Environmentally‐induced noise dampens and reddens with increasing trophic level in a complex food web

Stochastic variability of key abiotic factors including temperature, precipitation and the availability of light and nutrients greatly influences species’ ecological function and evolutionary fate. Despite such influence, ecologists have typically ignored the effect of abiotic stochasticity on the structure and dynamics of ecological networks. Here we help to fill that gap by advancing the theory of how abiotic stochasticity, in the form of environmental noise, affects the population dynamics of species within food webs. We do this by analysing an allometric trophic network model of Lake Constance subjected to positive (red), negative (blue), and non‐autocorrelated (white) abiotic temporal variability (noise) introduced into the carrying capacity of basal species. We found that, irrespective of the colour of the introduced noise, the temporal variability of the species biomass within the network both reddens (i.e. its positive autocorrelation increases) and dampens (i.e. the magnitude of variation decreases) as the environmental noise is propagated through the food web by its feeding interactions from the bottom to the top. The reddening reflects a buffering of the noise‐induced population variability by complex food web dynamics such that non‐autocorrelated oscillations of noise‐free deterministic dynamics become positively autocorrelated. Our research helps explain frequently observed red variability of natural populations by suggesting that ecological processing of environmental noise through food webs with a range of species’ body sizes reddens population variability in nature.     

Demographic stochasticity alters expected outcomes in experimental and simulated non‐neutral communities

Theory has shown that the effects of demographic stochasticity on communities may depend on the magnitude of fitness differences between species. In particular, it has been suggested that demographic stochasticity has the potential to significantly alter competitive outcomes when fitness differences are small (nearly neutral), but that it has negligible effects when fitness differences are large (highly non‐neutral). Here we test such theory experimentally and extend it to examine how demographic stochasticity affects exclusion frequency and mean densities of consumers in simple, but non‐neutral, consumer–resource communities. We used experimental microcosms of protists and rotifers feeding on a bacterial resource to test how varying absolute population sizes (a driver of demographic stochasticity) affected the probability of competitive exclusion of the weakest competitor. To explore whether demographic stochasticity could explain our experimental results, and to generalize beyond our experiment, we paired the experiment with a continuous‐time stochastic model of resource competition, which we simulated for 11 different fitness inequalities between competiting consumers. Consistent with theory, in both our experiments and our simulations we found that demographic stochasticity altered competitive outcomes in communities where fitness differences were small. However, we also found that demographic stochasticity alone could affect communities in other ways, even when fitness differences between competitors were large. Specifically, demographic stochasticity altered mean densities of both weak and strong competitors in experimental and simulated communities. These findings highlight how demographic stochasticity can change both competitive outcomes in non‐neutral communities and the processes underlying overall community dynamics.     

Testing the Wiegand–Milton model: A long‐term experiment to understand mechanisms driving vegetation dynamics in arid shrublands

The Wiegand and Milton (1996) simulation model predicts that vegetation dynamics in arid shrublands are characterized by event‐driven stochasticity (weather events), and demographic inertia (persistence of a species in a community) that lead to a lagged response in vegetation compositional change. Slow plant growth is one of the mechanisms driving slow vegetation change. We test this model at the same location (Tierberg Long‐term Ecological Research site) on which the model was based. Three dwarf shrub species, differing in palatability, were tracked over 25 years (1988–2014) at two levels of the past herbivory (pre‐1960) and three levels of the present herbivory (post‐1988). In the period between 1960 and 1988, all sites were grazed at the recommended agricultural stocking rate. For each species, plant density and a number of size attributes (basal diameter, height, canopy area) were surveyed. Analyses using a two‐way Analysis of Covariance (ANCOVA) took initial starting size into consideration. As the model predicted, event‐driven stochasticity (rainfall) resulted in an increase in density of the smaller size classes following a single large recruitment event across all grazing regimes for the palatable and unpalatable species. Size‐class distribution curve types remained unchanged illustrating that population demography remains unaffected for long periods and responses are slow (lagged response). Slow plant growth was evident in that there were no changes in height, canopy area, or density under present grazing regimes over the 25‐year period. Palatable species had a reduced canopy area and density compared to unpalatable species. Our findings provide empirical evidence supporting the predictions of the Wiegand and Milton (1996) model, notably event‐driven stochasticity, demographic inertia, and a lagged response in vegetation change in arid shrublands. In addition, our results support the model assumption of the significance of slow growth in long‐lived plant species and the influence of grazing regime.     

