A neutral metapopulation model of biodiversity in river networks

In this paper, we develop a stochastic, discrete, structured metapopulation model to explore the dynamics and patterns of biodiversity of riparian vegetation. In the model, individual plants spread along a branched network via directional dispersal and undergo neutral ecological drift. Simulation results suggest that in comparison to 2-D landscapes with non-directional dispersal, river networks with directional dispersal have lower local (alpha) and overall (gamma) diversities, but higher between-community (beta) diversity, implying that riparian species are distributed in a more localized pattern and more vulnerable to local extinction. The relative abundance patterns also change, such that higher percentages of species are in low-abundance, or rare, classes, accompanied by concave rank-abundance curves. In contrast to existing theories, the results suggest that in river networks, increased directional dispersal reduces alpha diversity. These altered patterns and trends result from the combined effects of directionality of dispersal and river network structure, whose relative importance is in need of continuing study. In addition, riparian communities obeying neutral dynamics seem to exhibit abrupt changes where large tributaries confluence; this pattern may provide a signature to identify types of interspecific dynamics in river networks.     

Time-dependent solutions of the spatially implicit neutral model of biodiversity

Previous research into the neutral theory of biodiversity has focused mainly on equilibrium solutions rather than time-dependent solutions. Understanding the time-dependent solutions is essential for applying neutral theory to ecosystems in which time-dependent processes, such as succession and invasion, are driving the dynamics. Time-dependent solutions also facilitate tests against data that are stronger than those based on static equilibrium patterns. Here I investigate the time-dependent solutions of the classic spatially implicit neutral model, in which a small local community is coupled to a much larger metacommunity through immigration. I present explicit general formulas for the eigenvalues, left eigenvectors and right eigenvectors of the models’s transition matrix. The time-dependent solutions can then be expressed in terms of these eigenvalues and eigenvectors. Some of these results are translated directly from existing results for the classic Moran model of population genetics (the Moran model is equivalent to the spatially implicit neutral model after a reparameterization); others of the results are new. I demonstrate that the asymptotic time-dependent solution corresponding to just these first two eigenvectors can be a good approximation to the full time-dependent solution. I also demonstrate the feasibility of a partial eigendecomposition of the transition matrix, which facilitates direct application of the results to a biologically relevant example in which a newly invading species is initially present in the metacommunity but absent from the local community.     

Dynamics of neutral biodiversity

Hubbell's neutral model has become a major paradigm in ecology. Whereas the steady-state structure is well understood, results about the dynamical aspects of the model are scarce. Here we derive dynamical equations for the Simpson diversity index. Both mean and variance of the diversity are proven to satisfy stable linear system dynamics. We show that in the stationary limit we indeed recover previous results, and we supplement this with numerical simulations to validate the dynamical part of our analytical computations. These findings are especially relevant for experiments in microbial ecology, where the Simpson diversity index can be accurately measured as a function of time.     

Testing predictions of the lake food web theory on pelagic communities of Australian reservoirs

Several predictions of the theory developed for pelagic food webs of the Northern Hemisphere were tested on water bodies of Eastern Australia. Eleven reservoirs, representing trophic and latitudinal gradients were sampled for nutrients, phytoplankton, zooplankton and pelagic fish. Two models of regression analysis, which analysed possible interactions between trophic levels were based on different sets of data. In one, each reservoir was represented by only one pair of observations – annual mean or single observation (“regional model”). In the other, seasonal means of four frequently sampled reservoirs similar in productivity were used (“temporal model”). Significant variation in total phytoplankton biovolume (TPB) was predicted by total phosphorus concentration (TP), total nitrogen concentration (TN), mean crustacean length and acoustic biomass of planktivorous fish in both models. This suggested that nutrient limitation, zooplankton grazing and positive effects of fish were probably important in controlling the biomass of primary producers at both regional and temporal scales. In the regional model, the biomass of fish was also negatively correlated with Daphnia biomass and mean crustacean length, suggesting that the trophic cascade hypothesis may be applicable to Eastern Australia for the considered range of reservoir productivities. The biovolume of cyanobacteria was not correlated to any variables tested in the regional model. In contrast, nutrient and food web variables had significant effects on cyanobacterial biovolume in the temporal model. This suggested that factors governing seasonal succession were probably more important for cyanobacteria than variation in reservoir productivity or location. Contrary to previous views, no negative relationship between total biomass of zooplankton and TPB was found in both models, suggesting that the community structure of zooplankton rather than its total biomass mediates top‐down effects. Many predictions of the food web theory remained robust in spite of substantial differences in animal taxonomy and physical environment of Australian ecosystems.     

