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Ecological and evolutionary dynamics under coloured environmental variation
Review
Ecological and evolutionary dynamics under coloured environmental variation Lasse Ruokolainen, Andreas Linde´n, Veijo Kaitala and Mike S. Fowler Integrative Ecology Unit, Department of Biological and Environmental Sciences, PO Box 65 (Viikinkaari 1), FIN-00014 University of Helsinki, Finland
Environmental variation is a ubiquitous component of individual, population and community processes in the natural world. Here, we review the consequences of spatio-temporally autocorrelated (coloured) environmental variation for ecological and evolutionary population dynamics. In single-species population models, environmental reddening increases (decreases) the amplitude of fluctuations in undercompensatory (overcompensatory) populations. This general result is also found in structurally more complex models (e.g. with space or species interactions). Environmental autocorrelation will also influence evolutionary dynamics as the changing environment is filtered through ecological dynamics. In the context of long-term environmental change, it becomes crucial to understand the potential impacts of different regimes of environmental variation at different scales of organization, from genes to species to communities. Natural populations exist in fluctuating environments Organisms in the natural world are constantly buffeted by exogenous forces that lead to changes in their population density. The term ‘environmental stochasticity’ reflects the unpredictability of the environment, generally encompassing a broad spectrum of variables that can change over time and space, affecting the birth, death and migration processes of individuals within a population. Typical examples of these variables include climatic factors, availability of light, nutrients and food, and water salinity. Recent changes in global climatic conditions [1] raise questions about the consequences of large-scale climatic forcing on ecosystems. Evidence is accumulating of unexpected responses to environmental perturbations and to human activities in ecosystems [2,3], particularly in combination with the loss and fragmentation of habitats [4]. In 1996, Halley [5] highlighted the importance of considering the temporal structure of environmental timeseries in ecological and evolutionary modelling. As well as changes in features such as the mean and variance of a stochastic variable, he pointed out that temporal structure was apparent in various natural and human-induced timeseries. Here, we review the progress that has been made in the fields of ecology and evolutionary biology since Halley’s ‘call to arms’. Corresponding author: Ruokolainen, L. ([email protected]).
The temporal structure (i.e. colour) of a time-series can be characterized in several ways, including the frequency spectrum and autocorrelation structure (Box 1). We focus on the impact of coloured noise [5,6] on ecological dynamics across different levels of organizational complexity and examine the effect of coloured noise in evolutionary dynamics. We highlight the need for more attention to be paid to examining the importance of environmental colour in the interaction between ecological and evolutionary dynamics. In general, natural environmental variation is thought to be positively autocorrelated (pink or red in colour) [11], that is, consecutive observations in a time-series are expected to be similar [12]. However, it is possible that long-term climate change will change natural regimes of environmental fluctuations [13,14], which might hamper predictions of population and community responses to environmental changes. This has consequences for the management of natural populations, including commercial fisheries, conservation projects, forestry, pest control and hunting. In addition, it can be difficult to predict population and community responses to environmental fluctuations if the mechanism (i.e. how environmental variables translate into population dynamical processes) is unknown [15]. How different environmental scenarios affect community stability depends on species demography [16], between-species interactions and community size [17,18], and the ecological role of community members [19]. As we discuss here, these issues call for a more detailed understanding of the underlying dynamical mechanisms in natural communities. The temporal structure of environmental variation in natural systems Many climatic variables have temporally reddened spectra and marine time-series are, in general, more reddened than terrestrial ones [11,20]; this is because large water bodies can buffer much of the rapid variation present in terrestrial locations [11]. Despite this generality, climatic processes that exhibit blue-shifted temporal dynamics do exist, such as the El Nin˜o Southern Oscillation with lags of 12–24 months [21]. The colour of an environmental variable depends on the timescale considered [22] (Figure 1); thus, this should be chosen carefully with respect to the life cycle of the focal organisms. The temporal structure of physical environments can also have anthropogenic causes. A simple example comes from the regulation of
0169-5347/$ – see front matter ß 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tree.2009.04.009 Available online 21 August 2009
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Box 1. Models of coloured environments Temporal environmental variation is usually modelled as a coloured process [5,6], in analogy with visible light, where different dominant frequencies in a stochastic time-series correspond to different colours. In blue noise, changes occur rapidly (high frequencies dominate), red indicates slow changes (low frequencies dominate), whereas no frequencies dominate in white noise. Such processes are most frequently modelled in the time domain using discrete time autoregressive (AR) processes, but can alternatively be considered in the frequency domain using sinusoidal (1/f) processes [5]. An AR process, describing an environmental variable e, can be modelled as (Equation I) [6]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi etþ1 ¼ ket þ vt 1 k2 ; [Equation I] where v is a random standard normal variable. Owing to the square root term, the variance of e will remain at unity, independent of its autocorrelation (k) [7,8]. The process produces blue noise when k < 0, red noise when k > 0, and white noise when k = 0 (Figure I).
