Numerous evolutionary studies have sought to explain the distribution of diversity across the limbs of the tree of life. At the same time, ecological studies have sought to explain differences in diversity and relative abundance within and among ecological communities. Traditionally, these patterns have been considered separately, but models that consider processes operating at the level of individuals, such as neutral biodiversity theory (NBT), can provide a link between them. Here, we compare evolutionary dynamics across a suite of NBT models. We show that NBT can yield phylogenetic tree topologies with imbalance closely resembling empirical observations. In general, metacommunities that exhibit greater disparity in abundance are characterized by more imbalanced phylogenetic trees. However, NBT fails to capture the tempo of diversification as represented by the distribution of branching events through time. We suggest that population-level processes might therefore help explain the asymmetry of phylogenetic trees, but that tree shape might mislead estimates of evolutionary rates unless the diversification process is modeled explicitly.
The tree of life is highly imbalanced. Some branches subtend clades containing many species, whereas others are represented by relatively few extant lineages (Purvis 1996; Mooers and Heard 1997). This phylogenetic imbalance is generally greater than can be explained by the equal-rates Markov model (ERM) (Guyer and Slowinski 1991, 1993; Heard 1992; Mooers 1995), which implies significant differences among lineages in their net rates of diversification (Heard 1996; Mooers and Heard 1997). To account for such variation, much emphasis has been placed on identifying key innovations that may have facilitated the proliferation of particular lineages (Simpson 1953; Van Valen 1971; Heard and Hauser 1995). For example, in fish, the decoupled pharyngeal jaw has been identified as contributing to the spectacular radiation of African cichlids (Liem 1973). In flowering plants, the list of putative traits is long, with particular focus on growth form, pollination mode, and method of dispersal (Ricklefs and Renner 1994; Dodd et al. 1999; Salamin and Davies 2004). However, biological traits frequently account for only a small proportion of the variation in species richness among clades (de Queiroz 2002). Moreover, within clades, rates appear too variable through time to be explained by the evolution of one or few key innovations (Davies et al. 2004).
Individual-based models, such as neutral biodiversity theory (NBT), offer an alternative hypothesis for rate variation among lineages based on differences in abundance rather than traits (Hubbell 2001). Like MacArthur and Wilson's (1963) island biogeography theory, NBT assumes that species richness arises as a dynamic equilibrium between demographic rates of species origination and extinction. However, in NBT, these dynamics are modeled at the individual level, rather than the species level, by characterizing demographic rates on a per-capita basis. NBT models generally assume demographic symmetry, meaning that per-capita rates of birth, death, dispersal, and speciation are identical for all community members, irrespective of species identity (Volkov et al. 2005). Given this per-capita symmetry assumption, the speciation rate of a lineage increases proportionally with its abundance. Thus, NBT models naturally give rise to differences among species in net rates of diversification due to abundance differences, rather than trait differences, reflecting stochastic differences in per-capita demographic rates.
NBT models frequently show a good fit to species-abundance data from some communities, such as species-rich tropical forests (Volkov et al. 2003, 2005), although niche-based models may yield species-abundance distributions of similar form (Chave et al. 2002). In a recent paper, Jabot and Chave (2009) demonstrated that under a point-mutation mode of speciation, in which new species have an incipient abundance of one individual, NBT can also yield phylogenetic tree topologies with similar imbalance (the disparity in species richness between sister clades) to empirical observations. However, NBT has been criticized because predictions regarding species lifetimes and speciation rates often disagree with fossil data (Lande et al. 2003; Ricklefs 2003; 2006; Nee 2005). Recent work indicates that reconciling theory with data will require relaxing NBT assumptions to encompass speciation modes that yield incipient abundances >1 individual (Hubbell 2003; Hubbell and Lake 2003; Rosindell et al. 2010) and the effects of environmental stochasticity on population dynamics (Allen and Savage 2007). Few studies have explored how NBT dynamics affect phylogenetic structure (see, e.g., Hubbell 2001; Mooers et al. 2007), and none have yet considered more biologically realistic speciation scenarios, which yield daughter species with incipient abundances >1 individual (e.g., allopatric speciation), or the sensitivity of phylogenetic tree shape to the spatial structure of the metacommunity.
