. Correlation between upper level traits and survivorship is not uncommon (e.g. for geographic range size of genera see Payne & Finnegan 2007; Harnik, Simpson & Payne 2012; Harnik et al. 2014), but without validation, it is potentially explainable by processes acting on those traits at a lower level producing upper level ‘sorting’ (see Vrba & Gould 1986; Gould 2002; and Grantham 2007). Unlike previous methods for detecting upper level selection (Simpson 2010; Powell & MacGregor 2011), the method we present here directly assesses the hypothesis that observed patterns of upper level survivorship are likely to be produced by arbitrarily grouped lower level units.

Caution is warranted when ascribing a low P value to upper level selection. Most importantly, this method tests the hypothesis that correlation between upper level traits and survival could be generated by arbitrarily grouped lower level units, and upper level selection can only be invoked as one potential explanation for the rejection of this null hypothesis. Further, Lewontin (1970) outlined three criteria for evolution to result from selection at a given level, paraphrased as phenotypic variation, differential fitness and heritability of phenotype. The method implemented here addresses only the first two criteria. However, previous work using a similar permutation approach detected heritability of species-level range sizes in North American molluscs across the K-Pg extinction (Jablonski 1987; Hunt et al. 2005 Harnik, Simpson & Payne 2012), so the third criterion may have been fulfilled in that case. Regardless, our analyses demonstrate that the differential survival across the K-Pg event with respect to geographic range of North American molluscan genus-level species groups (i) is unlikely to have been produced by random combinations of species and (ii) was not limited to North America, but extended to the global geographic ranges of these taxa. Importantly, our global analysis only considered molluscan taxa with representatives in the New World; future work may elucidate whether all genera of gastopods and bivalves across the K-Pg would show this effect.

We also note that while our upper level species groups were defined by their genus classification, our results need not apply exclusively to the genus level. Because all species with fewer than three distinct occurrences were removed (see Material and methods and Table S2), each of the taxonomic groups tested consisted of a minority of the species present in the original data set. Further, fossilized genera may or may not represent monophyletic groups. This may not preclude these species groups from serving as evolutionarily relevant individuals, or at least as subsampled proxies of evolutionarily relevant individuals. However, it does mean that more completely sampled genera might not show the same patterns, and that we cannot make claims about the exact taxonomic level putatively under selection in the data sets used here.

Our results from multiple mass extinction events, during which some taxa show evidence consistent with upper level selection, are in line with Jablonski's (1986) proposal of alternation of macroevolutionary regimes between times of mass and background extinction. On one hand, we found that the background extinction intervals tested showed little evidence for the evolutionary significance of genus-level species groups; however, as with any test of hypotheses in a frequentist framework, we must remain agnostic in instances in which we fail to reject the null hypothesis. Further, because only one level of grouping and trait were tested here, it is possible that the macroevolutionary regime shifted to different, untested levels and traits in data sets where we fail to reject the null hypothesis. Future analyses and applications of our method to other taxa and more thoroughly vetted data may provide a better understanding of the generality of regime change during mass extinctions.

Our results also bear on long-standing discussions concerning the extent to which taxonomic groupings can serve as evolutionary entities (for instance Dawkins 1976; Gould 2002; Okasha 2003; Hendricks et al. 2014). Here, we show that for at least some taxa, during some extinction events, observed macroevolutionary patterns differ significantly from what would be expected if genus-level species groups constituted arbitrary groupings of species. This finding is consistent with previous thinking that the geographic range of taxonomic groups above the species level may serve, during times of pronounced ecological turnover, as a biologically relevant emergent property affecting their survival.

It could be objected that survivorship of these species groups is related not positively towards geographic range, but negatively towards existence in certain locations – for instance, near the Yucatan peninsula during the K-Pg bolide impact (Schulte et al. 2010). However, the location of impact is stochastic with respect to global biogeography, and selection for existence outside of a randomly defined geographic locality is effectively positive selection for large range size. In such a scenario, taxa inhabiting too small an area are likely to be situated entirely within or outside the area subject to environmental perturbation. However, sets of species groups may have ranges both large and variable enough to experience differential survival of taxa with large ranges. If data from such a scenario returned a low P value from perspectev, we would correctly conclude that the pattern observed for those species groups was not simply a collective effect of differential survival with respect to range sizes at the species level.

