Patterns of biodiversity predicted by the neutral theory rely on a simple phenomenological model of speciation. To further investigate the effect of speciation on neutral biodiversity, we analyze a spatially-explicit neutral model based on population genetics. We define the metacommunity as a system of populations exchanging migrants and we use this framework to introduce speciation with little or no gene flow (allopatric and parapatric speciation). We find that with realistic mutation rates, our metacommunity model driven by neutral processes cannot support more than a few species. Adding natural selection in the population genetics of speciation increases the number of species in the metacommunity but the level of diversity found in Barro Colorado Island is difficult to reach.
Speciation is the "elephant in the room" of community ecology. As the ultimate source of biodiversity, its integration in ecology's theoretical corpus is necessary to understand community assembly. Yet, speciation is often completely ignored or stripped of its spatial dimension. Recent approaches based on network theory have allowed ecologists to effectively model complex landscapes. In this study, we use this framework to model allopatric and parapatric speciation in networks of communities and focus on the relationship between speciation, richness, and the spatial structure of communities. W…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system (i.e., the geography) by a square lattice where each site corresponds to a distinct ``patch''. A self-organizing hierarchical food web describes the prey-predator relations in the eco-system. The same species at different patches have identical food habits but differ from each other in their reproductive characteristic features. By carrying out computer simulati…
The evolutionary and ecological processes behind the origin of species are among the most fundamental problems in biology. In fact, many theoretical hypothesis on different type of speciation have been proposed. In particular, models of sympatric speciation leading to the formation of new species without geographical isolation, are based on the niche hypothesis: the diversification of the population is induced by the competition for a limited set of the available resources. On the other hand, neutral models of evolution have shown that stochastic forces are sufficient to generate coexistence o…
Neutral speciation mechanisms based on isolation by distance and sexual selection, termed topopatric, have recently been shown to describe the observed patterns of abundance distributions and species-area relationships. Previous works have considered this type of process only in the context of hermaphrodic populations. In this work we extend a hermaphroditic model of topopatric speciation to populations where individuals are explicitly separated into males and females. We show that for a particular carrying capacity speciation occurs under similar conditions, but the number of species generate…
Mimulus guttatus and M. nasutus are an evolutionary and ecological model sister species pair differentiated by ecology, mating system, and partial reproductive isolation. Despite extensive research on this system, the history of divergence and differentiation in this sister pair is unclear. We present and analyze a novel population genomic data set which shows that M. nasutus "budded" off of a central Californian M. guttatus population within the last 200 to 500 thousand years. In this time, the M. nasutus genome has accrued numerous genomic signatures of the transition to predominant selfing.…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of protein binding DNA for two geographically isolated populations. Our results predict that, despite neutral diffusion of hybrids in trait space, smaller populations have a higher rate of speciation, due to sequence entropy poising populations more closely to incompatible regions of phenotype space. A key lesson of this work is that non-trivial contributions of …
The impact of environmental fluctuation on species diversity is studied with a model of the evolutionary ecology of microorganisms. We show that environmental fluctuation induces evolutionary branching and assures the consequential coexistence of multiple species. Pairwise invasibility analysis is applied to illustrate the speciation process. We also discuss how fluctuation affects species diversity.
The speciation model proposed by Derrida and Higgs demonstrated that a sexually reproducing population can split into different species in the absence of natural selection or any type of geographic isolation, provided that mating is assortative and the number of genes involved in the process is infinite. Here we revisit this model and simulate it for finite genomes, focusing on the question of how many genes it actually takes to trigger neutral sympatric speciation. We find that, for typical parameters used in the original model, it takes of the order of $10^5$ genes. We compare the results wi…
Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. Here we consider a two island neutral model of speciation with continuous migration and study diversity patterns as a function of the migration probability, population size, and number of genes involved in reproductive isolation (dubbed as genome size). For small genomes, …
The general tendency for species number (S) to increase with sampled area (A) constitutes one of the most robust empirical laws of ecology, quantified by species-area relationships (SAR). In many ecosystems, SAR curves display a power-law dependence, $S\propto A^z$. The exponent $z$ is always less than one but shows significant variation in different ecosystems. We study the multitype voter model as one of the simplest models able to reproduce SAR similar to those observed in real ecosystems in terms of basic ecological processes such as birth, dispersal and speciation. Within the model, the s…
