The Neutral Theory of Biodiversity and Biogeography and Stephen Jay Gould Author(S): Stephen P

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The neutral theory of biodiversity and biogeography and Stephen Jay Gould Author(s): Stephen P. Hubbell Source: Paleobiology, 31(sp5):122-132. 2005. Published By: The Paleontological Society DOI: 10.1666/0094-8373(2005)031[0122:TNTOBA]2.0.CO;2 URL: http://www.bioone.org/doi/full/10.1666/0094- 8373%282005%29031%5B0122%3ATNTOBA%5D2.0.CO%3B2

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The neutral theory of biodiversity and biogeography and Stephen Jay Gould

Stephen P. Hubbell

Abstract.—Neutral theory in ecology is based on the symmetry assumption that ecologically similar species in a community can be treated as demographically equivalent on a per capita basis—equivalent in birth and death rates, in rates of dispersal, and even in the probability of speciating. Al- though only a ﬁrst approximation, the symmetry assumption allows the development of a quan- titative neutral theory of relative species abundance and dynamic null hypotheses for the assembly of communities in ecological time and for phylogeny and phylogeography in evolutionary time. Although Steve Gould was not a neutralist, he made use of ideas of symmetry and of null models in his science, both of which are fundamental to neutral theory in ecology. Here I give a brief over- view of the current status of neural theory in ecology and phylogeny and, where relevant, connect these newer ideas to Gould’s work. In particular, I focus on modes of speciation under neutrality, particularly peripheral isolate speciation, and their implications for relative species abundance and species life spans. Gould was one of the pioneers in the study of neutral models of phylogeny, but the modern theory suggests that at least some of the conclusions from these early neutral models were premature. Modern neutral theory is a remarkably rich source of new ideas to test in ecology and paleobiology, the potential of which has only begun to be realized.

Stephen P. Hubbell. Department of Plant Biology, University of Georgia, Athens, Georgia 30602, and Smithsonian Tropical Research Institute, Unit 0948, APO AA 34002-0948. E-mail: [email protected]

Accepted: 12 September 2004

Introduction generates a set of formal null hypotheses for the origin, maintenance, and loss of species in Many of Gould’s ideas generated controver- ecological communities or in phylogenies sy, but one for which he was never criticized (Hubbell 2001a). Gould understood the criti- was being a neutralist, which he most defi- cal importance of null models in his own sci- nitely was not. On the contrary, Gould argued ence (Gould et al. 1977), and in science in gen- that patterns of punctuated equilibria in phy- eral. He also understood their importance as logeny can be explained only if natural selec- a control on one’s own preconceptions and bi- tion operates not just among individuals with- ases, and what can happen when such con- in populations, but also among species and trols are absent or abused, as in the racist the- higher taxon levels (Gould 2002). Selection op- ories of human evolution, which Gould vig- erating at levels above the individual would of orously refuted (Gould 1981). In the 1970s, course imply that species and higher taxa dif- Gould and his collaborators used null models fer in fundamental ways that affect their rel- of phylogeny as a means to evaluate whether ative fitnesses on geological timescales, which the patterns generated solely by random birth- in turn affect their relative life spans in the fos- death processes were consistent with the sil record. punctuated equilibrium hypothesis of evolu- Although Gould was not a neutralist, there tion, with busts of speciation interspersed are at least two deep philosophical connec- with long periods of relative quietude (Raup tions between Gould and current neutral the- et al. 1973; Gould et al. 1977). They found that ory. The first is his recognition of the impor- randomly generated patterns were not consis- tance of null models in science, and more spe- tent with observed patterns, and so Gould and cifically Gould’s pioneering work using neu- company concluded that non-neutral selection tral models to study phylogeny. The unified processes must be at work in the phylogenies neutral theory of biodiversity and biogeogra- he studied. As it turns out, however, these phy is a recent example of such models, and it conclusions were somewhat premature, be-