In this study, we address three issues relevant to NBT dynamics. First, we assess how tree imbalance varies with speciation rate, migration, and incipient species abundance (mode of speciation). Owing to the per-capita speciation assumption, we would a priori expect tree imbalance to be lower for metacommunities that exhibit a more equitable (i.e., even) distribution of abundance among species because variation in instantaneous per-lineage rates of speciation at a given moment in time directly reflects variation in species abundance, and hence the form of the species abundance distribution. Because the point-mutation mode of speciation yields rank-abundance distributions that are steeper (i.e., less even) than those of other modes, such as random fission (Hubbell 2001), we hypothesize that tree imbalance will be greater for point-mutation speciation than for other modes. Second, we assess the effects of these three variables on the relative distribution of branching times from the root to the tips of the tree. It is possible that NBT might explain well one axis of tree shape but not another; we therefore compare simulated tree topologies with empirical data. Third, we explore the relative times to ecological equilibrium (stability in species richness and relative abundance) versus evolutionary equilibrium (stability in phylogenetic tree shape). This issue is relevant because NBT models generally assume dynamic equilibrium between rates of speciation and extinction via neutral demographic processes, whereas many evolutionary lineages are thought to be products of “adaptive radiations” during which species rapidly proliferate via natural selection to occupy a range of habitats (Schluter 2000). Although there is evidence suggesting that many clades may be at equilibrium with respect to speciation and extinction dynamics (Phillimore and Price 2008; Rabosky and Lovette 2008b), it remains possible that tree shape retains the imprint of these earlier nonequilibrial processes.
Although some NBT models have analytical solutions, or can be approximated using coalescence-based methods (e.g., Tavare 2005; Allen and Savage 2007; Rosindell et al. 2008; Haegeman and Etienne 2009), general solutions characterizing the combined effects of speciation mode and dispersal on phylogenetic-tree shape have yet to be derived. Here, we aim to help fill this gap using simulations.
We simulate NBT communities under a range of different scenarios, and then characterize the shape of the phylogenetic trees connecting the species in each community. Scenarios were chosen based on two insights from speciation theory (Coyne and Orr 2004). First, because nearly all speciation modes yield incipient-species abundances greater than one individual, we varied incipient-species abundance, following a similar approach to that of Hubbell and Lake (2003). Speciation via fission—where incipient species abundance is greater than one—might not be considered a strictly “per-individual” model; nonetheless, assuming the special case of speciation by fission as modeled by NBT, the per-lineage probability of speciation remains directly proportional to its abundance. Second, because spatial processes are critical in several modes of speciation, we investigated the effects of spatially explicit migration and speciation on the origin and maintenance of biodiversity. Within the spatial context, fission fits a model of speciation via vicariance or peripheral isolates (Hubbell and Lake 2003). In the homogeneous case, fission may be consistent with mutation-order speciation, in which reproductive isolation may evolve as a byproduct of sexual selection or conflict resolution between selfish genetic elements within individuals (e.g., linked to cytoplasmic male sterility or meiotic drive) (Palumbi 2009; Schluter 2000).