The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species

Invasive species are a serious threat to biodiversity worldwide and predicting whether an introduced species will first establish and then become invasive can be useful to preserve ecosystem services. Establishment is influenced by multiple factors, such as the interactions between the introduced individuals and the resident community, and demographic and environmental stochasticity. Field observations are often incomplete or biased. This, together with an imperfect knowledge of the ecological traits of the introduced species, makes the prediction of establishment challenging. Methods that consider the combined effects of these factors on our ability to predict the establishment of an introduced species are currently lacking. We develop an inference framework to assess the combined effects of demographic stochasticity and parameter uncertainty on our ability to predict the probability of establishment following the introduction of a small number of individuals. We find that even moderate levels of demographic stochasticity influence both the probability of establishment, and, crucially, our ability to correctly predict that probability. We also find that estimation of the demographic parameters of an introduced species is fundamental to obtain precise estimates of the interaction parameters. For typical values of demographic stochasticity, the drop in our ability to predict an establishment can be 30% when having priors on the demographic parameters compared to having their accurate values. The results from our study illustrate how demographic stochasticity may bias the prediction of the probability of establishment. Our method can be applied to estimate probability of establishment of introduced species in field scenarios, where time series data and prior information on the demographic traits of the introduced species are available.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

A mathematical synthesis of niche and neutral theories in community ecology

The debate between niche-based and neutral community theories centers around the question of which forces shape predominantly ecological communities. Niche theory attributes a central role to niche differences between species, which generate a difference between the strength of intra- and interspecific interactions. Neutral theory attributes a central role to migration processes and demographic stochasticity. One possibility to bridge these two theories is to combine them in a common mathematical framework. Here we propose a mathematical model that integrates the two perspectives. From a niche-based perspective, our model can be interpreted as a Lotka-Volterra model with symmetric interactions in which we introduce immigration and demographic stochasticity. From a neutral perspective, it can be interpreted as Hubbell's local community model in which we introduce a difference between intra- and interspecific interactions. We investigate the stationary species abundance distribution and other community properties as functions of the interaction coefficient, the immigration rate and the strength of demographic stochasticity.     

Evolution of aging through reduced demographic stochasticity – an extension of the pleiotropy theory to finite populations

In finite populations, there is selection against demographic stochasticity. In this study, it is shown that an increase in the rate of aging, here defined as an increase in early‐life survival at the expense of later survival, may reduce this form of stochasticity. In particular, a trade‐off between juvenile and adult survival is highly efficient in reducing demographic stochasticity. Therefore, aging may evolve as a response to selective pressure for reduced demographic stochasticity.     

Setting the absolute tempo of biodiversity dynamics

Neutral biodiversity theory has the potential to contribute to our understanding of how macroevolutionary dynamics influence contemporary biodiversity, but there are issues regarding its dynamical predictions that must first be resolved. Here we address these issues by extending the theory in two ways using a novel analytical approach: (1) we set the absolute tempo of biodiversity dynamics by explicitly incorporating population-level stochasticity in abundance; (2) we allow new species to arise with more than one individual. Setting the absolute tempo yields quantitative predictions on biodiversity dynamics that can be tested using contemporary and fossil data. Allowing incipient-species abundances greater than one individual yields predictions on how these dynamics, and the form of the species-abundance distribution, are affected by multiple speciation modes. We apply this new model to contemporary and fossil data that encompass 30 Myr of macroevolution for planktonic foraminifera. By synthesizing the model with these empirical data, we present evidence that dynamical issues with neutral biodiversity theory may be resolved by incorporating the effects of environmental stochasticity and incipient-species abundance on biodiversity dynamics.     

Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.     

Population demography and the evolution of helping behaviors

Limited dispersal may favor the evolution of helping behaviors between relatives as it increases their relatedness, and it may inhibit such evolution as it increases local competition between these relatives. Here, we explore one way out of this dilemma: if the helping behavior allows groups to expand in size, then the kin-competition pressure opposing its evolution can be greatly reduced. We explore the effects of two kinds of stochasticity allowing for such deme expansion. First, we study the evolution of helping under environmental stochasticity that may induce complete patch extinction. Helping evolves if it results in a decrease in the probability of extinction or if it enhances the rate of patch recolonization through propagules formed by fission of nonextinct groups. This mode of dispersal is indeed commonly found in social species. Second, we consider the evolution of helping in the presence of demographic stochasticity. When fecundity is below its value maximizing deme size (undersaturation), helping evolves, but under stringent conditions unless positive density dependence (Allee effect) interferes with demographic stochasticity. When fecundity is above its value maximizing deme size (oversaturation), helping may also evolve, but only if it reduces negative density-dependent competition.     

Species dynamics alter community diversity–biomass stability relationships

The relationship between community diversity and biomass variability remains a crucial ecological topic, with positive, negative and neutral diversity–stability relationships reported from empirical studies. Theory highlights the relative importance of Species–Species or Species–Environment interactions in driving diversity–stability patterns. Much previous work is based on an assumption of identical (stable) species‐level dynamics. We studied ecosystem models incorporating stable, cyclic and more complex species‐level dynamics, with either linear or non‐linear density dependence, within a locally stable community framework. Species composition varies with increasing diversity, interacting with the correlation of species' environmental responses to drive either positive or negative diversity–stability patterns, which theory based on communities with only stable species‐level dynamics fails to predict. Including different dynamics points to new mechanisms that drive the full range of diversity–biomass stability relationships in empirical systems where a wider range of dynamical behaviours are important.     

Distance decay of similarity,effects of environmental noise and ecological heterogeneity among species in the spatio‐temporal dynamics of a dispersal‐limited community

The joint spatial and temporal fluctuations in community structure may be due to dispersal, variation in environmental conditions, ecological heterogeneity among species and demographic stochasticity. These factors are not mutually exclusive, and their relative contribution towards shaping species abundance distributions and in causing species fluctuations have been hard to disentangle. To better understand community dynamics when the exchange of individuals between localities is very low, we studied the dynamics of the freshwater zooplankton communities in 17 lakes located in independent catchment areas, sampled at end of summer from 2002 to 2008 in Norway. We analysed the joint spatial and temporal fluctuations in the community structure by fitting the two‐dimensional Poisson lognormal model under a two‐stage sampling scheme. We partitioned the variance of the distribution of log abundance for a random species at a random time and location into components of demographic stochasticity, ecological heterogeneity among species, and independent environmental noise components for the different species. Non‐neutral mechanisms such as ecological heterogeneity among species (20%) and spatiotemporal variation in the environment (75%) explained the majority of the variance in log abundances. Overdispersion relative to Poisson sampling and demographic stochasticity had a small contribution to the variance (5%). Among a set of environmental variables, lake acidity was the environmental variable that was most strongly related to decay of community similarity in space and time.     

Species richness, environmental fluctuations, and temporal change in total community biomass

Theory and empirical results suggest that high biodiversity should often cause lower temporal variability in aggregate community properties such as total community biomass. We assembled microbial communities containing 2 to 8 species of competitors in aquatic microcosms and found that the temporal change in total community biomass was positively but insignificantly associated with diversity in a constant temperature environment. There was no evidence of any trend in variable temperature environments. Three non-exclusive mechanisms might explain the lack of a net stabilising effect of species richness on temporal change. (1) A direct destabilising effect of diversity on population level variances caused some populations to vary more when embedded in more diverse communities. (2) Similar responses of the different species to environmental variability might have limited any insurance effect of increased species richness. (3) Large differences in the population level variability of different species (i.e., unevenness) could weaken the relation between species richness and community level stability. These three mechanisms may outweigh the stabilising effects of increases in total community biomass with diversity, statistical averaging, and slightly more negative covariance in more diverse communities. Our experiment and analyses advocate for further experimental investigations of diversity-variability relations.     