᭧ 2005 The Paleontological Society. All rights reserved. 0094-8373/05/3102-0009/$1.00 GOULD AND NEUTRAL THEORY 123 cause there were several problems with the The Neural Theory and Relative formulations of the models that were not im- Species Abundance mediately apparent at the time. The origins of modern neutral theory in The other philosophical connection of neu- ecology can be traced back to the theory of is- tral theory to Gould is through the concept of land biogeography (MacArthur and Wilson symmetry and symmetry breaking. In the 1963, 1967). The theory of island biogeogra- neutral theory of biodiversity, all species are phy hypothesizes that ecological communities treated as symmetric, which means that, to a are assembled purely by dispersal. This and first approximation, all species are assumed to other dispersal assembly theories assert that be demographically identical on a per capita the species richness on islands or in local com- basis. The principal use of the neutral theory munities represents a dynamic equilibrium is to evaluate when, and to what degree, asym- between the rates of immigration of species metries among species are required to explain into the community and the rate of their sub- the assembly of observed ecological communities. Although Gould did not use this ter- sequent local extinction. Thus, such theories minology, nevertheless the concepts he wrote assert that communities are in taxonomic non- about were the same. Paleontology could be equilibrium with continual species turnover. described as the study of how morphological The theory of island biogeography is neutral symmetries are transmitted, broken, and re- because it assumes that species are identical established over evolutionary time. In phylog- (symmetric) in their probabilities of arrival enies, more closely related species are more and survival. This theory was, and remains, a similar (symmetric) than less related species radical departure from most contemporary (Harvey and Pagel 1991). At least for the living theory in ecology, which says that ecological species, the new tools of genomics and evo- nature is fundamentally asymmetric, that lutionary developmental biology promise to communities are equilibrium or near-equilib- answer many if not all of the recalcitrant clas- rium assemblages of niche-differentiated spe- sic questions in ontogeny and phylogeny cies, each of which is the best competitor in its (Gould 1977). These tools are revealing that own ecological niche (Chase and Leibold the symmetries of life run far deeper than any- 2003). There has been a persistent theoretical one ever supposed, as illustrated, for example, tension in ecology between these two conflict- by the discovery of ancient and phylogeneti- ing worldviews. Both perspectives have cally pervasive homeobox master regulatory strong elements of truth, although typically on genes (Carroll et al. 2001; Davidson 2001). very different spatial and temporal scales In this paper, I first present a brief synopsis (Hubbell 2001a). The theoretical quest has of the neutral theory (Hubbell 2001a; Volkov been the search for ways to reconcile and com- et al. 2003). The current theory is best devel- bine these divergent perspectives into a single oped for ecological scales of time and space. seamless theory for ecology. However, the unified neutral theory embodies The unified neutral theory of biodiversity more of a macroecological and deep-time per- begins to build a theoretical bridge between spective than do most contemporary theories these two perspectives by incorporating a dy- in ecology. This is because it is one of very few namic theory of relative species abundance theories in ecology to incorporate a process of into the theory of island biogeography (Hub- speciation explicitly. Here I focus mainly on bell 2001a; Bell 2000, 2001). As in the original the results for speciation, particularly periph- theory, the unified neutral theory treats spe- eral isolate speciation, and its implications for cies as identical (symmetric) in their per capita biodiversity, speciation rates, and species life vital rates of birth, death, and migration. Un- spans. I conclude with a brief prospect for the like the theory of island biogeography, how- future of symmetric neutral theory in ecology ever, the unified neutral theory makes the and paleobiology, and how new models with neutrality assumption at the individual level, symmetry broken in various ways promise to not the species level, a change that allows spe- move us forward. cies to differentiate in relative abundance 124 STEPHEN P. HUBBELL

