Environmental noise and population dynamics of the ciliated protozoa Tetrahymena thermophila in aquatic microcosms

Population theory predicts that the reddened environmental noise, especially in combination with high population growth rate, reddens population dynamics, increases population variability and strengthens environment–population correlation. We tested these predictions with axenic populations of ciliated protozoa Tetrahymena thermophila. Populations with low and high growth rate were cultured in a stable environment, and in environments with sublethal temperature fluctuations that had blue, white and red spectra (i.e. negatively autocorrelated, uncorrelated, or positively autocorrelated, respectively). Population size and biomass of individuals were determined at 3-h intervals for 18 days.
Dynamics of all populations were reddened, suggesting that internal mechanisms can redden the population spectra. However, population dynamics were reddest, variability highest, and environment–population correlation strongest in the red environment as predicted. Contrary to theoretical predictions and previous empirical findings, population growth rate (r_max being equal to 0.05 and 0.3 h⁻¹) had no effect on population dynamics.
Mean cell size and variability of cell size were affected by the presence and type of environmental noise suggesting that the physiological consequences of variability depend on colour. Environmental variability decreased mean population size and biomass and the decrease was strongest in rapidly fluctuating blue and white environments. The latter finding implies that rapid fluctuations are physiologically stressful, an effect that is not accounted for in the basic population models.     

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.     

Poor environmental tracking can make extinction risk insensitive to the colour of environmental noise

The relative importance of environmental colour for extinction risk compared with other aspects of environmental noise (mean and interannual variability) is poorly understood. Such knowledge is currently relevant, as climate change can cause the mean, variability and temporal autocorrelation of environmental variables to change. Here, we predict that the extinction risk of a shorebird population increases with the colour of a key environmental variable: winter temperature. However, the effect is weak compared with the impact of changes in the mean and interannual variability of temperature. Extinction risk was largely insensitive to noise colour, because demographic rates are poor in tracking the colour of the environment. We show that three mechanisms-which probably act in many species-can cause poor environmental tracking: (i) demographic rates that depend nonlinearly on environmental variables filter the noise colour, (ii) demographic rates typically depend on several environmental signals that do not change colour synchronously, and (iii) demographic stochasticity whitens the colour of demographic rates at low population size. We argue that the common practice of assuming perfect environmental tracking may result in overemphasizing the importance of noise colour for extinction risk. Consequently, ignoring environmental autocorrelation in population viability analysis could be less problematic than generally thought.     

Populations embedded in trophic communities respond differently to coloured environmental noise

Noise in environmental variables is often described as 'coloured', where colour describes the exponent beta of the scaling relationship between the amplitude of variability and its frequency of occurrence (1/f(beta)). Different environments are known to have different colours and models have shown that colour can have important impacts upon population persistence and dynamics. This study advances current knowledge about the impact of environmental colour using a trophic model (consumer-resource) experiencing environmental noise (temperature) in a biologically realistic manner--derived mechanistically from metabolic scaling theory. The model demonstrates that the variability of consumers and resources can respond differently to changing environmental colour, depending upon (i) their relative ability to track and over or undercompensate for environmental changes and (ii) the relative sensitivity of their equilibria to environmental changes. These results form the basis with which to interpret differences and facilitate comparisons of the variability of ecological communities across gradients of environmental colour.     

Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations

Populations fluctuate because of their internal dynamics, which can be nonlinear and stochastic, and in response to environmental variation. Theory predicts how the colour of environmental stochasticity affects population means, variances and correlations with the environment over time. The theory has not been tested for cycling populations, commonly observed in field systems. We applied noise of different colours to cycling laboratory beetle populations, holding other statistical properties of the noise fixed. Theory was largely validated, but failed to predict observations in sufficient detail. The main period of population cycling was shifted up to 33% by the colour of environmental stochasticity. Noise colour affected population means, variances and dominant periodicities differently for populations that cycled in different ways without noise. Our results show that changes in the colour of climatic variability, partly caused by humans, may affect the main periodicity of cycling populations, possibly impacting industry, pest management and conservation.     

