The effects of archipelago spatial structure on island diversity and endemism: predictions from a spatially‐structured neutral model

Islands are particularly suited to testing hypotheses about the ecological and evolutionary mechanisms underpinning community assembly. Yet the complex spatial arrangements of real island systems have received little attention from both empirical studies and theoretical models. Here, we investigate the extent to which the spatial structure of archipelagos affects species diversity and endemism. We start by proposing a new spatially structured neutral model that explicitly considers archipelago structure, and then investigate its predictions under a diversity of scenarios. Our results suggest that considering the spatial structure of archipelagos is crucial to understanding their diversity and endemism, with structured island systems acting both as “museums” and “cradles” of biodiversity. These dynamics of diversification may change the traditionally expected pattern of decrease in species richness with distance from the mainland, even potentially leading to increasing patterns for taxa with high speciation rates in archipelagos off species‐poor continental areas. Our results also predict that, within spatially structured archipelagos, metapopulation dynamics and evolutionary processes can generate higher diversity on islands more centrally placed than at the periphery. We derive from our results a set of theoretical predictions, potentially testable with empirical data.     

A mean field model for competition: from neutral ecology to the Red Queen

Individual species are distributed inhomogeneously over space and time, yet, within large communities of species, aggregated patterns of biodiversity seem to display nearly universal behaviour. Neutral models assume that an individual's demographic prospects are independent of its species identity. They have successfully predicted certain static, time‐independent patterns. But they have generally failed to predict temporal patterns, such as species ages or population dynamics. We construct a new, multispecies framework incorporating competitive differences between species, and assess the impact of this competition on static and dynamic patterns of biodiversity. We solve this model exactly for the special case of a Red Queen hypothesis, where fitter species are continually arising. The model predicts more realistic species ages than neutral models, without greatly changing predictions for static species abundance distributions. Our modelling approach may allow users to incorporate a broad range of ecological mechanisms.     

The onion model, a simple neutral model for the evolution of diversity in bacterial biofilms

Bacterial biofilms are particularly resistant to a wide variety of antimicrobial compounds. Their persistence in the face of antibiotic therapies causes significant problems in the treatment of infectious diseases. Seldom have evolutionary processes like genetic drift and mutation been invoked to explain how resistance to antibiotics emerges in biofilms, and we lack a simple and tractable model for the genetic and phenotypic diversification that occurs in bacterial biofilms. Here, we introduce the 'onion model', a simple neutral evolutionary model for phenotypic diversification in biofilms. We explore its properties and show that the model produces patterns of diversity that are qualitatively similar to observed patterns of phenotypic diversity in biofilms. We suggest that models like our onion model, which explicitly invoke evolutionary process, are key to understanding biofilm resistance to bactericidal and bacteriostatic agents. Elevated phenotypic variance provides an insurance effect that increases the likelihood that some proportion of the population will be resistant to imposed selective agents and may thus enhance persistence of the biofilm. Accounting for evolutionary change in biofilms will improve our ability to understand and counter diseases that are caused by biofilm persistence.     

Species-area relationships from a spatially explicit neutral model in an infinite landscape

We use recently developed technical methods to study species–area relationships from a spatially explicit extension of Hubbell's neutral model on an infinite landscape. Our model includes variable dispersal distances and exhibits qualitatively different behaviour from the cases of nearest-neighbour dispersal and finite periodic landscapes that have previously been studied. We show that different dispersal distances and even different dispersal kernels produce identical species–area curves up to rescaling of the two axes. This scaling property provides a straightforward method for fitting the model to empirical data. The species–area curves display all three phases observed empirically and enable the exponent describing the power law relationship for species–area curves to be identified as the gradient at the central phase. This exponent can take all values between 0 and 1 and is given by a simple function of the speciation rate, independent of all other model variables.     

