Viability in a pink environment: why "white noise" models can be dangerous

Analysis of long time series suggests that environmental fluctuations may be accurately represented by 1/ f   noise (pink noise), where temporal correlation is found at several scales, and the range of fluctuations increases over time. Previous studies on the effects of coloured noise on population dynamics used first or second order autoregressive noise. I examined the importance of coloured noise for extinction risk using true 1/ f   noise. I also considered the problem of estimating extinction risk with a limited sample of environmental variation. Pink noise environments increased extinction risk in random walk models where environmental variation affected the growth rate. However, pink noise environments decreased extinction risk in the Ricker model where environmental variation modified the carrying capacity. Underestimation of environmental variance almost always yielded underestimation of extinction risk. For either population viability analysis or management, we should carefully consider the long-term behaviour of the environment as well as how we include environmental noise in population models.     

Extinctions in competitive communities forced by coloured environmental variation

Understanding the relationships between environmental fluctuations, population dynamics and species interactions in natural communities is of vital theoretical and practical importance. This knowledge is essential in assessing extinction risks in communities that are, for example, pressed by changing environmental conditions and increasing exploitation. We developed a model of density dependent population renewal, in a Lotka–Volterra competitive community context, to explore the significance of interspecific interactions, demographic stochasticity, population growth rate and species abundance on extinction risk in populations under various autocorrelation (colour) regimes of environmental forcing. These factors were evaluated in two cases, where either a single species or the whole community was affected by the external forcing. Species' susceptibility to environmental noise with different autocorrelation structure depended markedly on population dynamics, species' position in the abundance hierarchy and how similarly community members responded to external forcing. We also found interactions between demographic stochasticity and environmental noise leading to a reversal in extinction probabilities from under- to overcompensatory dynamics. We compare our results with studies of single species populations and contrast possible mechanisms leading to extinctions. Our findings indicate that abundance rank, the form of population dynamics, and the colour of environmental variation interact in affecting species extinction risk. These interactions are further modified by interspecific interactions within competitive communities as the interactions filter and modulate the environmental noise.     

Mischaracterising density dependence biases estimated effects of coloured covariates on population dynamics

Environmental effects on population growth are often quantified by coupling environmental covariates with population time series, using statistical models that make particular assumptions about the shape of density dependence. We hypothesized that faulty assumptions about the shape of density dependence can bias estimated effect sizes of temporally autocorrelated covariates. We investigated the presence of bias using Monte Carlo simulations based on three common per capita growth functions with distinct density dependent forms (θ-Ricker, Ricker and Gompertz), autocorrelated (coloured) ‘known’ environmental covariates and uncorrelated (white) ‘unknown’ noise. Faulty assumptions about the shape of density dependence, combined with overcompensatory intrinsic population dynamics, can lead to strongly biased estimated effects of coloured covariates, associated with lower confidence interval coverage. Effects of negatively autocorrelated (blue) environmental covariates are overestimated, while those of positively autocorrelated (red) covariates can be underestimated, generally to a lesser extent. Prewhitening the focal environmental covariate effectively reduces the bias, at the expense of the estimate precision. Fitting models with flexible shapes of density dependence can also reduce bias, but increases model complexity and potentially introduces other problems of parameter identifiability. Model selection is a good option if an appropriate model is included in the set of candidate models. Under the specific and identifiable circumstances with high risk of bias, we recommend prewhitening or careful modelling of the shape of density dependence.     