Accommodating environmental variation in population models: metaphysiological biomass loss accounting

1. There is a pressing need for population models that can reliably predict responses to changing environmental conditions and diagnose the causes of variation in abundance in space as well as through time. In this 'how to' article, it is outlined how standard population models can be modified to accommodate environmental variation in a heuristically conducive way. This approach is based on metaphysiological modelling concepts linking populations within food web contexts and underlying behaviour governing resource selection. Using population biomass as the currency, population changes can be considered at fine temporal scales taking into account seasonal variation. Density feedbacks are generated through the seasonal depression of resources even in the absence of interference competition. 2. Examples described include (i) metaphysiological modifications of Lotka-Volterra equations for coupled consumer-resource dynamics, accommodating seasonal variation in resource quality as well as availability, resource-dependent mortality and additive predation, (ii) spatial variation in habitat suitability evident from the population abundance attained, taking into account resource heterogeneity and consumer choice using empirical data, (iii) accommodating population structure through the variable sensitivity of life-history stages to resource deficiencies, affecting susceptibility to oscillatory dynamics and (iv) expansion of density-dependent equations to accommodate various biomass losses reducing population growth rate below its potential, including reductions in reproductive outputs. Supporting computational code and parameter values are provided. 3. The essential features of metaphysiological population models include (i) the biomass currency enabling within-year dynamics to be represented appropriately, (ii) distinguishing various processes reducing population growth below its potential, (iii) structural consistency in the representation of interacting populations and (iv) capacity to accommodate environmental variation in space as well as through time. Biomass dynamics provide a common currency linking behavioural, population and food web ecology. 4. Metaphysiological biomass loss accounting provides a conceptual framework more conducive for projecting and interpreting the population consequences of climatic shifts and human transformations of habitats than standard modelling approaches.     

Non-linear biological responses to environmental noise affect population extinction risk

Non-linearities are commonly observed in the responses of organisms to environment. They potentially modify the qualitative and quantitative properties of population dynamics. We studied how non-linear responses to environment, or "noise filters", influence population variability and extinction risk by introducing coloured noise to the growth rate in the Hassell single-species model. The consequences of noise filtering were analysed by comparing the model dynamics with linearly filtered and non-linearly filtered noise that have the same mean. Three biologically plausible filters we used: saturating, unimodal optimum type, and sigmoid responses.
Filtering can either decrease or increase population variability when compared to linear noise response. The effect of noise filtering on variability is most pronounced with stable population dynamics and the outcome depends on the filter type, population growth rate, and noise colour.
Non-linear noise filtering predominantly increases extinction risks when population growth rate is low (R<5). As an exception, saturating filter has a window of decreased risk at very low growth rate and reddened environment. In the unstable range of the dynamics (15These results suggest that accounting for the non-linear responses to environment should be considered when estimating extinction risks and population variability. Moreover, the non-linear responses make noise colour a more important factor in these analyses.     

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.     

Trophic interactions affect the population dynamics and risk of extinction of basal species in food webs

This paper addresses effects of trophic complexity on basal species, in a Lotka–Volterra model with stochasticity. We use simple food web modules, with three trophic levels, and expose every species to random environmental stochasticity and analyze (1) the effect of the position of strong trophic interactions on temporal fluctuations in basal species’ abundances and (2) the relationship between fluctuation patterns and extinction risk. First, the numerical simulations showed that basal species do not simply track the environment, i.e. species dynamics do not simply mirror the characteristics of the applied environmental stochasticity. Second, the extinction risk of species was related to the fluctuation patterns of the species.More specifically, we show (i) that despite being forced by random stochasticity without temporal autocorrelation (i.e. white noise), there is significant temporal autocorrelation in the time series of all basal species’ abundances (i.e. the spectra of basal species are red-shifted), (ii) the degree of temporal autocorrelation in basal species time series is affected by food web structure and (iii) the degree of temporal autocorrelation tend to be correlated to the extinction risks of basal species.Our results emphasize the role of food web structure and species interactions in modifying the response of species to environmental variability. To shed some light on the mechanisms we compare the observed pattern in abundances of basal species with analytically predicted patterns and show that the change in the predicted pattern due to the addition of strong trophic interactions is correlated to the extinction risk of the basal species. We conclude that much remain to be understood about the mechanisms behind the interaction among environmental variability, species interactions, population dynamics and vulnerability before we quantitatively can predict, for example, effects of climate change on species and ecological communities. Here, however, we point out a new possible approach for identifying species that are vulnerable to environmental stochasticity by checking the degree of temporal autocorrelation in the time series of species. Increased autocorrelation in population fluctuations can be an indication of increased extinction risk.     