Biodiversity may regulate the temporal variability of ecological systems

The effect of biodiversity on natural communities has recently emerged as a topic of considerable ecological interest. We review studies that explicitly test whether the number of species in a community (species richness) regulates the temporal variability of aggregate community (total biomass, productivity, nutrient cycling) and population (density, biomass) properties. Theoretical studies predict that community variability should decline with increasing species richness, while population variability should increase. Many, but not all, empirical studies support these expectations. However, a closer look reveals that several empirical studies have either imperfect experimental designs or biased methods of calculating variability. Furthermore, most theoretical studies rely on highly unrealistic assumptions. We conclude that evidence to support the claim that biodiversity regulates temporal variability is accumulating, but not unequivocal. More research, in a broader array of ecosystem types and with careful attention to methodological considerations, is needed before we can make definitive statements regarding richness‐variability relationships.     

Differential effects of functional traits on aboveground biomass in semi-natural grasslands

Despite increasing evidence on the importance of species functional characteristics for ecosystem processes, two major hypotheses suggest different mechanisms: the ‘mass ratio hypothesis’ assumes that functional traits of the dominant species determine ecosystem processes, while the ‘complementarity hypothesis’ predicts that resource niches may be used more completely when a community is functionally more diverse. Here, we present a method which uses two different groups of biotic predictor variables being (1) abundance‐weighted mean (=aggregated) trait values and (2) functional trait diversity based on Rao's quadratic diversity (FD_Q) to test the competing hypotheses on biodiversity–ecosystem functioning relationships after accounting for co‐varying abiotic factors. We applied this method to data recorded on biodiversity–biomass relationships and environmental variables in 35 semi‐natural temperate grasslands and used a literature‐based matrix of fourteen plant functional traits to assess the explanatory power of models including different sets of predictor variables. Aboveground community biomass did not correlate with species richness. Abiotic factors, in particular soil nitrogen concentration, explained about 50% of variability in aboveground biomass. The best model incorporating functional trait diversity explained only about 30%, while the best model based on aggregated trait values explained about 54% of variability in aboveground biomass. The inclusion of all predictor variable groups in a combined model increased the predictive power to about 75%. This model comprised soil nitrogen concentration as abiotic factor, aggregated traits being indicative for species competitive dominance (rooting depth, leaf distribution, specific leaf area, perennial life cycle) and functional trait diversity in vegetative plant height, leaf area and life cycle. Our study strongly suggests that abiotic factors, trait values of the dominant species and functional trait diversity in combination may best explain differences in aboveground community biomass in natural ecosystems and that their isolated consideration may be misleading.     

How variation between individuals affects species coexistence

Although the effects of variation between individuals within species are traditionally ignored in studies of species coexistence, the magnitude of intraspecific variation in nature is forcing ecologists to reconsider. Compelling intuitive arguments suggest that individual variation may provide a previously unrecognised route to diversity maintenance by blurring species‐level competitive differences or substituting for species‐level niche differences. These arguments, which are motivating a large body of empirical work, have rarely been evaluated with quantitative theory. Here we incorporate intraspecific variation into a common model of competition and identify three pathways by which this variation affects coexistence: (1) changes in competitive dynamics because of nonlinear averaging, (2) changes in species’ mean interaction strengths because of variation in underlying traits (also via nonlinear averaging) and (3) effects on stochastic demography. As a consequence of the first two mechanisms, we find that intraspecific variation in competitive ability increases the dominance of superior competitors, and intraspecific niche variation reduces species‐level niche differentiation, both of which make coexistence more difficult. In addition, individual variation can exacerbate the effects of demographic stochasticity, and this further destabilises coexistence. Our work provides a theoretical foundation for emerging empirical interests in the effects of intraspecific variation on species diversity.     