SIMULATING METACOMMUNITY DYNAMICS
We investigated the effects of stochastic population-level processes on tree shape by varying the following demographic parameters: migration rate, m (0.005–0.8 individual−1 time step−1); per-capita speciation rate, υ (10−4−10−2 individual−1 time step−1); and incipient-species abundance, JS. We ran 1000 replicates for each parameter combination, for a metacommunity of size Jm= 104 individuals. At each time step in the simulation, an individual is chosen at random from the metacommunity and suffers one of two fates. First, with probability υ, the “ancestral” species to which this individual belongs undergoes speciation, which entails reassigning JS individuals to an incipient “daughter” species. We considered four scenarios to span the possible range of values for JS. At one end of this continuum lies the “point mutation” mode of speciation (Hubbell 2001), which corresponds to a fixed value of JS= 1 individuals. The other end corresponds to an “equal splits” mode of speciation, where half of the individuals comprising the ancestral species are assigned to the descendant. In the spatially explicit case, individuals are assigned to the new species only within the focal patch. “Random fission” lies between the two extremes (Hubbell 2001), and corresponds to the scenario where JS is a random uniform deviate between 1 and half the size of the ancestral species. Finally, we consider a fixed incipient species-abundance of JS= 10 individuals, following the modeling approach of Allen and Savage (2007).
Second, with probability 1 −υ, this individual dies and is replaced by the daughter of a randomly chosen individual. For the aspatial simulations, this individual is chosen from among all metacommunity members with equal probability. These models encapsulate, but are not necessarily limited to, a sympatric mode of speciation. For the spatial simulations, the metacommunity is divided into patches, and an individual is then chosen from within the patch with probability 1−m, and from a neighboring patch (i.e., eight-patch Moore neighborhood) with probability m, which corresponds to a migration event. For the spatial simulations presented in the Results, the metacommunity was comprised of JM= 104 individuals that were subdivided into a 10 × 10 square grid with fixed 100 individuals per patch. To explore sensitivity to boundary effects, main models were repeated assuming a wrapped torus (i.e., joining grid edges so that left meets right, and top meets bottom). As m approaches 0, each 100-individual patch can be viewed as an isolated metacommunity. Importantly, for the case where m= 1, metacommunity dynamics remain distinct from the aspatial model because migration is restricted to the immediate neighborhood.
The dynamics described above ensure that metacommunity size is held constant at JM individuals, so JM time steps corresponds to a single generation. Each simulation was run for 104 generations starting from a monospecific metacommunity, which was sufficient time to achieve a steady state with respect to phylogenetic tree shape and the form of the species abundance distribution in most cases (Results).
We assessed phylogenetic tree shape using two metrics. First, we estimated β of the beta-splitting model from Blum and François (2006) using the R package apTreeshape (Bortolussi et al. 2006). The parameter β was estimated using maximum likelihood based on the conditional probability, p(i | n), that the left sister clade is of size i given that the parent clade is of size n:
where Γ (z) is the Gamma function, and an(β) is a normalization factor (Blum and François 2006). In contrast to Colless’ index, IC, which is the most commonly used imbalance metric (Mooers et al. 2007), β is unbiased with respect to species richness, which facilitates comparisons among trees of different size. Trees where β < 0 are more imbalanced than those generated by the Yule (1925) model, which assumes that all species have identical stochastic per-lineage rates of speciation, whereas trees with β > 0 are more balanced than Yule expectations. To compare β estimates from our simulations to those observed empirically, we also calculated β for phylogenetic trees in TreeBASE (http://www.treebase.org/), following Blum and François (2006). Analyses were restricted to the set of 701 completely bifurcating trees because β can only be calculated for such trees, and resolving polytomies can introduce bias in tree imbalance (Mooers et al. 1995). Putative outgroups were pruned from the trees prior to calculating β (for further details see Blum and François 2006) to facilitate comparison with our simulated data. The comparison between simulated and empirical trees should be interpreted cautiously because TreeBASE is a nonrandom subset of published phylogenies. Consequently, some taxa may be represented in multiple trees, and empirically estimated imbalance metrics may be biased owing to incomplete taxonomic sampling, errors in tree reconstruction, and misidentification of outgroups (Heard 1992; Mooers 1995; Mooers and Heard 1997; Heath et al. 2008).
