The punctuated equilibrium model predicts that phenotypic change is concentrated into pulses associated with speciation, with little change otherwise accruing in established lineages. Palaeontological tests of this model have generally lacked an adequate phylogenetic and modelling framework, whereas tests relying on extant populations lack direct constraints on the evolutionary dynamics within lineages.
This study extends a modelling approach developed in comparative studies and applies it to a clade with a rich fossil record, the deep-sea ostracode genus Poseidonamicus. Using a phylogenetic framework and an independent set of shape traits plus body size, a model was fit that allows estimation of anagenetic (within-lineage) evolution, cladogenetic (speciational) change and geographic variation within species.
Maximum-likelihood parameter estimates suggested dominantly speciational change for only one or two shape traits, depending on model assumptions. For the remaining shape traits and body size, the contribution of anagenesis was always substantial. Confidence limits on these solutions were quite broad (although narrower when multiple traits were analysed jointly), with most traits consistent with both strongly anagenetic and strongly cladogenetic change.
Whereas uncertainty about phylogenetic topology and species limits has little influence on the conclusions, assuming stasis instead of Brownian motion within lineages shifted support to solutions in which speciational change was more dominant, although several traits remained dominantly explained by anagenetic evolution.
These results suggest that for the traits and taxa examined, anagenesis contributes substantially to long-term divergence. The uncertainty in the results highlights the analytical difficulty of decomposing anagenetic and cladogenetic sources of phenotypic evolution, even with fossil constraints. When model uncertainty is taken into account, the task of doing so using observations from entirely extant populations is even more daunting.
The model of punctuated equilibrium makes two central claims about how phenotypes evolve (Eldredge & Gould 1972). The first is that species do not change much once they are established, a pattern referred to as stasis. Second, lasting phenotypic changes are concentrated into pulses associated with the formation of new species during cladogenesis. The first of these claims has been investigated extensively by palaeontologists, who have documented numerous examples of stasis within fossil lineages, although other patterns occur with reasonable frequency (Gingerich 1985; Erwin & Anstey 1995; Levinton 2001; Hunt 2007c, 2008b; Hopkins & Lidgard 2012). The second claim, that rates of change are elevated at speciation, has proven far more difficult to assess with the fossil record. With only a handful of cases studies claiming to have sampled cladogenetic events in detail (Gingerich 1976; Kellogg 1983; Lazarus 1986), the inference of pulsed change at speciation has mostly relied on presumed consequences of allopatric speciation (Eldredge & Gould 1972), stratigraphic overlap between putative ancestor and descendant species (Gould 2002), and from considerations that observed rates of change within lineages are too slow to produce the total divergence seen in clades (Stanley 1978).
To test more directly the relative importance of changes within species vs. those accompanying cladogenesis, ideally one would want to take ancestor to descendant sequences and stitch them into a phylogenetic framework. This approach was taken in a series of studies by Alan Cheetham and colleagues that examined the Caribbean bryozoan genus Metrarabdotos (Cheetham 1986, 1987; Jackson & Cheetham 1990; Cheetham, Jackson & Hayek 1993, 1994; Cheetham, Sanner & Jackson 2007). These authors considered in careful detail the species limits, phylogeny and genetic basis of morphological traits, finding that the evolutionary history of this clade was dominated by minor fluctuations within lineages and much larger transitions between related species. Collectively, they are widely viewed as the most rigorous palaeontological test of punctuated equilibrium's predictions, and there is a notable dearth of similar studies that attempt to combine ancestor–descendant sequences and phylogenetic information to address this issue (see also Bookstein, Gingerich & Kluge 1978; Pachut & Anstey 2009).
Parallel to the palaeontological investigations of punctuated equilibrium, a series of methods were developed to test for elevated rates of change at cladogenesis without the benefit of a fossil record. One class of approaches makes comparisons across clades, testing for correlations between morphological divergence and a proxy for the number of speciation events (Stanley 1975; Ricklefs 2004; Adams et al. 2009; Bokma 2010). A second class of methods dissects changes within a single clade using only terminal taxa in a phylogenetic framework. Pagel (1994, 1998) used a tree-scaling parameter to estimate a point on the continuum between fully anagenetic and fully cladogenetic change. Bokma (2002) developed an approach based on a more explicit evolutionary model, that of Brownian motion (BM) within lineages coupled with a pulse of change associated with speciation (see also Mooers & Schluter 1998; Ricklefs 2006). [Analogous methods also exist for discrete characters (Goldberg & Igic 2012; Magnuson-Ford & Otto 2012)]. Species missing from the analysis because they are extinct or otherwise unsampled can confound these attempts because their absence leads to the underestimation of the number of speciation events, and therefore, the opportunity for speciational change. Implementations of Bokma's model therefore attempt to estimate the number of speciations missing from a phylogeny using reconstructed rates of speciation and extinction (Bokma 2008; Mattila & Bokma 2008; Ingram 2011).
