The University of Chicago

On Age and Species Richness of Higher Taxa. Author(s): Tanja Stadler, Daniel L. Rabosky, Robert E. Ricklefs, and Folmer Bokma Source: The American Naturalist, Vol. 184, No. 4 (October 2014), pp. 447-455 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/10.1086/677676 . Accessed: 07/11/2015 19:47 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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vol. 184, no. 4

the american naturalist

october 2014

On Age and Species Richness of Higher Taxa Tanja Stadler,1 Daniel L. Rabosky,2 Robert E. Ricklefs,3 and Folmer Bokma4,* 1. Department of Biosystems Science and Engineering, Eidgeno¨ssische Technische Hochschule (ETH), Zurich, Switzerland; 2. Department of Ecology and Evolutionary Biology and Museum of Zoology, University of Michigan, Ann Arbor, Michigan 48109; 3. Department of Biology, University of Missouri, St. Louis, Missouri 63121; 4. Department of Ecology and Environmental Sciences, S90187 Umea˚ University, Umea˚, Sweden Submitted December 11, 2013; Accepted March 17, 2014; Electronically published August 29, 2014 Online enhancement: appendix.

abstract: Many studies have tried to identify factors that explain differences in numbers of species between clades against the background assumption that older clades contain more species because they have had more time for diversity to accumulate. The finding in several recent studies that species richness of clades is decoupled from stem age has been interpreted as evidence for ecological limits to species richness. Here we demonstrate that the absence of a positive age-diversity relationship, or even a negative relationship, may also occur when taxa are defined based on time or some correlate of time such as genetic distance or perhaps morphological distinctness. Thus, inferring underlying processes from distributions of species across higher taxa requires caution concerning the way in which higher taxa are defined. When this definition is unclear, crown age is superior to stem age as a measure of clade age. Keywords: birth-death process, diversification, macroevolution, phylogenetics, speciation.

Why some groups of organisms are species rich and others are species poor is a fundamental question in evolutionary biology (Hutchinson 1959). Four general explanations have been proposed for the disparity in species richness among higher taxa. First, clades may vary in age, so that older groups have had more time to accumulate species (McPeek and Brown 2007). Second, clades might vary with respect to their net rate of species accumulation, so that more rapidly diversifying clades contain more species. Third, the species richness of clades might wax and wane predictably through time, such that some old clades have low species richness (Pyron and Burbrink 2012; Quental and Marshall 2013). Finally, diversity might be limited by ecological factors, with variation in species richness arising from differences in the ecological space available to members of different clades (Ricklefs 2007; Ricklefs et al. 2007; Rabosky 2009, 2010; Barraclough 2010). * Corresponding author; e-mail: [email protected]. Am. Nat. 2014. Vol. 184, pp. 447–455. 䉷 2014 by The University of Chicago. 0003-0147/2014/18404-55148$15.00. All rights reserved. DOI: 10.1086/677676

The first explanation predicts that older clades contain more species than younger clades, because older clades have had more time to accumulate species. Also if diversification rates vary among clades, as the second explanation assumes, species richness should on average remain positively related to clade age (Rabosky 2009, 2010; Ricklefs 2009). The remaining two models need not predict a positive relationship between clade age and species richness. Some very old but low-diversity clades (e.g, coelacanths, lungfishes, rhynchocephalians) were characterized by much higher diversity in the past (Stanley 1979), implying that at least some named higher taxa have undergone pronounced declines in species richness through time. Likewise, ecological constraints on clade diversification through time can lead to a decoupling between the ages of clades and their species richness. A number of recent studies have addressed—from different points of view—the relationship between the ages of clades and the numbers of species they contain (Magallo´n and Sanderson 2001; Bokma 2003; Ricklefs 2003, 2006, 2007, 2009; McPeek and Brown 2007; Ricklefs et al. 2007; Rabosky 2009; Rabosky et al. 2007, 2012). While one study suggested that crown age of clades explains species richness (McPeek and Brown 2007), several others have reported nonexistent or even negative relationships between clade age and extant species richness, apparently consistent with the hypothesis that ecological factors regulate species richness (Ricklefs 2006, 2009; Ricklefs et al. 2007; Rabosky 2009; Rabosky et al. 2012). Here we demonstrate that the manner in which higher taxa are defined can lead to a decoupling between clade age and species richness, challenging the notion that these patterns result from clade-specific differences in evolutionary or ecological processes. We investigate the expected relationship between clade age and species richness when age (or some proxy like genetic distance or phenotypic disparity) is used as a criterion to define clades. We demonstrate that the absence of positive stem age–diversity relationships, or even a negative relationship, can arise

