Modelling niche and neutral dynamics: on the ecological interpretation of variation partitioning results

Many studies have attempted to disentangle the effects of neutral and niche‐mediated processes on community composition using partial Mantel tests and variance partitioning on dissimilarity matrices. Recently, doubts about the reliability of these methods have emerged. Here we explore how the results are affected by three confounding factors that may affect ecological data to different degrees: spatial autocorrelation of the environmental variables, length of the compositional gradient, and sampling noise. We document that the statistical hypotheses tested in these methods may or may not correspond to the ecological hypotheses of interest. A major discrepancy emerges if a large proportion of sampling units in the analysed dataset share no species, in which case compositional dissimilarities saturate to a fixed maximum value although explanatory dissimilarities do not. With increasing dissimilarity saturation, the explanatory power of regression models decrease, which may lead to the erroneous conclusion that the ecological processes represented by the explanatory variables are not operating. A survey of recent literature suggests that there is a general lack of awareness of this problem, although it appears to affect > 10% of relevant studies. Our simulations show that if dissimilarity saturation is due to a long ecological gradient, extended dissimilarities essentially solve the problem for any degree of saturation. Using distances from a hybrid multidimensional scaling alleviates the saturation problem when the degree of saturation is < 60%. However, neither correction method can provide a solution to problems caused by insufficient sampling. How the presence of multiple explanatory gradients in combination with sampling noise affects overall analysis performance remains to be clarified.     

Only noise can induce chaos in discrete populations

Motivated by the papers from Ellner and Turchin 2005 and Dennis et al. 2003 we investigate the possibility to detect chaos in noisy ecological systems. One message of our paper is that if a dynamic model is available and if this model predicts chaotic behaviour, one should consider its discrete-state, noisy version when fitting numerical predictions to observations. We emphasize that deterministic discrete-state models behave periodically, thus only the interaction of these deterministic skeletons with random noise can produce non-regular dynamics. We detect and describe a relatively sharply defined range of the noise (the grey zone) where the gradual transition from periodic to chaotic behaviour happens. This zone, the upper border of which can be predicted analytically, is identified in experimental data as well as in numerical simulations. In the grey zone the global, statistical behaviour will approach the statistics produced by the chaotic, continuous model, and in this sense we claim that noise can produce chaos.     

Discrete and continuous state population models in a noisy world

Simple ecological models operate mostly with population densities using continuous variables. However, in reality densities could not change continuously, since the population itself consists of integer numbers of individuals. At first sight this discrepancy appears to be irrelevant, nevertheless, it can cause large deviations between the actual statistical behaviour of biological populations and that predicted by the corresponding models. We investigate the conditions under which simple models, operating with continuous numbers of individuals can be used to approximate the dynamics of populations consisting of integer numbers of individuals. Based on our definition for the (statistical) distance between the two models we show that the continuous approach is acceptable as long as sufficiently high biological noise is present, or, the dynamical behaviour is regular (non-chaotic). The concepts are illustrated with the Ricker model and tested on the Tribolium castaneum data series. Further, we demonstrate with the help of T. castaneum's model that if time series are not much larger than the possible population states (as in this practical case) the noisy discrete and continuous models can behave temporarily differently, almost independently of the noise level. In this case the noisy, discrete model is more accurate [OR has to be applied].     

The risk of competitive exclusion during evolutionary branching: Effects of resource variability, correlation and autocorrelation

Evolutionary branching has been suggested as a mechanism to explain ecological speciation processes. Recent studies indicate however that demographic stochasticity and environmental fluctuations may prevent branching through stochastic competitive exclusion. Here we extend previous theory in several ways; we use a more mechanistic ecological model, we incorporate environmental fluctuations in a more realistic way and we include environmental autocorrelation in the analysis. We present a single, comprehensible analytical result which summarizes most effects of environmental fluctuations on evolutionary branching driven by resource competition. Corroborating earlier findings, we show that branching may be delayed or impeded if the underlying resources have uncorrelated or negatively correlated responses to environmental fluctuations. There is also a strong impeding effect of positive environmental autocorrelation, which can be related to results from recent experiments on adaptive radiation in bacterial microcosms. In addition, we find that environmental fluctuations can lead to cycles of repeated branching and extinction.     