through ecological drift (demographic stochasticity). The persistence times of species under drift are then dictated by their abundances, so that the extinction rate is a genuine prediction of the theory, not a free parameter as it was in the original theory of island biogeography. In the unified neutral theory, the ‘‘metacommunity’’ replaces the mainland source area concept of the theory of island biogeography. The metacommunity is the phy- logeographic unit within which most member species spend their entire evolutionary life- FIGURE 1. The fit of the unified neutral theory to the times. The neutral theory also generates a nat- dominance-diversity curve for tropical tree species in a ural length scale—the biogeographic correla- 50-ha permanent plot of rainforest in Lambir Hills Na- tion length—that measures the size of meta- tional Park, Sarawak, Borneo. The dotted line extending diagonally down to the right is the best-fit metacom- communities. In the theory of island bioge- munity curve for ␪ϭ310, assuming no dispersal limi- ography, however, the size of the source area tation (m ϭ 1). The relative abundance for the 50-ha plot ␪ϭ ϭ is not defined. was best fit with 310 and m 0.18. The error bars are Ϯ one standard deviation. The heavier solid line is Previous theories of relative species abun- the observed dominance-diversity curve. Note the ex- dance have been largely static, phenomeno- cellent fit even for very rare species. This fit to 1197 spe- ␪ logical models (e.g., Preston 1948, 1960) and cies is achieved with just three parameters, , m, and local community size J, the latter of which is known from involve fitting generic statistical distributions the plot census data (J ϭ 324,592). whose parameters are not clearly derivable from first principles in population biology (Hubbell 2005). Because the previous models retical and empirical attention in ecology than are not dynamic or mechanistic, they do not relative species abundance, attention that is generate hypotheses about how basic demo- fully justified. One of the most important in- graphic processes affect species richness and sights gained from the unified neutral theory the distribution of relative species abundance. is that speciation rates and patterns of relative In contrast, the parameters of the neutral the- species abundance on large spatio-temporal ory of relative species abundance all have scales are inextricably and causally linked. At straightforward biological interpretations, large biogeographic scales and between punc- such as per capita birth and death rates, dis- tuational events, the steady-state diversity persal rates, and rates of speciation. Incorpo- and distribution of relative species abundance rating a process of speciation was especially are set by the balance between speciation and key to developing a neutral theory of relative extinction rates. Relative species abundance is species abundance. Lacking a speciation directly involved in this steady state because mechanism for generating new diversity, the species extinctions are not drawn at random older phenomenological models have been with respect to the abundances of species. generally unable to make predictions about Both theoretically and empirically, we know the expected patterns of relative species abun- that rare species are more extinction prone dance on large biogeographic spatial scales (Richter-Dyn and Goel 1972; Lande et al. and evolutionary timescales. Fits of the neu- 1993). Although high global abundance ap- tral theory to relative abundance data are of- pears to offer little or no protection from the ten quite good, especially in species-rich com- agents of mass extinction (Jablonski 2001, munities such as tropical rain forests (Fig. 1). 2002), there is evidence that abundant and The importance of studying relative species geographically widespread taxa are more per- abundance, especially on large landscape sistent during ‘‘normal’’ times (Jablonski scales, cannot be overstated. Apart from spe- 1995; Jackson 1995). cies richness, no other general attribute of eco- The correlation between global abundance logical communities has received more theo- and taxon longevity implies that during ‘‘nor- GOULD AND NEUTRAL THEORY 125 mal’’ times, the diversity steady state is main- munity’’) under the simplest mode of specia- tained principally by the balance between the tion (‘‘point mutation’’ speciation; see below). origination of new species and the extinction However, this fundamental distribution be- of mostly rare species. This conclusion is im- comes modified on local scales under dispers- portant in considering tests of the apparent al limitation and on large spatial scales under dynamic quiescence of diversity between different modes of speciation, and these mod- punctuational events. If rare species are hard- ified distributions are more lognormal-like er to find in the fossil record than common (Hubbell 2001a; Volkov et al. 2003; Hubbell species, there will be a built-in sampling bias and Borda-de-A´ gua 2004). that will underestimate taxon turnover rates The formal connection between speciation during these periods. As data sets improve for and relative species abundance in the meta- fossil assemblages to include ever rarer taxa, I community can be shown by simultaneously predict that estimated turnover rates for pe- deriving the distribution of relative species riods between punctuational events will abundance and the speciation rate from the steadily rise. In studies of paleocommunities, fundamental dynamical equations of popula- relative species abundance has played a less tion growth under neutrality (see the Appen- prominent role than species richness, but this dix for details). Under the metacommunity situation is changing as improved data sets distribution of relative species abundance, become available (e.g., Kidwell 2001). How- which is the log-series, the expected mean ͗␾ ͘ ever, there are already data to support high number of species with n individuals n is rates of taxon turnover during periods of di- given by versity steady states in some taxa, even in the xn absence of analyses of relative abundance data ͗␾͘ϭ␣ , n n (e.g., Patzkowsky and Holland 1997). Because relative species abundance is fun- where parameter x is a positive number Ͻ1, damental to any discussion of speciation un- and ␣ is the diversity parameter, known as der the neutral theory, it is important to re- Fisher’s ␣. Fisher’s ␣ (Fisher et al. 1943) is the view briefly the formal connection between oldest, most famous, and most widely used the two subjects. Since publication of my book measure of species diversity in ecology (Ma- (Hubbell 2001a), there have been many signif- gurran 1988). One reason it is used so widely icant changes and improvements in the math- is that it is remarkably stable in the face of in- ematical framework of the theory (Houch- creasing sample sizes of relative abundance mandzadeh and Vallade 2003; Vallade and data from communities. Until the unified neu- Houchmandzadeh 2003; Volkov et al. 2003; tral theory, however, there has been no clear Etienne and Olff 2004; Hubbell 2004; McKane theoretical explanation for the stability and et al. 2004). One of the advantages of the new universality of Fisher’s ␣ nor any biological in- framework is that several important problems terpretation of parameter x of the logseries. in the symmetric neutral theory that were ad- Neutral theory explains that the diversity dressed only by simulations (numerical ex- parameter, Fisher’s ␣, is so stable and univer- periments) in my book are now tractable to sal because it is a linear function of the average analytical solutions. In particular, we have speciation rate across the entire metacommun- made substantial progress in understanding ity as well as of the size of the metacommun- the relationship of neutral theory to the two ity, defined as the sum of the population sizes most celebrated statistical distributions used of all species in the metacommunity. Fisher’s to describe the distribution of relative species ␣–called ␪ by Hubbell (2001a)—is a dimen- abundance: the logseries (Fisher et al. 1943), sionless, fundamental biodiversity number and the lognormal (Preston 1948). The neutral that crops up over and over again throughout theory clarifies the situation and shows that the neutral theory. Neutral theory also dem- the logseries is the fundamental distribution onstrates that parameter x of the logseries is of relative species abundance expected at equal to the ratio of the average per capita large spatiotemporal scales (the ‘‘metacom- birth rate to the average per capita death rate 126 STEPHEN P. HUBBELL of all species in the metacommunity (Volkov cause under this