Regime shift and robustness of organism-created environments: A model for microbial ecosystems

Organism-environment interactions are different from organism-resource interactions in two respects: (1) resources can only be consumed by organisms whereas environmental conditions can be increased or decreased depending on the species; (2) high resource conditions generally stimulate the growth of organisms, whereas extreme environmental conditions are not necessarily favored because each species usually has an optimum range for growth. To investigate the properties of an organism-environment feedback system, we analyze a model for microbial ecosystems in which a single microorganism species can modify the environmental pH. We demonstrate that the equilibrium level of the environmental pH can be partially regulated at a relatively constant value even if the pH in the influx to the ecosystem changes over a wide range. For species that acidify the medium, the equilibrium pH is somewhat lower than the pH optimal for the species. The pH-stabilizing effect of microorganisms is stronger if their growth is self-limited by the environmental pH. When the influx becomes sufficiently alkaline, the population of the organism suddenly disappears and the environmental pH changes abruptly. The system shows bi-stability and hysteresis and therefore differs from a standard resource competition model composed of a single species that consumes resources.     

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.     

Calling at the highway: The spatiotemporal constraint of road noise on Pacific chorus frog communication

Loss of acoustic habitat due to anthropogenic noise is a key environmental stressor for vocal amphibian species, a taxonomic group that is experiencing global population declines. The Pacific chorus frog (Pseudacris regilla) is the most common vocal species of the Pacific Northwest and can occupy human‐dominated habitat types, including agricultural and urban wetlands. This species is exposed to anthropogenic noise, which can interfere with vocalizations during the breeding season. We hypothesized that Pacific chorus frogs would alter the spatial and temporal structure of their breeding vocalizations in response to road noise, a widespread anthropogenic stressor. We compared Pacific chorus frog call structure and ambient road noise levels along a gradient of road noise exposures in the Willamette Valley, Oregon, USA. We used both passive acoustic monitoring and directional recordings to determine source level (i.e., amplitude or volume), dominant frequency (i.e., pitch), call duration, and call rate of individual frogs and to quantify ambient road noise levels. Pacific chorus frogs were unable to change their vocalizations to compensate for road noise. A model of the active space and time (“spatiotemporal communication”) over which a Pacific chorus frog vocalization could be heard revealed that in high‐noise habitats, spatiotemporal communication was drastically reduced for an individual. This may have implications for the reproductive success of this species, which relies on specific call repertoires to portray relative fitness and attract mates. Using the acoustic call parameters defined by this study (frequency, source level, call rate, and call duration), we developed a simplified model of acoustic communication space–time for this species. This model can be used in combination with models that determine the insertion loss for various acoustic barriers to define the impact of anthropogenic noise on the radius of communication in threatened species. Additionally, this model can be applied to other vocal taxonomic groups provided the necessary acoustic parameters are determined, including the frequency parameters and perception thresholds. Reduction in acoustic habitat by anthropogenic noise may emerge as a compounding environmental stressor for an already sensitive taxonomic group.     

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。     

Environmental robustness and the adaptability of populations

Recent work has shown that genetic robustness can either facilitate or impede adaptation. But the impact of environmental robustness on adaptation remains unclear. Environmental robustness helps ensure that organisms consistently develop the same phenotype in the face of "environmental noise" during development. Under purifying selection, those genotypes that express the optimal phenotype most reliably will be selectively favored. The resulting reduction in genetic variation tends to slow adaptation when the population is faced with a novel target phenotype. However, environmental noise sometimes induces the expression of an alternative advantageous phenotype, which may speed adaptation by genetic assimilation. Here, we use a population-genetic model to explore how these two opposing effects of environmental noise influence the capacity of a population to adapt. We analyze how the rate of adaptation depends on the frequency of environmental noise, the degree of environmental robustness in the population, the distribution of environmental robustness across genotypes, the population size, and the strength of selection for a newly adaptive phenotype. Over a broad regime, we find that environmental noise can either facilitate or impede adaptation. Our analysis uncovers several surprising insights about the relationship between environmental noise and adaptation, and it provides a general framework for interpreting empirical studies of both genetic and environmental robustness.     