Non-genetic inheritance and the patterns of antagonistic coevolution

ABSTRACT: BACKGROUND: Antagonistic species interactions can lead to coevolutionary genotype or phenotype frequency oscillations, with important implications for ecological and evolutionary processes. However, direct empirical evidence of such oscillations is rare. The rarity of observations is generally attributed to inherent difficulties of ecological and evolutionary long-term studies, to weak or absent interaction between species, or to the absence of negative frequency-dependence. RESULTS: Here, we show that another factor - non-genetic inheritance, mediated for example by epigenetic mechanisms - can completely eliminate oscillations even if only a small fraction of offspring are affected. We analytically derive the threshold value of this fraction at which the dynamics change from oscillatory to stable, and investigate how selection, mutation and generation times differences between the two species affect the threshold value. These results strongly suggest that the lack of phenotype frequency oscillations should not be attributed to the lack of strong interactions between antagonistic species. CONCLUSIONS: Given increasing evidence of non-genetic effects on the outcomes of antagonistic species interactions, we suggest that these effects should be incorporated into ecological and evolutionary models of interacting species.     

Noise, predation risk compensation and vigilance in the chaffinch Fringilla coelebs

Background noise should in theory hinder detection of auditory cues associated with approaching danger. We tested whether foraging chaffinches Fringilla coelebs responded to background noise by increasing vigilance, and examined whether this was explained by predation risk compensation or by a novel stimulus hypothesis. The former predicts that only inter-scan interval should be modified in the presence of background noise, not vigilance levels generally. This is because noise hampers auditory cue detection and increases perceived predation risk primarily when in the head-down position, and also because previous tests have shown that only interscan interval is correlated with predator detection ability in this system. Chaffinches only modified interscan interval supporting this hypothesis. At the same time they made significantly fewer pecks when feeding during the background noise treatment and so the increased vigilance led to a reduction in intake rate, suggesting that compensating for the increased predation risk could indirectly lead to a fitness cost. Finally, the novel stimulus hypothesis predicts that chaffinches should habituate to the noise, which did not occur within a trial or over 5 subsequent trials. We conclude that auditory cues may be an important component of the trade-off between vigilance and feeding, and discuss possible implications for anti-predation theory and ecological processes.     

Biotic resistance to exotic invasions: its role in forest ecosystems,confounding artifacts,and future directions

Biotic resistance, the ability of communities to resist exotic invasions, has long attracted interest in the research and management communities. However, inconsistencies exist in various biotic resistance studies and less is known about the current status and knowledge gaps of biotic resistance in forest ecosystems. In this paper, we provide a brief review of the history and mechanisms of the biotic resistance hypothesis, and summarize the central topics and knowledge gaps related to biotic resistance with a special emphasis on forest ecosystems. Overall, although the amount of research efforts on biotic resistance in forest ecosystems has increased since the mid-2000s, aspects such as resistance to exotic pests and pathogens remain understudied. In addition, we synthesize ecological and statistical explanations of observed inconsistencies and provide suggestions for future research directions. Some of the observed inconsistencies on biotic resistance can be attributed to (1) the interactive or additive effects of other ecological processes and (2) the statistical artifacts of modifiable areal unit problem. With the advancement of new statistical knowledge and tools, along with availability of big data, biotic resistance research can be greatly improved with the simultaneous consideration of key ecological processes, the attention to various scales involved, and the addition of understudied systems.     

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

From noise to knowledge: how randomness generates novel phenomena and reveals information

Noise, as the term itself suggests, is most often seen a nuisance to ecological insight, a inconvenient reality that must be acknowledged, a haystack that must be stripped away to reveal the processes of interest underneath. Yet despite this well‐earned reputation, noise is often interesting in its own right: noise can induce novel phenomena that could not be understood from some underlying deterministic model alone. Nor is all noise the same, and close examination of differences in frequency, colour or magnitude can reveal insights that would otherwise be inaccessible. Yet with each aspect of stochasticity leading to some new or unexpected behaviour, the time is right to move beyond the familiar refrain of “everything is important” (Bjørnstad & Grenfell 2001 ). Stochastic phenomena can suggest new ways of inferring process from pattern, and thus spark more dialog between theory and empirical perspectives that best advances the field as a whole. I highlight a few compelling examples, while observing that the study of stochastic phenomena are only beginning to make this translation into empirical inference. There are rich opportunities at this interface in the years ahead.     