Speciation and the neutral theory of biodiversity

The neutral theory of biodiversity purports that patterns in the distribution and abundance of species do not depend on adaptive differences between species (i.e. niche differentiation) but solely on random fluctuations in population size (“ecological drift”), along with dispersal and speciation. In this framework, the ultimate driver of biodiversity is speciation. However, the original neutral theory made strongly simplifying assumptions about the mechanisms of speciation, which has led to some clearly unrealistic predictions. In response, several recent studies have combined neutral community models with more elaborate speciation models. These efforts have alleviated some of the problems of the earlier approaches, while confirming the general ability of neutral theory to predict empirical patterns of biodiversity. However, the models also show that the mode of speciation can have a strong impact on relative species abundances. Future work should compare these results to diversity patterns arising from non‐neutral modes of speciation, such as adaptive radiations.     

Relaxing the zero-sum assumption in neutral biodiversity theory

The zero-sum assumption is one of the ingredients of the standard neutral model of biodiversity by Hubbell. It states that the community is saturated all the time, which in this model means that the total number of individuals in the community is constant over time, and therefore introduces a coupling between species abundances. It was shown recently that a neutral model with independent species, and thus without any coupling between species abundances, has the same sampling formula (given a fixed number of individuals in the sample) as the standard model [Etienne, R.S., Alonso, D., McKane, A.J., 2007. The zero-sum assumption in neutral biodiversity theory. J. Theor. Biol. 248, 522-536]. The equilibria of both models are therefore equivalent from a practical point of view. Here we show that this equivalence can be extended to a class of neutral models with density-dependence on the community-level. This result can be interpreted as robustness of the model, i.e. insensitivity of the model to the precise interaction of the species in a neutral community. It can also be interpreted as a lack of resolution, as different mechanisms of interactions between neutral species cannot be distinguished using only a single snapshot of species abundance data.     

A genome-wide departure from the standard neutral model in natural populations of Drosophila

We analyze nucleotide polymorphism data for a large number of loci in areas of normal to high recombination in Drosophila melanogaster and D. simulans (24 and 16 loci, respectively). We find a genome-wide, systematic departure from the neutral expectation for a panmictic population at equilibrium in natural populations of both species. The distribution of sequence-based estimates of 2Nc across loci is inconsistent with the assumptions of the standard neutral theory, given the observed levels of nucleotide diversity and accepted values for recombination and mutation rates. Under these assumptions, most estimates of 2Nc are severalfold too low; in other words, both species exhibit greater intralocus linkage disequilibrium than expected. Variation in recombination or mutation rates is not sufficient to account for the excess of linkage disequilibrium. While an equilibrium island model does not seem to account for the data, more complicated forms of population structure may. A proper test of alternative demographic models will require loci to be sampled in a more consistent fashion.     

Invasibility of neutral communities

Comparative data in invasion ecology show that (i) disturbance enhances community invasibility, (ii) there is a positive relationship between residence time of an invader and its success, (iii) there are broadly constant proportions of newly arrived species to those that become established and dominant (“tens rule”), and (iv) invasive species have higher growth rates in comparison with non-invasive species. I use a simple neutral model to test whether these patterns occur in communities with all species identical and no species-specific interactions. In the model, local communities are grouped into continents with immigration rates smaller between than within the continents. Species coming from the other continent are considered to be alien and their fates are recorded. In the model, disturbance predictably increases species numbers and numbers of individuals of aliens. However, the model makes different predictions on effects of disturbance on three processes involved in alien species spreading: establishment (positive effect of disturbance), naturalization (negative effect) and dominance (positive effect). The predictions do not change if variation of growth rates is incorporated into the model. The model also predicts positive relationship between residence time and abundance. Total community size had little effect on success of alien species. The broad agreement of the predictions of the neutral model with the patterns from the field suggests that some of these general patterns of community invasibility are to some degree fully independent of any specific biological assumptions and by themselves may not provide many insights on underlying biological processes. Aggregate data should therefore be used with great caution and statistical patterns must be removed by means of generating null model predictions.     

