FORTY YEARS AGO the theory of island biogeography challenged the Huchinsonian niche assembly paradigm in community ecology by postulating that ecological communities on islands were nonequilibrium collections of species assembled and disassembled solely by immigration and local extinction. Although the implications of this postulate were not fully appreciated at that time, the theory’s elegantly simple graphical representation of the immigration-extinction equilibrium implied that species were ecologically equivalent—symmetric—in their probabilities of immigrating to an island and going extinct once there. Recasting the symmetry assumption on a per capita basis and adding speciation, the extended theory predicts not only species richness but also relative species abundance. The symmetry assumption is equivalent to asking how many of the properties of ecological communities are captured by the mean, ignoring species differences. Clearly the mean can only give us a first approximation, but how good an approximation is it? This paper examines this question in a species-rich tropical tree community on Barro Colorado Island (BCI) in a plot whose dynamics my colleagues and I have followed for the past quarter century. Before examining the BCI results, however, I explain the underlying symmetry assumption of the theory of island biogeography, first, because there is some disagreement whether the theory makes this assumption, and second, because this assumption is the theoretical foundation for extending the theory to predict relative species abundance.
Although it is called an equilibrium theory, the theory of island biogeography can only be narrowly construed as such because it predicts continual species turnover, rather than a stable species composition in ecological communities. This is quite a radical idea that then—as now—flies squarely in the face of prevailing theory in community ecology. Contemporary theory is largely based on the Hutchinsonian niche paradigm, which states that each species has a unique niche or functional role that it performs better than any other species (Chase and Leibold 2003). According to this hypothesis, ecological communities are limited-membership, closed sets of species coexisting in competitive equipoise and that resist invasion of all other species. In contrast, the theory of island biogeography—in its famous graphical representation of crossing immigration and extinction curves as a function of island species richness—asserts that ecological communities are open assemblages of species that approach a steady state species richness that is dynamic, not a static species composition. The species are not labeled in the theory, which means the theory assumes that species are essentially interchangeable, i.e., equivalent in their likelihood of arriving on an island, or of going extinct after arrival.
MacArthur and Wilson did not discuss the fact that their theory assumes species symmetry. Indeed, much of the latter half of their monograph was devoted to discussing topics such as differences among species in the timing and order of immigration events or in probabilities of extinction once established on the island. In the original presentation, the immigration and extinction curves were drawn concave downward, which MacArthur and Wilson explained as follows: Immigration rate should slow with increasing numbers of species on the island because rapidly dispersing species should arrive sooner than slowly dispersing species, because competition from already established species reduces the colonization success of later arriving species, and because immigrants can no longer be counted if their species is already present on the island. Extinction rates, on the other hand, should accelerate with increasing numbers of species due to a larger number of potential competitive interactions among species and decreasing average population sizes as the island filled up (MacArthur and Wilson 1967, Schoener, this volume). Later, MacArthur and Wilson introduced a second version of the graphical representation of the equilibrium in which the immigration and extinction lines were linear (Schoener, this volume).
The graphical representation of island biogeography theory implies symmetry because, according to the theory, it does not matter which species contribute to balancing immigration and extinction rates on any given island. The single state variable in the model is the number of species on the island. All species in the original theory are treated as identical. Without this assumption, the model’s reduction of island community dynamics to counting species does not logically work. This is true even of the version of the theory with downwardly concave immigration and extinction curves. This concavity makes late-arriving species experience lower successful immigration rates and higher extinction rates. However, this modification does not alter the basic fact that any species arriving late, regardless of whether it is a good colonizer or competitor, will exhibit the same rate changes (Hubbell 2001). Likewise, all species respond in an identical manner to variation in the size of the island and its distance from the mainland source area.
Figure 10.1. The classical immigration-extinction graph of the equilibrium species richness on an island generated by two versions of neutral theory. Immigration rates are circles and extinction rates are triangles. Panel A: The linear version is mathematically expected when the symmetry assumption is made at the species level, in which each source area species has an equal probability of immigrating to the island, and of going extinct once there. In this example there were 100 species in the source area To estimate rates of immigration and extinction, individual immigration and extinction events were binned into short (10 unit) time intervals and plotted against mean number of species on the island in that time interval. Points represent the scatter over an ensemble of 10 stochastic runs. Panel B: The curvilinear version (arises when the symmetry assumption is made at the individual level, in which case the relative abundances of the species in the source area affect the probability of immigration (common species are more likely to immigrate than rare species). Extinction rates are a function of local species abundance on the island and accelerate as species become rarer with increasing numbers of species on the island. In this example there were 150 species in the source area (“metacommunity”) whose abundances were determined by a value of 20 for biodiversity number θ of neutral theory (Fisher’s α) and a metacommunity (source area) size of 10,000. The immigration rate 
was 0.5. The degree of asymmetry of the immigration and extinction curves varies and is a function of the immigration rate, the size of the island (measured by the sum of the population sizes on the island), and the value of θ.
It is easy to demonstrate how both the linear and curvilinear graphical versions of the immigration-extinction equilibrium in island biogeography arise from symmetric neutral theory (figure 10.1). The difference between the two versions is due to the level at which one makes the symmetry assumption, either at the species level—the level of the assumption in the theory of island biogeography—or at the individual level, which is the level of the assumption in neutral theory. If one makes the symmetry assumption at the species level, then species per se are equally likely to immigrate or go extinct, and in this case, one obtains the linear immigration-extinction graph. Figure 10.1a presents the results of an ensemble of ten stochastic simulations of the colonization of an island assuming equivalence at the species level. However, one can change the symmetry assumption to apply at the individual level, not at the species level, a change which means that each source-area individual—not each species—has an equal probability of immigrating, irrespective of the species to which it belongs. With this change in the level of the symmetry assumption, neutral theory is able to extend the theory of island biogeography to encompass relative species abundance both in the source area and on the island. One can prove that the expected distribution of relative species abundance in a continuous source area (the “metacommunity”) is Fisher’s logseries (Hubbell 2001, Volkov et al 2003). There is recent empirical evidence that the logseries distribution applies at large landscape scales in Amazonia (Hubbell et al. 2008).