mode, new species arise as et al. 2003) (see Appendix). This ratio is very lineages founded by single individuals, and slightly less than unity when the distribution most of these lineages go extinct quickly. of relative species abundance in the metacom- ‘‘Random-fission’’ speciation creates new spe- munity is in steady state. This means that at cies by the random uniform partition of an an- equilibrium diversity, there is a minute excess cestral species into two daughter species. Spe- of deaths over births, and this small deficit in cies life spans are much longer under ‘‘ran- births is exactly balanced by the slow rate of dom fission’’ speciation because this mode introduction of new species into the metacom- produces the largest average population size munity. Thus, under the framework of the of new species. Large founding population unified neutral theory, the fundamental dis- sizes buffer species from rapid extinction, tribution of relative species abundance at which, in turn, increases the steady state spe- large landscape scales is directly derivable cies richness in the metacommunity. In my from the speciation rate, the size of the meta- book I suggested that random fission specia- community, and the average rates of birth and tion is the analog to Mayr’s allopatric specia- death in the metacommunity. tion model (Hubbell 2001a). However, we now have a more complete and general formulation The Neutral Theory and Speciation of the problem, in a mode of speciation we call Coyne and Orr (2004) have recently re- ‘‘peripheral isolate’’ speciation (Hubbell and viewed current evidence in favor of various Lake 2003), which is discussed below. modes of speciation. They favor the biological Ricklefs (2003) has recently argued that species concept, which leads them naturally to these two modes of speciation are unrealistic a focus on the origin and maintenance of re- because ‘‘point mutation’’ speciation produces productive isolation. They conclude that, de- too many short-lived species, whereas ‘‘ran- spite modest evidence for the hybrid origin of dom fission’’ speciation leads to overly long- some species or for other mechanisms of sym- lived species. In my response, (Hubbell 2003), patric speciation, the vast majority of species I argued that the problems with ‘‘point mu- arise through allopatric speciation, following tation’’ speciation were easily resolved if one closely the now classical model of Mayr viewed this mode as actually a model of the (1963). The biological species concept is, of fate of all lineages, most of which die out rap- course, not very useful in paleontology be- idly, and only a very few of which survive and cause tests of reproductive isolation are not become numerous enough to be discovered possible. However, from the perspective of and sufficiently reproductively isolated to be neutral theory, the only question about speci- called ‘‘good species.’’ The ‘‘point mutation’’ ation that matters is how the mode of specia- mode is the only known speciation mecha- tion affects the mean size of the founding pop- nism that gives rise to Fisher’s ␣ and the log- ulation of new species. This is the critical ques- series distribution for the metacommunity. tion because initial population size deter- Whenever metacommunity relative species mines not only the mean life span of a species, abundance distributions are observed to be but also steady-state species richness and rel- consistent with the logseries, such a finding ative species abundance in the metacommun- necessarily implies that the population sizes at ity. origination must be small to very small. Spe- In my book, I studied two modes of speci- cies that arise by sudden changes in ploidy ation, ‘‘point mutation’’ speciation and ‘‘ran- number or by hybridization are good candi- dom fission’’ speciation (Hubbell 2001a). I dates for origins by ‘‘point mutation’’ specia- chose to study these two modes because they tion. represent the end extremes of a speciation Regarding ‘‘random fission’’ speciation, continuum in terms of the size of founding however, I think Ricklefs’s point is well taken, populations and the predicted life spans of and certainly most current data seem to be in- new species. Mean species life spans are very consistent with the ‘‘random fission’’ mode. In short under ‘‘point mutation’’ speciation, be- response to Ricklefs, Jeff Lake and I have ex- GOULD AND NEUTRAL THEORY 127 plored the consequences of a third and intermediate mode of speciation, dubbed ‘‘peripheral isolate’’ speciation (Hubbell 2003; Hubbell and Lake 2003). Under this mode, founding populations are not as small as singleton- founded lineages, nor as large as those under ‘‘random fission,’’ but nevertheless are fairly modest in size. ‘‘Peripheral isolate’’ speciation is probably commonplace. Most species are distributed as discontinuous metapopulations, and it seems likely that new species FIGURE 2. As the initial size of species populations at arise from one or more of the local isolated origination increases, more species are present at steady demes of metapopulations. This mode of spe- state in the metacommunity, for a fixed speciation rate. The figure shows an example of the effect of varying ciation does indeed produce species having population size at origination on the steady-state me- intermediate life spans and equilibrium metacommunity species richness and distribution of rela- tacommunities with intermediate species rich- tive species abundance (‘‘dominance-diversity’’ curves), for a fixed value of the fundamental biodiver- ness and relative species abundance distribu- sity number ␪ (Fisher’s ␣) and for a metacommunity av- tions (Hubbell and Lake 2003). If the incipient erage per capita birth/death ratio of x ϭ 0.9999. The species originate in small populations, how- numbers beside each dominance-diversity curve are the initial population sizes at the origination of new species. ever, empirically they may be difficult to dis- The steepest dominance-diversity curve for a founding tinguish from ‘‘point mutation’’ speciation population size of unity corresponds to the logseries events. distribution for the limiting case of ‘‘point mutation’’ speciation. In my book, only the ‘‘point mutation’’ mode was solved analytically (Hubbell 2001a). Now, however, all three modes of speciation, Thus, one will consistently overestimate the including ‘‘peripheral isolate’’ speciation, speciation rate by fitting the ‘‘point mutation’’ have been solved analytically (I. Volkov per- speciation equations to relative abundance sonal communication 2004). Although the an- data. By how much the speciation rate is over- alytical results will be reported elsewhere, we estimated will depend on the mean size of pe- can make three general statements about the ripheral isolate populations at origination. findings here. The first conclusion is that the Figure 3 shows that speciation rates under general case is ‘‘peripheral isolate’’ speciation; ‘‘peripheral isolate’’ speciation are orders of the other two modes are special cases of this magnitude smaller than those expected under general mode. The second conclusion con- ‘‘point mutation’’ speciation. The curves rep- firms the simulation results of Hubbell (2001a) resent the ratio of the speciation rate under and Hubbell and Lake (2003) that increasing ‘‘peripheral isolate’’ speciation to the specia- the size of the founding population greatly in- tion rate under ‘‘point mutation’’ speciation creases the steady-state species richness in the that yields an equivalent metacommunity spe- metacommunity. Figure 2 shows this effect for cies richness, as a function of the population a value of Fisher’s ␣ (Hubbell’s ␪)of10,fora size of the isolate at speciation. Thus, the in- birth-death ratio of 0.9999, and for various val- tercept for all curves is a ratio of 1.0 for an ini- ues of the size of the peripheral isolate at the tial population size of unity, which corre- point of speciation. sponds to the ‘‘point mutation’’ limiting case. The third conclusion addresses one of the A smaller and smaller speciation rate is re- main concerns of Ricklefs (2003) about speci- quired to achieve the same metacommunity ation rates that are too high under ‘‘point mu- diversity the larger the founding peripheral tation’’ speciation. Because of the slower rate isolate population becomes, and the closer the of extinction of new species under ‘‘peripheral average metacommunity birth/death rate ra- isolate’’ speciation, a given level of species tio approaches unity. richness in the metacommunity can be ex- Testing these predictions about speciation plained by a much slower rate of speciation. and relative species abundance in metacom- 128 STEPHEN P. HUBBELL