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448 The American Naturalist purely from the manner by which higher taxa are defined. Our analysis should not be interpreted as evidence against the existence of ecological limits to species richness. However, it emphasizes that we should be cautious about ascribing particular causal mechanisms to diversity patterns until we can eliminate the possibility that such patterns resulted from the manner by which higher taxa are recognized (Rabosky 2010). “Algorithms” for the Delimitation of Higher Taxa The various “algorithms” by which human perceptual biases led to the delimitation of some clades as higher taxa, while ignoring many other possible groupings, remain relatively intractable. It is clear, however, that taxonomic practice leading to the recognition of higher taxa is partly subjective and differs between groups of species. Obviously, this makes it difficult to derive analytical expressions for the relation between clade age and species richness. Therefore, we will consider different definitions of higher taxa when below we investigate the relationship between stem age (i.e., the time of split that separates the clade from the rest of the tree), crown age (i.e., the age of the most recent common ancestor of the extant members of the clade) and species richness. First (i), we consider a stringent definition in which all lineages existing at some time h before the present serve to define stem lineages leading to extant higher taxa (fig. 1). Then (ii) we relax

the definition by assuming that basal lineages are sampled from an interval [hmax hmin]. Finally (iii) we consider a very liberal definition in which stem lineages for higher taxa are randomly sampled from all branches in the phylogeny. To obtain analytical results we must assume a model for the diversification of clades. For each of the three taxon definitions (i–iii) we consider two scenarios. (a) Following most previous studies of species numbers in higher taxa (e.g., Raup et al. 1973; Raup 1985; Foote et al. 1999; Magallo´n and Sanderson 2001; Nee 2001; Bokma 2003; Ricklefs 2007; Stadler 2010; Stadler and Bokma 2013), we assume a constant-rates birth-death process (crBDP; Kendall 1948; Bailey 1964) where speciation rates are constant across taxa. In addition, (b) we investigate variable rates, assuming that speciation and extinction rates differ between taxa but are constant within taxa. Let l and m denote the speciation and extinction rates, respectively, so that the net rate of diversification is l ⫺ m, and the species turnover rate is m/l. Under the crBDP these rates are equal for all species within a clade and constant over time, so that the number of species n in a clade of age t is geometrically distributed (given n 1 0) with expectation e(l ⫺ m)h (Bailey 1964). In other words, the number of species in a clade is expected to increase exponentially unless l ≤ m. Hence, all else being equal, we would expect older taxa to contain more species. (Under alternative models of diversification, the number of species

h to clade 1 clade 2 to clade 3

clade 4

tsc stem age

crown age

Time

Figure 1: The Sibley-Ahlquist model for defining higher taxa. Named higher taxa are clades with crown ages younger than some time h but with stem ages older than h. If this definition is applied consistently to a complete phylogenetic tree, h will intersect the branch leading from the stem ancestor to the crown ancestor for each named clade. Here, h defines four clades (crown groups not shown for clades 1 and 3). Crown clades 2 and 4 are denoted by bold branches. The length of the branch between stem ancestor and crown clade is denoted by tsc (shown here for clade 4). Note that clade 2, with low species richness, is associated with a younger crown age, an older stem age, and a longer waiting time tsc between stem and crown groups, relative to the more species-rich clade 4.