There are two potential limitations to these phylogenetic approaches for detecting elevated rates of speciational evolution. First, the signal for anagenetic vs. cladogenetic change is subtle: it hinges upon whether the magnitude of divergence between species is more strongly correlated with elapsed time (as predicted by anagenetic change) or with the number of speciation events (as predicted by cladogenetic change) since their common ancestor. These two quantities are often estimated with substantial error, and published analyses sometimes find nearly equivalent support for both dominantly anagenetic and dominantly cladogenetic solutions (Mattila & Bokma 2008; Ingram 2011). Second, in the absence of any direct record of changes within species, these approaches are only able to separate anagenetic from cladogenetic change with help from strong evolutionary assumptions, namely that traits evolve within lineages according to BM, and that missing speciations can be accurately estimated using a constant-rates, birth–death process. While not unreasonable, both assumptions are frequently violated (Hunt 2007c; Rabosky, Slater & Alfaro 2012; see also Ezard, Thomas & Purvis 2013) and the robustness of this approach in the face of such violations is unknown.
Separating the contributions of cladogenesis and anagenesis to trait evolution would be easier with independent constraints on one of these components. The fossil record can provide such constraints in the form of ancestor–descendant sequences of populations. Differences between such populations reflect only anagenesis because they are separated by time but not speciation events. Here, I illustrate this potential of the fossil record in a case study examining evolutionary patterns in the deep-sea ostracode genus Poseidonamicus. Ancestor–descendant sequences of populations are integrated with a phylogenetic hypothesis of this genus, and these jointly allow for the estimation of the anagenetic and cladogenetic components of trait evolution. These analyses take advantage of the strong analytical framework developed in phylogenetic studies while leveraging the fossil record as a key source of historic data.
Materials and methods
Fossil Populations and Phylogeny
This study focuses on deep-sea members of the genus Poseidonamicus, a monophyletic group that originated late in the Eocene and survives to the present day (Hunt 2007b). Phylogenetic relationships among species derive from a parsimony analysis of 42 characters related to carapace shape and the presence and nature of pores, ridges and other morphological features (Hunt 2007b). Importantly, the operational units scored for this analysis were spatially and temporally restricted populations, not species. After combining populations with compatible character codings (Hunt 2007b), this analysis produced a set of 42 507 equally parsimonious trees. Most of the conflict among these trees involved relationships among populations within traditionally defined species; the backbone of species relationships was generally well resolved (Hunt 2007b).
Populations with mutually compatible or similar codings for the cladistic characters were grouped to form species units. (Table S1). Some morphological variation was permitted within these species, the nature of which was informed by existing species concepts within this genus. Determining which morphological variants warrant species rank is necessarily subjective, but the consequences of adopting alternative species-level taxonomies are explored below. The species groupings were applied to all 42 507 equally parsimonious trees and each resulting species tree was scaled to absolute time using the geological ages of the fossil populations (Hunt 2007a,b). This temporal scaling was carried out using the function timePaleoPhy in the R package paleotree version 1.4 (Bapst 2012), setting a minimum branch length of 0·5 Myr and using the argument type = ‘mbl’. A minimum branch length is enforced because fossil occurrences only provide a minimum age for nodes, and without modification, they result in scaled trees with many zero-length branches. Such branches are unrealistic and analytically problematic (Hunt & Carrano 2010; Bapst 2013), although there are other ways of extending them using rates of sampling (Bapst 2013) or morphological evolution (Ruta, Wagner & Coates 2006).
The consistency of each of these species trees with stratigraphy was measured as the sum of its branch lengths; larger sums represent longer intervals of time for which a tree implies the existence of lineages that are not sampled. The species tree with the lowest summed branch length was selected and pruned to include only those species with morphometric data. This tree became the focal tree for subsequent analysis; the remaining trees were used in sensitivity analyses as described below. The focal tree has 14 species-level lineages encompassing 51 populations with morphometric trait data (Fig. 1).