Second, we calculated the γ statistic of Pybus and Harvey (2000), which characterizes the distribution of internode distances from the root of the tree to the tips. Under a pure birth process, γ follows a standard normal distribution; γ > 0 indicates internal nodes are closer to the tips than expected under the pure birth process, whereas γ < 0 indicates that internal nodes are closer to the root than expected (Pybus and Harvey 2000). It is not possible to extract calibrated trees with branch lengths directly from TreeBASE. We therefore contrast our simulations with empirical estimates of γ (245 phylogenetic trees) from McPeek (2008).
To assess the relationships of these shape metrics to the form of the species abundance distribution, we characterized evenness using Simpson's index, D:
Greater values of D correspond to greater evenness in the form of the species abundance distribution.
For the aspatial simulations, which assume no dispersal limitation, tree imbalance, as indexed by β, increased moving from fission with equal splits and random fission to point mutation (Fig. 1A), which generates the lowest incipient-species abundances, JS (=1), and therefore the most inequitable split of individuals among daughter species. The simulations yielded β estimates spanning the range of empirically observed values (Table 1, Fig. 1A). Random fission and fission with equal splits yielded tree topologies with β values greater than Yule expectations (both P < 0.01 from Mann–Whitney test), implying that these speciation modes result in phylogenetic topologies more balanced than expected if all lineages had an equal probability of diversifying. For both fission and point mutation, variance in β decreased with increasing speciation rate, υ. However, average imbalance increased with υ for point-mutation speciation (Kruskal–Wallis chi-squared = 51.21, df = 2, P < 0.001; Fig. 1B), but was independent of υ for fission with equal splits (Kruskal–Wallis chi-squared = 1.88, df = 2, P= 0.39; Fig. 1B).
Table 1. Tree shape (β and γ) statistics, and respective demographic parameters for each of the various simulation models (Methods)
Tree size* (min/max)
*Median values from 1000 replicates.
For the spatial simulations, imbalance tended to increase with migration, m, although the strength of this relationship also varied with mode of speciation (Table 1 and Fig. 1C). For fission with equal splits, the effect of migration rate on tree imbalance was pronounced (Kruskal–Wallis chi-squared = 2990.87, df = 3, P < 0.001) over the full range of migration rates. By contrast, for point mutation, the trend was much weaker at moderate-to-high rates of migration (Fig 1C), although still highly significant overall (Kruskal–Wallis chi-squared = 1357.88, df = 3, P < 0.001).
In general, metacommunities that exhibit greater phylogenetic-tree imbalance, as indexed by β, also exhibit greater disparity in abundance among species, as indexed by Simpson's D (Fig. 2). These findings are as expected given the proportional relationship between per-species speciation rate and abundance in NBT models. Importantly, however, the strengths and magnitudes of these relationships vary with migration rate, m, and speciation mode (Table 2, Fig. 2). Equivalent slopes for the homogeneous case differ significantly (Table 2), and the slope of β against D for fission is weakly negative (P= 0.04), with greater imbalance in metacommunities with a more even distribution of abundance (Fig. 2) in this case of random splitting of parental abundances among daughter lineages.
Table 2. Regression coefficients for the model of tree imbalance (β) against Simpson's D with varying migration rates (m) and for the homogeneous case (see also Fig. 2).
*Simpson's D values were log +2 transformed prior to model fitting.
We found time to equilibrium in phylogenetic balance (evolutionary equilibrium) was of the same order of magnitude (103–104 generations, depending upon speciation rate) as time to ecological equilibrium, here quantified using Simpson's D (Fig. S1). Unsurprisingly, average time to evolutionary equilibrium was more rapid for fission; there was relatively more variation around the dynamic equilibrium in tree balance for low speciation rates (see also the large interquartile range for point mutation in the boxplot for υ= 0.0001, Fig. 1B). Extrapolating our simulated communities of size 104 individuals to natural metacommunities, in which JM may be several orders of magnitude larger than in our simulations, or to those which have experienced nonlinear evolutionary dynamics, for example, adaptive radiations and/or mass extinctions, is not straightforward. Nonetheless, we include these results because the relative time equilibrium states might be of interest, and to facilitate comparison between models.