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.     

Co‐occurrence is not evidence of ecological interactions

There is a rich amount of information in co‐occurrence (presence–absence) data that could be used to understand community assembly. This proposition first envisioned by Forbes (1907) and then Diamond (1975) prompted the development of numerous modelling approaches (e.g. null model analysis, co‐occurrence networks and, more recently, joint species distribution models). Both theory and experimental evidence support the idea that ecological interactions may affect co‐occurrence, but it remains unclear to what extent the signal of interaction can be captured in observational data. It is now time to step back from the statistical developments and critically assess whether co‐occurrence data are really a proxy for ecological interactions. In this paper, we present a series of arguments based on probability, sampling, food web and coexistence theories supporting that significant spatial associations between species (or lack thereof) is a poor proxy for ecological interactions. We discuss appropriate interpretations of co‐occurrence, along with potential avenues to extract as much information as possible from such data.     

Can You Sequence Ecology? Metagenomics of Adaptive Diversification

Few areas of science have benefited more from the expansion in sequencing capability than the study of microbial communities. Can sequence data, besides providing hypotheses of the functions the members possess, detect the evolutionary and ecological processes that are occurring? For example, can we determine if a species is adapting to one niche, or if it is diversifying into multiple specialists that inhabit distinct niches? Fortunately, adaptation of populations in the laboratory can serve as a model to test our ability to make such inferences about evolution and ecology from sequencing. Even adaptation to a single niche can give rise to complex temporal dynamics due to the transient presence of multiple competing lineages. If there are multiple niches, this complexity is augmented by segmentation of the population into multiple specialists that can each continue to evolve within their own niche. For a known example of parallel diversification that occurred in the laboratory, sequencing data gave surprisingly few obvious, unambiguous signs of the ecological complexity present. Whereas experimental systems are open to direct experimentation to test hypotheses of selection or ecological interaction, the difficulty in “seeing ecology” from sequencing for even such a simple system suggests translation to communities like the human microbiome will be quite challenging. This will require both improved empirical methods to enhance the depth and time resolution for the relevant polymorphisms and novel statistical approaches to rigorously examine time-series data for signs of various evolutionary and ecological phenomena within and between species.     

Ecological limitations to the resilience of coral reefs

The decline of coral reefs has been broadly attributed to human stressors being too strong and pervasive, whereas biological processes that may render coral reefs fragile have been sparsely considered. Here we review several ecological factors that can limit the ability of coral reefs to withstand disturbance. These include: (1) Many species lack the adaptive capacity to cope with the unprecedented disturbances they currently face; (2) human disturbances impact vulnerable life history stages, reducing reproductive output and the supply of recruits essential for recovery; (3) reefs can be vulnerable to the loss of few species, as niche specialization or temporal and spatial segregation makes each species unique (i.e., narrow ecological redundancy); in addition, many foundation species have similar sensitivity to disturbances, suggesting that entire functions can be lost to single disturbances; and (4) feedback loops and extinction vortices may stabilize degraded states or accelerate collapses even if stressors are removed. This review suggests that the degradation of coral reefs is due to not only the severity of human stressors but also the “fragility” of coral reefs. As such, appropriate governance is essential to manage stressors while being inclusive of ecological process and human uses across transnational scales. This is a considerable but necessary upgrade in current management if the integrity, and delivery of goods and services, of coral reefs is to be preserved.     

Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models

The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planck equation, the linear noise approximation or the macroscopic rate equation. The inverse problem of estimating the parameters of the underlying network model can be approached in deterministic and stochastic ways, and available methods often compare individual or mean concentration traces obtained from experiments with theoretical model predictions when maximizing likelihoods, minimizing regularized least squares functionals, approximating posterior distributions or sequentially processing the data. In this article we assume that the biological reaction network can be observed at least partially and repeatedly over time such that sample moments of species molecule numbers for various time points can be calculated from the data. Based on the chemical master equation we furthermore derive closed systems of parameter dependent nonlinear ordinary differential equations that predict the time evolution of the statistical moments. For inferring the reaction rate parameters we suggest to not only compare the sample mean with the theoretical mean prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. As a consequence both deterministic and stochastic parameter inference algorithms may be improved with respect to accuracy and efficiency. We demonstrate the potential of moment fitting for parameter inference by means of illustrative stochastic biological models from the literature and address topics for future research.     