A new sampling formula for neutral biodiversity

The neutral model of biodiversity, proposed by Hubbell (The Unified Neutral Theory of Biodiversity and Biogeography, Princeton University Press, Princeton, NJ, 2001) to explain the diversity of functionally equivalent species, has been subject of hot debate in community ecology. Whereas Hubbell studied the model mostly by simulations, recently analytical treatments have yielded expressions of the expected number of species of a particular abundance in a local community with dispersal limitation. Moreover, a formula has been offered for the joint likelihood of observing a given species‐abundance dataset in a local community with dispersal limitation, but this formula is too complicated to allow practical applications. Here, I present a much simplified expression that can be regarded as an enhanced version of the famous Ewens sampling formula. It can be used in maximum likelihood methods for quick estimation of the model parameters, using all information in the data, and for model comparison. I also show how to rapidly generate examples of species‐abundance distributions for a given set of model parameters and how to calculate Simpson's diversity index.     

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.     

Field theory for biogeography: a spatially explicit model for predicting patterns of biodiversity

Predicting the variation of biodiversity across the surface of the Earth is a fundamental issue in ecology, and in this article we focus on one of the most widely studied spatial biodiversity patterns: the species–area relationship (SAR). The SAR is a central tool in conservation, being used to predict species loss following global climate change, and is striking in its universality throughout different geographical regions and across the tree of life. In this article we draw upon the methods of quantum field theory and the foundation of neutral community ecology to derive the first spatially explicit neutral prediction for the SAR. We find that the SAR has three phases, with a power law increase at intermediate scales, consistent with decades of documented empirical patterns. Our model also provides a building block for incorporating non-neutral biological variation, with the potential to bridge the gap between neutral and niche-based approaches to community assembly.
Ecology Letters (2010) 13: 87–95     

A neutral model of edge effects

In this paper a spatially implicit neutral model for explaining the edge effects between habitats is proposed. To analyze this model we use two different approaches: a discrete approach that is based on the Master equation for a one step jump process and a continuous approach based on the approximation of the discrete jump process with the Kolmogorov-Fokker-Planck forward and backward equations. The discrete and continuous approaches are applied to analyze the species abundance distributions and the time to species extinction. Moreover, with the aid of the continuous approach a realistic classification of the behavior of species in local communities is developed. The species abundance dynamics at the edge between two distinct habitats is compared with those located in the homogeneous interior habitats using species abundance distributions and the first time to species extinction. We show that the structure of the links between local community and the metacommunity plays an important role on species persistence. Specifically, species at the edge between two distinct metacommunities have higher extinction rate than those in the interior habitats connected only to one metacommunity. Moreover, the same species might be persistent in the homogeneous interior habitat, but its probability of extinction from the edge local community could be very high.     

The neutral effective migration rate in a mainland-island context

Genetic influx into a population often does not correspond to the real migration rate (m) of individuals, due to class structure within the population. The effective migration rate (m(e)) is a concept to measure gene flow in such a situation. The ratio of the effective migration rate to the real migration rate (m(e)/m) is called the gene flow factor, and represents the degree of gene flow modification. Prior authors proposed different definitions of the effective migration rate. These may be categorized into two groups: the neutral effective migration rate and the selective effective migration rate. In this article, we construct a general model of a class-structured population with a mainland-island structure. Using the model, we prove that the gene flow factor of the neutral effective migration rate converges to the mean reproductive value of immigrants if the limit is taken with the real migration rate converging to zero. This limit theorem provides a novel interpretation of gene flow and can be used to derive approximation formulae of the neutral effective migration rate. We illustrate this method analyzing two examples, sex ratio distortion due to extrinsic factors and hybrid zones with underdominance.     

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.     