When species have different relative abundances in the source area, then species no longer have equal probabilities of immigrating to the island. Common species are more likely to arrive before rare species. The individual-level symmetry assumption gives rise to the concave-curvilinear immigration curve in which the probability of species immigrations are ordered stochastically by ranked species abundances in the source area (figure 10.1b). Neutral theory requires no assumptions about differing dispersal abilities of species or interactions among species to generate curvilinear immigration and extinction curves, so it is a very parsimonious theory—more so even than the theory of island biogeography, because one no longer needs to specify the extinction rate, which is a prediction of the theory and arises through the demographic stochasticity of island populations. In the example shown, the immigration curve is much higher than the extinction curve; the degree of asymmetry is a function of the immigration rate and is less for slower immigration rates. However, the approach to equilibrium from an empty island is generally much faster than the loss of species through extinction from an “over-saturated” island. Asymmetric curves tend to occur because a colonization event requires the arrival of only one individual of a given species, whereas extinction requires the death of all individuals of a species on the island.
As MacArthur and Wilson point out, many species do differ in their colonizing ability and in their susceptibility to extinction. However, neutral theory says that simply observing curvilinear immigration and extinction rates is not sufficient evidence because species differences in immigration and extinction could be due primarily to differences in species abundance. It is possible that differences in source-area abundance of species may be many orders of magnitude greater than differences in dispersal ability and therefore could dominate the immigration process; this is an important open question for future research. In fact, neutral theory is a rich source of many detailed predictions about how the actual shapes of the immigration rate and extinction rate curves should change as a result of island size and immigration rate and the distribution of relative species abundance in the source area. For example, under low rates of immigration, the theory predicts that one may observe a bimodal extinction cure as a function of number of species on the island. This can happen because, under low immigration rates, some island species that colonized the island early have a chance to build to large population sizes, causing a bump in early extinctions in rare species before equilibrium species diversity is reached. To my knowledge, this result was not anticipated by island biogeography theory; it is a prediction that has never been made before, and has yet to be tested empirically.
I turn now to discussing the BCI results and evaluating their consistency with the theory of island biogeography and its extension the symmetric neutral theory. This paper discusses the following findings from empirical and theoretical studies of the BCI plot. (1) Although tree species in the BCI forest exhibit many differences, nevertheless island biogeography theory—and its neutral theory extensions—does quite a good job fitting both the aggregate community static and dynamic data. (2) Density dependence—the supposed signature of a diversity-regulated, niche-differentiated community—although strong and pervasive in the BCI tree community, especially in the early life history stages, nevertheless is not strong enough to regulate tree populations at the scale of the entire 50 ha plot. (3) A key ingredient in island biogeography is dispersal limitation, and all BCI species are strongly dispersal and recruitment limited. (4) Virtually all BCI tree species are ecological equivalents or near equivalents in their nutrient niches, so R* competition theory, the iconic niche-assembly theory in plat ecology, does not work for BCI trees. (5) Contrary to popular belief, simple evolutionary models show that ecological equivalence, the key concept of neutral theory, can evolve easily and often in communities of competing, dispersal-limited species. I discuss each of these findings, but in reverse order.
The core idea of neutral theory is ecological equivalence or near equivalence. A legitimate question is whether ecological equivalence among competing species can evolve, and if it can, how likely is it to do so. I have argued that ecological equivalence can and will arise easily and often under selective regimes that should be commonplace (Hubbell 2006). To study this problem, I adapted a model from Hurtt and Pacala (1995), who studied a model community of dispersal-limited competing species, each of which was the best competitor for some set of microsites. When dispersal was not limiting, such that offspring of each species reached every site, then each species won those sites for which it was the best competitor. However, under dispersal limitation, many species won by default sites for which they were not the best competitor—because the best competitor did not reach the site. Hurtt and Pacala showed that dispersal limitation can delay competitive exclusion nearly indefinitely, even of species that were inferior competitors to some other species in every microsite. Dispersal limitation delayed competitive exclusion longer the more species-rich the community became.
Hurtt and Pacala (1995) did not study the evolution of niches, however, so I added genetics, modeling the evolution of a quantitative trait of many genes of small, additive effect that adapted species to particular microsites (Hubbell 2006). I considered three selective scenarios under chronic dispersal limitation (figure 10.2). In scenario 1, environmental (microsite) variation was fine-grained, and each species experienced the full range of microsite variation over the range of the species. Under this scenario, species exhibited convergent evolution, converging on nearly identical distributions of genotypes matching the frequency of the different microsites they encountered, irrespective of the number of other species doing the same thing, and regardless of starting conditions. Under scenario 2, environmental (microsite) variation was coarse-grained and spatially autocorrelated, but nevertheless all species still experienced the full range of microsite variation over their geographic range. Under this scenario, species evolved into polymorphic generalists, consisting of locally adapted ecotypes. This case might seem like niche differentiation, but it is fundamentally different because the niches of all species overlapped broadly across their polymorphisms, and there was no limiting similarity (figure 10.2). Finally, in scenario 3, environmental (microsite) variation was again coarse-grained and spatially autocorrelated, but in this case, the species did not encounter the full range of environments (microsites). Only under this scenario did species evolve classical niche differentiation with limiting similarity. I expect all three selective regimes to be commonplace, and ecological equivalence or near-equivalence evolved under two out of three selective regimes. These ecologically equivalent or near-equivalent species persisted without extinction for at least 10,000 generations, the duration of the model simulations (Hubbell 2006).
Figure 10.2. Three scenarios for the evolution of ecological niches in a dispersal-limited community of 10 species. Top 10 panels under each scenario are the distributions of genotype frequencies (percentages) for a metric trait with values ranging from 0-40 in each of the 10 species after 10,000 generations. Bottom panel under each scenario is the frequency distribution of environmental states, which ranged in value from 0 to 40. Selection favored juveniles having the genotype value (number of alleles) most closely matching the environmental state value. Scenario 1: environment is fine-grained, each species is exposed to the full range of environmental variation; result: convergent evolution, broadly overlapping niches with genotype frequencies similar to the frequencies of environmental states encountered. Scenario 2: environment is coarse-grained and patchy, such that local populations of a species are not fully exposed to all environmental variation, but the range of the species span the full range of environmental variation; result: species evolve into polymorphic generalists with local ecotypes, but no limiting niche similarity between species. Scenario 3: environment is coarse-grained and patchy and species are not exposed to the full range of environmental variation over their evolutionary history; result: classical niche differentiation. Under this scenario, the species were ordered for illustration to better reveal the staggered niche distributions.
A question might arise as to whether these results are obtained only on local spatial scales. Subsequent to the analyses in Hubbell (2006), Jeff Lake, Luís Borda-de-Agua, and I (unpublished) have explored these models on much larger spatial scales and with more explicit functional traits. As long as strong dispersal limitation applies (which becomes stronger on larger spatial scales), and the selective regimes are the same, then we obtain the same qualitative results on large scales. Of course, real environments are spatially autocorrelated, and they are more likely to differ the farther apart they are separated. Therefore it is not surprising that niche differentiation should generally be greater among species separated by larger distances.