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Age and Species Richness of Higher Taxa 449 is also expected to increase over time, but the increase may be other than exponential.)

E[log (n)Fh, l, m, tstem] p E[log (n)Fh, l, m], E[log (n)Fh, l, m, tcrown] p E[log (n)Fl, m, tcrown] p log (2) ⫹ E[log (n)Fh p tcrown , l, m].

Stringent Definition of Higher Taxa (i) Consider a complete phylogenetic tree for a clade generated under a constant rate of diversification and draw a line through the tree at some time h (fig. 1). We define higher taxa as those groups with a stem age older than h but with a crown age younger than h. This strict definition was applied to higher taxa of birds by Sibley and Ahlquist (1990), who defined families (with some exceptions based on traditional taxonomic practice) by drawing a line through the avian phylogeny at 9 units of genetic distance (corresponding to approximately 40 Ma), as mathematically formalized in Stadler and Bokma (2013). Following this practice, each intersected lineage in figure 1 represents a clade containing the extant species that descended from it. Figure 1 illustrates that a clade is a crown group with a stem age older than h but a crown age younger than h. Our aim is to derive analytical expressions for the relationship between stem age tstem, crown age tcrown, and species richness n, for a crBD model with a stringent definition of higher taxa. If we assume speciation and extinction rates l and m and cutoff time h, then species richness n, stem age tstem, and crown age tcrown are random outcomes of the crBD process. We calculate the expectation of tstem, tcrown, and n, given h, l, and m. As we consider clades with surviving species, we condition all expressions on the process not dying out before the present time: E[tstemFh, l, m] p h⫹

[1 ⫺ (m/l)e⫺(l⫺m)h] log {1/[1 ⫺ (m/l)e⫺(l⫺m)h]} , (1) (l ⫺ m)(m/l)e⫺(l⫺m)h E[tcrownFh, l, m] p h 1 ⫺ , ⫺(l⫺m)h 1⫺e l⫺m

E[tcrownFh, l ⫺ m] p

(2)

E[log (n)Fh, l, m] p (l ⫺ m)h ⫺ log

[

]

1 ⫺ (m/l) . 1 ⫺ (m/l)e⫺(l⫺m)h

(3)

Equations (1)–(3) are proven in the appendix, available online. Note that the expectations for tstem and log(n) depend on h, l ⫺ m, and m/l, while tcrown only depends on h and l ⫺ m. In addition, we calculate the expected species richness n given stem age tstem or crown age tcrown:

(4)

(5)

Equation (4) follows from equation (3), because given l, m, and h, then tstem is a random outcome of the crBD process. Equation (5) involves equation (3) because each of the two lineages descending from the basal split at crown age tcrown is expected to have E[log(n)Fh p tcrown , l, m] descendants at present. We will now discuss how stem age, crown age, and species richness n, are expected to correlate for a fixed h. First we consider constant speciation and extinction rates (see “Constant Diversification Rates [i-a]”) followed by variable rates (i-b). In these analyses, we set h p 1 without loss of generality, because this defines one time unit as the time to the cut of the tree. A process with an arbitrary age h can be rewritten as h p 1 (i.e., the process is scaled by 1/h), because multiplying l and m by h (meaning l and m are multiplied by h while m/l remains constant), ages in the tree are just scaled by 1/h, which is easy to verify for crown age and stem age based on equations (2) and (3). Constant Diversification Rates (i-a) If we fix l and m (and h p 1), we of course also obtain fixed expectations for stem age, crown age, and number of extant species from equations (1)–(3). Still, equations (4) and (5) provide insight into clade age and species richness relationships. First, the stringent definition of a higher taxon yields no correlation between stem age and size of a clade, because each lineage at time h has the same expected number of present-day descendants, independent of stem age (eq. [4]). Another way to see this is that in a given tree with k higher taxa, each permutation of the k subtrees attached to the k ancestral lineages present at age h is equally likely, so there is no correlation between stem age and clade size. This observation holds independently of conditioning the tree on having a fixed age, a fixed final number of species, or both; we never expect a correlation between stem age and species richness under the crBDP if clades are delimited using a stringent criterion. The same conclusion was reached already in 1976 by Farris, who showed that when two sister taxa diversify at the same (but not necessarily constant) rate, then all possible partitions of n species between the sister taxa are equally likely. Our argument can be regarded as the generalization of Farris’s (1976) result to k “sister” taxa. While there is no correlation between stem age and clade size, according to equation (5), there is a positive relationship between crown age and species richness, as clades with