The procedure outlined here requires a time-calibrated phylogenetic hypothesis, but it is agnostic as to how this is generated. Instead of the parsimony analysis employed here, one could use Bayesian analysis (Ronquist et al. 2012) or methods that incorporate stratigraphy and allow for some species to be ancestral to others (Fisher 1994; Wagner 1995; Marcot & Fox 2008).
Body size was measured as ln-transformed valve length (see Hunt & Roy 2006), and shape variables were taken as the first six principal component axes from a Procrustes analysis of ten anatomic landmarks defined by the intersection of ridges, pores and other features of the valve (Hunt 2007a)(Fig. 2a). Collectively, these components encompass 75% of the variance in the original data (PCs 1–6 individually account for 25%, 17%, 12%, 8%, 7% and 6%, respectively). All variables were standardized by the pooled, within-population variation for each trait, effectively transforming them into standard deviation units, similar in strategy to measuring evolutionary rates in haldanes (Gingerich 2009).
Critics of punctuated equilibrium have long noted the potential circularity of defining species on the basis of morphology and then testing if those same traits differ by species (Levinton & Simon 1980; Erwin & Anstey 1995). Importantly, in the present study, species boundaries were established from the cladistic characters, not on the basis of these morphometric or size traits. The morphometric data are not entirely independent of species differences – some of the cladistic characters relate indirectly to features that influence the position of the morphometric landmarks. Nevertheless, this correspondence is weak, and its effect should be far less of a concern here than in studies that use a single data set to both define species and trace evolutionary difference between them.
The model employed here is an extension of that developed by Bokma (2002). This model features evolution as Brownian motion within lineages with an anagenetic rate of per Myr. Lineage splitting adds a pulse of cladogenetic change at a rate of per speciation event. Both sources of change are nondirectional, adding an increment of trait change per unit time or speciation event that is normally distributed around zero. One additional source of morphological difference not modelled explicitly by Bokma is geographic variation within species. Here, population means are modelled as draws from a normal distribution with a mean equal to the species mean and a variance equal to VG. Thus, the expected difference in a trait value between two populations is distributed normally, with a mean of zero and a variance of
where t and s are elapsed time and number of speciation events that separate the two species. The same relationship holds for ancestor–descendant populations within a single species, except that s = 0 and the middle term disappears.
Visualizing Differences Within and Between Species
Shape differences within and between species can be visualized by ordinating the trait variables and plotting the populations and their phylogenetic topology with respect to morphology and absolute time, similar to the iconic figure by Cheetham (1986; updated in Cheetham, Sanner & Jackson 2007). The primary focus of the present study is the magnitude of morphological difference between sister species compared with the changes within species. One can more accurately show local differences by dividing the phylogeny into sections and performing the ordination separately on a few species at a time, although of course one then loses the ability to compare differences across the whole clade. This is similar in strategy to what was carried out by Cheetham, except that he ordinated separately pairs of species inferred to have an ancestor–descendant relationship. The first axis of a nonmetric multidimensional scaling ordination was used to represent morphology for this visualization, although a principal components analysis produces a similar arrangement of populations.
The genealogical structure of this data set is summarized in Fig. 1. A phylogenetic backbone connects the oldest populations of each sampled species; this backbone spans all known speciation events in this clade. Following Bokma (2002, 2008), these populations are jointly multivariate normally distributed, centred on the ancestral trait state of the root, with a covariance matrix equal to
where ΣA and ΣC are the variance–covariance matrices from anagenesis and cladogenetic change, respectively, diag (VG) is a matrix with the geographic variance parameter along the diagonal, and error is a diagonal matrix of squared standard errors of trait means of the tip populations. The likelihood of the model is then the density function of the multivariate normal with the above parameters, evaluated at the observed data points.
Added to the tips of this backbone is a set of ancestor–descendant populations capturing evolutionary change within established species. The log likelihood calculations for ancestor–descendant series follows Hunt (2006), modified to include geographic variation as described above for populations collected from different localities. Under the assumed model, the ancestor–descendant series span evolutionary transitions independent from each other and from the phylogenetic backbone, and so the log likelihood for a set of parameters (, VG) is equal to the log likelihood of the phylogenetic backbone plus the sum of the log likelihoods for all the ancestor–descendant series. Because traits were standardized by within-population variance, they are all on a comparable scale. As a result, one can estimate parameters within individual traits, or jointly by summing log likelihoods over multiple traits, each considered univariately, assuming that evolutionary dynamics are shared across traits.