Applying ecological models to communities of genetic elements: the case of neutral theory

A promising recent development in molecular biology involves viewing the genome as a mini‐ecosystem, where genetic elements are compared to organisms and the surrounding cellular and genomic structures are regarded as the local environment. Here, we critically evaluate the prospects of ecological neutral theory (ENT), a popular model in ecology, as it applies at the genomic level. This assessment requires an overview of the controversy surrounding neutral models in community ecology. In particular, we discuss the limitations of using ENT both as an explanation of community dynamics and as a null hypothesis. We then analyse a case study in which ENT has been applied to genomic data. Our central finding is that genetic elements do not conform to the requirements of ENT once its assumptions and limitations are made explicit. We further compare this genome‐level application of ENT to two other, more familiar approaches in genomics that rely on neutral mechanisms: Kimura's molecular neutral theory and Lynch's mutational‐hazard model. Interestingly, this comparison reveals that there are two distinct concepts of neutrality associated with these models, which we dub ‘fitness neutrality’ and ‘competitive neutrality’. This distinction helps to clarify the various roles for neutral models in genomics, for example in explaining the evolution of genome size.     

Epistasis can lead to fragmented neutral spaces and contingency in evolution

In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space--namely, that networks of genomes encoding the same phenotype may not be connected by single mutational moves. We use the folding of RNA sequences into secondary structures as a model genotype-phenotype map and explore the neutral spaces corresponding to networks of genotypes with the same phenotype. In most of these networks, we find that it is not possible to connect all genotypes to one another by single point mutations. Instead, a network for a phenotypic structure with n bonds typically fragments into at least 2(n) neutral components, often of similar size. While components of the same network generate the same phenotype, they show important variations in their properties, most strikingly in their evolvability and mutational robustness. This heterogeneity implies contingency in the evolutionary process.     

Batesian mimicry promotes pre‐ and postmating isolation in a snake mimicry complex

We evaluated whether Batesian mimicry promotes early‐stage reproductive isolation. Many Batesian mimics occur not only in sympatry with their model (as expected), but also in allopatry. As a consequence of local adaptation within both sympatry (where mimetic traits are favored) and allopatry (where nonmimetic traits are favored), divergent, predator‐mediated natural selection should disfavor immigrants between these selective environments as well as any between‐environment hybrids. This selection might form the basis for both pre‐ and postmating isolation, respectively. We tested for such selection in a snake mimicry complex by placing clay replicas of sympatric, allopatric, or hybrid phenotypes in both sympatry and allopatry and measuring predation attempts. As predicted, replicas with immigrant phenotypes were disfavored in both selective environments. Replicas with hybrid phenotypes were also disfavored, but only in a region of sympatry where previous studies have detected strong selection favoring precise mimicry. By fostering immigrant inviability and ecologically dependent selection against hybrids (at least in some habitats), Batesian mimicry might therefore promote reproductive isolation. Thus, although Batesian mimicry has long been viewed as a mechanism for convergent evolution, it might play an underappreciated role in fueling divergent evolution and possibly even the evolution of reproductive isolation and speciation.     

DNA barcoding and community assembly—A simple solution to a complex problem

Identifying the current and past processes driving community assembly is critical in the effort to understand the Earth's biodiversity and its response to future environmental change. But while studies on community assembly often emphasize the role of contemporary ecological drivers, it has been particularly challenging to account for the effects of past processes in shaping present‐day communities. In this issue of Molecular Ecology, Hao et al. (2020) provide a holistic analysis of factors driving the assembly of diverse communities of Lepidoptera in two mountain ranges in northeastern China. The authors use an impressively large data set and exceptionally comprehensive analyses to test how processes of range expansion and gene flow, speciation and extinction, dispersal limitation, environmental filtering and competition have led to present‐day diversity patterns. A key novelty of this work is the exhaustive use of DNA barcodes, relatively simple yet powerful molecular markers, to tackle complex biological questions. The authors elegantly show the utility of DNA barcoding data for research beyond simple taxonomic assignment. Their approach is remarkable as it manages to integrate population genetics, phylogenetic history, species diversity and ecology into a well‐rounded picture of community assembly. With this work, Hao et al. demonstrate the great promise of DNA barcoding for exhaustive community analysis of even highly diverse and complex systems, raising the bar for future research.     