Bayesian change-point analyses in ecology

Ecological and biological processes can change from one state to another once a threshold has been crossed in space or time. Threshold responses to incremental changes in underlying variables can characterize diverse processes from climate change to the desertification of arid lands from overgrazing. Simultaneously estimating the location of thresholds and associated ecological parameters can be difficult: ecological data are often 'noisy', which can make the identification of the locations of ecological thresholds challenging. We illustrate this problem using two ecological examples and apply a class of statistical models well-suited to addressing this problem. We first consider the case of estimating allometric relationships between tree diameter and height when the trees have distinctly different growth modes across life-history stages. We next estimate the effects of canopy gaps and dense understory vegetation on tree recruitment in transects that transverse both canopy and gap conditions. The Bayesian change-point models that we present estimate both threshold locations and the slope or level of ecological quantities of interest, while incorporating uncertainty in the change-point location into these estimates. This class of models is suitable for problems with multiple thresholds and can account for spatial or temporal autocorrelation.     

A statistical model for the genetic origin of allometric scaling laws in biology

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling (power-law) relationships between size and rate. Although such allometric relationships may be under genetic determination, their precise genetic mechanisms have not been clearly understood due to a lack of a statistical analytical method. In this paper, we present a basic statistical framework for mapping quantitative genes (or quantitative trait loci, QTL) responsible for universal quarter-power scaling laws of organic structure and function with the entire body size. Our model framework allows the testing of whether a single QTL affects the allometric relationship of two traits or whether more than one linked QTL is segregating. Like traditional multi-trait mapping, this new model can increase the power to detect the underlying QTL and the precision of its localization on the genome. Beyond the traditional method, this model is integrated with pervasive scaling laws to take advantage of the mechanistic relationships of biological structures and processes. Simulation studies indicate that the estimation precision of the QTL position and effect can be improved when the scaling relationship of the two traits is considered. The application of our model in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship of third-year stem height with third-year stem biomass. The model proposed here has implications for genetic, evolutionary, biomedicinal and breeding research.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

Analyzing tropical forest tree species abundance distributions using a nonneutral model and through approximate Bayesian inference

The neutral theory of biodiversity challenges the classical niche-based view of ecological communities, where species attributes and environmental conditions jointly determine community composition. Functional equivalence among species, as assumed by neutral ecological theory, has been recurrently falsified, yet many patterns of tropical tree communities appear consistent with neutral predictions. This may mean that neutral theory is a good first-approximation theory or that species abundance data sets contain too little information to reject neutrality. Here we present a simple test of neutrality based on species abundance distributions in ecological communities. Based on this test, we show that deviations from neutrality are more frequent than previously thought in tropical forest trees, especially at small spatial scales. We then develop a nonneutral model that generalizes Hubbell's dispersal-limited neutral model in a simple way by including one additional parameter of frequency dependence. We also develop a statistical method to infer the parameters of this model from empirical data by approximate Bayesian computation. In more than half of the permanent tree plots, we show that our new model fits the data better than does the neutral model. Finally, we discuss whether observed deviations from neutrality may be interpreted as the signature of environmental filtering on tropical tree species abundance distributions.     

Statistical inferences in phylogeography

In conventional phylogeographic studies, historical demographic processes are elucidated from the geographical distribution of individuals represented on an inferred gene tree. However, the interpretation of gene trees in this context can be difficult as the same demographic/geographical process can randomly lead to multiple different genealogies. Likewise, the same gene trees can arise under different demographic models. This problem has led to the emergence of many statistical methods for making phylogeographic inferences. A popular phylogeographic approach based on nested clade analysis is challenged by the fact that a certain amount of the interpretation of the data is left to the subjective choices of the user, and it has been argued that the method performs poorly in simulation studies. More rigorous statistical methods based on coalescence theory have been developed. However, these methods may also be challenged by computational problems or poor model choice. In this review, we will describe the development of statistical methods in phylogeographic analysis, and discuss some of the challenges facing these methods.