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.     

Genetically informed ecological niche models improve climate change predictions

We examined the hypothesis that ecological niche models (ENMs) more accurately predict species distributions when they incorporate information on population genetic structure, and concomitantly, local adaptation. Local adaptation is common in species that span a range of environmental gradients (e.g., soils and climate). Moreover, common garden studies have demonstrated a covariance between neutral markers and functional traits associated with a species’ ability to adapt to environmental change. We therefore predicted that genetically distinct populations would respond differently to climate change, resulting in predicted distributions with little overlap. To test whether genetic information improves our ability to predict a species’ niche space, we created genetically informed ecological niche models (gENMs) using Populus fremontii (Salicaceae), a widespread tree species in which prior common garden experiments demonstrate strong evidence for local adaptation. Four major findings emerged: (i) gENMs predicted population occurrences with up to 12‐fold greater accuracy than models without genetic information; (ii) tests of niche similarity revealed that three ecotypes, identified on the basis of neutral genetic markers and locally adapted populations, are associated with differences in climate; (iii) our forecasts indicate that ongoing climate change will likely shift these ecotypes further apart in geographic space, resulting in greater niche divergence; (iv) ecotypes that currently exhibit the largest geographic distribution and niche breadth appear to be buffered the most from climate change. As diverse agents of selection shape genetic variability and structure within species, we argue that gENMs will lead to more accurate predictions of species distributions under climate change.     

Environmental colour intensifies the Moran effect when population dynamics are spatially heterogeneous

Evidence for synchronous fluctuations of spatially separated populations is ubiquitous in the literature, including accounts within and across taxa. Among the few mechanisms explaining this phenomenon is the Moran effect, whereby independent populations are synchronized by spatially correlated environmental disturbances. The body of research on the Moran effect predominantly assumes that environmental disturbances within a local site are serially uncorrelated; that is, successive observations in time at a particular local site are independent. Yet, many environmental variables are known to possess strong temporal autocorrelation – a character which has often been described as 'colour'. The omission of environmental colour from research on the Moran effect may be due in part to the lack of methods capable of generating sets of time series with a desired colour and spatial correlation. Here I present a novel and simple method designated as 'phase partnering' to generate such sets of time series and I investigate the combined impact of spatial correlation and environmental colour on population synchrony in two common models of population dynamics. For linear population dynamics, and for a subset of nonlinear population dynamics, coloured environments intensify the Moran effect when population dynamics are spatially heterogeneous; in coloured environments the spatial correlation between populations more closely mimics the spatial correlation between their respective environments. Given that most environmental variables are coloured, these results imply that the Moran effect may be a far more significant driver of regional-scale population and interspecific synchrony than is currently believed.     

Pink landscapes: 1/f spectra of spatial environmental variability and bird community composition

Temporal and spatial environmental variability are predicted to have reddened spectra that reveal increases in variance with the period or length sampled. However, spectral analyses have seldom been performed on ecological data to determine whether these predictions hold true in the case of spatial environmental variability. For a 50 km long continuous transect of 128 point samples across a heterogeneous cultural landscape in the Czech Republic, both habitat composition and bird species composition decomposed by standard ordination techniques did indeed exhibit reddened spectra. The values of main ordination axes have relationships between log spectral density and log frequency with slopes close to -1, indicating 1/f, or 'pink' noise type of variability that is characterized by scale invariance. However, when habitat composition was controlled for and only residuals for bird species composition were analysed, the spectra revealed a peak at intermediate frequencies, indicating that population processes that structure bird communities but are not directly related to the structure of the environment might have some typical correlation length. Spatial variability of abundances of individual species was mostly reddened as well, but the degree was positively correlated to their total abundance and niche position (strength of species-habitat association). If 'pink' noise type of variability is as generally typical for spatial environmental variability as for temporal variability, the consequences may be profound for patterns of species diversity on different spatial scales, the form of species-area relationships and the distribution of abundances within species ranges.     