R* competition theory (Tilman 1982, 1988) postulates that plant species coexist by virtue of partitioning limiting nutrients through an interaction of spatially variable nutrient supply rates and species-specific uptake rates for these nutrients. R* theory is also called resource-ratio theory because plants use nutrients in relatively fixed tissue ratios, and in R* theory the outcome of competition for multiple nutrients depends on ratios of supply rates of limiting nutrients in relation to ratios of consumption rates by competing species. R* theory is very parameter-rich, and the species-specific values of these parameters are unknown for BCI tree species. Nevertheless, there are strong qualitative predictions that we can test, and we summarize our findings for three of these predictions here.
We mapped all soil macronutrients except S and most micronutrients across the BCI plot (John et al. 2007). We analyzed species richness across three primary gradients of macronutrients in the BCI plot, ratios of N/P, Ca/K, and Mn/Mg, chosen because they were statistically independent from each other, and because these six macronutrients are generally thought to include the nutrients that are most often limiting. Spatial variogram analysis revealed that virtually all of the spatial autocorrelation in nutrients occurs on spatial scales of 200 m or less, so the appropriate scale for testing the effects of variation in nutrients on species richness is on spatial scales of less than 4 hectares. There is one to two orders of magnitude variation in these nutrient ratios across the plot. Here we report only the results for the N/P gradients, but the conclusions are identical to those reached from considering the nutrient ratios of Ca/K and Mn/Mg. We will publish the full results elsewhere (Hubbell et al. unpublished).
The first prediction of R* theory is that species richness should increase with the spatial variance in nutrient ratios. There is considerable variation in local species richness to explain. For example, on a scale of 400 m2, species richness varies from 26 to 81 species. Does local variation in nutrient ratios explain this variation in species diversity and composition? The answer appears to be no. We found no relationship between species richness and spatial variance in nutrient ratios (Hubbell et al. unpublished). Figure 10.3 shows the results on the N/P gradient at a spatial scale of 400 m2, and we obtained similar results at all spatial scales and for other nutrient ratios. We did find by principal-component analysis that a linear combination of Ca, P, and Zn explained over 40% of the variation in species richness (John et al. 2007). However, this nutrient interaction is not predicted by R* theory, but probably reflects an underlying interaction between these nutrients that is not captured by R* theory, as discussed below.
The second qualitative prediction is that if one moves across gradients of limiting nutrients or their ratios, there should be a sequence of species replacements (figure 10.4). We tested this prediction on the ten most abundant species, which constitute 52% of all individuals. One would expect competition to be the most intense, and nutrient partitioning to be the most evident, among these very abundant species. However, these species remain relatively invariant, with some fluctuations in abundance across the three primary gradients of macronutrients (figure 10.4) (Hubbell et al. unpublished).
Figure 10.3. Lack of relationship between species richness per 400 m2 in the BCI plot and position on the N/P gradient across the plot. Species richness varies from 26 to 81 species on this spatial scale. similar qualitative results were obtained on Ca/K and Mn/Mg gradients, and on different spatial scales, ranging um to 4 ha.
Figure 10.4. Lack of species replacements over the N/P gradient among the 10 most abundant species in the BCI plot. These 10 species represent more than half of all stems in the forest, and should show niche differentiation for limiting nutrients if it exists. Similar results were obtained on the Ca./K and Mn/Mg gradients.
Figure 10.5. Evidence of nutrient niche generalization over the N/P gradient among the 10 most abundant species in the BCI plot. The heavy gray line is the distribution of the proportion of quadrats having a given value of the N/P ratio in the plot, which is the null distribution of the proportion of species abundance that is expected if they are indifferent to the nutrient ratio variation. The thin lines are for each of the 10 species. The species lines do not differ significantly from the null distribution. Similar results were obtained on the Ca/K and Mn/Mg gradients.
A third prediction is that the nutrient niches of BCI species should minimally overlap on nutrient gradients. The null expectation is that the proportion of the individuals of a given species occurring at a given nutrient ratio should match the proportion of plot area exhibiting that nutrient ratio. The most common species should exhibit strong nutrient niche differentiation. However, this is not what we observe. Virtually all species show very broad niche overlap in their distributions, many species conforming very closely to the null expectation. For example, the ten most abundant species are all nutrient generalists on the three gradients; we illustrate these results for the N/P gradient in figure 10.5. The distributions conform to the null expectation, i.e., they are indifferent to position on the nutrient gradient. This said, about 70% of BCI species distributions deviate significantly from the null distribution, consistent with our previous findings (John et al. 2007). However, our very large sample sizes allow us to detect significance in quantitatively small deviations from the null. Moreover, many of the species that deviate from the null expectation do not differ from each other (e.g., figure 10.6). In fact, all BCI species overlap to a very large extent in niche breadth on all three nutrient gradients. Of the 187 species abundant enough to test, in 155 species the intersection of their niche breadths was > 95% of the union of their niche breaths on these nutrient gradients and in 139 species it was >99% (Hubbell et al. unpublished). We conclude that BCI species are nearly ecologically equivalent for the major macronutrients likely to be limiting to them, and that the primary explanation for the coexistence of so many BCI tree species is not likely to lie in niche partitioning of nutrient gradients.
Figure 10.6. About 70% of BCI species deviate from the null distribution of one or more nutrient ratio gradients. However, many of these species, although they differ from the null distribution, are not distributed differently from each other. For example, here are the distributions of 10 species that show a slight skewing of abundance toward the high end of the N/P gradient in the plot, but do not differ from each other. The heavy line is the null distribution.
The mathematics of R* theory is internally consistent, so what is going on? One possibility is that BCI tree species do not actually compete for these nutrients, but this seems very unlikely. A second possibility is that the niche differentiation is in regard to other macro- and micronutrients not yet examined, which remains to be tested. A third possibility is that our measurements of soil nutrient concentrations do not accurately reflect the supply rates of these nutrients; but we have tested this possibility, and there is a very high positive correlation (>0.9) between soil concentrations and levels of nutrient availability to plants (Dalling, personal communication).