Custom R (R Core Team 2012) functions were written to search parameter space for maximum-likelihood estimates of model parameters using the R function optim. Profile confidence intervals (Meeker & Escobar 1995) were generated as the set of parameter values within C units of the maximum-likelihood solution where C is half the 95% quantile for the chi-square distribution with degrees of freedom equal to the number of free parameters of the model (here, three parameters of interest translate to C = 3·907). The functions and data needed to perform this analysis were archived at the Dryad repository (http://dx.doi.org/10.5061/dryad.6s146).
The output from this model fitting produces parameter estimates for and VG. To facilitate comparing the relative importance of anagenetic vs. speciational evolutionary change, two derived quantities were calculated from the maximum-likelihood parameter estimates. The first is simply the ratio of the cladogenetic to anagenetic rates, . This ratio is interpretable as the magnitude of the pulse of change associated with speciation, in units of millions of years of anagenetic change. For example, when = 5, speciational change is as large as the accumulated change expected in 5 million years of anagenetic evolution. The second quantity computes, for a single species, the proportion of its total evolutionary change that can be attributed to the pulse associated with its formation. This proportion of cladogenetic change is equal to ), where T is the longevity of a typical species, here taken as eight million years, a reasonable figure for Poseidonamicus. Other metrics are available for summarizing the relative importance of anagenetic vs. cladogenetic changes for whole clades, rather than species-level lineages (Mattila & Bokma 2008; Ingram 2011).
Testing The Method Via Simulation
The ability of this approach to discriminate different scenarios of anagenetic vs. cladogenetic change was assessed by fitting this model to series of simulated data sets that used the observed data as a template (Supporting Information). These analyses showed that this approach can reliably fit this model with data similar to that available for Poseidonamicus (Fig. S1).
The outcome from this model-fitting exercise is downstream of a series of methodological steps and decisions, many of which have the potential to introduce considerable uncertainty to the results. Three sources of uncertainty were explored: uncertainty in the phylogenetic topology, uncertainty in grouping populations into species and uncertainty in the model of phenotypic change within lineages.
To explore the effects of uncertainty in the phylogenetic topology, the model-fitting procedure was repeated on a sample of trees derived from the 42 507 equally parsimonious species trees described above. This is a large number of trees overall, but after conspecific populations were condensed to a single species and species lacking morphometric data were pruned from the analysis, only 99 unique trees remained. The above model was fit to each of these 99 equally parsimonious trees.
Varying species limits
Model fitting was also repeated across a range of different schemes for grouping populations into species. Results are presented for two end-member scenarios of an extremely lumped (11 sampled species) and an extremely split (19 sampled species) species-level taxonomy (Table S1). As for the standard species limits, the topology most consistent with stratigraphy (that with the lowest summed branch lengths) under alternative species limits was used as the focal tree.
Palaeontologically sampled ancestor–descendant series capture only a portion of the history of that species, so one must rely on a model to fill in the predicted change over the unobserved portion. Under the model of Brownian motion used here, the expected variance in evolutionary outcomes scales linearly with elapsed time, and so rather substantial change can be imputed for the unsampled portions of species' stratigraphic ranges. This is inconsistent with views of stasis as stable, nonaccumulating fluctuations around a steady mean (Sheets & Mitchell 2001; Gould 2002; Eldredge et al. 2005). If this view is accurate, using BM will systematically overestimate the amount of anagenetic change that is expected within lineages.
To evaluate this potential model sensitivity, an alternative model assuming stasis within lineages was also fit. In this model, trait values are independent and normally distributed with variance VA around a steady mean (Sheets & Mitchell 2001; Hunt 2006). This model was parameterized differently than previous work (Hunt 2006, 2008a), so as to avoid the need to separately estimate the mean trait value across many lineages and traits (Supporting Information). Under this model, the proportion of a species' evolutionary change accounted for by the pulse of change at its formation is .