Sampling Hubbell's neutral theory of biodiversity

In the context of neutral theories of community ecology, a novel genealogy‐based framework has recently furnished an analytic extension of Ewens’ sampling multivariate abundance distribution, which also applies to a random sample from a local community. Here, instead of taking a multivariate approach, we further develop the sampling theory of Hubbell's neutral spatially implicit theory and derive simple abundance distributions for a random sample both from a local community and a metacommunity. Our result is given in terms of the average number of species with a given abundance in any randomly extracted sample. Contrary to what has been widely assumed, a random sample from a metacommunity is not fully described by the Fisher log‐series, but by a new distribution. This new sample distribution matches the log‐series expectation at high biodiversity values (θ > 1) but clearly departs from it for species‐poor metacommunities (θ < 1). Our theoretical framework should be helpful in the better assessment of diversity and testing of the neutral theory by using abundance data.     

The zero-sum assumption in neutral biodiversity theory

The neutral theory of biodiversity as put forward by Hubbell in his 2001 monograph has received much criticism for its unrealistic simplifying assumptions. These are the assumptions of functional equivalence among different species (neutrality), the assumption of point mutation speciation, and the assumption that resources are continuously saturated, such that constant resource availability implies constant community size (zero-sum assumption). Here we focus on the zero-sum assumption. We present a general theory for calculating the probability of observing a particular species-abundance distribution (sampling formula) and show that zero-sum and non-zero-sum formulations of neutral theory have exactly the same sampling formula when the community is in equilibrium. Moreover, for the non-zero-sum community the sampling formula has this same form, even out of equilibrium. Therefore, the term "zero-sum multinomial (ZSM)" to describe species abundance patterns, as coined by Hubbell [2001. The Unified Neutral Theory of Biodiversity and Biogeography, Princeton University Press, Princeton, NJ], is not really appropriate, as it also applies to non-zero-sum communities. Instead we propose the term "dispersal-limited multinomial (DLM)", thus making explicit one of the most important contributions of neutral community theory, the emphasis on dispersal limitation as a dominant factor in determining species abundances.     

Productivity-diversity relationships in lake plankton communities

One of the most intriguing environmental gradients connected with variation in diversity is ecosystem productivity. The role of diversity in ecosystems is pivotal, because species richness can be both a cause and a consequence of primary production. However, the mechanisms behind the varying productivity-diversity relationships (PDR) remain poorly understood. Moreover, large-scale studies on PDR across taxa are urgently needed. Here, we examined the relationships between resource supply and phyto-, bacterio-, and zooplankton richness in 100 small boreal lakes. We studied the PDR locally within the drainage systems and regionally across the systems. Second, we studied the relationships between resource availability, species richness, biomass and resource ratio (N:P) in phytoplankton communities using Structural Equation Modeling (SEM) for testing the multivariate hypothesis of PDR. At the local scale, the PDR showed variable patterns ranging from positive linear and unimodal to negative linear relationships for all planktonic groups. At the regional scale, PDRs were significantly linear and positive for phyto- and zooplankton. Phytoplankton richness and the amount of chlorophyll a showed a positive linear relationship indicating that communities consisting of higher number of species were able to produce higher levels of biomass. According to the SEM, phytoplankton biomass was largely related to resource availability, yet there was a pathway via community richness. Finally, we found that species richness at all trophic levels was correlated with several environmental factors, and was also related to richness at the other trophic levels. This study showed that the PDRs in freshwaters show scale-dependency. We also documented that the PDR complies with the multivariate model showing that plant biomass is not mirroring merely the resource availability, but is also influenced by richness. This highlights the need for conserving diversity in order to maintain ecosystem processes in freshwaters.     

The HKA test revisited: a maximum-likelihood-ratio test of the standard neutral model

We present a maximum-likelihood-ratio test of the standard neutral model, using multilocus data on polymorphism within species and divergence between species. The model is based on the Hudson-Kreitman-Aguade (HKA) test, but allows for an explicit test of selection at individual loci in a multilocus framework. We use coalescent simulations to show that the likelihood-ratio test statistic is conservative, particularly when the assumption of no recombination is violated. Application of the method to polymorphism data from 18 loci from a population of Arabidopsis lyrata provides significant evidence for a balanced polymorphism at a candidate locus thought to be linked to the centromere. The method is also applied to polymorphism data in maize, providing support for the hypothesis of directional selection on genes in the starch pathway.     