A fourth possibility is that BCI tree species do not conform to one or more assumptions of the mathematics of R* theory. One assumption is that species are nutrient specialists, but this is not true of the vast majority of BCI tree species. Another false assumption is that the essential macro- and micronutrients are taken up independently. Over the past quarter century since R* theory was developed, there have been major advances in understanding of the mineral nutrition of plants (Epstein and Bloom 2005) that have not yet been incorporated into the theory of resource competition. One of the main research findings is that many nutrients are not taken up independently. For example, Ca facilitates the uptake of many cations and anions. Another false assumption of R* theory is that nutrient uptake and growth parameters are invariant over time and the same among all individuals of a given species. Nutrient uptake parameters vary among individuals and even in the same individual over time. Plants regulate their internal tissue stoichiometry of macro- and micronutrients against concentration gradients in the environment, and they do this by changing enzymatic pathways and affinities in nutrient uptake depending on the concentrations to which they are exposed. Plants can also adaptively change their mycorrhizal associates as nutrient environments change, favoring associates that are better at facilitating uptake of nutrients such as P over different concentration ranges.
These and other findings suggest that we need a new resource-based theory for testing the importance of nutrients to coexistence of species in plant communities, including tropical tree communities. Regardless of the development of new theory, there is little doubt that most BCI species are nutrient generalists with broadly overlapping niches. In terms of the model of the evolution of ecological equivalence summarized above (Hubbell 2006), the origin of this near-ecological equivalence is presumably response to selection from similarly variable nutrient regimes over the evolutionary history of these species.
What about niche differentiation along other niche dimensions, such as light and water availability gradients? There is a strong axis of niche differentiation at the guild level with regard to light. However, there are many nearly equivalent shade-tolerant species, many more than the number of shade-intolerant species (figure 10.7). The large number of shade-tolerant species could be a problem for niche theory because one would expect light to be more finely partitioned when it is abundant than when it is scarce (Hubbell 2005). Although competition for light is intense in the closed-canopy BCI forest, shade is not species-specific nor a resource to be partitioned. The most parsimonious hypothesis to explain these results is simply that most BCI tree species have experienced shady environments over their evolutionary history, each converging on adaptations for tolerating shade stress, irrespective of the number of species following the same adaptive trajectory. We therefore do not believe that light partitioning is a strong candidate to explain the high tree species richness of the BCI forest.
What about hydrological niches, as in the hypothesis made by Silvertown et al. (1999) that different species have different drought tolerances? We do find a considerable range in seedling drought sensitivity among Panamanian tree species (Englebrecht et al. 2007). We have tested drought tolerance in about 70 species across the isthmus of Panama, from the wet Caribbean side to the more seasonal and drier Pacific side, and the ratio of population density of species in dry versus wet sites across the isthmus is significantly correlated, although weakly, with drought sensitivity (R2<0.2) (Englebrecht et al. 2007). On small spatial scales (the 50 ha BCI plot), seasonal water availability appears to act as an environmental filter determining which species can persist in the seasonally drier parts of the plot (the plateau). However, virtually all of the more drought-resistant species also are present in (i.e., not excluded from) the wetter areas (slopes) of the plot and grow right alongside the less drought-tolerant species.
Figure 10.7. Axis of niche differentiation with respect to light availability. Each point represents the mean phenotype of a single species. The species at the upper left are shade tolerant (high survival in shade, low maximal growth rate in high light), whereas species’ at the lower right are shade intolerant (low survival in shade, high maximum growth rate in full sun). There are many more shade-tolerant species than shade-intolerant species, posing a potential difficulty for niche theory in explaining why low light environments would be more finely partitioned than high light environments. A simple hypothesis is that species have niche-converged on shade tolerance because more species have experienced shady environments more persistently over evolutionary time than sunny environments, irrespective of the number of species following the same evolutionary trajectory.
In summary, if one examines the nutrient, light, and hydrological gradients in the BCI plot, there are many nearly equivalent species at each point along each gradient, and I am unaware of any niche-based theory that predicts how many species will be found at any given position along these gradients (Hubbell 2005). This is not to say that new dimensions of niche differentiation will not be discovered in the future to explain all of these locally co-occurring species; but at the moment, a simpler hypothesis suffices, namely, that species in each guild have been subject to similar environments and selection pressures over their evolutionary history and have converged on a similar suite of traits that adapt them to these shared environments, irrespective of the number of other species evolving the same, or a very similar, suite of traits. If Hurtt and Pacala (1995) are correct, dispersal limitation prevents competitive exclusion among these niche-convergent species. According to this view, the number of tree species in the BCI is more a reflection of larger-scale evolutionary-biogeographic processes that dictate the number of species in the regional species pool.
We have already discussed the theoretical evidence that dispersal limitation can promote long-term species coexistence in communities (Tilman 1994, Hurtt and Pacala 1995). Dispersal limitation is the failure of seeds to arrive at all sites favorable for the growth and survival of a given species, and recruitment limitation is the failure to recruit germinated seedlings in a site similarly favorable for growth and survival. I will lump both processes under the rubric of dispersal limitation for purposes of the present discussion. We have been studying seed dispersal in BCI trees in the 50 ha plot for the past 21 years, sampling seed rain biweekly in a network of 200 seed traps, and following seedling germination in three 1 m2 quadrats next to each of the traps (Hubbell et al. 1999, Muller-Landau et al. 2002, Dalling et al. 2002, Wright et al. 2002). The results show that only a small number of species managed to deposit seeds in a substantial fraction of the traps. In the first decade, only 5 species deposited at least one seed in over half of the traps, whereas 50% of the >200 species whose seeds were collected somewhere at least once, managed to deliver at least one seed to only 5 or fewer traps over a decade (figure 10.8) (Hubbell et al. 1999).
Jacaranda copia (Bignoniaceae) is the best disperser of any species whose seeds were collected in the seed traps. At least one seed of this species arrived in every trap during the first decade, and no other species came close to this record. Despite this, even J. copaia is recruitment limited because it requires very large light gaps to survive, and gaps of sufficient size for successful regeneration of this species average more than 100 m from adults of this species in the BCI forest. We studied dispersal in this species using microsatellite markers (Jones et al. 2006). We genotyped potential parents and maternal tissue from seeds collected after dispersal. This is a light-demanding canopy emergent that is under strong selection for dispersal because the large gaps it requires to regenerate are few and far apart. The genetic data indicated that, although more than 91% of the seeds landed within 100 m of the mother, 57% of sapling recruits (reaching the census size of 1 cm DBH) were from the tail of the dispersal kernel, more than 100 m from the mother.
Figure 10.8. Evidence for community-wide dispersal limitation among BCI trees. Seeds were collected weekly in a network of 200 traps throughout the BCI plot. Of the 260 species collected over a decade, only a dozen species deposited seeds in more than half of the traps, whereas half of all species dispersed seeds to 5 or fewer traps in a decade. After Hubbell et al. (1999).