cent species-level taxa, an estimate of ␪ from the deep-time structure of the phylogeny may be more accurate, and this in turn may help us assess how much modern diversity we are still missing. Ironically, it may well be that fossil assemblages can be used to test these ideas better than living taxa can, providing a much deeper time perspective.

Gould’s Contribution to Neutral Theory and a Modern Update FIGURE 3. Holding species richness in the metacommunity constant, we can calculate the speciation rate As mentioned, Gould and a number of his under ‘‘peripheral isolate’’ speciation that is necessary colleagues made a pioneering contribution to to produce the same species richness relative to the speciation rate required under ‘‘point mutation’’ speciation neutral theory in their early studies of neutral (initial size ϭ 1). These relative speciation rates are in- phylogenies. After the publication of Eldredge dependent of the starting value of the fundamental bio- and Gould (1972) on the theory punctuated diversity number ␪ (Fisher’s ␣) under ‘‘point mutation’’ speciation, but they do depend on the mean per capita equilibrium, one of the questions that arose birth rate to death rate ratio, x. For large metacommun- was whether randomly generated phylogenies ities, x is expected to be extremely close to unity, so that would produce patterns similar to those seen even moderate-sized peripheral isolates will result in a reduction of the effective speciation rate by several to in the fossil record, which, depending on the many orders of magnitude over than required under taxon, often exhibited sudden, episodic in- ‘‘point mutation’’ speciation to produce the same me- creases in diversity, separated by longer peri- tacommunity diversity. ods of relatively calm and steady diversity levels. In part to try to answer this question, munities will be a considerable challenge. The Raup et al. (1973) and Gould et al. (1977) took best tests will involve independent measures a ‘‘demographic approach’’ to phylogeny, in of speciation rates and metacommunity sizes, which they modeled monophyletic clades so that we have independently derived esti- evolving as a stochastic birth-death branching mates of the fundamental biodiversity num- process, picking up from the much earlier ber ␪. However, there are genuine empirical work of Yule (1925). In these models, lineages difficulties. One is that, if ‘‘peripheral isolate’’ were assigned ‘‘birth’’ and ‘‘death’’ rates. speciation is the dominant mode but the av- When the birth rate exceeded the death rate, erage size of the founding populations is the general outcome of these models was ex- small, then ecologists, and especially paleon- ponential growth in the number of descendant tologists, may have considerable difficulty in lineages, and somewhat slower growth if all finding and recognizing these nascent species, extinct lineages were pruned out. In no cases leading us to underestimate the true specia- did the models yield the punctuational pattern tion rates, potentially seriously. One possible postulated by Eldredge and Gould. In the last approach to testing the theory relies on the decade, in a series of elegant papers, Nee and fact that the structure of phylogenetic trees is his collaborators have provided analytical so- expected to be fractal with a single scaling do- lutions to these models to study the process of main under ‘‘point mutation’’ speciation, ‘‘phylogenetic reconstruction’’ (e.g., Nee et al. whereas it is expected to be compound fractal 1994). Nee argued that observed phylogenies under ‘‘peripheral isolate’’ speciation (Hub- exhibit clades that are too ‘‘bushy,’’ with some bell 2001b). In the former case, the neutral the- subclades containing too many species rela- ory says that we should expect a linear relative to the predictions of the null models, and tionship between ␪ and the fractal dimension argued that this was strong evidence for non- of the phylogeny (Hubbell 2001b). Because the random processes in clade evolution. deep-time, higher taxonomic divisions of phy- These models meshed very well with logenetic clades leading to modern species are Gould’s concepts about species, which he has better sampled and known than the most re- long argued can be treated as analogous to in- GOULD AND NEUTRAL THEORY 129 dividuals when it comes to species-level selec- er total birth rate per unit time (opportunities tion (Gould 2001). Indeed, in the unified neu- for speciation) than in the case of rare species. tral theory under ‘‘point mutation’’ speciation, This effect will make certain subclades much the hypothesis that new species arise from in- more speciose than expected under Gould- dividually founded lineages blurs the distinc- type neutral models of phylogeny. Third, the tion between species and individuals. This unified neutral theory produces a genuine di- said, there is a fundamental difference be- versity steady state at equilibrium between tween species and individuals that led the speciation and extinction. As mentioned, there original neutral models of cladogenesis of is increasing evidence that these diversity Raup et al. (1973) and Gould et al. (1977)—and equilibria between punctuational events (Eld- their analytical counterparts (Nee et al. redge and Gould 1972, 1988) are dynamic 1994)—astray. The essential problem lies in steady states with continual species turnover the failure to take the relative abundance of (Patzkowsky and Holland 1997). In contrast, lineages into account: populations have abun- Gould’s neutral theory does not produce a di- dances, individuals do not. In the models of versity steady state, but instead produces ex- Raup, Gould, and Nee the evolutionary unit is ponential growth in the number of surviving the lineage, and lineages have assigned prob- lineages (Nee et al. 1994). This is because in abilities of speciating or going extinct. How- Gould’s theory, lineages have preassigned ever, in the unified neutral theory, the evolu- birth and death rates that do not change with tionary unit is the individual, and lineages per lineage abundance. se have no preassigned speciation and extinc- Current evidence gives equivocal support tion rates. Instead, the probability of speciat- to these various predictions of the unified neu- ing or going extinct is determined by lineage tral theory. As mentioned, there is evidence abundance, which is dictated in turn by the that globally abundant taxa do indeed have fundamental biodiversity number ␪ (or Fish- longer evolutionary life spans, at least during er’s ␣). In the models of Gould and Raup, lin- ‘‘normal’’ extinction times (Jablonski 1995; eage abundances are ignored completely, yet Jackson 1995), but this pattern breaks down the abundance of a lineage (i.e., a species) will during mass extinctions (Jablonski 2001, have a profound effect on the time to extinc- 2002). In molluscs and foraminifera, there are tion of the lineage. Models that are pure birth- well-established relationships between dis- death branding processes trace the fate of lin- persal ability and global abundance. However, eages as if they had equal probabilistic fates, there is also evidence that dispersal ability but this is not true because the fate of globally and global abundance are negatively correlat- abundant lineages is very different on average ed with rates of speciation, suggesting that from the fate of rare and local endemics. Including lineage abundance changes many gene flow is a major cohesive force in main- of the conclusions of the original neutral the- taining the integrity of species (Jablonski and ory of phylogeny and suggests a series of test- Roy 2003). It should be noted that increased able hypotheses. First, globally abundant spe- dispersal is expected to reduce the slope of the cies are expected to be much older on average species-area relationship (Hubbell 2001a). than rare species, a result consistent with the This occurs for two reasons. One reason is now classical theory of stochastic extinction simply more complete mixing. The other rea- (Richter-Dyn and Goel 1972). However, there son is extinctions of rare species caused by in- is no such expectation under Gould’s theory creased dispersal of common species and the because lineage abundance is not considered. overwhelming mass effect of their greater ab- Second, these globally abundant and wide- solute birth rates (even when per capita birth spread metacommunity species are expected rates are the same). Thus, even in a fully neu- to be the ancestors of many more modern spe- tral model at a per capita level, increasing dis- cies than are rare and local species. This is a persal can cause a reduction of metacommun- consequence not only of their much longer ex- ity diversity through increasing the extinction pected life spans, but also of their much high- rate of rare species (Hubbell 2001a). 130 STEPHEN P. HUBBELL