Limiting similarity and functional diversity along environmental gradients

Recent developments in community models emphasize the importance of incorporating stochastic processes (e.g. ecological drift) in models of niche‐structured community assembly. We constructed a finite, spatially explicit, lottery model to simulate the distribution of species in a one‐dimensional landscape with an underlying gradient in environmental conditions. Our framework combines the potential for ecological drift with environmentally‐mediated competition for space in a heterogeneous environment. We examined the influence of niche breadth, dispersal distances, community size (total number of individuals) and the breadth of the environmental gradient on levels of species and functional trait diversity (i.e. differences in niche optima). Three novel results emerge from this model: (1) niche differences between adjacent species (e.g. limiting similarity) increase in smaller communities, because of the interaction of competitive effects and finite population sizes; (2) immigration from a regional species pool, stochasticity and niche‐assembly generate a bimodal distribution of species residence times (‘transient’ and ‘resident’) under a heterogeneous environment; and (3) the magnitude of environmental heterogeneity has a U‐shaped effect on diversity, because of shifts in species richness of resident vs. transient species. These predictions illustrate the potential importance of stochastic (although not necessarily neutral) processes in community assembly.     

Extinction in relation to demographic and environmental stochasticity in age-structured models

The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.     

Using root traits to understand temporal changes in biodiversity effects in grassland mixtures

Biodiversity–ecosystem functioning (BEF) studies typically show that species richness enhances community biomass, but the underlying mechanisms remain debated. Here, we combine metrics from BEF research that distinguish the contribution of dominant species (selection effects, SE) from those due to positive interactions such as resource partitioning (complementarity effects, CE) with a functional trait approach in an attempt to reveal the functional characteristics of species that drive community biomass in species mixtures. In a biodiversity experiment with 16 plant species in monocultures, 4‐species and 16‐species mixtures, we used aboveground biomass to determine the relative contributions of CE and SE to biomass production in mixtures in the second, dry year of the experiment. We also measured root traits (specific root length, root length density, root tissue density and the deep root fraction) of each species in monocultures and linked the calculated community weighted mean (CWM) trait values and trait diversity of mixtures to CE and SE. In the second year of the experiment, community biomass, CE and SE increased compared to the first year. The contribution of SE to this positive effect was greater than that of CE. The increased contribution of SE was associated with root traits: SE increased most in communities with high abundance of species with deep, thick and dense roots. In contrast, changes in CE were not related to trait diversity or CWM trait values. Together, these results suggest that increased positive effects of species richness on community biomass in a dry year were mainly driven by increased dominance of deep‐rooting species, supporting the insurance hypothesis of biodiversity. Positive CE indicates that other positive interactions did occur, but we could not find evidence that belowground resource partitioning or facilitation via root trait diversity was important for community productivity in our biodiversity experiment.     

Sex and stochasticity affect range expansion of experimental invasions

Understanding and predicting range expansion are key objectives in many basic and applied contexts. Among dioecious organisms, there is strong evidence for sex differences in dispersal, which could alter the sex ratio at the expansion's leading edge. However, demographic stochasticity could also affect leading‐edge sex ratios, perhaps overwhelming sex‐biased dispersal. We used insects in laboratory mesocosms to test the effects of sex‐biased dispersal on range expansion, and a simulation model to explore interactive effects of sex‐biased dispersal and demographic stochasticity. Sex‐biased dispersal created spatial clines in the sex ratio, which influenced offspring production at the front and altered invasion velocity. Increasing female dispersal relative to males accelerated spread, despite the prediction that demographic stochasticity would weaken a signal of sex‐biased dispersal. Our results provide the first experimental evidence for an influence of sex‐biased dispersal on invasion velocity, highlighting the value of accounting for sex structure in studies of range expansion.