Colour lightness of dragonfly assemblages across North America and Europe

Dark‐coloured ectotherms absorb energy from the environment at higher rates than light‐coloured ectotherms. The thermal melanism hypothesis (TMH) states that this physical mechanism links the colour lightness of the body surfaces of ectotherms to their thermal environment and hence to their geographical distribution. Studies on different insect taxa in Europe found support for this prediction of the TMH. However, whether these results hold also for other biogeographical regions remains unclear. Here, we quantify and map the colour lightness of dragonfly species in North America and directly compare our results to previously published findings for Europe. We estimated the colour lightness of 152 North American dragonfly species from published illustrations, compiled their distribution data from the literature and combined all these data with six biologically relevant environmental variables. We evaluated the importance of phylogenetic autocorrelation for the spatial variation of mean colour lightness of dragonfly assemblages (grid cells of approximately 50 × 50 km size) by repeating all analyses also for the phylogenetically predicted component of the colour lightness of species and the species‐specific deviation from this prediction. We also accounted for spatial autocorrelation with autoregressive error models. All statistical approaches showed that dragonfly assemblages from both continents consistently tended to be darker coloured in regions with cold climates and lighter coloured in regions with warm climates. Regression slopes, however, were significantly less steep, and the amount of variance explained by environmental variables was lower for North America than for Europe. Our results highlight the importance of colour lightness for the distribution of dragonfly species, but they also indicate that idiosyncrasies of the continents modify the general pattern.     

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。     

Extinction risk, coloured noise and the scaling of variance

The impact of temporally correlated fluctuating environments (coloured noise) on the extinction risk of populations has become a main focus in theoretical population ecology. In this study we particularly focus on the extinction risk in strongly correlated environments. Here, we found that, in contrast to moderate auto-correlation, the extinction risk was highly dependent on the process of noise generation, in particular on the method of variance scaling. Such scaling is commonly applied to avoid variance-driven biases when comparing the extinction risk under white and coloured noise. We show that for strong auto-correlation often-used scaling techniques lead to a high variability in the variances of the resulting time series and thus to deviations in the subsequent extinction risk. Therefore, we present an alternative scaling method that always delivers the target variance, even in the case of strong auto-correlation. In contrast to earlier techniques, our very intuitive method is not bound to auto-regressive processes but can be applied to all types of coloured noises. We strongly recommend our method to generate time series when the target of interest is the effect of noise colour on extinction risk not obscured by any variance effects.     

Rod outer segments are designed for optimum photon detection

The proposal that rod outer segment length is optimal with respect to photon absorption and noise control is extended and tested in a number of species. We find good agreement with our optimality criterion in duplex retinae where rods act as detectors of one or a few photons, but not in all rod retinae nor in those which are exposed to significant photic environmental noise.     

Weighted averaging,logistic regression and the Gaussian response model

The indicator value and ecological amplitude of a species with respect to a quantitative environmental variable can be estimated from data on species occurrence and environment. A simple weighted averaging (WA) method for estimating these parameters is compared by simulation with the more elaborate method of Gaussian logistic regression (GLR), a form of the generalized linear model which fits a Gaussian-like species response curve to presence-absence data. The indicator value and the ecological amplitude are expressed by two parameters of this curve, termed the optimum and the tolerance, respectively. When a species is rare and has a narrow ecological amplitude — or when the distribution of quadrats along the environmental variable is reasonably even over the species' range, and the number of quadrats is small — then WA is shown to approach GLR in efficiency. Otherwise WA may give misleading results. GLR is therefore preferred as a practical method for summarizing species' distributions along environmental gradients. Formulas are given to calculate species optima and tolerances (with their standard errors), and a confidence interval for the optimum from the GLR output of standard statistical packages.Nomenclature follows Heukels-van der Meijden (1983).We would like to thank Drs I. C. Prentice, N. J. M. Gremmen and J. A. Hoekstra for comments on the paper. We are grateful to Ir. Th. A. de Boer (CABO, Wageningen) for permission to use the data of the first example.     