Neutral models and the deviation from neutral pattern metric

Ecological variables are inherently spatial with arrangement on the landscape often directly attributed to underlying processes. Historically, assumptions regarding the relationships among scale, pattern, and process have been used to characterize landscapes as well as compare multiple landscapes or changes in landscapes over time. Despite the utility of landscape comparisons, they often fail to adequately link scale, pattern, or process, and far too frequently are presented as logical interpretations leading to prediction of pattern to process relationships. Pattern metrics and measures of spatial autocorrelation have evolved to characterize and model landscape phenomena. Unfortunately, the two are quite often misapplied. This research presents an alternative metric, Deviation from Neutral (DFN), which permits the comparison of multiple landscapes.     

Species diversity in neutral metacommunities: a network approach

Biologists seek an understanding of the processes underlying spatial biodiversity patterns. Neutral theory links those patterns to dispersal, speciation and community drift. Here, we advance the spatially explicit neutral model by representing the metacommunity as a network of smaller communities. Analytic theory is presented for a set of equilibrium diversity patterns in networks of communities, facilitating the exploration of parameter space not accessible by simulation. We use this theory to evaluate how the basic properties of a metacommunity – connectivity, size, and speciation rate – determine overall metacommunity γ -diversity, and how that is partitioned into α - and β -components. We find spatial structure can increase γ -diversity relative to a well-mixed model, even when θ is held constant. The magnitude of deviations from the well-mixed model and the partitioning into α - and β -diversity is related to the ratio of migration and speciation rates. γ -diversity scales linearly with metacommunity size even as α - and β -diversity scale nonlinearly with size.     

Factors contributing to the accumulation of reproductive isolation: A mixed model approach

The analysis of large datasets describing reproductive isolation between species has been extremely influential in the study of speciation. However, the statistical methods currently used for these data limit the ability to make direct inferences about the factors predicting the evolution of reproductive isolation. As a result, our understanding of iconic patterns and rules of speciation rely on indirect analyses that have clear statistical limitations. Phylogenetic mixed models are commonly used in ecology and evolution, but have not been applied to studies of reproductive isolation. Here I describe a flexible framework using phylogenetic mixed models to analyze data collected at different evolutionary scales, to test both categorical and continuous predictor variables, and to test the effect of multiple predictors on rates and patterns of reproductive isolation simultaneously. I demonstrate the utility of this framework by re‐analyzing four classic datasets, from both animals and plants, and evaluating several hypotheses that could not be tested in the original studies: In the Drosophila and Bufonidae datasets, I found support for more rapid accumulation of reproductive isolation in sympatric species pairs compared to allopatric species pairs. Using Silene and Nolana, I found no evidence supporting the hypothesis that floral differentiation elevates postzygotic reproductive isolation. The faster accumulation of postzygotic isolation in sympatry is likely the result of species coexistence determined by the level of postzygotic isolation between species. In addition, floral trait divergence does not appear to translate into pleiotropic effects on postzygotic reproductive isolation. Overall, these methods can allow researchers to test new hypotheses using a single statistical method, while remedying the statistical limitations of several previous methods.     

Allopatry increases the balance of phylogenetic trees during radiation under neutral speciation

The shape of a phylogenetic tree is defined by the sequence of speciation events, represented by its branching points, and extinctions, represented by branch interruptions. In a neutral scenario of parapatry and isolation by distance, species tend to branch off the original population one after the other, leading to highly unbalanced trees. In this case the degree of imbalance, measured by the normalized Sackin index, grows linearly with species richness. Here we claim that moderate values of imbalance for trees with large number of species can occur if the geographic distribution involves more than one deme (allopatry) and speciation is parapatric within demes. The combined values of balance (normalized Sackin index) and species richness provide an estimate of how many demes were involved in the process if it happened in such neutral scenario. We also show that the spatial division in demes moderately slows down the diversification process, portraying a neutral mechanism for structuring the branch length distribution of phylogenetic trees.