Subsidiary analyses on data sets of varying unit richness, with selection simulated across a range of intensities, selectivities, stochastic variation (‘noise’) and survivorship probability types (binary vs. continuous) give some insight into the effects of confounding variables on perspectev's efficacy (detailed in File S3). Almost all simulations of upper level selection with slope >1 gave < 0·05, and almost all simulations of lower level selection gave > 0·05. Interestingly, while adding noise to the selection process decreased sensitivity of analyses, it also increased specificity by weakening the signal of lower level selection. It may be hypothesized that low unit richness will make upper level survivorship patterns reducible to lower level patterns, with the extreme example of all groupings having only one constituent unit, making upper- and lower level selection identical. There is some evidence for this: in the case of continuous survivorship probability, simulations of lower level selection under mean unit richness of 1·1 consistently gave P  values <0·05 for groupings. However, this effect was diminished with increased noise and was not observed in simulations with binary survivorship probability.

The effect of permutation on trait values is also important to consider. As shown in File S5, in geographically widespread data sets permuted species groups tended to have larger ranges than observed species groups. However, because correlation rather than covariance was used to measure selective effect, differences in scale between ranges of observed and permuted genera are not expected to significantly impact our results. Further, as also shown in File S5 for MNAK and MGK, although the difference is not as large as in observed species groups, surviving permuted species groups nevertheless show larger ranges than victim species groups.

The differential survival of upper level groupings with regard to emergent properties is almost certainly of importance to conservation efforts, as species and ecosystems continue to turn over at a global scale (Carpenter et al. 2008; Wake & Vredenburg 2008; Barnosky et al. 2011), and potentially shift macroevolutionary regimes. Future work using the approach developed here could test the hypothesis that certain groups of species or ecological groups are expected in the future to undergo differential survival with respect to traits not reducible to the species level. If shown to be the case, this may suggest that some communities are better managed as functional units, rather than as collections of species with separate management plans.

Ultimately, perspectev provides a framework for testing hypotheses such as these. This framework is extendable to virtually any well-defined upper/lower level grouping system, such as Linnean taxa, monophyletic clades and ecological groups. Further, it contains a diverse library of trait functions including geographic range size, trait variation and mean pairwise genetic distance and can also accept user-written trait functions. Survivorship probability may be either binary (as in historical extinctions) or expressed probabilistically, allowing prediction of whether upper level groupings will survive differentially with respect to traits that are not reducible to lower levels. While these variations of the test are not explored in detail here, a demonstration of their implementation is available as a tutorial (see Data accessibility). In demonstrating the method, we find evidence consistent with previous studies suggesting that upper level selection occurred in North American molluscs during the K-Pg mass extinction, and we extend this result to the same genera globally. Importantly, there are two related questions these analyses seek to answer. First, with respect to natural selection, have higher taxonomic groupings in the past undergone differential survival with respect to irreducible traits? Secondly, and much more broadly, in what circumstances and with what biological effect has this phenomenon shaped evolutionary history, and to what extent can it be expected to shape the future? We believe these analyses have shown that the first question can be answered in the affirmative. For the second question, we have released our method as the R package perspectev and invite others to contribute to finding the answers.


We thank Michael Foote, James Crampton and other maintainers of FRED for providing the data set for Cenozoic molluscs, and David Jablonski for helpful discussions of data sources. Suggestions made by an anonymous editor substantially improved the model of selection used; comments by Carl Simpson, Megan Morikawa, Liam Revell and two anonymous reviewers improved the manuscript. Hoehn's work was supported by an A.B. Duke Research Grant, Goldwater Scholarship and Marshall Scholarship; Harnik's work was supported, in part, by a National Evolutionary Synthesis Center Postdoctoral Fellowship (National Science Foundation grant EF-0905606). We gratefully acknowledge the researchers who collected these data and those who compiled the data in the Paleobiology Database. This is Paleobiology Database publication number 234.

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