Cell death in lake phytoplankton communities

1. The fraction of living and dead phytoplankton cells in seven Florida lakes was assessed by using the cell digestion assay, a non‐staining membrane permeability test. The cell digestion assay is an effective method to analyse cell viability in complex natural phytoplankton communities. 2. The lakes examined ranged widely in phytoplankton abundance and community composition. The variability in the percentage of living cells (% LC) was high among the taxonomic groups forming the different phytoplankton communities, ranging from 19.7% to 98% LC. 3. All cells within single cyanobacteria filaments were determined to be either dead or alive, suggesting physiological integration of the cells within colonies. 4. Within each lake, the dominant taxa generally exhibited the highest proportion of living cells. A high proportion of living cells was found to be a characteristic of the different taxa forming the communities of eutrophic lakes. The average value for the % LC for all groups comprising the phytoplankton communities in each of the lakes ranged from 29.9 ± 7.2 to 80.4 ± 4.0 (mean ± SE) and varied strongly and positively with chlorophyll a concentration. 5. These results suggest phytoplankton cell death to be an important process structuring phytoplankton communities in lakes, particularly in oligotrophic ones.     

Modes of speciation and the neutral theory of biodiversity

Hubbell's neutral theory of biodiversity has generated much debate over the need for niches to explain biodiversity patterns. Discussion of the theory has focused on its neutrality assumption, i.e. the functional equivalence of species in competition and dispersal. Almost no attention has been paid to another critical aspect of the theory, the assumptions on the nature of the speciation process. In the standard version of the neutral theory each individual has a fixed probability to speciate. Hence, the speciation rate of a species is directly proportional to its abundance in the metacommunity. We argue that this assumption is not realistic for most speciation modes because speciation is an emergent property of complex processes at larger spatial and temporal scales and, consequently, speciation rate can either increase or decrease with abundance. Accordingly, the assumption that speciation rate is independent of abundance (each species has a fixed probability to speciate) is a more natural starting point in a neutral theory of biodiversity. Here we present a neutral model based on this assumption and we confront this new model to 20 large data sets of tree communities, expecting the new model to fit the data better than Hubbell's original model. We find, however, that the data sets are much better fitted by Hubbell's original model. This implies that species abundance data can discriminate between different modes of speciation, or, stated otherwise, that the mode of speciation has a large impact on the species abundance distribution. Our model analysis points out new ways to study how biodiversity patterns are shaped by the interplay between evolutionary processes (speciation, extinction) and ecological processes (competition, dispersal).     

Biomass and biodiversity in species-rich tritrophic communities

We consider a tritrophic system with one basal and one top species and a large number of primary consumers, and derive upper and lower bounds for the total biomass of the middle trophic level. These estimates do not depend on dynamical regime, holding for fixed point, periodic, or chaotic dynamics. We have two kinds of estimates, depending on whether the predator abundance is zero. All these results are uniform in a self-limitation parameter, which regulates prey diversity in the system. For strong self-limitation, diversity is large; for weak self-limitation, it is small. Diversity depends on the variance of species’ parameter values. The larger this variance, the lower the diversity, and vice versa. Moreover, variation in the parameters of the Holling type II functional response changes the bifurcation character, with the equilibrium state with nonzero predator abundance losing stability. If that variation is small then the bifurcation can lead to oscillations (the Hopf bifurcation). Under certain conditions, there exists a supercritical Hopf bifurcation. We then find a connection between diversity and Hopf bifurcations. We also show that the system exhibits top-down regulation and a hump-shaped diversity-productivity curve.We then extend the model by allowing species to experience self-regulation. For this extended model, explicit estimates of prey diversity are obtained. We study the dynamics of this system and find the following. First, diversity and system dynamics crucially depend on variation in species parameters. We show that under certain conditions, the system undergoes a supercritical Hopf bifurcation. We also establish a connection between diversity and Hopf bifurcations. For strong self-limitation, diversity is large and complex dynamics are absent. For weak self-limitation, diversity is small and the equilibrium with non-zero predator abundance is unstable.     

Species diversity in local neutral communities

We extend the neutral theory of macroecology by deriving biodiversity models (relative species abundance and species-area relationships) in a local community-metacommunity system in which the local community is embedded within the metacommunity. We first demonstrate that the local species diversity patterns converge to that of the metacommunity as the size (scale) of the embedded local community increases. This result shows that in continuous landscapes no sharp boundaries dividing the communities at the two scales exist; they are an artificial distinction made by the current spatially implicit neutral theory. Second, we remove the artificial restriction that speciation cannot occur in a local community, even if the effects of local speciation are small. Third, we introduce stochasticity into the immigration rate, previously treated as constant, and demonstrate that local species diversity is a function not only of the mean but also of the variance in immigration rate. High variance in immigration rates reduces species diversity in local communities. Finally, we show that a simple relationship exists between the fundamental diversity parameter of neutral theory and Simpson's index for local communities. Derivation of this relationship extends recent work on diversity indices and provides a means of evaluating the effect of immigration on estimates of the fundamental diversity parameter derived from relative species abundance data on local communities.