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。     

Synchrony of spatial populations induced by colored environmental noise and dispersal

Spatial synchrony of oscillating populations has been observed in many ecological systems, and its influences and causes have attracted the interest of ecologists. Spatially correlated environmental noises, dispersal, and trophic interactions have been considered as the causes of spatial synchrony. In this study, we develop a spatially structured population model, which is described by coupled-map lattices and incorporates both dispersal and colored environmental noise. A method for generating time series with desired spatial correlation and color is introduced. Then, we use these generated time series to analyze the influence of noise color on synchrony in population dynamics. The noise color refers to the temporal correlation in the time series data of the noise, and is expressed as the degree of (first-order) autocorrelation for autoregressive noise. Patterns of spatial synchrony are considered for stable, periodic and chaotic population dynamics. Numerical simulations verify that environmental noise color has a major influence on the level of synchrony, which depends strongly on how noise is introduced into the model. Furthermore, the influence of noise color also depends on patterns of dispersal between local populations. In addition, the desynchronizing effect of reddened noise is always weaker than that of white noise. From our results, we notice that the role of reddened environmental noise on spatial synchrony should be treated carefully and cautiously, especially for the spatially structured populations linked by dispersal.     

Noisy clues to the origin of life

The origin of stable self-replicating molecules represents a fundamental obstacle to the origin of life. The low fidelity of primordial replicators places restrictions on the quantity of information encoded in a primitive nucleic acid alphabet. Further difficulties for the origin of life are the role of drift in small primordial populations, reducing the rate of fixation of superior replicators, and the hostile conditions increasing developmental noise. Thus, mutation, noise and drift are three different stochastic effects that are assumed to make the evolution of life improbable. Here we show, to the contrary, how noise present in hostile early environments can increase the probability of faithful replication, by amplifying selection in finite populations. Noise has negative consequences in infinite populations, whereas in finite populations, we observe a synergistic interaction among noise sources. Hence, two factors formerly considered inimical to the origin of life-developmental noise and drift in small populations-can in combination give rise to conditions favourable to robust replication.     

Extracting Information from the Power Spectrum of Synaptic Noise

In cortical neurons, synaptic "noise" is caused by the nearly random release of thousands of synapses. Few methods are presently available to analyze synaptic noise and deduce properties of the underlying synaptic inputs. We focus here on the power spectral density (PSD) of several models of synaptic noise. We examine different classes of analytically solvable kinetic models for synaptic currents, such as the "delta kinetic models," which use Dirac delta functions to represent the activation of the ion channel. We first show that, for this class of kinetic models, one can obtain an analytic expression for the PSD of the total synaptic conductance and derive equivalent stochastic models with only a few variables. This yields a method for constraining models of synaptic currents by analyzing voltage-clamp recordings of synaptic noise. Second, we show that a similar approach can be followed for the PSD of the the membrane potential (Vm) through an effective-leak approximation. Third, we show that this approach is also valid for inputs distributed in dendrites. In this case, the frequency scaling of the Vm PSD is preserved, suggesting that this approach may be applied to intracellular recordings of real neurons. In conclusion, using simple mathematical tools, we show that Vm recordings can be used to constrain kinetic models of synaptic currents, as well as to estimate equivalent stochastic models. This approach, therefore, provides a direct link between intracellular recordings in vivo and the design of models consistent with the dynamics and spectral structure of synaptic noise.     

A general theory of environmental noise in ecological food webs

We examine the effects of environmental noise on populations that are parts of simple two-species food webs. We assume that the species are strongly interacting and that one or the other population is affected by the noise signal. Further assuming that a stable equilibrium with positive population densities exists, we are able to perform a complete frequency analysis of the system. If only one of the populations is subject to noise, the relative noise response by both populations is fully determined by the sign of a single element of the Jacobian matrix. The analysis is readily extended to cases when both species are affected by noise or when the food web has more than two species. The general conclusion about relative responses to noise is then less unambiguous, but the power spectra describing the frequency composition of the population variabilities are nevertheless completely determined. These results are entirely independent on the exact nature of the interaction (i.e., predation, competition, mutualism) between the populations. The results show that the interpretation of the "color" of ecological time series (i.e., the frequency composition of population variability over time) may be complicated by species interactions. The propagation of noise signals through food webs and the importance of web structure for the expected response of all parts of the web to such signals is a challenging field for future studies.     