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5 4 3 2

log(species richness)

Different taxa may have different rates of speciation and extinction. For h p 1, we now vary l and m in order to investigate the consequences of unequal diversification rates for the relationship between clade age and species richness. First we note that for different l ⫺ m we obtain the orange and red lines in figure 2 for different fixed clade ages. However, for different l ⫺ m, the clade ages may not be equally distributed along the orange and red lines. We investigate this dependence of clade age on l ⫺ m and m/l in figure 2 by plotting in black the expected stem and crown age (eqq. [1], [2]) as a function of the expected number of species (eq. [3]) for l ⫺ m and m/l p 0.25 (dotted), 0.5 (solid), and 0.75 (dashed). First, the plot reveals that for a certain net speciation rate l ⫺ m, expected stem age depends little on the turnover rate m/l, because the dotted, solid, and dashed lines for m/l p 0.25, 0.5, and 0.75 roughly coincide. Second, and most importantly, the correlation between diversification rate and stem age is negative. This can be seen in figure 2 from the intersections of the relation between species richness and expected stem age (e.g., solid black line) with the relations between stem age and species richness for l ⫺ m p 1, 2, ..., 5 (red lines). In other words, if net rates of diversification l ⫺ m differ between higher taxa, then clades with low diversification rate l ⫺ m are expected to be old and contain few species, while clades with high diversification rate l ⫺ m are expected to be young and contain many species. That is because a taxon with a low net speciation rate is expected to be species poor but is also expected to have a longer basal lineage (or stem, crossing the h taxon definition) and hence to be older than a taxon with a high net speciation rate. This leads to the perhaps counterintuitive expectation that old clades are species poor if rates of speciation differ between clades, and demonstrates that a negative correlation between stem age and number of species in empirical data might indicate differences in net speciation rates between clades. The expected crown age of clades defined through h depends only on the net diversification rate and not on the species turnover rate. Therefore, this relationship is illustrated in figure 2 by only one solid black line (and no dotted or dashed lines). This solid black line intersects the orange lines that indicate the relations between crown age

1

Varying Diversification Rates (i-b)

0

an earlier first split have more opportunity to accumulate species. This is illustrated in figure 2, where orange lines indicate the expected positive relation between crown age and species richness (eq. [5]), and red lines the absence of a correlation between stem age and species richness (eq. [4]), for m/l p 0.5 and l ⫺ m p 1, 2, ..., 5.

6

450 The American Naturalist

0.0

0.5

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1.5

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clade age Figure 2: Relation between stem age, crown age, and expected number of species per higher taxon under the stringent and relaxed definition of higher taxa. Orange, red, and black lines correspond to h p 1. Orange and red lines from bottom to top plot species richness for given crown (orange, eq. [5]) and stem ages (red, eq. [4]) for fixed l ⫺ m p 1, ..., 5). Black lines indicate the relation between clade age and species richness given crown age (eqq. [1], [3]) or stem age (eqq. [1], [2]). The gray curve represents the same relationships as the black curve but for h p 1.5 (i.e., the axis is stretched by 1.5). Stem age and species richness depend on m/l which is set to 0.5 for all solid lines. Changing m/l has a minor influence on the pattern: m/l p 0.25 is plotted with black dots, and m/l p 0.75 is plotted with black dashes. Increasing h from 1 to 1.5 for fixed l ⫺ m is plotted for the crown age in green and the stem age in blue (l ⫺ m p 2, 3).