Bayesian methods for comparing species physiological and ecological response curves

Many ecological questions require information on species' optimal conditions or critical limits along environmental gradients. These attributes can be compared to answer questions on niche partitioning, species coexistence and niche conservatism. However, these comparisons are unconvincing when existing methods do not quantify the uncertainty in the attributes or rely on assumptions about the shape of species' responses to the environmental gradient. The aim of this study was to develop a model to quantify the uncertainty in the attributes of species response curves and allow them to be tested for substantive differences without making assumptions about the shape of the responses. We developed a model that used Bayesian penalised splines to produce and compare response curves for any two given species. These splines allow the data to determine the shape of the response curves rather than making a priori assumptions. The models were implemented using the R2OpenBUGS package for R, which uses Markov Chain Monte Carlo simulation to repetitively fit alternative response curves to the data. As each iteration produces a different curve that varies in optima, niche breadth and limits, the model estimates the uncertainty in each of these attributes and the probability that the two curves are different. The models were tested using two datasets of mosses from Antarctica. Both datasets had a high degree of scatter, which is typical of ecological research. This noise resulted in considerable uncertainty in the optima and limits of species response curves, but substantive differences were found. Schistidium antarctici was found to inhabit wetter habitats than Ceratodon purpureus, and Polytrichastrum alpinum had a lower optimal temperature for photosynthesis than Chorisodontium aciphyllum under high light conditions. Our study highlights the importance of considering uncertainty in physiological optima and other attributes of species response curves. We found that apparent differences in optima of 7.5 °C were not necessarily substantive when dealing with noisy ecological data, and it is necessary to consider the uncertainty in attributes when comparing the curves for different species. The model introduced here could increase the robustness of research on niche partitioning, species coexistence and niche conservatism.     

Colour Terms Affect Detection of Colour and Colour-Associated Objects Suppressed from Visual Awareness

The idea that language can affect how we see the world continues to create controversy. A potentially important study in this field has shown that when an object is suppressed from visual awareness using continuous flash suppression (a form of binocular rivalry), detection of the object is differently affected by a preceding word prime depending on whether the prime matches or does not match the object. This may suggest that language can affect early stages of vision. We replicated this paradigm and further investigated whether colour terms likewise influence the detection of colours or colour-associated object images suppressed from visual awareness by continuous flash suppression. This method presents rapidly changing visual noise to one eye while the target stimulus is presented to the other. It has been shown to delay conscious perception of a target for up to several minutes. In Experiment 1 we presented greyscale photos of objects. They were either preceded by a congruent object label, an incongruent label, or white noise. Detection sensitivity (d’) and hit rates were significantly poorer for suppressed objects preceded by an incongruent label compared to a congruent label or noise. In Experiment 2, targets were coloured discs preceded by a colour term. Detection sensitivity was significantly worse for suppressed colour patches preceded by an incongruent colour term as compared to a congruent term or white noise. In Experiment 3 targets were suppressed greyscale object images preceded by an auditory presentation of a colour term. On congruent trials the colour term matched the object’s stereotypical colour and on incongruent trials the colour term mismatched. Detection sensitivity was significantly poorer on incongruent trials than congruent trials. Overall, these findings suggest that colour terms affect awareness of coloured stimuli and colour- associated objects, and provide new evidence for language-perception interaction in the brain.     

Host egg pigmentation protects developing parasitoids from ultraviolet radiation

Parasites rely on their hosts not only for nutrition and reproduction, but also for protection against natural enemies and adverse climatic conditions. In host‐parasite interactions, protective characteristics of both players are important to consider regarding damaging effects of environmental hazards. While ultraviolet radiation (UVR) is pervasive and harmful to organisms in general, its impact on parasite fitness remains understudied. Moreover, studies that do examine the effects of UV exposure on parasitic organisms tend to neglect host traits, which may vary inter‐ or intra‐specifically and thus confer different levels of environmental protection. We examined in the laboratory whether the UV‐protective value of host egg pigmentation could also benefit parasitoids, using the egg parasitoid Telenomus podisi and the predatory stink bug Podisus maculiventris. This host species lays eggs of variable pigmentation levels from light to dark grey, an adaptation protecting its own embryos from UVR. We showed that higher levels of host egg pigmentation protect parasitoids subjected to a developmental exposure to UVR, increasing emergence rates by up to 86% and reducing development time by up to 4%. This protective effect of host pigmentation was context‐dependent, being less pronounced at low UVR intensity and towards the end of parasitoid development. Parasitoids that emerged from darker‐coloured eggs exposed to UVR were of slightly larger size than those developing in light‐coloured eggs, but other fitness‐related traits (fecundity, longevity, sex ratio) were unaffected. This study provides the first experimental evidence that host pigmentation can increase host suitability for parasitic organisms, and emphasizes the importance of considering trait variation in interacting species when investigating the susceptibility of ecological communities to important abiotic environmental factors.     

