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

Consequences of Local Conspecific Density Effects for Plant Diversity and Community Dynamics

Conspecific density dependence (CDD) in plant populations is widespread, most likely caused by local-scale biotic interactions, and has potentially important implications for biodiversity, community composition, and ecosystem processes. However, progress in this important area of ecology has been hindered by differing viewpoints on CDD across subfields in ecology, lack of synthesis across CDD-related frameworks, and misunderstandings about how empirical measurements of local CDD fit within the context of broader ecological theories on community assembly and diversity maintenance. Here, we propose a conceptual synthesis of local-scale CDD and its causes, including species-specific antagonistic and mutualistic interactions. First, we compare and clarify different uses of CDD and related concepts across subfields within ecology. We suggest the use of local stabilizing/destabilizing CDD to refer to the scenario where local conspecific density effects are more negative/positive than heterospecific effects. Second, we discuss different mechanisms for local stabilizing and destabilizing CDD, how those mechanisms are interrelated, and how they cut across several fields of study within ecology. Third, we place local stabilizing/destabilizing CDD within the context of broader ecological theories and discuss implications and challenges related to scaling up the effects of local CDD on populations, communities, and metacommunities. The ultimate goal of this synthesis is to provide a conceptual roadmap for researchers studying local CDD and its implications for population and community dynamics.

Processes governing species richness in communities exposed to temporal environmental stochasticity: A review and synthesis of modelling approaches

Research into the processes governing species richness has often assumed that the environment is fixed, whereas realistic environments are often characterised by random fluctuations over time. This temporal environmental stochasticity (TES) changes the demographic rates of species populations, with cascading effects on community dynamics and species richness. Theoretical and applied studies have used process-based mathematical models to determine how TES affects species richness, but under a variety of frameworks. Here, we critically review such studies to synthesise their findings and draw general conclusions. We first provide a broad mathematical framework encompassing the different ways in which TES has been modelled. We then review studies that have analysed models with TES under the assumption of negligible interspecific interactions, such that a community is conceptualised as the sum of independent species populations. These analyses have highlighted how TES can reduce species richness by increasing the frequency at which a species becomes rare and therefore prone to extinction. Next, we review studies that have relaxed the assumption of negligible interspecific interactions. To simplify the corresponding models and make them analytically tractable, such studies have used mean-field theory to derive fixed parameters representing the typical strength of interspecific interactions under TES. The resulting analyses have highlighted community-level effects that determine how TES affects species richness, for species that compete for a common limiting resource. With short temporal correlations of environmental conditions, a non-linear averaging effect of interspecific competition strength over time gives an increase in species richness. In contrast, with long temporal correlations of environmental conditions, strong selection favouring the fittest species between changes in environmental conditions results in a decrease in species richness. We compare such results with those from invasion analysis, which examines invasion growth rates (IGRs) instead of species richness directly. Qualitative differences sometimes arise because the IGR is the expected growth rate of a species when it is rare, which does not capture the variation around this mean or the probability of the species becoming rare. Our review elucidates key processes that have been found to mediate the negative and positive effects of TES on species richness, and by doing so highlights key areas for future research.

Age-dependent extinction and the neutral theory of biodiversity

Red Queen (RQ) theory states that adaptation does not protect species from extinction because their competitors are continually adapting alongside them. RQ was founded on the apparent independence of extinction risk and fossil taxon age, but analytical developments have since demonstrated that age-dependent extinction is widespread, usually most intense among young species. Here, we develop ecological neutral theory as a general framework for modeling fossil species survivorship under incomplete sampling. We show that it provides an excellent fit to a high-resolution dataset of species durations for Paleozoic zooplankton and more broadly can account for age-dependent extinction seen throughout the fossil record. Unlike widely used alternative models, the neutral model has parameters with biological meaning, thereby generating testable hypotheses on changes in ancient ecosystems. The success of this approach suggests reinterpretations of mass extinctions and of scaling in eco-evolutionary systems. Intense extinction among young species does not necessarily refute RQ or require a special explanation but can instead be parsimoniously explained by neutral dynamics operating across species regardless of age.

Macroecological laws describe variation and diversity in microbial communities

How the coexistence of many species is maintained is a fundamental and unresolved question in ecology. Coexistence is a puzzle because we lack a mechanistic understanding of the variation in species presence and abundance. Whether variation in ecological communities is driven by deterministic or random processes is one of the most controversial issues in ecology. Here, I study the variation of species presence and abundance in microbial communities from a macroecological standpoint. I identify three macroecological laws that quantitatively characterize the fluctuation of species abundance across communities and over time. Using these three laws, one can predict species' presence and absence, diversity, and commonly studied macroecological patterns. I show that a mathematical model based on environmental stochasticity, the stochastic logistic model, quantitatively predicts the three macroecological laws, as well as non-stationary properties of community dynamics.