In summary, the trap data and the genetic results indicate that all BCI tree species are dispersal and recruitment limited. This is a key assumption of the theory of island biogeography and of neutral theory.
A great deal of attention has been paid to the question of density dependence in tropical forests, particularly to the hypotheses of Janzen (1970) and Connell (1971) about the role of enemies in maintaining high species diversity in tropical forests. Janzen and Connell independently proposed that an interaction of dispersal and seed predation would prevent monodominance by any single species by lowering the probability of self-replacement of a given species at the same location. We have been testing a generalization of this hypothesis, measuring not only losses in the seed-to-seedling transition, but also density dependence in subsequent growth and survival of juvenile individuals, as a function of local conspecific population density. Using data from the seed rain/seedling germination study, Harms et al. (2000) demonstrated that there was pervasive density dependence throughout the BCI tree community in the seed-to-seedling transition. If a species deposited more seeds in a given trap, it had lower per capita seedling germination in the adjacent seedling plots than when a species deposited fewer seeds in a given trap. This effect was species-specific: traps with more seeds of other species did not increase the mortality of seeds of a given focal species.
In 2001, to study density dependence in a spatially stratified sampling design covering the entire 50 ha plot, we began a study of seedling recruitment, growth, and survival in 20,000 1 m2 seedling plots in a 5 m grid over the entire plot. This grid puts 2 to 5 traps under the crown of every single canopy tree in the plot. We have analyzed seedling survival during the first three years of this study in 48,956 established seedlings and small saplings of 235 species (Comita and Hubbell, 2009). When we tested for density dependence across all species, there was a significant negative effect of conspecific seedling and adult densities on conspecific growth and survival. In contrast, heterospecific neighbors had no effect on seedling growth and a positive effect on survival. At the species level, the density of conspecific neighbor seedlings had a significant negative effect on survival for 45 of the 59 species (76%) that were sufficiently abundant to test. We expect the percentage of species showing negative density dependence to increase as the length of the study increases. The expectation is based on the fact that we know that density-dependent effects on growth and survival persist into the sapling and subadult stages of BCI tree species as well (Hubbell et al. 2001, Ahumada et al. 2004). Smaller saplings show a greater depression of relative growth rate than do larger subadult trees from conspecific neighbors. These juvenile life stages last for decades in many species, so even small effects can accumulate over the lifespan of individual trees. Pervasive interspecific frequency dependence, although weak in comparison with intraspecific density dependence, has also been detected at the community level (Wills et al. 1997, 2006).
However, the primary question we are posing here is, do Jansen-Connell density-dependent effects regulate BCI tree populations? Given the strength, pervasiveness, and persistence of the negative conspecific density effects in the BCI community, there is no doubt any longer that these effects promote local diversity in the BCI forest by reducing the probability of conspecific self replacement. However, this is different from the question of whether these Janzen-Connell effects regulate the adult population sizes of BCI tree species. Several empirical observations and theoretical considerations cast serious doubt on this possibility.
Figure 10.9. Effect of number of conspecific neighbors on relative growth rate (percentage growth) over the decade, 1990–2000, as a function of distance from a focal plant, for focal plants 1–4 cm DBH. Light gray circles: Effect of close conspecific neighbors, within 5 m of the focal plant. Dark gray triangles: Effects of conspecific neighbors from 5 to 10 m from the focal plant. Black circles: Effects of conspecific neighbors from 15 to 20 m from the focal plant. The data for 10 to 15 m are not shown for graph clarity. The negative effect of a conspecific neighbor on the growth rate of a focal plant is about an order of magnitude weaker at a distance of 15–20 m than it is at a distance of 0–5 m.
The most important of these observations is that the strength of the negative density dependence on conspecific recruitment, growth, and survival decays to background levels over very short distances, measured in a few tens of meters, usually less than 20 m (figure 10.9) (Ahumada et al. 2004, Hubbell et al. 2001). Therefore, there is little or no force of density dependence acting at the scale of the entire plot on adult tree population densities—or even on spatial scales of a few hectares. Janzen-Connell effects do reduce the probability that a given tree will replace itself at the same location in the forest, so they increase the mixing of species and species richness on a local spatial scale. However, they are not sufficiently strong and spatially extensive to regulate adult population abundances on landscape scales. This conclusion is consistent with the observation that, despite locally negative effects on survival of conspecific neighbors, seedling survival is positively correlated with species abundance in the BCI tree community at the whole plot level (Comita and Hubbell, 2009).
One can reach the same conclusion on theoretical grounds (Zillio et al. 2005, Hubbell 2008). Without delving into the mathematics, the logic is clear from a simple verbal argument. Consider a perfect Janzen-Connell effect, such that no species can replace itself in the same location. However, suppose that species i can replace any of the other S−1 species in the forest. Turning this around, any of the S−1 species in the forest can replace the ith species at a given location. Unless and until a species approaches monodominance, this constraint on the population growth of the ith species is very weak in a species-rich forest such as BCI. It is weak even in a forest consisting of only a few dozen species, such as a typical mid-latitude temperate forest. Janzen-Connell effects are also prevalent in relatively species-poor temperate forests, so one must also conclude that these effects are not responsible for the latitudinal gradient in tree species richness either (HilleRisLambers et al. 2000). These findings mean that Janzen-Connell effects are not the “cause” of tree species richness in tropical forests. What these effects do is mix species more thoroughly in a small area and maintain whatever species are present, but they do not dictate how many species participate overall in this mixing.
The relevance of these findings regarding the application of neutral theory to plant communities—and also probably to many animal communities—is that density dependence is a very local-scale phenomenon that becomes an unimportant force in population dynamics at larger spatial scales. Zillio et al. (2005) showed that patterns of beta diversity in tropical forests on local to biogeographic spatial scales are consistent with a loss of density dependence on scales of a few tens of meters. Patterns of relative species abundance in the BCI plot are also consistent with a loss of density dependence at densities above a few tens of trees (Volkov et al. 2005). These conclusions on density dependence have profound implications for ecology, biogeography, and conservation biology, namely. that our familiar notions of population regulation do not apply in macroecology on landscape spatial scales, scales on which population growth becomes very close to, and indistinguishable from, density independence (i.e., neutrality).