As for imbalance, we also observed large variation in the distribution of branching times, γ, but with simulations falling outside the relatively narrow estimates from empirical studies (range: −8.09 to 4.96; McPeek 2008; Fig. 3). Overall, our simulations yield positively skewed γ, exceeding the maximum empirical observation. In the homogeneous case, γ increases moving from point mutation to random fission and fission with equal splits (Fig. 3A), mirroring trends for decreasing tree imbalance. Speciation rate had large impact on γ (Fig. 3B), more pronounced than observed effects on tree imbalance, with faster rates leading to higher γ. In the spatial model, γ decreases with migration rate (m), and is generally less than observed for the homogeneous case, but remains positively skewed, (Fig. 3C). Time to equilibrium in γ was negatively correlated with speciation rate, and generally longer than observed for imbalance, but was largely insensitive to speciation mode (although equilibrium values differ) (Fig. S2).
Here we demonstrate that, for a variety of scenarios, the evolutionary dynamics of NBT models can yield phylogenetic trees with levels of imbalance similar to empirical estimates from TreeBASE (Fig. 1). However, NBT dynamics fail to capture the tempo of diversification, as represented by the distribution of branching events through time (Fig. 3). There is a growing body of evidence suggesting imbalance is a common feature of the tree of life (e.g., Heard 1992; Mooers 1995; Purvis 1996; Mooers and Heard 1997; Blum and François 2006; Jabot and Chave 2009). Much previous work has invoked trait differences among taxa to explain significant tree imbalance (e.g., life history, Salamin and Davies 2004; flower form, Hodges and Arnold 1995; fruit type, Smith 2001). Our findings suggest that tree imbalance may be at least partly attributable to demographic stochasticity, but the mismatch in the distribution of branching times, γ, between simulations and empirical studies remains to be resolved. Critically, our simulations reveal that γ can vary widely even under equilibrium conditions (see also Rabosky and Lovette 2008a; Fordyce 2010).
The influence of demographic stochasticity on phylogenetic tree shape is likely superimposed on that of other nonneutral processes related to key innovations, environmental changes, and their interactions (Harvey et al. 1994; de Queiroz 2002), and perhaps on nonequilibrium processes related to mass extinctions and adaptive radiations. Times to phylogenetic equilibrium varied with tree-shape statistic, suggesting that different aspects of tree topology might reflect more these nonneutral versus neutral processes, depending upon the particular evolutionary history of the clade.
In our simulations, the point-mutation mode yielded imbalance estimates most similar to those calculated from the treeBASE data (Fig. 1A, see also Jabot and Chave 2009). Although the point mutation mode has been criticized as unrealistic (e.g., Ricklefs 2003; Nee 2005), it is important to recognize that our simulated metacommunities were comprised of far fewer individuals (Jm= 104 individuals) than metacommunities in nature (e.g., ∼1010 for neotropical trees, Ricklefs 2003), and that we would expect relatively high imbalance for speciation modes other than point-mutation provided that Js≪Jm. Under a fission mode of speciation, in which ancestral abundance is split more or less evenly between daughter species (i.e., random fission or equal splits), the rank abundance distributions is shallower, yielding balanced phylogenetic topologies—fitting predictions from Losos and Adler's (1995) latency model, in which speciating lineages undergo a refractory period during which further speciation is unlikely, in this instance mediated by changes in abundance.
Holding other factors constant (e.g., incipient-species abundance and dispersal limitation), the fundamental biodiversity number, θ, increases proportionally with per-capita speciation rate and metacommunity size (Hubbell 2001). Because communities with large θ are characterized as having a more equitable allocation of abundances among species, one would expect phylogenetic tree imbalance to decline with increases in θ, and hence with increases in per-capita speciation rate and metacommunity size (Jabot and Chave 2009). Although these expectations were consistent with our findings for point mutation, this was not the case for the fission mode of speciation. Taken together, these findings indicate that the relationship between phylogenetic tree imbalance and the form of the species-abundance distribution, characterized in part by θ, is mediated by details of the speciation process. More generally, they highlight the primary role of incipient-species abundance in influencing speciation–extinction dynamics, as demonstrated by the theoretical work of Allen and Savage (2007) and Rosindell et al. (2010).