Ordinations of the populations reveal a variety of patterns within species (Fig. 3). Some species, such as P. miocenicus and P. rudis, show minimal variation over substantial periods of time. Other lineages, however, show morphological changes through their histories that are about as large as the differences between closely related species (e.g. P. major, P. pintoi and P. riograndensis). However, this figure is incomplete in that it does not indicate which differences are associated with shifts in locality (geographic variation). Moreover, different ordination strategies would produce somewhat different looking patterns. Accordingly, we must look to the model-fitting results for a better test of the importance of anagenetic vs. cladogenetic morphological change.
The maximum-likelihood parameter estimates for the model evaluated here indicate a substantial speciational component of change only for PC 1; all other shape traits and body size yield cladogenetic rates () that are at or near zero (Table 1). For PC 1, the ratio of cladogenetic to anagenetic rates is 6·59, indicating that its pulse of change associated with speciation is as large as the expected anagenetic change accruing over more than 6 million years. A speciational pulse of this magnitude would account for about 45% of the total evolutionary change occurring in a typical Poseidonamicus species (Table 1).
Table 1. Maximum-likelihood parameter estimates for a model with Brownian motion within lineages and cladogenetic change associated with speciation. All traits were standardized to standard deviation units before analysis, so values of 1·0 are equal to within-population trait variance. , the anagenetic rate of change; , the cladogenetic rate; VG, geographic variance within species. The last two columns are the ratio of the rates of cladogenetic to anagenetic change and the proportion of change within a typical species that can be attributed to its speciational pulse of change. In brackets, after the latter are its 95% confidence interval
% Cladogenetic [95% CI]
PC 1–6 jointly
As in previous studies using this model, estimation uncertainty around the best-fitting model can be quite broad. Although the best solutions for all traits except PC 1 imply completely anagenetic change, other solutions that imply substantial or even dominantly cladogenetic change are within the 95% confidence interval (Table 1). The exceptions are PC 4 and body size, as the confidence limits for both are broad but exclude scenarios in which cladogenetic change dominates. Discriminating power is improved by optimizing the model over all shape traits jointly (Table 1, Fig. 4). When PCs 1-6 are analysed together, there is strong support only for models in which anagenetic change accounts for the majority of phenotypic change. A potential disadvantage of optimizing the model over multiple traits is that this may mix the more speciational signal of PC 1 with more dominantly anagenetic evolution of the other traits. If only PCs 2–6 are fit jointly, support for dominantly anagenetic change is even clearer: the 95% CI on the proportion of cladogenetic change narrows to 0–28%.
Phylogenetic uncertainty has little effect on these results, as analyses performed over 99 equally parsimonious trees hardly differ from those on the focal tree (Fig. 5, left column). Different hypotheses about species limits also had little effect (Fig. 5). Employing vary narrow species limits (a highly split taxonomy) implied that PC 1 was somewhat less influenced by speciational change and that PCs 2 and 3 were somewhat more speciational, relative to the standard hypothesis of species limits. But the overall picture of dominantly anagenetic evolution is qualitatively unchanged.
The assumption that evolution proceeds as BM within lineages turns out to be more influential. Assuming stasis instead within lineages increases the importance of speciational change for PC 1, PC 4 and body size, but the remaining shape traits (PCs 2, 3, 5 and 6) are still estimated to have cladogenetic rates of zero (Table 2, Fig. 5). Overall, switching the anagenetic model from BM to stasis improves log likelihoods and model support (Table 3). The support advantage for stasis is moderate for PCs 1 and 2, but overwhelming (Akaike weights > 0·95) for all other traits.
Table 2. Maximum-likelihood parameter estimates for a model with stasis within lineages and cladogenetic change associated with speciation. Format follows Table 1. VA, the variance associated with within-lineage stasis
% Cladogenetic [95% CI]
PC 1–6 jointly
Table 3. Log likelihoods and AIC scores for models that assume BM vs. stasis within lineages. Because these two modes have the same number of parameters, ΔAIC scores are determined completely by the differences in log likelihood (logL) between the models. Stasis is preferred over BM for all traits
Akaike weight BM
Akaike weight Stasis
PC 1–6 jointly
Anagenetic Vs. Cladogenetic Change in Poseidonamicus
The results on a whole do not support the punctuated equilibrium notion that phenotypic change accumulates dominantly associated with speciation events, at least for most traits examined. The best model solutions indicate no detectable pulse of change at speciation for all traits except for PC 1 when BM is assumed within lineages; results are more mixed under the better-supported model that postulates stasis, rather then BM, within lineages. Even under stasis, however, anagenesis contributes substantially to divergence in body size and four of six shape traits, although confidence intervals around these solutions are quite broad.