There are currently two mechanistic versions of neutral theory. The original version (Hubbell 2001, Volkov et al. 2003, Vallade and Houchmandzadeh 2003, McKane et al. 2004, Etienne 2005) embodies the mechanism in the theory of island biogeography, namely, dispersal limitation. According to this mechanism, relative species abundances are dictated by the steady state between the arrival of immigrants to a particular community and their local extinction. The loss of all diversity is prevented by adding a slow trickle of new species into the source area or metacommunity, from which the immigrants to the local community are drawn. Under this version of neutral theory, rare species are less frequent than species of intermediate abundance in the local community because they are more prone to local extinction and, once they go locally extinct, they take longer to reimmigrate than do common species.
The other version of neutral theory embodies a mechanism of symmetric density and frequency dependence (Volkov et al. 2005). In this version, there are fewer rare species in the community because they have a higher per capita growth rate than do common species. Thus populations of rare species tend to grow in abundance relative to common species and thereby graduate out of the rare abundance categories, depleting the steady-state frequency of rare species in the community. This rare species advantage is captured in the ratio of the average per capita birth rate to the death rate, b/d (Volkov et al. 2005). At low population sizes, the birth rate exceeds the death rate (b/d > 1), but at higher population rates, b/d is very close to, but slightly less than, unity. In the theory there is a parameter c which determines the strength of the density dependence. The larger the value of c, the higher the threshold abundance of species that enjoy a growth rate advantage (Volkov et al. 2005).
Dispersal limitation and density dependence are independent mechanisms, and both can operate simultaneously to varying degrees. Remarkably, both mechanisms under neutrality fit the static data on relative tree species abundance in the BCI plot equally well, and data from other 50 ha plots as well (Volkov et al. 2005) (figure 10.10). Although we cannot distinguish the quality of their fits to the static relative abundance data, we can do so in the fit to the dynamic data from the BCI plot. One of the surprising findings over the past quarter century is just how dynamic the BCI forest is (Hubbell 2008). More than half (55.8%, 179) of BCI species have changed by more than 25% in total abundance since 1982, and 36 species (11.2%) have changed by more than 100%. Large changes were not restricted to just uncommon or rare species, but also occurred in common to very common species (Hubbell 2008). The dynamism of the BCI tree community gives us considerable power to test the two versions of neutral theory.
Figure 10.10. Fits of the two versions of neutral theory to the static BCI relative species abundance data. Observed relative abundance data are given by the bar histogram. Species are binned into doubling classes of abundance. The light gray line and ovals is the fit of the dispersal limitation version of the theory, which is the original version in Hubbell (2001) and the generalization of island biogeography theory. The unconnected dark gray ovals are the fit of the symmetric density dependence version of the theory. The quality of the fits is equally good and cannot be distinguished from the static data alone. After Volkov et al. (2005).
We can compare the predictions of a neutral model community in which species are stabilized by stochastic density dependence versus one in which species drift in abundance solely under the influence of immigration and extinction and demographic stochasticity. We compare the two model predictions for what should happen to the decay in community similarity over time. There are a number of possible ways to measure community similarity, but a simple way is to regress the logarithm of species abundance at time t + τ on the logarithm of the abundance of the same species at time t, where τ is the time lag separating the abundance snapshots of the tree community. We then can use the R2 of this regression as a measure of community similarity, i.e., the proportion of variance in log abundance of species at time t + τ explained by the log abundance of the same species at time t (we add one individual to the abundances before log transforming them so we can include species that are not present at a particular census). Under both versions of neutral theory, the R2 decays over time, reaching an asymptotic low R2 value after some time period. Under the stochastic density dependence model, this asymptote is reached quite quickly, and theory predicts the R2 decay curve to be obviously curvilinear and asymptoting even on short time scales such as a quarter of a century. However, under the immigration-extinction model, the original theory of island biogeography, the R2 decay curve is expected to take much longer to reach its asymptote, on the order of 3,000 years (Azaele et al. 2006), and the curve is predicted to decay essentially as a straight line for periods as short as 25 years (Hubbell 2008). Which curve do we observe?
Figure 10.11. Observed near-normal distribution of the intrinsic rates of increase of BCI tree species, centered on r = 0, over the 23 year time interval, 1982–2005.
We can compute the expected curve under density dependence by assuming that populations are fluctuating stochastically around fixed carrying capacities. The intrinsic rates of increase of BCI tree species over the past 25 years are nearly normally distributed around zero (figure 10.11). We can sample this distribution to produce expected changes in abundance of BCI tree species and project changes in their abundances from 1980 to 2005 in five-year intervals, matching the census intervals. I did this in an ensemble of 100 runs and calculated the mean decay curve in R2 that resulted. To compute the expected decay curve under immigration-extinction, I simulated the changes expected in species abundances assuming the average per capita death rate observed in the BCI plot, and the fundamental biodiversity number θ and the dispersal parameter m of neutral theory, estimated from the static relative abundance data from the first census of the plot (Hubbell 2001, Volkov et al. 2003). The R2 obtained for each lag interval was averaged with all lags of similar length, e.g., all five-year lags between censuses, all ten-year lags, and so on. I then compared the fit of the two model decay curves to the actual decay curve observed in the BCI tree community.
The conclusion from fitting the two versions of neutral theory is clear-cut and unambiguous: the immigration-extinction version fits the observed dynamic data on decay in community similarity with time, and the density-dependence version does not (figure 10.12). The observed decay curve is nearly perfectly linear, not curvilinear, with an R2 of 0.997. The fit of the immigration-extinction model is impressive, especially considering that the fit is not a regression, but the fitted line was derived completely independently by estimating the values of θ and m from the static relative abundance data of the first BCI census—completely independently from the dynamic data of changes in the BCI tree community over the subsequent quarter century.
Figure 10.12. Predicted curves for the decay of community similarity under the dispersal limitation version of neutral theory (straight solid line), and under a model of symmetric density dependence, in which species are assumed to be stochastically fluctuating around fixed carrying capacities (curved dashed line). The two curves represent the expected decay in community similarity as measured by the decline in R2 over time of the autoregression of log species abundances at time t + τ on the log of the abundances of the same species at prior time t for all possible combinations of 5-year inter-census time lags. The observed decay in R2 is almost perfectly linear (top solid straight line) (coefficient of determination is 0.997); the error bars are 1 standard error of the mean across all inter-census time lags. The curve for density-dependence (bottom curved line) is the mean of an ensemble of 1000 runs. The error bars are one standard error of the mean. The line fit through the linear decay data is not a regression but is the prediction of the dispersal limitation (island biogeography) version of neutral theory. The values of the fundamental biodiversity number θ and dispersal parameter m were 40 and 0.09, respectively, and were obtained independently from fitting the static relative abundance data from the first census in 1982.