and species richness for l ⫺ m p 1, 2, ..., 5. These points of intersection reveal that if net rates of diversification l ⫺ m differ between higher taxa, then clades with low diversification rate l ⫺ m are expected to have a young crown age and contain few species. Summarizing, if rates of speciation and extinction differ between higher taxa, then taxa with high diversification rate l ⫺ m are expected to have an old crown age, a young stem age and contain many species, and vice versa for taxa with low diversification rate. To highlight that an h different from 1 merely stretches the axis, we plotted the expected crown and stem ages of clades for h p 1.5 and m/l p 0.5 in gray in figure 2. Relaxed Definition of Higher Taxa (ii) The avian tribes and families (Sibley and Ahlquist 1990; Sibley and Monroe 1990) that were analyzed by Ricklefs (2006) and Rabosky (2009) were defined applying strict and clear definitions of higher taxa based on an ultrametric phylogeny, making them particularly useful for illustrative

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Age and Species Richness of Higher Taxa 451 purpose. However, in most other groups of species, taxa have been defined in a far less tractable fashion, generally as groups of species showing comparable levels of morphological distinctness. Nevertheless, such taxonomies may show broad similarities to those based on ultrametric phylogenies. (Sibley and Ahlquist 1990 made some minor exceptions to their strict definition to match traditional taxonomy.) Thus, the definition using constant h that we analyzed above does not generally apply to higher taxa but can serve as a basis to investigate less stringent definitions of taxa. Instead of assuming that all higher taxa are defined with a strict genetic distance h, that is, by drawing a line through the phylogeny exactly at time h (fig. 1), we now assume that taxa are defined by sampling higher taxon stem lineages from the time window [hmin, hmax]. This is a less stringent definition, because some taxa may have crown ages exceeding the stem ages of other taxa. Constant Diversification Rates (ii-a) To investigate the case of relaxed definition of taxa, we again first assume a constant net speciation rate l ⫺ m. For fixed l ⫺ m but increasing h, we have tstem, tcrown, and n increasing (eqq. [1]–[3]). This is illustrated in figure 2 where for l ⫺ m p 2 and l ⫺ m p 3 (and m/l p 0.5), the relationship between clade age and species richness for 1 ! h ! 1.5 is shown for crown age (green) and stem age (blue). Thus, under the relaxed definition of higher taxa, we expect a positive correlation between clade age (both stem and crown) and size. However, the strength of this correlation depends on the interval [hmin, hmax] and vanishes in the case of stem age for hmin and hmax approaching each other (i.e., hmin p h p hmax), as we have shown above. Varying Diversification Rates (ii-b) We now consider the case where basal lineages are sampled from the interval [hmin, hmax] and where l ⫺ m varies between taxa. (We fix m/l p 0.5 as we showed above that it only has minor influence on the outcome.) For each fixed h but varying l ⫺ m, the relationship between species richness and crown age is positive, as shown by the black line in figure 2. When h varies but l ⫺ m is constant, we also have a positive relationship, as indicated by the green lines in figure 2. If both h and l ⫺ m vary, we maintain a positive relationship between crown age and species richness. For 2 ! l ⫺ m ! 3 and 1 ! h ! 1.5, the relevant area of relationships is the area enclosed by the green, black, and gray lines in figure 2. The relation between stem age and clade size is more complicated: if h is fixed, then size differences between clades are due to differences in l ⫺ m and the relation