Poseidonamicus is probably one of the most intensively studied genera among deep-sea ostracodes (Benson 1972; Whatley et al. 1986; Hunt 2007b), and the present study included all named species except for three described very recently from the modern Southern Ocean (Brandao & Paplow 2011). However, it is very likely that still other species are not yet known to science, and indeed, I have observed some specimens that belong to undescribed species too rare to include in these analyses. Missing speciations, if not accounted for, bias solutions towards inflated cladogenetic rates because pulses that are attributed to a single speciation event are in reality spread over several. As a consequence, the magnitude of each pulse – and therefore – is overestimated (Supporting Information, Fig. S2). Thus, not attempting to infer unsampled speciation events is conservative with respect to the conclusion that anagenetic change is an important component of evolutionary change.
It may be slightly surprising that using a highly split and a highly lumped species-level taxonomy had rather little effect on the analyses here, although it is hard to know the generality of this finding. The standard species-level taxonomy here, like that of Cheetham and colleagues, employed species limits that are somewhat narrower than traditional species concepts. Many deep-sea ostracode species are reported to have very broad distributions, often spanning multiple ocean basins (Coles, Ayress & Whatley 1990). This is perhaps unexpected for organisms lacking dispersal stages and, for most taxa, the ability to swim. Indeed, some recent morphological and genetic work suggests that at least some of the broad ranging ‘species’ identifications may mask cryptic diversity (Brandão, Sauer & Schon 2010; Brandão 2013). For the standard taxonomy in the present study, the recognized species encompass populations from the same or neighbouring ocean basins; none have the nearly global distributions ascribed to some deep-sea species.
Those features used to differentiate species in the present study are not the same as those analysed for their evolutionary mode. This tactic was used to avoid the potential circularity of dividing populations into species using some traits, and then testing if those species differ particularly in those same traits (Levinton & Simon 1980). However, one might counter that features that distinguish species are those in which much of the evolutionary change has been concentrated, and by avoiding such traits, one thereby misses important aspects of change. This is a valid point, and it highlights some of the difficulties of dealing with species in the fossil record. Nevertheless, if punctuated equilibrium is fundamentally correct, one should see its signal in all phenotypic traits, including those not used to define species. In fact, such traits may offer a clearer test of punctuated equilibrium than species-defining features because they are the only ones for which a signal of speciational change cannot be an artefact of how species are recognized. Another avenue for possibly avoiding potential circularity of species definition in the fossil record would be to develop methods to simultaneously estimate species limits, phylogeny and evolutionary models, but such an approach is likely to be a daunting technical challenge.
The Role of Geographic Variation
One pleasing feature of the modelling approach taken here is that once a population-level phylogeny and hypothesis of species limits are specified, all differences between populations are naturally accounted for by either anagenetic change, cladogenetic change or geographic variation. This last source of variation is not often incorporated into phylogenetic approaches (but see Freckleton & Jetz 2009), and in the present study, VG is mostly a nuisance parameter – not of primary interest in itself, but necessary to properly estimate rates of anagenetic and cladogenetic change. Nevertheless, it is an important source of variation, roughly equal in magnitude to within-population trait variance (Tables 1 and 2). For the most strongly cladogenetic trait, PC 1, the magnitude of geographic variation is about half the size of the pulse of change at speciation and for PCs 1–6 considered jointly, geography adds as much variation as about five million years of anagenetic evolution (Table 1). The contribution of geographic variation is particularly important in the present context because it creates differences between populations that are not correlated with elapsed time, and thus, may potentially mimic speciational change.
This modelled geographic variation is included here in addition to measurement error (Ives, Midford & Garland 2007). These two sources of intraspecific variation are not equivalent. Measurement error reflects sampling noise in estimating the mean trait value for species; it ignores spatial structure among specimens, and it is of known magnitude that decreases with the number of individuals measured, rather than being a free parameter of the model. The specific model of geographic variation used here is simple and unstructured. One could implement more complex models in which trait differences increase with physical distance or with environmental dissimilarity, but there is rather limited geographic sampling within species in the present study and thus little ability to distinguish among such scenarios. Although including geographic variation can add realism to evolutionary models, adding another source of difference between populations can complicate model optimization. For any anagenetic or cladogenetic rate estimate, there are other solutions that fit nearly as well that have somewhat lower rates coupled with higher estimates for geographic variation, and vice versa. This trade-off between evolutionary and geographic sources of variation contributes to the broad confidence limit on the relative importance of anagenetic and cladogenetic evolution.