We also consider simulations that incorporate spatial structure and migration between neighboring patches, and thus correspond broadly to allopatric and peripatric modes of speciation. In general, we find that, as migration rates increase, so does tree imbalance, consistent with the observation that species abundance is more unevenly distributed in spatially structured metacommunities with high migration rates (Hubbell 2001). The relationship between phylogenetic imbalance and ecological evenness is tighter for point mutation than for fission (Table 2). We suggest this difference reflects the greater dynamism in species’ rank abundances when incipient species abundance is large. Under point mutation the rank order of species is relatively stable, and migration influences tree shape via its effect on abundance evenness, as evident in the shape of the rank abundance curve (Fig. S3). However, under fission, abundances change rapidly with each speciation event—allowing species to traverse the ranks rapidly. The single patch case, in which migration is unbounded, differs for the spatial model with high migration because, in the latter, migration remains restricted to the immediate neighborhood, as also reflected in the differing shapes of the respective rank abundance distributions (Fig. S3).
Phylogenetic imbalance uses only information on tree topology. However, calibrated phylogenies also contain information on relative branching times, and these too can be compared across trees using the γ statistic (Pybus and Harvey 2000). Imbalance and γ are not expected to be independent under most models (Mooers et al. 2007), nonetheless, they capture two largely complementary axes of tree shape. A credible diversification model should demonstrate a good fit to both metrics. Here we find that γ values from our simulations were generally much greater and more variable than empirical estimates. This may either indicate that the macroevolutionary dynamics of NBT models are unrealistic, or it may reflect the fact that empirical estimates tend to be biased. Because older, more abundant lineages are less likely to be excluded than younger lineages in incompletely sampled trees, empirical estimates from poorly sampled trees are likely to be negatively biased (Pybus and Harvey 2000). However, even for relatively well-sampled phylogenies, negative γ's may be common (e.g., McPeek 2008; Phillimore and Price 2008; Rabosky and Lovette 2008b), whereas γ from NBT simulations is frequently positively skewed (see also Mooers et al. 2007). Perhaps the key insight from these findings is that, even under equilibrium conditions, with constant rates and zero net diversification, γ can depart significantly from zero. Our results call into question the frequent use of the γ statistic to detect trends in diversification rates through time (see also McPeek 2008; Rabosky and Lovette 2008a; Cusimano and Renner 2010; Fordyce 2010).
Our results demonstrate that stochastic population-level processes can have a large influence on tree shape for equilibrium communities. The uneven distribution of species across the branches of the tree of life is often poorly explained by differences in biology and ecology. NBT provides an alternative model, in which diversification is independent of lineage-specific traits. Using simulations, we show that NBT dynamics can generate phylogenetic tree topologies that overlap with those observed among empirical studies, but do not capture well the tempo of their diversification. Perhaps even more importantly, because our simulations demonstrate that tree shape can be highly sensitive to specific details of the speciation process, the search for correlates of diversification and diversification rate shifts must also consider the process of speciation.
Associate Editor: D. Posada
We thank S. Hubbell and P. Gowaty for stimulating discussion. We also thank D. Rabosky for providing us with gamma estimates from empirical trees, and M. Blum for help in implementing the beta-splitting model and associated R-code for querying TreeBASE. J. Chave, S. Heard, and an anonymous reviewer provided valuable comments on a previous version of this manuscript. TJD and CJM were supported in part as Postdoctoral Associates at the National Center for Ecological Analysis and Synthesis, a Center funded by NSF (Grant #EF-0553768), the University of California, Santa Barbara, and the State of California. CJM also acknowledges support from Microsoft Research Ltd., Cambridge, United Kingdom. LBA was supported by the National Science Foundation grant DEB 0346488.