Conclusions tions—who have supported my ecological research over the past 25 years, and the Although the neutral theory is simple, it development of the neutral theory over the nevertheless fits many macroecological pat- past ten years. I thank the Center for Tropical terns as well as or better than current niche Forest Science of the Smithsonian Tropical Re- theory in ecology. Perhaps the deepest ques- search Institute for permission to analyze the tion raised by neutral theory is why it per- relative species abundance data for tree spe- forms so well despite its symmetry assump- cies in the 52-hectare plot in Lambir Hills Na- tions. I expect that some of the best and most tional Park, Sarawak (Fig. 1). rigorous tests will come from paleobiology. One of the most important conclusions from Literature Cited neutral theory is that processes of speciation Bell, G. 2000. The distribution of abundance in neutral com- and macroecological patterns of species rich- munities. American Naturalist 155:606–617. ness and relative species abundance are inex- ———. 2001. Neutral macroecology. Science 201:2413–2417. tricably and causally linked. This finding sug- Carroll, S. B., J. K. Grenier, and S. D. Weatherbee. 2001. From DNA to diversity: molecular genetics and the evolution of an- gests that understanding relative species imal design. Blackwell Scientific, Oxford. abundance in fossil communities better will Chase, J. M., and M. A. Leibold. 2003. Ecological niches: lining provide further insights into both speciation classical and contemporary approaches. University of Chi- cago Press, Chicago. and extinction processes. There are encour- Chave, J. 2004. Neutral theory and community ecology. Ecology aging signs that major improvements in data Letters 7:241–253. on patterns of relative species abundance in Coyne, J. A., and H. A. Orr. 2004. Speciation. Sinauer, Sunder- land, Mass. fossil assemblages are possible (Kidwell Davidson, E. 2001. Genomic regulatory systems. Academic 2001), and this would be a major boon in test- Press, New York. ing the predictions of the unified neutral the- Eldredge, N., and S. J. Gould. 1972. Punctuated equilibria: an alternative to phyletic gradualism. Pp. 82–115 in T. J. M. ory with fossil data. It is also extremely im- Schopf, ed. Models in paleobiology. Freeman, Cooper, San portant to obtain improved spatial data on the Francisco. geographic range of fossil communities. ———. 1988. Punctuated equilibrium prevails. Nature 332:211– 212. Symmetric neutral theory will be a rich Etienne, R. S., and H. Olff. 2004. A novel genealogical approach source of hypotheses and tests about com- to neutral biodiversity theory. Ecology Letters 7:170–175. munity assembly rules. I predict that one of Fisher, R. A., A. S. Corbet, and C. B. Williams. 1943. The relation between the number of species and the number of individuals the most productive uses of the unified neu- in a random sample of an animal population. Journal of An- tral theory will be in testing when, how, and imal Ecology 12:42–58. to what extent symmetry is broken in actual Gould, S. J. 1977. Ontogeny and phylogeny. Harvard University Press, Cambridge. ecological communities. The theory is still in ———. 1981. The mismeasure of man. Norton, New York. its infancy; and there are many exciting, un- ———. 2002. The structure of evolutionary theory. Belknap resolved theoretical challenges in and beyond Press of Harvard University Press, Cambridge. Gould, S. J., D. M. Raup, J. J. Sepkoski Jr., T. J. M. Schopf, and D. the unified neutral theory to tackle for years S. Simberloff. 1977. The shape of evolution: a comparison of to come (Chave 2004). I also anticipate that the real and random clades. Paleobiology 3:23–40. legacy of the exciting, challenging, and still Harvey, P. H., and M. D. Pagel. 1991. The comparative method in evolutionary biology. Oxford University Press, Oxford. unanswered questions left by Steve Gould in Houchmandzadeh, B., and M. Vallade. 2003. Clustering in neu- paleobiology will continue to inspire major tral ecology. Physical Review E 68: Art. No. 061912. new contributions to our understanding of the Hubbell, S. P. 2001a. The unified neutral theory of biodiversity and biogeography. Princeton University Press, Princeton, N.J. assembly of ecological communities, past and ———. 2001b. The unified neutral theory of biodiversity and present. biogeography: a synopsis of the theory and some challenges ahead. Pp. 393–411 in J. Silvertown and J. Antonovics, eds. In- tegrating ecology and evolution in a spatial context. Blackwell Acknowledgments Scientific, Oxford. ———. 2003. Modes of speciation and the lifespans of species I thank the National Science Foundation, the under neutrality: a response to the comment of Robert E. John D. and Catherine T. MacArthur Founda- Ricklefs. Oikos 100:193–199. tion, the Pew Charitable Trusts, the John Si- ———. 2005. Neutral theory in ecology and the evolution of functional equivalence. Ecology (in press). mon Guggenheim Foundation, and many oth- Hubbell, S. P., and J. Lake. 2003. The neutral theory of bioge- er donors—individuals and private organiza- ography and biodiversity: and beyond. Pp. 45–63 in T. Black- GOULD AND NEUTRAL THEORY 131