Although geographic variation is a statistical nuisance in the current model, it may well be important in an evolutionary sense. Some models suggest that geographic variation can be the raw material for phenotypic changes associated with speciation. Under ‘incipient divergence’ and similar models (Futuyma 1987, 2010; Rosenblum et al. 2012), phenotypic shifts are occurring continually within local populations but they are fleeting as divergent populations are extirpated or assimilated by gene flow. In these scenarios, speciation is important in that it makes permanent, and therefore detectable in the fossil record, morphological changes that allow the recognition of new species. In terms of the parameters of the model used here, these models postulate that geographic variation can be converted into cladogenetic change. Other scenarios can be supposed by which VG is converted into anagenetic change through differentiation and extinction of demes within species. Although potentially important, these processes are operating at a grain finer than the modelling framework employed here, and their investigation thus requires different analytical tools.
Differences Among Traits
Across various permutations of phylogeny, species limits and model assumptions, PC 1 consistently shows more evidence of speciational change than do the other traits. Shape variation represented by this axis is complex, but it includes a substantial component of dorsal–ventral narrowing and anterior–posterior elongation (Fig. 2b). This aspect of shape distinguishes males from females in Poseidonamicus (Hunt 2007b) and many other podocopid ostracodes, as the large sperm and bulky copulatory apparatus of males are accommodated by an elongation of the carapace (van Morkhoven 1962; Cohen & Morin 1990). It is possible that the signal of more speciational evolution in PC 1 reflects episodes of sexual selection related to sperm competition, although one might expect this mechanism to co-occur with speciation more in traits related to mate recognition rather than male reproductive investment (McPeek et al. 2008).
Although the results for body size are similar to those for most shape traits, the anagenetic rate of change is much higher for body size, about 10-fold so when compared with the rate estimated from PCs 1–6 jointly (Table 1). This increased rate of within-lineage change is likely related to climate-driven trends towards increased body size in Poseidonamicus and other deep-sea ostracode lineages through the Cenozoic (Hunt & Roy 2006; Hunt et al. 2010).
Implications For Future Work
In the present study, the fossil record supplies what is not available for studies on extant species: a direct view of phenotypic changes occurring within species. Yet, despite these observations that independently constrain rates of anagenetic change, fitting the Bokma model to individual traits produce confidence limits that do not much constrain the relative dominance of anagentic and cladogenetic change. Although these limits do narrow when the model is optimized over multiple traits and would be expected to narrow when applied to clades more diverse than Poseidonamicus, these results highlight the difficulty of decomposing evolutionary change into speciational and within-lineage components.
Perhaps most troubling for attempts to apply this approach to exclusively extant organisms is the assumption of Brownian motion within lineages. Patterns consistent with BM are observed within fossil lineages with some frequency (Hunt 2007c), but the temporal scaling of morphological divergences (Uyeda et al. 2011) and rates of change (Hunt 2012) within fossil lineages do not support the assumption of unbounded, BM-like dynamics within established lineages. Instead, these studies suggest evolutionary dynamics within lineages are intermediate between BM and stasis, but closer to the latter. Indeed, in the present study switching from BM to stasis within lineages improved model log likelihoods for all traits (Table 3). Repeated observations within the same lineage allow us to compare the support for alternative assumptions in this case study, but the same is not possible for studies of extant populations. Moreover, one cannot even fit this model with data from exclusively extant populations when anagenetic evolution is modelled as stasis. Under this scenario, each speciation adds an amount of evolutionary change equal to VA + , but there is no way to separate the contribution of the speciational pulse () from the subsequent variation in stasis (VA) because neither accumulates with time.
I thank the editors for organizing this special issue, and for the invitation to submit this manuscript. G. Miller, R. Benson, C. Sanford and S. Schellenberg helped with access to specimens, and G. Slater provided helpful feedback. I thank F. Bokma, P. Wagner and an anonymous reviewer for their helpful suggestions for improving the manuscript.