These results do not “prove” that the BCI tree community is dynamically neutral. Indeed, we have presented evidence that the life histories of BCI tree species are not all ecologically equivalent. Moreover, when species names are attached to BCI trees, there are emerging signs of directional, non-neutral change in species composition of the BCI tree community (Feeley et al., unpublished). Species of higher wood density and slower growth rates are slowly and steadily increasing in abundance, possibly as a result of climate change, but the cause is not completely proven yet. Neutral theory assumes constant environments, and if environments change, then the competitive balance among species that had neutral or near-neutral dynamics under the old environmental regime may expose species differences that previously went unrecognized as important to determining which species persist and which ones do not under changing environments. Nevertheless, despite the slow, directional changes in the BCI forest, neutral theory still does a very good job of fitting the static and dynamic data on relative species abundance in the BCI plot. The precision of the fits of neutral theory to both the static and dynamic data must mean that neutral theory—as a first-moment approximation to be sure—captures much of the true behavior of the BCI tree community. Arguments that the theory of island biogeography and its neutral theory extensions, are “cartoonish” (Laurance 2008, this volume) are a mischaracterization of the theory’s continuing utility. For an application of neutral theory to a question in conservation biology, namely, how many tree species there are in the Amazon, and how many of them are likely to go extinct, see Hubbell et al. (2008).
Indeed, I would argue that neutral theory provides a solid theoretical foundation on which to build a new non-neutral, niche-based theory of ecology from the perspective of statistical mechanics (Hubbell 1995, 1997, 2001, Bell 2001, Volkov et al. 2003, 2005, 2007, Vallade and Houchmandzadeh 2003, Alonzo and McKane 2004, McKane et al. 2004, Etienne 2005, He 2005, Azaele et al. 2006, Volkov et al., in press). These developments will add “higher-moment” processes as needed to achieve new levels of realism and precision. However, the guiding principle in theory development should always be to start simple and add complexity slowly, step by step, but only when absolutely necessary, kicking and screaming the whole time.
I thank Jonathan Losos, Bob Ricklefs, and Patty Gowaty for valuable comments on the first draft of this paper. The BCI forest dynamics research project was made possible by National Science Foundation grants to Stephen P. Hubbell: DEB-0640386, DEB-0425651, DEB-0346488, DEB-0129874, DEB-00753102, DEB-9909347, DEB-9615226, DEB-9615226, DEB-9405933, DEB-9221033, DEB-9100058, DEB-8906869, DEB-8605042, DEB-8206992, and DEB-7922197, support from the Center for Tropical Forest Science, the Smithsonian Tropical Research Institute (STRI), the John D. and Catherine T. MacArthur Foundation, the Andrew Mellon Foundation, the Celera Foundation, and numerous private individuals, and through the hard work of over 100 students, postdocs, and assistants from ten countries over the past quarter century. The nutrient mapping of the BCI plot was made possible by an NSF grant to Jim Dalling and Kyle Harms, and the analysis of the soil chemistry was done by Joe Yavitt. The plot project is part the Center for Tropical Forest Science (CTFS), a pantropical network of large-scale forest dynamics plots modeled after the BCI project. I am especially grateful to Robin Foster, who began the project with me in 1980 and who met the botanical identification needs of the census through the early years, to Salomon Aguilar, Rick Condit, Jim Dalling, Kyle Harms, Suzanne Loo de Lau, Rolando Perez, and Joe Wright, for their long-term collaboration on the BCI project, and to Ira Rubinoff, Director of STRI, for his constant support of and belief in the project. I thank Liz Losos and Stuart Davies for their management of CTFS.
Ahumada, J. A., S. P. Hubbell, R. Condit, and R. B. Foster. 2004. Long-term tree survival in a neotropical forest: The influence of local biotic neighborhood. In Forest Diversity and Dynamism: Findings from a Network of Large-Scale Tropical Forest Plots, ed. E. Losos and E. G. Leigh Jr., 408–32. Chicago: University of Chicago Press.
Alonzo, D., and A. J. McKane. 2004. Sampling Hubbell’s neutral theory of biodiversity. Ecology Letters 7:901–10.
Azaele, S., S. Pigolotti, J. R. Banavar, and A. Maritan. 2006. Dynamical evolution of ecosystems. Nature 444: 926–28.
Bell, G. 2001. Neutral macroecology. Science 293:2413–16.
Chase, J. M., and M. A. Leibold. 2003. Ecological Niches: Linking Classical and Contemporary Approaches. Chicago: University of Chicago Press.
Comita, L., and S. P. Hubbell. 2009. Local neighborhood and species’ shade tolerance influence survival in a diverse seedling bank. Ecology 90:328–34.
Connell, J. H. 1971. On the role of natural enemies in preventing competitive exclusion in some marine animals and in rain forest trees. In Dynamics of Populations, ed. P. J. den Boer and G. R. Gradwell, 298–312. Wageningen, The Netherlands: Centre for Agricultural Publishing and Documentation.
Dalling, J. W., H. C. Muller-Landau, S. J. Wright, and S. P. Hubbell. 2002. Role of dispersal in recruitment limitation in six pioneer species. Journal of Ecology 90: 714–27.
Donnelas, M., S. R. Connolly, and T. P. Hughes. 2006. Coral reef diversity refutes the neutral theory of biodiversity. Nature 440: 80–82.
Engelbrecht, B.M.J., L. Comita, R. Condit, T. A. Kursar, M. T. Tyree, and S. P. Hubbell 2007. Drought sensitivity shapes species distribution patterns in tropical forests. Nature 447:80–82.
Epstein, E., and A. J. Bloom. 2005. Mineral Nutrition of Plants. Sunderland, MA: Sinauer Associates.
Etienne, R. 2005. A new sampling formula for neutral biodiversity. Ecology Letters 8: 493–504.
Feeley, K. J., S. J. Davies, R. Peres, R. Condit, R. B. Foster, and S. P. Hubbell. Unpublished. Directional changes in the composition of a tropical forest due to climate change. Proceedings of the National Academy of Sciences U.S.A. (submitted).
Harms, K. E., J. S. Wright, O. Calderón, A. Hernández, and E. A. Herre. 2000. Pervasive density-dependent recruitment enhances seedling diversity in tropical forests. Nature 404: 493—95.
He, F. L., 2005. Deriving a neutral model of species abundance from fundamental mechanisms of population dynamics. Functional Ecology 19: 187–93.
HilleRisLambers, J., J. S. Clark, and B. Beckage. 2000. Density-dependent mortality and the latitudinal gradient in species diversity. Nature 417:732–35.
Hubbell, S. P. 1979. Tree dispersion, abundance and diversity in a tropical dry forest. Science 203: 1299–309.