between stem age and species richness is negative, as illustrated by the (dotted, solid, or dashed) black lines in figure 2. This will similarly be the case if hmin ≈ hmax. However, if hmin and hmax get further apart while l ⫺ m is constant, the relation becomes positive. Thus, when both l ⫺ m and h vary, the relationship between stem age and species richness may be negative (if variation in l ⫺ m is dominant) or positive (if variation in h is dominant). When 2 ! l ⫺ m ! 3 and 1 ! h ! 1.5 we expect a positive relationship, in the area enclosed by the blue, black, and gray curves in figure 2 (although whether a positive relation is observed depends on the sampling distribution of ages and species numbers). Liberal Definition of Higher Taxa (iii) Finally, we consider a scenario where higher taxa are defined by randomly choosing basal lineages, so that each branch irrespective of its position in the phylogeny is equally likely to be the stem lineage of a “higher” taxon. Now we condition our calculations on having picked a clade with stem age tstem, and the model has remaining parameters l and m. This liberal definition of higher taxa can be regarded as the extreme of the relaxed definition above, where hmin p 0 and hmax p ⬁ (and where different h may be chosen with different probabilities). Constant Diversification Rates (iii-a) Under the liberal definition of higher taxa and the crBDP, expected clade size is simply E[nFl, m, tstem] p

[

(l ⫺ m)tstem ⫺ log

(6)

]

1 ⫺ (m/l) . 1 ⫺ (m/l)e⫺(l⫺m)t stem

Using equation (3), we can relate crown age to stem age: E[tcrownFl, m, tstem] p E[tcrownFl ⫺ m, tstem] p

(7)

tstem 1 ⫺ . 1 ⫺ e⫺(l⫺m)t stem l ⫺ m

These equations are plotted in figure 3, which shows the positive correlation expected between stem age (black), crown age (gray), and diversity. As equation (6) depends on m/l, we evaluated it for m/l p 0.25, 0.5, and 0.75. Because l ⫺ m and time always appear as a product, which can be easily checked if multiplying equation (7) by l ⫺ m, changing l ⫺ m is equivalent to changing the timescale. This means that by increasing l ⫺ m, we simply shrink the horizontal axis in figure 3 by the same factor.

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452 The American Naturalist Table 1: Expected correlation of the numbers of species of higher taxa with stem age and crown age for different definitions of higher taxa, when speciation and extinction rates are constant across higher taxa or variable between higher taxa

Varying Diversification Rates (iii-b) Consider again varying diversification rates l and m. For all values of l ⫺ m, species richness increases with clade age. Differences in l ⫺ m may introduce additional variation in species richness between clades, lowering the correlation of species richness with clade age. However, the expected correlation always remains positive.

Definition

l and m

Correlation with tstem

Correlation with tcrown

Strict (i)

Constant Variable Constant Variable Constant Variable

0 ⫺ ⫹ ⫺ to ⫹ ⫹ ⫹

⫹ ⫹ ⫹ ⫹ ⫹ ⫹

Comparing the Strict, Relaxed, and Liberal Definition

Relaxed (ii)

Summarizing the analytical results above, we found that crown age is always positively correlated with species richness. This result is independent of the definition of higher taxa and independent of variation in speciation and extinction rates, provided that rates of speciation and extinction are constant through time. For stem ages, the correlation depends on the definition of higher taxa and on diversification rate heterogeneity among clades. When rates of speciation and extinction are equal across taxa, we expect no correlation between stem age and size under the strict definition of higher taxa. Under the relaxed and liberal definition of higher taxa, however, we expect clades with older stem ages to contain more species. If rates of speciation and extinction differ between taxa, we expect a negative relation between stem age and species richness under the strict definition but a positive relation under the liberal definition. The relaxed definition represents a gradient between those extremes: if hmin ≈ hmax, then the relation between clade age and size resembles that expected under the strict definition (i.e., negative correlation),

Liberal (iii)

Note: The plus sign stands for positive, the minus sign for negative, and 0 for no correlation.

whereas if hmin K hmax, the relation resembles that of the liberal definition (i.e., positive correlation). These findings are summarized in table 1.