A test of sensory exploitation in the swordtail characin (Corynopoma riisei) based on colour matching between female prey and a male ornament

The sensory exploitation hypothesis states that pre-existing biases in female sensory systems may generate strong selection on male signals to match such biases. As environmental conditions differ between populations, sexual preferences resulting from natural selection are expected to vary as well. The swordtail characin (Corynopoma riisei) is a species in which males carry a flag-like ornament growing from the operculum that has been proposed to function as a prey mimic to attract females. Here, we investigated if female plasticity in feeding preferences is associated with plasticity in preference for an artificial male ornament in this species. Females were trained for 10 days by offering them differently coloured food items and were then tested for changes in preferences for differently coloured artificial male ornaments according to foraging experience. We found a rapid and pronounced change in female preference for the colouration of the artificial ornament according to food training. Thus our results support the possibility that sensory exploitation may act as a driving force for female preferences for male ornaments in this species.     

Dynamic phenotypic clustering in noisy ecosystems

In natural ecosystems, hundreds of species typically share the same environment and are connected by a dense network of interactions such as predation or competition for resources. Much is known about how fixed ecological niches can determine species abundances in such systems, but far less attention has been paid to patterns of abundances in randomly varying environments. Here, we study this question in a simple model of competition between many species in a patchy ecosystem with randomly fluctuating environmental conditions. Paradoxically, we find that introducing noise can actually induce ordered patterns of abundance-fluctuations, leading to a distinct periodic variation in the correlations between species as a function of the phenotypic distance between them; here, difference in growth rate. This is further accompanied by the formation of discrete, dynamic clusters of abundant species along this otherwise continuous phenotypic axis. These ordered patterns depend on the collective behavior of many species; they disappear when only individual or pairs of species are considered in isolation. We show that they arise from a balance between the tendency of shared environmental noise to synchronize species abundances and the tendency for competition among species to make them fluctuate out of step. Our results demonstrate that in highly interconnected ecosystems, noise can act as an ordering force, dynamically generating ecological patterns even in environments lacking explicit niches.     

Population dynamics and the colour of environmental noise.

The effect of red, white and blue environmental noise on discrete-time population dynamics is analyzed. The coloured noise is superimposed on Moran-Ricker and Maynard Smith dynamics, the resulting power spectra are less than examined. Time series dominated by short- and long-term fluctuations are said to be blue and red, respectively. In the stable range of the Moran-Ricker dynamics, environmental noise of any colour will make population dynamics red or blue depending the intrinsic growth rate. Thus, telling apart the colour of the noise from the colour of the population dynamics may not be possible. Population dynamics subjected to red and blue environmental noises show, respectively, more red or blue power spectra than those subjected to white noise. The sensitivity to differences in the noise colours decreases with increasing complexity and ultimately disappears in the chaotic range of the population dynamics. These findings are duplicated with the Maynard Smith model for high growth rates when the strength of density dependence changes. However, for low growth rates the power spectra of the population dynamics with noise are red in stable, periodic and aperiodic ranges irrespective of the noise colour. Since chaotic population fluctuations may show blue spectra in the deterministic case, this implies that blue deterministic chaos may become red under any colour of the noise.