The impact of stochasticity on the behaviour of nonlinear population models: synchrony and the Moran effect

Environmental variation is ubiquitous, but its effects on nonlinear population dynamics are poorly understood. Using simple (unstructured) nonlinear models we investigate the effects of correlated noise on the dynamics of two otherwise independent populations (the Moran effect), i.e. we focus on noise rather than dispersion or trophic interaction as the cause of population synchrony. We find that below the bifurcation threshold for periodic behaviour (1) synchrony between populations is strongly dependent on the shape of the noise distribution but largely insensitive to which model is studied, (2) there is, in general, a loss of synchrony as the noise is filtered by the model, (3) for specially structured noise distributions this loss can be effectively eliminated over a restricted range of distribution parameter values even though the model might be nonlinear, (4) for unstructured models there is no evidence of correlation enhancement, a mechanism suggested by Moran, but above the bifurcation threshold enhancement is possible for weak noise through phase-locking, (5) rapid desynchronisation occurs as the chaotic regime is approached. To carry out the investigation the stochastic models are (a) reformulated in terms of their joint asymptotic probability distributions and (b) simulated to analyse temporal patterns.     

The effects of synaptic noise on measurements of evoked excitatory postsynaptic response amplitudes.

Spontaneously occurring synaptic events (synaptic noise) recorded intracellularly are usually assumed to be independent of evoked postsynaptic responses and to contaminate measures of postsynaptic response amplitude in a roughly Gaussian manner. Here we derive analytically the expected noise distribution for excitatory synaptic noise and investigate its effects on amplitude histograms. We propose that some fraction of this excitatory noise is initiated at the same release sites that contribute to the evoked synaptic event and develop an analytical model of the interaction between this fraction of the noise and the evoked postsynaptic response amplitude. Recording intracellularly with sharp microelectrodes in the in vitro hippocampal slice preparation, we find that excitatory synaptic noise accounts for up to 70% of the intracellular recording noise, when inhibition is blocked pharmacologically. Up to 20% of this noise shows a significant correlation with the evoked event amplitude, and the behavior of this component of the noise is consistent with a model which assumes that each release site experiences a refractory period of approximately 60 ms after release. In contrast with classical models of quantal variance, our models predict that excitatory synaptic noise can cause the apparent variance of successive peaks in an excitatory synaptic amplitude histogram to decrease from left to right, and in some cases to be less than the variance of the measured noise.     

Experimentally increased noise levels change spatial and singing behaviour

The reasons why animal populations decline in response to anthropogenic noise are still poorly understood. To understand how populations are affected by noise, we must understand how individuals are affected by noise. By modifying the acoustic environment experimentally, we studied the potential relationship between noise levels and both spatial and singing behaviour in the European robin (Erithacus rubecula). We found that with increasing noise levels, males were more likely to move away from the noise source and changed their singing behaviour. Our results provide the first experimental evidence in a free ranging species, that not merely the presence of noise causes changes in behaviour and distribution, but that the level of noise pollution plays a crucial role as well. Our results have important implications for estimating the impact of infrastructure which differs in the level of noise produced. Thus, governmental planning bodies should not only consider the physical effect on the landscape when assessing the impact of new infrastructure, but also the noise levels emitted, which may reduce the loss of suitable habitats available for animals.     

Engineering stochasticity in gene expression

Stochastic fluctuations (noise) in gene expression can cause members of otherwise genetically identical populations to display drastically different phenotypes. An understanding of the sources of noise and the strategies cells employ to function reliably despite noise is proving to be increasingly important in describing the behavior of natural organisms and will be essential for the engineering of synthetic biological systems. Here we describe the design of synthetic constructs, termed ribosome competing RNAs (rcRNAs), as a means to rationally perturb noise in cellular gene expression. We find that noise in gene expression increases in a manner proportional to the ability of an rcRNA to compete for the cellular ribosome pool. We then demonstrate that operons significantly buffer noise between coexpressed genes in a natural cellular background and can even reduce the level of rcRNA enhanced noise. These results demonstrate that synthetic genetic constructs can significantly affect the noise profile of a living cell and, importantly, that operons are a facile genetic strategy for buffering against noise.     