Empirical Data

4 3 2 0

1

log(species richnes)

5

6

To exemplify the above considerations, we analyzed an approximately complete species-level reconstructed avian phylogeny (Jetz et al. 2012; we used the maximum clade credibility tree of the avian subtree for the tips with genetic data and the Hackett backbone). We investigated the relationship between clade age and log(species richness) fitting a linear model using the function lm and testing for significance using Pearson’s test within the function

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clade age Figure 3: Relation between stem age (black), crown age (gray; eq. [7]), and expected number of species (eq. [6]) per higher taxon under the liberal definition of higher taxa. Stem age depends on m/l, as illustrated for m/l p 0.25 (dotted), 0.5 (solid), and 0.75 (dashed). Here l ⫺ m p 1; the plot for general l ⫺ m p D is equivalent to the plot for l ⫺ m p 1 with the abscissa scaled by a factor D.

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Age and Species Richness of Higher Taxa 453

Discussion Several studies have investigated relations between species richness and ages of higher taxa. Three methodological articles (Magallo´n and Sanderson 2001; Bokma 2003; Paradis 2003) prominently featuring the idea that E[n] p e(l ⫺ m)t have together been cited by more than 500 articles. Furthermore, Rabosky et al. (2012) investigated the behavior of a simple model where higher taxa originate under a Poisson process (see also Aldous et al. 2008; Maruvka et al. 2013). They found that such a model was expected to result in positive relationships between stem clade age and species richness, even when rates of species diversification varied among clades, provided that rates within clades were constant through time. As we have shown here, the expectation of a positive relationship between stem age

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cor.test in the R package stats (http://cran.r-project.org). We first collapsed lineages so as to obtain a phylogeny of families as defined by traditional taxonomy (fig. 4B). In that phylogeny, log(species richness) is positively related with crown age (slope 0.040, p p 1.77e⫺06) but not with stem age (slope 0.009, p p .202). As we have summarized in table 1, the absence of a significant relation between species richness and stem age does not mean that special diversification processes are acting, involving, for example, ecological limits. Absence of a relation may simply be due to the way in which families were defined. Indeed, if we collapse clades in a random tree of the posterior avian phylogenies provided by Jetz et al. (2012), according to the stringent taxon definition (we chose h p 40 Ma, see fig. 4A), we also obtain a positive relation between log(species richness) and crown age (0.070, p p 2.96e⫺11) and no relation of log(species richness) and stem age (⫺0.007, p p .569). Such correlation patterns are also recovered in simulated trees: when simulating trees with n p 10,000, l ⫺ m p 0.070, and m/l p 0.5 and then again collapsing clades at 40 Ma, all 10 simulated trees show a positive relation between log(species richness) and crown age (0.071–0.078, p ! 10e⫺15) while only in one tree a significant correlation between log(species richness) and stem age is observed (p p .01, all other trees p p .31, ..., .98). We emphasize that the commonly used ecological models to explain the absence of a relation between stem age and species richness do not fit the bird data here. Such ecological models predict no relation between crown age and species richness, while the bird data show a significant positive relation. On the other hand, our model with stringent higher taxon definition predicts the observed positive relation between crown age and species richness, and no relation between stem age and species richness. Table 2 provides a summary of these regression analyses.

0

clade age Figure 4: Analysis of a species-level reconstructed phylogeny of approximately 10,000 present-day bird species. A, Relation between clade age (red for crown and blue for stem age) and species richness when a strict cutoff is applied at 40 Ma. B, Relation between clade age and species richness when clades represent taxonomically defined families. Gray lines are linear regression lines. Black is the expected relationship when only the crown age slope is used from the regression.

and species richness may be incorrect, as it depends on the particular model of diversification and definition of higher taxa. Many studies have identified young taxa as “unexpectedly” species rich, but our results show that such patterns can result from the manner in which higher taxa are delimited. For example, under scenarios i-b and ii-b, clades with young stem ages are expected to contain not fewer but more species than clades with old stem ages (table 1). In other words, studies may have incorrectly identified