burn and K. Gaston, eds. Macroecology: concepts and con- population dynamics under the unified neutral theory (Volkov sequences. Blackwell Scientific, Oxford. et al. 2003). This new formulation incorporates birth and death ´ Hubbell, S. P., and L. Borda-de-Agua. 2004. The unified neutral rates explicitly. Let bn,k and dn,k be the probabilities of birth and

theory of biogeography and biogeography: reply. Ecology 85: death of an arbitrary species k at abundance n. Let Pn,k(t)bethe 3175–3178. probability that species k is at abundance n at time t. Then the Jablonski, D. 1995. Extinctions in the fossil record. Pp. 25–44 in rate of change of this probability is given by J. H. Lawton and R. M. May, eds. Extinction rates. Oxford Uni- dp (t) n,k ϭ ϩ Ϫ ϩ versity Press, Oxford. pnϩ1,kn(t)d ϩ1,knp Ϫ1,kn(t)b Ϫ1,kn,kn,kn,kp (t)(b d ). (A1) ———. 2001. Lesson from the past: evolutionary impacts of dt mass extinction. Proceedings of the National Academy of Sci- This equation is straightforward and easy to understand. The ences USA 98:5393–5398. first term on the right represents the transition from abundance ———. 2002. Survival without recovery after mass extinctions. n ϩ 1ton, due to a death. The second term is the transition from Proceedings of the National Academy of Sciences USA 99: abundance n Ϫ 1ton due to a birth. The last two terms are losses 8139–8144. to Pn,k(t) because they are transitions away from abundance n to Jablonski, D., and K. Roy. 2003. Geographical ranges and spe- either n ϩ 1orn Ϫ 1 through a birth or death, respectively. On ciation in fossil and living molluscs. Proceedings of the Royal first consideration, equation (1) appears to be little more than a Society of London B 270:401–406. bookkeeping exercise, but it is actually much more. Because it is Jackson, J. B. C. 1995. Constancy and change in the life of the written as a recursive function on abundance, it allows an equi- sea. Pp. 45–54 in J. H. Lawton and R. M. May, eds. Extinction librium solution to be found for species of arbitrary abundance rates. Oxford University Press, Oxford. n. When all derivatives at all abundances are set equal to zero, Kidwell, S. M. 2001. Preservation of species abundance in ma- then the solution is said to satisfy ‘‘detailed balance,’’ which rine death assemblages. Science 294:1091–1094. means that each abundance transition is in equilibrium. Now let MacArthur, R. H., and E. O. Wilson. 1963. An equilibrium the- ϭ Pn,k denote this equilibrium. Then Pn,k PnϪ1,k:(bnϪ1,k/dn,k), and ory of insular zoogeography. Evolution 17:373–387. more generally, this corresponds to a global equilibrium solu- ———. 1967. The theory of island biogeography. Princeton Uni- tion for the metacommunity: versity Press, Princeton, N.J. nϪ1 b Magurran, A. E. 1988. Ecological diversity and its measure- ϭ ͹ i,k Pn,k P0,k . (A2) ϭ ment. Princeton University Press, Princeton, N.J. i 0 diϩ1,k Mayr, E. 1963. Animal species and evolution. Belknap Press of Note that the probability of being at abundance n is a function Harvard University Press, Cambridge. of the product of the ratios of birth rate to death rate over all McKane, A. J., D. Alonso, and R. V. Sole. 2004. Analytic solution abundances below n. Because the P ’s must sum to unity, we of Hubbell’s model of local community dynamics. Theoretical n,k can find the value of P from this sum, and therefore all other Population Biology 65:67–73. 0,k terms as well. Nee, S., R. M. May, and P. H. Harvey. 1994. The reconstructed Now consider a symmetric neutral community of S species evolutionary process. Philosophical Transactions of the Royal that are all alike on a demographic basis, such that they all have Society of London B 344:305–311. the same birth rates and death rates; that is, b ϵ b and d ϵ Patzkowsky, M. F., and S. M. Holland. 1997. Patterns of turnover n,k n n,k d (i.e., the species identifier k doesn’t matter, and we denote the in Middle to Upper Ordovician brachiopods of the eastern n probabilities by P ). We can introduce speciation by recognizing United States: a test of coordinated stasis. Paleobiology 23: n a special ‘‘birth rate’’ in this general metacommunity solution; 420–443. i.e., b ϭ␯, the speciation rate. The mean number of species with Preston, F. W. 1948. The commonness, and rarity, of species. 0 n individuals, ͗␾ ͘, in a community of S identical species is sim- Ecology 29:254–283. n ply proportional to P : ———. 1960. Time and space variation of species. Ecology 41: n 611–627. nϪ1 b ͗␾ ͘ ϭ ͹ i n SP0 . (A3) Raup, D. M., S. J. Gould, T. J. M. Schopf, and D. S. Simberloff. ϭ i 0 diϩ1 1973. Stochastic models of phylogeny and the evolution of diversity. Journal of Geology 81:525–542. From equation (3) we are now in a position to derive Fisher’s Richter-Dyn, N., and S. S. Goel. 1972. On the extinction of a col- logseries under density independence. Density independence onizing species. Theoretical Population Biology 3:406–433. means that the birth rate of a species of current abundance n is Ricklefs, R. E. 2003. A comment on Hubbell’s zero-sum ecolog- simply n times the birth rate of a species with abundance 1; i.e., ϭ ical drift model. Oikos 100:187–193. bn nb1, or density independence. Similarly, suppose that the ϭ Yule, G. U. 1925. A mathematical theory of evolution, based on death rates are density independent, dn nd1. Substituting these the conclusions of Dr. J. C. Willis, F. R. S. Philosophical Trans- expressions into equation (3), we immediately obtain Fisher’s actions of the Royal Society of London B 213:21–87. logseries:

Vallade, M., and B. Houchmandzadeh. 2003. Analytical solution n bb ··· bxϪ ͗␾ ͘ ϭ 01 n 1 ϭ␪ of a neutral model of biodiversity. Physical Review E 68: Art. nMSP M 0 , (A4) dd ··· dn No. 061902. 12 n ϭ Volkov, I., J. R. Banavar, S. P. Hubbell, and A. Maritan. 2003. where the subscript M refers to the metacommunity, x bn/dn ϭ ϭ ϭ␯ ␪ϭ␣ϭ ␯ Neutral theory and relative species abundance in ecology. Na- b1/d1 b/d, b0 ,and SmP0 /b of Fisher’s logseries. ture 424:1035–1037. The derivation of equation (4) reveals that the mysterious parameter x of the logseries is now biologically interpretable: x is the ratio of the density-independent, per capita birth rate to per Appendix capita death rate. Note that when one introduces speciation, pa- A full ecological explanation of Fisher’s logseries in terms of rameter x must be slightly less than 1 to maintain a finite me- population dynamics is now available from new theoretical re- tacommunity size. At very large spatial scales, the total birth sults on the neutral theory of relative species abundance. This and death rates must be nearly in material balance, resulting in explanation emerges from a more general theoretical formula- a metacommunity b/d ratio only infinitesimally less than unity. tion of the equations of demographic stochasticity that underpin The very slight deficit in birth rates versus death rates at the 132 STEPHEN P. HUBBELL

⌫ ϭ #ϱ zϪ1 Ϫt Ϫ metacommunity biodiversity equilibrium is made up by the where (z) 0 t e dt which is equal to z 1)! for integer z, very slow input of new species. and ␥ϭ[m(J Ϫ 1)]/(1 Ϫ m). As in Hubbell 2001a, parameter m Thus, we now have a complete derivation of the logseries and is the immigration rate. Equation (5) was derived by making the its parameters ␪ and x, from the neutral theory. It is interesting following functional substitutions for the per capita birth and that Hubbell (2001a) derived ␪ following a completely different death rates in equation (2): route from the one taken by Volkov et al. (2003), so we now have Ϫ ␮ further insights into parametric relationships under the unified nJ n k n b ϭ (1 Ϫ m) ϩ m 1 Ϫ and n,k ΂΃΂Ϫ ΃ ΂ ΃΂ ΃ neutral theory. The greatest significance of this result, however, JJ 1 JJM is demonstrating that the logseries relative species abundance Ϫ ␮ distribution arises at the metacommunity speciation-extinction nJ n k n d ϭ (1 Ϫ m) ϩ m 1 Ϫ (A6) n,k ΂΃΂Ϫ ΃ ΂ ΃΂΃ equilibrium when the birth and death rates are density inde- JJ 1 JJM pendent and the metacommunity is symmetric (all species ex- ␮ th hibit the same mean per capita rates). where k is the abundance of the k species in the metacom- The expected relative species abundance distribution on is- munity under the logseries, and JM is the size of the metacom- lands under dispersal limitation (the classical problem in the munity. The first (second) term of bn,k and dn,k is the probability theory of island biogeography) is not the logseries, however, but of an increase or decrease by one individual, the kth species in is a distribution that resembles a skewed lognormal (Hubbell the local community, as a function of whether an immigration 2001a). The second advance in the unified neutral theory is the event occurred (did not occur), respectively. discovery of an analytical solution for the relative species abun- The expression in equation (5) can be solved numerically dance distribution in a local community under immigration quite accurately. Programs in C are attached electronically to from the metacommunity (Volkov et al. 2003), previously avail- the paper by Hubbell and Borda-de-A´ gua (2004). As the im- ͗␾ ͘ able only by simulation (Hubbell 2001a). Once again, let n be migration rate m decreases, the relative species abundance dis- the mean number of species with n individuals. Then tribution in the local community given by equation (5) becomes ⌫ ␥ ͗␾͘ϭ␪ J! ( ) progressively more skewed. Thus, as islands or local commu- n n!(J Ϫ n)! ⌫(J ϩ␥) nities become more isolated, rare species become rarer and common species become commoner. The degree of skewness of the ␥ ⌫ ϩ ⌫ Ϫ ϩ␥Ϫ Ϫ ␪ ϫ ͵ (n y) (J n y) y relative species abundance distribution is also a function of lo- ⌫ ϩ ⌫ ␥Ϫ exp΂΃␥ dy (A5) 0 (1 y) ( y) cal community size (Hubbell and Borda-de-A´ gua 2004).