We have simulated the evolution of age structured populations whose individuals represented by their diploid genomes were distributed on a square lattice. The environmental conditions on the whole territory changed simultaneously in the same way by switching on or off some requirements. Mutations accumulated in the genes dispensable during a given period of time were neutral, but they could cause a genetic death of individuals if the environment required their functions again. Populations survived due to retaining some surplus of genetic information in the individual genomes. The changes of th…
Species richness varies widely across the tree of life, and there is great interest in identifying ecological, geographic, and other factors that affect rates of species proliferation. Recent methods for explicitly modeling the relationships among character states, speciation rates, and extinction rates on phylogenetic trees- BiSSE, QuaSSE, GeoSSE, and related models - have been widely used to test hypotheses about character state-dependent diversification rates. Here, we document the disconcerting ease with which neutral traits are inferred to have statistically significant associations with …
An ongoing debate in ecology concerns the impacts of ecological drift and selection on community assembly. Here, we show that there is a sharp phase transition in diverse ecological communities between a selection dominated regime (the niche phase) and a drift dominated regime (the neutral phase). Simulations and analytic arguments show that the niche phase is favored in communities with large population sizes and relatively constant environments, whereas the neutral phase is favored in communities with small population sizes and fluctuating environments. Our results demonstrate how apparently…
We demonstrate how niche theory and Hubbell's original formulation of neutral theory can be blended together into a general framework modeling the combined effects of selection, drift, speciation, and dispersal on community dynamics. This framework connects many seemingly unrelated ecological population models, and allows for quantitative predictions to be made about the impact of niche stabilizing and destabilizing forces on population extinction times and abundance distributions. In particular, the existence of niche stabilizing forces in our blended framework can simultaneously resolve two …
The origin of diversification and coexistence of genes and species have been traditionally studied in isolated biological levels. Ecological and evolutionary views have focused on the mechanisms that enable or constrain species coexistence, genetic variation and the genetics of speciation, but a unified theory linking those approaches is still missing. Here we introduce evolutionary graphs in the context of neutral theories of molecular evolution and biodiversity to provide a framework that simultaneously addresses speciation rate and joint genetic and species diversities. To illuminate this q…
The theory of island biogeography[1] asserts that an island or a local community approaches an equilibrium species richness as a result of the interplay between the immigration of species from the much larger metacommunity source area and local extinction of species on the island (local community). Hubbell[2] generalized this neutral theory to explore the expected steady-state distribution of relative species abundance (RSA) in the local community under restricted immigration. Here we present a theoretical framework for the unified neutral theory of biodiversity[2] and an analytical solution f…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory.…
Hubbell's neutral theory of biodiversity has successfully explained the observed composition of many ecological communities but it relies on strict demographic equivalence among species and provides no room for evolutionary processes like selection, adaptation and speciation. Here we show how to embed the neutral theory within the Darwinian framework. In a fitness landscape with a quadratic maximum, typical of quantitative traits, selection restricts the extant species to have traits close to optimal, so that the fitness differences between surviving species are small. For sufficiently small m…
The ecological principle of limiting similarity dictates that species similar in resource requirements will compete, with the superior eventually excluding the inferior competitor from the community. The observation that nonetheless apparently similar species comprise a significant proportion of the diversity in any given community has led to suggestions that competition may not in fact be an important regulator of community structure and assembly. Here we apply a recently introduced metric of species interaction, fractional (relative) abundance, to tree species of the tropical wet forest of B…
Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to environmental variations due to the storage effect. This paper provides a systematic and comprehensive discussion of these two contradicting tendencies, using the metacommunity version of the recently proposed time-average neutral model of biodiversity which incorporates environmental stochasticity and demographic noise and allows for extinction and speciation. We …
Using game theory we provide mathematical proof that if a species of asexually reproducing microbes does not possess maximum variability in competitive abilities amongst its individual organisms, then that species is vulnerable to replacement by competitors. Furthermore, we prove that such maximally variable species are neutral towards each other in competition for limited resources; they coexist. Our proof is constructive: given one species which does not possess maximum variability, we construct a species with the same (or lower) mean competitive ability which can invade, in the sense that i…
We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in which no intrinsic advantage is ascribed to a particular type of the variable unit, for example a gene, appearing in the theory. In many cases these models are exactly solvable and furthermore go some way to describing observed features of genetic, ecological and linguistic systems.