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454 The American Naturalist Table 2: Strength of relation between log(species richness) and clade age for clades in the avian phylogeny Crown age

Cutoff at 40 Families

Stem age

Slope

Intercept

Correlation

Slope

Intercept

Correlation

.070 .040

.523 1.626

.478 (P p 2.96e⫺11) .434 (P p 1.77e⫺06)

⫺.007 .009

2.793 2.266

⫺.044 (P p .569) .121 (P p .202)

Note: Clades were defined both with a stringent definition (40 Ma) as well as through traditional taxonomy (families).

young taxa as unexpectedly species rich because they neglected how taxa were defined, and consequently incorrectly expected young taxa to be species poor. McPeek and Brown (2007) compared a sample of distantly related taxa of various age, thus adopting a definition of higher taxa like our scenario iii (liberal). They found that clade age correlates positively with species richness but only in comparisons across major groups (birds, mammals, insects, etc.) and not within these groups. Studies focusing on more closely related taxa, potentially resembling our strict (i) or relaxed (ii) taxon definitions, report no or negative correlations between stem age and species richness (Ricklefs 2006; Ricklefs et al. 2007; Rabosky 2009; our fig. 4 and table 2). Furthermore, a phylogenetically controlled analysis involving 1,400 clades of multicellular eukaryotes, found no relationship between stem age and clade size at any timescale (Rabosky et al. 2012). Failing to detect a correlation may in part be due to reduced statistical power, as taxon definitions (i) and (ii) yield a narrower range of taxon ages than definition (iii). However, narrower age ranges cannot explain negative relations. We therefore suggest that the nonpositive correlations are an artifact of the definition of higher taxa, instead of signatures of the diversification process. Overall, we should be cautious about ascribing particular causal mechanisms to clade diversity patterns until we can eliminate the possibility that such patterns result from artifacts of the manner by which higher taxa are recognized. In summary, it is unlikely that the strict definition of higher taxa applied by Sibley and Ahlquist (1990) applies to many other data sets, and unfortunately, definitions of higher taxa vary between groups of organisms in an often intractable fashion. Therefore, in many cases the expected relation between species richness and stem age of taxa remains unknown. However, irrespective of the definition of higher taxa and irrespective of whether or not speciation and extinction rates are constant across taxa, under all the scenarios we considered we expect species richness to increase with crown age of taxa (table 1). Therefore, tests aiming to determine whether species richness is determined by clade age, diversification rate, ecological limits, or some other factors affecting macroevolutionary dynamics, should use crown age and not stem age. When crown ages are unavailable, it may be possible to apply a stringent

clade definition retrospectively, placing h at the most recent time where the phylogeny is believed to contain all lineages. In general, it is important to bear in mind that the many ways in which higher taxa are recognized pose significant challenges for macroevolutionary studies of species richness patterns.

Acknowledgments We thank G. Thomas for providing the maximum clade credibility bird tree. We thank S. Claramunt, A. Pyron, and the editors for valuable comments on an earlier version of the manuscript. T.S. thanks the Swiss National Science Foundation and ETH Zurich for funding. D.L.R. acknowledges the support of National Science Foundation grant DEB-1256330. R.E.R. thanks the curators of the University of Missouri for funding. F.B. thanks the Swedish research councils VR and Formas for funding.

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Associate Editor: Daniel L. Roelke Editor: Troy Day

“The Bill-fish (Scomberesox Storerii), Fig. 113, which but fifteen years since I saw stranded on the shore by the thousands, driven in by its devouring pursuers, has gradually decreased, till at the present time it has nearly, if not quite, been driven away, and I think that during the past year there was not one specimen seen at Provincetown.” From “The Habits and Migrations of Some of the Marine Fishes of Massachusetts” by James H. Blake (The American Naturalist, 1870, 4:513–521).

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On age and species richness of higher taxa.

Many studies have tried to identify factors that explain differences in numbers of species between clades against the background assumption that older...
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