Uncovering the rules of microbial community invasions

Understanding the ecological and evolutionary processes determining the outcome of biological invasions has been the subject of decades of research with most work focusing on macro-organisms. In the context of microbes, invasions remain poorly understood despite being increasingly recognized as important. To shed light on the factors affecting the success of microbial community invasions, we perform simulations using an individual-based nearly neutral model that combines ecological and evolutionary processes. Our simulations qualitatively recreate many empirical patterns and lead to a description of five general rules of invasion: (1) larger communities evolve better invaders and better defenders; (2) where invader and resident fitness difference is large, invasion success is essentially deterministic; (3) propagule pressure contributes to invasion success, if and only if, invaders and residents are competitively similar; (4) increasing the diversity of invaders has a similar effect to increasing the number of invaders; and (5) more diverse communities more successfully resist invasion.

Cross-scale neutral ecology and the maintenance of biodiversity

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 scale. For tropical forest data where neutrality has been extensively tested before now, we apply this approach and identify an incompatibility between neutral fits at regional and local scales. We use this approach derive a sharp quantification of what remains to be explained by non-neutral processes at the local scale, setting a quantitative target for more general models for the maintenance of biodiversity.

The Red Queen model of recombination hot-spot evolution: a theoretical investigation

In humans and many other species, recombination events cluster in narrow and short-lived hot spots distributed across the genome, whose location is determined by the Zn-finger protein PRDM9. To explain these fast evolutionary dynamics, an intra-genomic Red Queen model has been proposed, based on the interplay between two antagonistic forces: biased gene conversion, mediated by double-strand breaks, resulting in hot-spot extinction, followed by positive selection favouring new PRDM9 alleles recognizing new sequence motifs. Thus far, however, this Red Queen model has not been formalized as a quantitative population-genetic model, fully accounting for the intricate interplay between biased gene conversion, mutation, selection, demography and genetic diversity at the PRDM9 locus. Here, we explore the population genetics of the Red Queen model of recombination. A Wright–Fisher simulator was implemented, allowing exploration of the behaviour of the model (mean equilibrium recombination rate, diversity at the PRDM9 locus or turnover rate) as a function of the parameters (effective population size, mutation and erosion rates). In a second step, analytical results based on self-consistent mean-field approximations were derived, reproducing the scaling relations observed in the simulations. Empirical fit of the model to current data from the mouse suggests both a high mutation rate at PRDM9 and strong biased gene conversion on its targets.

This article is part of the themed issue ‘Evolutionary causes and consequences of recombination rate variation in sexual organisms’.

Inferring processes of cultural transmission: the critical role of rare variants in distinguishing neutrality from novelty biases

Neutral evolution assumes that there are no selective forces distinguishing different variants in a population. Despite this striking assumption, many recent studies have sought to assess whether neutrality can provide a good description of different episodes of cultural change. One approach has been to test whether neutral predictions are consistent with observed progeny distributions, recording the number of variants that have produced a given number of new instances within a specified time interval: a classic example is the distribution of baby names. Using an overlapping generations model, we show that these distributions consist of two phases: a power-law phase with a constant exponent of [Formula: see text], followed by an exponential cut-off for variants with very large numbers of progeny. Maximum-likelihood estimations of the model parameters provide a direct way to establish whether observed empirical patterns are consistent with neutral evolution. We apply our approach to a complete dataset of baby names from Australia. Crucially, we show that analyses based on only the most popular variants, as is often the case in studies of cultural evolution, can provide misleading evidence for underlying transmission hypotheses. While neutrality provides a plausible description of progeny distributions of abundant variants, rare variants deviate from neutrality. Further, we develop a simulation framework that allows the detection of alternative cultural transmission processes. We show that anti-novelty bias is able to replicate the complete progeny distribution of the Australian dataset.This article is part of the themed issue 'Process and pattern in innovations from cells to societies'.

Reinterpreting maximum entropy in ecology: a null hypothesis constrained by ecological mechanism

Simplified mechanistic models in ecology have been criticised for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in ecology to make predictions constrained by just a handful of state variables, like total abundance or species richness. But an outstanding question remains: what principle tells us which state variables to constrain? Here we attempt to solve both problems simultaneously, by translating a given set of mechanisms into the state variables to be used in MaxEnt, and then using this MaxEnt theory as a null model against which to compare mechanistic predictions. In particular, we identify the sufficient statistics needed to parametrise a given mechanistic model from data and use them as MaxEnt constraints. Our approach isolates exactly what mechanism is telling us over and above the state variables alone.