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we present a new technique, based on interface dynamics analysis, and apply it to the neutral dynamics in one, two and three spatial dimensions. New results are derived for the correlation length and for the main characteristics of the communit…
Recently there has been growing interest in the use of Maximum Relative Entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast, here we propose MaxREnt as a tool for applying statistical mechanics to ecology. We use MaxREnt to explain and predict species abundance patterns in ecological communities in terms of the most probable behaviour under given environmental constraints, in the same way that statistical mechanics explains and predicts the behaviour of thermodynamic systems. We show that MaxREnt unifies a number of different ecological patterns: (i) at relatively loc…
One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances changes with spatial scale, and this gap has hampered attempts to use observed species abundances as a way to quantify what non-neutral processes are needed to fully explain observed patterns. To address this, we introduce a new formulation of spatial neutral biodiversity theory and derive analytical predictions for the way abundance distributions change with sca…
Niche and neutral theory are two prevailing, yet much debated, ideas in ecology proposed to explain the patterns of biodiversity. Whereas niche theory emphasizes selective differences between species and interspecific interactions in shaping the community, neutral theory supposes functional equivalence between species and points to stochasticity as the primary driver of ecological dynamics. In this work, we draw a bridge between these two opposing theories. Starting from a Lotka-Volterra (LV) model with demographic noise and random symmetric interactions, we analytically derive the stationary …
A fundamental problem in community ecology is to understand how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we present a simple, analytically tractable, presence-absence (PA) model for community assembly and use it to ask how ecological traits such as the strength of competition, the amount of diversity, and demographic and environmental stochasticity affect species composition in a community. In the PA model, species are treated as stochastic binary variables that can either be present or absent in a…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic [${\cal{O}} ({\sqrt N})$] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems - age size relationships and species extinction ti…
A neutral ecology model is simulated on an island chain, in which neighbouring islands can exchange individuals but only the first island is able to receive immigrants from a metacommunity. It is found by several measures that biodiversity decreases along the chain, being highest for the first island. Subtle changes in taxon abundance distributions can be detected when islands in the chain are compared to diversity-matched single islands. The results potentially apply to human microbial diversity, but highlight the difficulty of using static single-site taxon abundance distributions to discrim…
We study the evolution of the network properties of a populated network embedded in a genotype space characterised by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution produces two distinct types of network. When a specific genotype is only able to influence a few other genotypes, the ecology consists of separate non-interacting clusters in genotype space. When different types may influence a large number of other sites, the network becomes one large interconnected cluster. The distribution of interaction strengths -- but n…
Environmental fluctuations have important consequences in the organization of ecological communities, and understanding how such a variability influences the biodiversity of an ecosystem is a major question in ecology. In this paper, we analyze the case of two species competing for the resources within the framework of the neutral theory in the presence of environmental noise, devoting special attention on how such a variability modulates species fitness. The environment is dichotomous and stochastically alternates between periods favoring one of the species while disfavoring the other one, pr…
Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and selection within the framework of a formal theory, able eventually to predict the dynamics and fate of evolving populations. However, a large body of empirical evidence collected over the last decades strongly suggests that some of the assumptions of those classical models necessitate a deep revision. The viability of organisms is not dependent on a unique and op…
Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest) --regardless of the species they belong to-- have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species w…
Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple statistical physics process, namely the diffusion of seeds. The model has three parameters: the speciation rate, the size of the meta-community in which the studied tree-community is embedded, and the average surviving time of the seeds. By extensive computer simulations we aim the reproduction of relevant statistical measures derived from the experimental dat…
Understanding factors that shape biodiversity and species coexistence across scales is of utmost importance in ecology, both theoretically and for conservation policies. Species-area relationships (SARs), measuring how the number of observed species increases upon enlarging the sampled area, constitute a convenient tool for quantifying the spatial structure of biodiversity. While general features of species-area curves are quite universal across ecosystems, some quantitative aspects can change significantly. Several attempts have been made to link these variations to ecological forces. Within …
We develop an analysis of the cryptocurrency market borrowing methods and concepts from ecology. This approach makes it possible to identify specific diversity patterns and their variation, in close analogy with ecological systems, and to characterize the cryptocurrency market in an effective way. At the same time, it shows how non-biological systems can have an important role in contrasting different ecological theories and in testing the use of neutral models. The study of the cryptocurrencies abundance distribution and the evolution of the community structure strongly indicates that these s…
Neutral theories have played a crucial and revolutionary role in fields such as population genetics and biogeography. These theories are critical by definition, in the sense that the overall growth rate of each single allele/species/type vanishes. Thus each species in a neutral model sits at the edge between invasion and extinction, allowing for the coexistence of symmetric/neutral types. However, in finite systems, mono-dominated states are ineludibly reached in relatively short times owing to demographic fluctuations, thus leaving us with an unsatisfactory framework to rationalize empiricall…
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate λ. We assume that types are clonally inherited. We consider two classes of speciation models in this setting. In the immigration model, new individuals of an entirely new species singly enter the population at constant rate μ(e.g., from the mainland into the island). In the mutation model, each individual independently experiences point mutations in its germ line, at const…
Why, contrary to theoretical predictions, do marine microbe communities harbor tremendous phenotypic heterogeneity? How can so many marine microbe species competing in the same niche coexist? We discovered a unifying explanation for both phenomena by investigating a non-cooperative game that interpolates between individual-level competitions and species-level outcomes. We identified all equilibrium strategies of the game. These strategies are characterized by maximal phenotypic heterogeneity. They are also neutral towards each other in the sense that an unlimited number of species can co-exist…
Genetic analysis was carried out in order to provide insights into differentiation among populations of two interfertile oak species, Quercus petraea and Quercus robur. Gene flow between the two species, local adaptations and speciation processes in general, may leave differential molecular signatures across the genome. Three interspecific pairs of natural populations from three ecologically different regions, one in central Europe (SW Germany) and two in the Balkan Peninsula (Greece and Bulgaria) were sampled. Grouping of highly informative SSR loci was made according to the component of vari…
Power-law-distributed species counts or clone counts arise in many biological settings such as multispecies cell populations, population genetics, and ecology. This empirical observation that the number of species $c_{k}$ represented by $k$ individuals scales as negative powers of $k$ is also supported by a series of theoretical birth-death-immigration (BDI) models that consistently predict many low-population species, a few intermediate-population species, and very high-population species. However, we show how a simple global population-dependent regulation in a neutral BDI model destroys the…