Black noise and population persistence

Biological populations are susceptible to random variation in environmental influences such as temperature and moisture. This variability (or noise) can determine population size and, ultimately, cause extinctions. Extinction risk depends on noise colour or the amount of short- and long-term variation. Most environmental noise is reddened: the variation is dominated by long-term fluctuations. Recent modelling has shown that moderately reddened noise affects populations differently from the white noise used in earlier studies. However, some geophysical phenomena, such as temperature and river height, can have deeply reddened ''brown'' or even ''black'' spectra. We find that, compared to environments characterized by red noise, very long population persistence times are more likely for black noise. Unlike previous work incorporating a simple autoregressive model of reddened noise, our model suggests that the large variation associated with persistence in a red-noise environment limits our ability to predict the fate of particular populations subject to this noise colour. Thus, we identify the colour of noise experienced by a population (red or black) as a crucial factor in any attempt to manage or conserve that population.     

Population synchrony and environmental variation: an experimental demonstration

Understanding the causes of population synchrony is an important issue for population management. Its study in field populations involves disentangling the effects of dispersal and correlated environmental noise. Here we report on an experimental investigation of the synchronizing effects of noise in closed laboratory populations of a soil mite, Sancassania berlesei . Mite life-histories are highly plastic with respect to resource availability (which is a function of food supply and population density). By varying the food supply we imposed environmental variation. We show that (a) population synchrony is a function of environmental synchrony, (b) perceived population synchrony depends on the life-history stage counted, and (c) average population synchrony tends to be lower than environmental synchrony: even when populations were supplied with food with a correlation of 1.0, the correlation between populations was 0.63 (bootstrapped 95%CI 0.54–0.71). This supports recent theoretical work suggesting that the Moran theorem (indicating that population synchrony equals environmental synchrony) generally overestimates the population synchrony of nonlinear systems.     

A Simple Screen to Identify Promoters Conferring High Levels of Phenotypic Noise

Genetically identical populations of unicellular organisms often show marked variation in some phenotypic traits. To investigate the molecular causes and possible biological functions of this phenotypic noise, it would be useful to have a method to identify genes whose expression varies stochastically on a certain time scale. Here, we developed such a method and used it for identifying genes with high levels of phenotypic noise in Salmonella enterica ssp. I serovar Typhimurium (S. Typhimurium). We created a genomic plasmid library fused to a green fluorescent protein (GFP) reporter and subjected replicate populations harboring this library to fluctuating selection for GFP expression using fluorescent-activated cell sorting (FACS). After seven rounds of fluctuating selection, the populations were strongly enriched for promoters that showed a high amount of noise in gene expression. Our results indicate that the activity of some promoters of S. Typhimurium varies on such a short time scale that these promoters can absorb rapid fluctuations in the direction of selection, as imposed during our experiment. The genomic fragments that conferred the highest levels of phenotypic variation were promoters controlling the synthesis of flagella, which are associated with virulence and host–pathogen interactions. This confirms earlier reports that phenotypic noise may play a role in pathogenesis and indicates that these promoters have among the highest levels of noise in the S. Typhimurium genome. This approach can be applied to many other bacterial and eukaryotic systems as a simple method for identifying genes with noisy expression.     

Red environmental noise and the appearance of delayed density dependence in age-structured populations

Previous work suggests that red environmental noise can lead to the spurious appearance of delayed density dependence (DDD) in unstructured populations regulated only by direct density dependence. We analysed the effect of noise reddening on the pattern of spurious DDD in several variants of the density-dependent age-structured population model. We found patterns of spurious DDD in structured populations with either density-dependent fertility or density-dependent survival of the first age class, inconsistent with predictions from unstructured population models. Moreover, we found that nonspurious negative DDD always emerges in populations with deterministic chaotic dynamics, regardless of population structure or the type of environmental noise. The effect of noise reddening in generating spurious DDD is often negligible in the chaotic region of population deterministic dynamics. Our findings suggest that differences in species' life histories may exhibit different patterns of spurious DDD (owing to noise reddening) than predicted by unstructured models.     

Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis

Cellular signaling systems show astonishing precision in their response to external stimuli despite strong fluctuations in the molecular components that determine pathway activity. To control the effects of noise on signaling most efficiently, living cells employ compensatory mechanisms that reach from simple negative feedback loops to robustly designed signaling architectures. Here, we report on a novel control mechanism that allows living cells to keep precision in their signaling characteristics – stationary pathway output, response amplitude, and relaxation time – in the presence of strong intracellular perturbations. The concept relies on the surprising fact that for systems showing perfect adaptation an exponential signal amplification at the receptor level suffices to eliminate slowly varying multiplicative noise. To show this mechanism at work in living systems, we quantified the response dynamics of the E. coli chemotaxis network after genetically perturbing the information flux between upstream and downstream signaling components. We give strong evidence that this signaling system results in dynamic invariance of the activated response regulator against multiplicative intracellular noise. We further demonstrate that for environmental conditions, for which precision in chemosensing is crucial, the invariant response behavior results in highest chemotactic efficiency. Our results resolve several puzzling features of the chemotaxis pathway that are widely conserved across prokaryotes but so far could not be attributed any functional role.     

The learning advantage: bird species that learn their song show a tighter adjustment of song to noisy environments than those that do not learn

Song learning has evolved within several avian groups. Although its evolutionary advantage is not clear, it has been proposed that song learning may be advantageous in allowing birds to adapt their songs to the local acoustic environment. To test this hypothesis, we analysed patterns of song adjustment to noisy environments and explored their possible link to song learning. Bird vocalizations can be masked by low‐frequency noise, and birds respond to this by singing higher‐pitched songs. Most reports of this strategy involve oscines, a group of birds with learning‐based song variability, and it is doubtful whether species that lack song learning (e.g. suboscines) can adjust their songs to noisy environments. We address this question by comparing the degree of song adjustment to noise in a large sample of oscines (17 populations, 14 species) and suboscines (11 populations, 7 species), recorded in Brazil (Manaus, Brasilia and Curitiba) and Mexico City. We found a significantly stronger association between minimum song frequency and noise levels (effect size) in oscines than in suboscines, suggesting a tighter match in oscines between song transmission capacity and ambient acoustics. Suboscines may be more vulnerable to acoustic pollution than oscines and thus less capable of colonizing cities or acoustically novel habitats. Additionally, we found that species whose song frequency was more divergent between populations showed tighter noise–song frequency associations. Our results suggest that song learning and/or song plasticity allows adaptation to new habitats and that this selective advantage may be linked to the evolution of song learning and plasticity.     

On luck and sex

Sex has many costs with respect to asexual reproduction, so its ubiquity is a puzzle. There has been a continuing effort to identify general circumstances in which aspects of sex generate an evolutionary advantage over asexual reproduction. Here we focus on the generality that individuals can experience good and bad "luck" at various stages of their life history regardless of genotype, and on the interindividual nature of sex. Sexual outcrossing combines genetic information from individuals with potentially different experiences, so it is conceivable that sex might reduce the contribution of individual luck to noise in inheritance. In a simple way, we derive expressions for noise in inheritance in terms of some sources of within-generation ecological noise. We demonstrate that interindividual reproduction can indeed dampen the effects of ecological noise better than lone-individual modes, but there are conditions under which it does not. Empirical and theoretical work on plants, modeled here, suggest noise dampening conditions. Ecological noise dampening operates alongside other features of sex such as recombination and segregation and, because noise in inheritance weakens the role of selection in genetic change, we speculate that noise dampening may offer a benefit to be deducted from the costs of sex. We also suggest that the amount of selfing relative to outcrossing observed in natural populations may be influenced by the amount of individual-level ecological noise in a given habitat.     

Persistence in fluctuating environments

Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations are key factors that can facilitate or disrupt coexistence. To better understand this interplay between these deterministic and stochastic forces, we develop a mathematical theory extending the nonlinear theory of permanence for deterministic systems to stochastic difference and differential equations. Our condition for coexistence requires that there is a fixed set of weights associated with the interacting populations and this weighted combination of populations’ invasion rates is positive for any (ergodic) stationary distribution associated with a subcollection of populations. Here, an invasion rate corresponds to an average per-capita growth rate along a stationary distribution. When this condition holds and there is sufficient noise in the system, we show that the populations approach a unique positive stationary distribution. Moreover, we show that our coexistence criterion is robust to small perturbations of the model functions. Using this theory, we illustrate that (i) environmental noise enhances or inhibits coexistence in communities with rock-paper-scissor dynamics depending on correlations between interspecific demographic rates, (ii) stochastic variation in mortality rates has no effect on the coexistence criteria for discrete-time Lotka–Volterra communities, and (iii) random forcing can promote genetic diversity in the presence of exploitative interactions.

One day is fine, the next is black.—The Clash