Understanding how biodiversity unfolds through time under neutral theory

Theoretical predictions for biodiversity patterns are typically derived under the assumption that ecological systems have reached a dynamic equilibrium. Yet, there is increasing evidence that various aspects of ecological systems, including (but not limited to) species richness, are not at equilibrium. Here, we use simulations to analyse how biodiversity patterns unfold through time. In particular, we focus on the relative time required for various biodiversity patterns (macroecological or phylogenetic) to reach equilibrium. We simulate spatially explicit metacommunities according to the Neutral Theory of Biodiversity (NTB) under three modes of speciation, which differ in how evenly a parent species is split between its two daughter species. We find that species richness stabilizes first, followed by species area relationships (SAR) and finally species abundance distributions (SAD). The difference in timing of equilibrium between these different macroecological patterns is the largest when the split of individuals between sibling species at speciation is the most uneven. Phylogenetic patterns of biodiversity take even longer to stabilize (tens to hundreds of times longer than species richness) so that equilibrium predictions from neutral theory for these patterns are unlikely to be relevant. Our results suggest that it may be unwise to assume that biodiversity patterns are at equilibrium and provide a first step in studying how these patterns unfold through time.

Species-abundance distributions under colored environmental noise

Natural communities at all spatiotemporal scales are subjected to a wide variety of environmental pressures, resulting in random changes in the demographic rates of species populations. Previous analyses have examined the effects of such environmental variance on the long-term growth rate and time to extinction of single populations, but studies of its effects on the diversity of communities remain scarce. In this study, we construct a new master-equation model incorporating demographic and environmental variance and use it to examine how statistical patterns of diversity, as encapsulated by species-abundance distributions (SADs), are altered by environmental variance. Unlike previous diffusion models with environmental variance uncorrelated in time (white noise), our model allows environmental variance to be correlated at different timescales (colored noise), thus facilitating representation of phenomena such as yearly and decadal changes in climate. We derive an exact analytical expression for SADs predicted by our model together with a close approximation, and use them to show that the main effect of adding environmental variance is to increase the proportion of abundant species, thus flattening the SAD relative to the log-series form found in the neutral case. This flattening effect becomes more prominent when environmental variance is more correlated in time and has greater effects on species' demographic rates, holding all other factors constant. Furthermore, we show how our model SADs are consistent with those from diffusion models near the white noise limit. The mathematical techniques we develop are catalysts for further theoretical work exploring the consequences of environmental variance for biodiversity.

Backbones of evolutionary history test biodiversity theory for microbes

Identifying the ecological and evolutionary mechanisms that determine biological diversity is a central question in ecology. In microbial ecology, phylogenetic diversity is an increasingly common and relevant means of quantifying community diversity, particularly given the challenges in defining unambiguous species units from environmental sequence data. We explore patterns of phylogenetic diversity across multiple bacterial communities drawn from different habitats and compare these data to evolutionary trees generated using theoretical models of biodiversity. We have two central findings. First, although on finer scales the empirical trees are highly idiosyncratic, on coarse scales the backbone of these trees is simple and robust, consistent across habitats, and displays bursts of diversification dotted throughout. Second, we find that these data demonstrate a clear departure from the predictions of standard neutral theories of biodiversity and that an alternative family of generalized models provides a qualitatively better description. Together, these results lay the groundwork for a theoretical framework to connect ecological mechanisms to observed phylogenetic patterns in microbial communities.

A neutral theory with environmental stochasticity explains static and dynamic properties of ecological communities

Understanding the forces shaping ecological communities is crucial to basic science and conservation. Neutral theory has made considerable progress in explaining static properties of communities, like species abundance distributions (SADs), with a simple and generic model, but was criticised for making unrealistic predictions of fundamental dynamic patterns and for being sensitive to interspecific differences in fitness. Here, we show that a generalised neutral theory incorporating environmental stochasticity may resolve these limitations. We apply the theory to real data (the tropical forest of Barro Colorado Island) and demonstrate that it much better explains the properties of short-term population fluctuations and the decay of compositional similarity with time, while retaining the ability to explain SADs. Furthermore, the predictions are considerably more robust to interspecific fitness differences. Our results suggest that this integration of niches and stochasticity may serve as a minimalistic framework explaining fundamental static and dynamic characteristics of ecological communities.

Unifying ecology and macroevolution with individual-based theory

A contemporary goal in both ecology and evolutionary biology is to develop theory that transcends the boundary between the two disciplines, to understand phenomena that cannot be explained by either field in isolation. This is challenging because macroevolution typically uses lineage-based models, whereas ecology often focuses on individual organisms. Here, we develop a new parsimonious individual-based theory by adding mild selection to the neutral theory of biodiversity. We show that this model generates realistic phylogenies showing a slowdown in diversification and also improves on the ecological predictions of neutral theory by explaining the occurrence of very common species. Moreover, we find the distribution of individual fitness changes over time, with average fitness increasing at a pace that depends positively on community size. Consequently, large communities tend to produce fitter species than smaller communities. These findings have broad implications beyond biodiversity theory, potentially impacting, for example, invasion biology and paleontology.