Spatial ecology of large herbivore populations

Models of the dynamics of large herbivore populations represent density feedbacks on the population growth rate either directly or indirectly through interactions with vegetation resources. Neither approach incorporates the spatial heterogeneity that is an essential feature of most natural environments, and modifies the population dynamics generated. This is especially true for large herbivores exploiting food resources that are rooted in space but temporally variable in quantity and quality both seasonally and annually. In this review I explore how environmental variation at different spatiotemporal scales influences the abundance of herbivore populations controlled via resources, predators or social mechanisms. Changes in abundance can be spatially disparate and dependent on different resource components at different stages of the seasonal cycle, including buffer resources restricting population crashes in extremely adverse years. GPS telemetry enables movement responses generating spatial patterns to be documented in fine spatiotemporal detail, including migration and dispersal. Models incorporating spatial heterogeneity either implicitly or explicitly are outlined, exemplifying how herbivores cope with temporal variability by exploiting spatial variability in resources and conditions. Global human dominance is generating widened climatic variation while opportunities for herbivore movements are becoming constricted. Theoretical population ecologists need to shift their focus from the workings of demographic structure towards effects of changing environmental contexts, in order to project the likely trajectories of large herbivore populations through the Anthropocene.     

Adaptive host preference and the dynamics of host-parasitoid interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) "ideal free" parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) "evolving" parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

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。     

Metapopulation structure of the specialized herbivore Macrosiphoniella tanacetaria (Homoptera,Aphididae)

We investigated population dynamics, genetic diversity and spatial structure in the aphid species Macrosiphoniella tanacetaria, a specialist herbivore feeding on tansy, Tanacetum vulgare. Tansy plants (genets) consist of many shoots (ramets), and genets are grouped in sites. Thus, aphids feeding on tansy can cluster at the level of ramets, genets and sites. We studied aphid population dynamics in 1997 and 2001 and found that within sites: (i). at any time, aphids used only a fraction of the available ramets and genets; (ii). at the level of ramets, most aphid colonies survived only one week; (iii). at the level of genets, mean survival time was less than 4 weeks; and (iv). colonization and extinction events occurred throughout the season. We sampled aphids in seven sites in the Alsace region, France (4-45 km apart) and two sites in Germany in 1999 to study genetic structure within and between populations. Genetic analyses using nine microsatellite loci showed that: (i). genotypic variability was high, (ii). none of the populations was in Hardy-Weinberg equilibrium, (iii). heterozygote deficits and linkage disequilibria were frequent, and (iv). all populations were genetically differentiated, even at a small geographical scale. Renewed sampling of the Alsace sites in 2001 showed that three populations had become extinct and significant genetic changes had occurred in the remaining four populations. The frequencies of extinction and colonization events at several spatial scales suggest a hierarchical metapopulation structure for M. tanacetaria. Frequent population turnover and drift are likely causes for the genetic differentiation of M. tanacetaria populations.     

Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

Adaptive Host Preference and the Dynamics of Host–Parasitoid Interactions

Models of two independent host populations and a common parasitoid are investigated. The hosts have density-dependent population growth and only interact indirectly by their effects on parasitoid behavior and population dynamics. The parasitoid is assumed to experience a trade-off in its ability to exploit the two hosts. Three alternative types of parasitoid are investigated: (i) fixed generalists whose consumption rates are those that maximize fitness; (ii) “ideal free” parasitoids, which modify their behavior to maximize their rate of finding unparasitized hosts within a generation; and (iii) “evolving” parasitoids, whose capture rates change between generations based on quantitative genetic determination of the relative attack rates on the two hosts. The primary questions addressed are: (1) Do the different types of adaptive processes stabilize or destabilize the population dynamics? (2) Do the adaptive processes tend to equalize or to magnify differences in host densities? The models show that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.     

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.