———. 1995. Towards a theory of biodiversity and biogeography on continuous landscapes. In Preparing for Global Change: A Midwestern Perspective, ed. G. R. Carmichael, G. E. Folk, and J. L. Schnoor, 173–201. Amsterdam: Academic.
———. 1997. A unified theory of biogeography and relative species abundance and its application to tropical rain forests and coral reefs. Coral Reefs 16 (suppl.):S9–S21.
———. 2001. The Unified Neutral Theory of Biodiversity and Biogeography. Princeton Monographs in Population Biology, Princeton, NJ: Princeton University Press.
———. 2005. Neutral theory in ecology and the hypothesis of functional equivalence. Functional Ecology 19: 166–77.
———. 2006. Neutral theory in ecology and the evolution of ecological equivalence. Ecology 87: 1387–98.
———. 2008. Approaching tropical forest complexity, and ecological complexity in general, from the perspective of symmetric neutral theory. In Tropical Forest Community Ecology, ed. W. Carson and S. Schnitzer, 143–59. Oxford: Blackwell.
Hubbell, S. P., J. A. Ahumada, R. Condit, and R. B. Foster. 2001. Local neighbourhood effects on long-term survival of individual trees in a neotropical forest. Ecological Research 16: 859–75.
Hubbell, S. P., R. B. Foster, S. O’Brien, B. Wechsler, R. Condit, K. Harms, S. J. Wright, and S. Loo de Lau. 1999. Light gaps, recruitment limitation and tree diversity in a Neotropical forest. Science 283: 554–57.
Hubbell, S. P., K. E. Harms, J. W. Dalling, R. John, and J. B. Yavitt. Unpublished. Nutrient-based niches in a neotropical tree community: A test of nutrient-ratio (R*) competition theory. Science (submitted).
Hubbell, S. P., F-L. He, R. Condit, L. Borda-de-Agua, J. Kellner, and H. ter Steege. 2008. How many tree species are there in the Amazon, and how many of then will go extinct? Proceedings of the National Academy of Sciences U.S.A. 105 (Suppl. 1): 11498–504.
Hurtt, G. C., and S. W. Pacala. 1995. The consequences of recruitment limitation: Reconciling chance, history, and competitive differences between plants. Journal of Theoretical Biology 176:1–12.
Janzen, D. 1970. Herbivores and the number of tree species in tropical forests. American Naturalist 104:501–28.
John, R., J. Dalling, K. E. Harms, J. B. Yavit, R. F. Stallard, M. Mirabello, S. P. Hubbell, R. Valencia, H. Navarrete, M. Vallejo, and R. B. Foster. 2007. Soil nutrients influence spatial distributions of tropical tree species. Proceedings of the National Academy of Sciences U.S.A. 104:864–69.
Jones, F. A., J. Chen, G.-J. Weng, and S. P. Hubbell. 2005. A genetic evaluation of long distance and directed dispersal in the Neotropical tree, Jacaranda copaia (Bignoniaceae). American Naturalist 166:543–55.
Laurance, W. H. 2008. Theory meets reality: How habitat fragmentation research has transcended island biogeographic theory. Biological Conservation 141:1731–44.
MacArthur, R. H., and E. O. Wilson. 1967. The Theory of Island Biogeography. Princeton, NJ: Princeton University Press.
McKane, A. J., D. Alonso, and R. V. Solé. 2004. Analytical solution of Hubbell’s model of local community dynamics. Theoretical Population Biology 65:67–73.
Muller-Landau, H. C., S. J. Wright, O. Calderon, S. P. Hubbell, and R. B. Foster. 2002. Assessing recruitment limitation: Concepts, methods, and case-studies from a tropical forest. In Seed Dispersal and Frugivory: Ecology, Evolution and Conservation, ed. D. J. Levey, W. R. Silva, and M. Galetti, 35–53. New York: CAB International.
Silvertown, J. M., E. Dodd, J.J.G. Gowing, and J. O. Mountford. 1999. Hydrologically defined niches reveal a basis for species richness in plant communities. Nature 400:61–63.
Tilman, D. 1982. Resource Competition and Community Structure. Princeton Monographs in Population Biology. Princeton, NJ: Princeton University Press.
———. 1988. Plant Strategies and the Dynamics and Structure of Plant Communities. Princeton, NJ: Princeton University Press.
———. 1994. Competition and biodiversity in spatially structured habitats. Ecology 75: 2–16.
Vallade, M., and B. Houchmandzadeh. 2003. Analytical solution of a neutral model of biodiversity. Physical Review E 68:061902.
Volkov, I., J. R. Banavar, F.-L. He, S. P. Hubbell, and A. Maritan. 2005. Density dependence explains tree species abundance and diversity in tropical forests. Nature 438: 658–61.
Volkov I., J. R. Banavar, S. P. Hubbell, and A. Maritan 2003. Neutral theory and the relative abundance of species in ecology. Nature 424:1035–37.
———. 2007. Patterns of relative species abundance in rain forests and coral reefs. Nature 450: 45–49.
Volkov I., J. R. Banavar, S. P. Hubbell, and A. Maritan. 2009. Infering species interactions in tropical forests. Procedings of the National Academy of Sciences (in press).
Wills, C., R. Condit, R. Foster, and S. P. Hubbell, 1997. Strong density- and diversity-related effects help to maintain tree species diversity in a Neotropical forest. Proceedings of the National Academy of Sciences U.S.A. 94: 1252–57.
Wills, C., K. E. Harms, R. Condit, D. King, J. Thompson, F. L. He, H. Muller-Landau, P. Ashton, E. Losos, L. Comita, S. Hubbell, J. LaFrankie, S. Bunyavejchewin, H. S. Dattaraja, S. Davies, S. Esufali, R. Foster, R. John, S. Kiratiprayoon, S. Loo de Lau, M. Massa, C. Nath, Md. Nur Supardi Noor, A. R. Kassim, R. Sukumar, H. S. Suresh, I.-F. Sun, S. Tan, T. Yamakura, and J. Zimmerman. 2006. Non-random processes maintain diversity in tropical forests. Science 311: 527–31.
Wright, S. J., H. Muller-Landau, O. Calderón, and A. Hernandez. 2002. Annual and spatial variation in seedfall and seedling recruitment in a neotropical forest. Ecology 86: 848–50.
Zillio, T., I. Volkov, S. P. Hubbell, J. R. Banavar, and A. Maritan. 2005. Spatial scaling relationships in ecology. Physical Review Letters 95:098101.