An alternative for AR-processes is sinusoidal (1/f) processes [5]. In general, this can be used for theoretical studies as an alternative for white noise. Sinusoidal noise (1/f) time-series can be generated by summing random-phase (uf) sine waves following the power law amplitude = 1/fb/2, where f is the frequency and b is the spectral exponent [9], giving Equation II Ft ¼
n=2 X f ¼1
1 f
b=2
sin
2p ft þuf ; n
[Equation II]
where t is the time unit and n is period length. b < 0 generates blue noise (Figure Ia), b = 0 results in white noise (Figure Ib) and b > 0 leads to reddened noise. Depending on the value of parameter b, 1/f noise can be called pink (Figure Ic), brown, or black (Figure Id) [10]. The autocorrelation (k) or the spectral exponent (b) can both be estimated from natural time-series (e.g. Figure Ie). The estimated colour is likely to be biased towards white in variables containing measurement error because such errors are usually temporally uncorrelated.
Figure I. Models of coloured environments. (a–d) Typical coloured noise time-series, generated using autoregressive (Equation I, darker lines) or 1/f methods (Equation II, lighter lines): (e) The annual North Atlantic Oscillation (NAO) index from 1822 to 2000 is approximately white. Autocorrelation coefficients (k) and spectral exponents (b) for time-series are embedded in the figure. In (e), these statistics are estimated from the NAO time-series, whereas in (a–d) they represent parameters in Equations I and II.
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Figure 2. Anthropogenic action leading to variation in the colour of environmental conditions. (a) Temporal variation in the water level (m above sea level) at Lokka reservoir (67849’ N, 27844’ E) in northern Finland during 1968–2008. The surface area of the lake varies between 216 m2 and 418 m2 owing to regulation of the water level. Until mid-1981 (red line), autocorrelation in water-level variation was significantly positive (k = 0.72); since then (black line), the variation has had zero autocorrelation (estimates based on samples taken every fourth month). This switch is due to a change in the regulation pattern. Data provided by Finnish National Environmental Institute (SYKE). (b) Three of the most important fish species in the Lokka reservoir. The breeding success of two of these species [(i) white fish (Coregonus lavaretus) and (ii) pike (Esox lucius)] depends on shallow water habitats, thus regulation of the water level will affect the amount of available breeding habitat. The third species is perch (Perca fluviatilis) (iii). Reproduced with permission from the Finnish Game and Fisheries Research Institute. Figure 1. Dependence of observed temporal autocorrelation on the scale and period of investigation, as well as on chance (sampling effects). The sample autocorrelation coefficients (k) for the North Atlantic Oscillation (NAO) are estimated with sliding time-windows of varying length. The (a) annual NAO (from 1822 to 2008) and (b) monthly NAO (1993–2008) are considered. The investigated time period is defined by the time of the first observation (X-axis; unit year) and time-series length [Y-axis; the time-units are (a) year and (b) month]. Different colours refer to different sample autocorrelations; blue indicates k < 0, whereas red indicates k > 0.
water level at the Lokka reservoir in northern Finland (Figure 2a), which leads to variation in the available habitat volume of economically significant fish species (Figure 2b). Increases in the frequency and severity of extreme climatic events have been predicted [1], which will also change the colour of environmental variables in the future. The general patterns of temporal structure in biotic and abiotic environmental factors might also differ from each other [23]. For example, mast seeding events [24] can create blue-shifted resource environments for granivorous animals. As we discuss next, coloured environmental variation can interact with population processes, with
important consequences for the resulting population dynamical patterns. Single-species populations in coloured environments The behaviour of unstructured single-species population models in coloured environments has been studied intensively [6,7,25–36]. Much of the research has concentrated on the risk of population extinction under different environmental conditions, which generally involves considering the colour and/or variance of population fluctuations over time. The observed responses depend on model assumptions; for example, how population demography is influenced by the environment [15,37] (Box 2). However, one general pattern that emerges is that noise colour interacts with density dependence to produce the observed response [23,32]. A population with undercompensating growth reacts slowly to environmental changes (i.e. has reddened dynamics) [32]. By contrast, an overcompensating population rapidly 557
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Box 2. How does environment affect population demography? In population models, environment variation is often assumed to affect individuals equally, through the rates of reproduction, mortality or dispersal. One modelling approach is to alter the percapita growth rate ( pgr) by multiplying the deterministic model prediction with exp(bet) [40], where et is environment at time t and b is its effect (Figure I). For example, in the Ricker model, we would have Equation I: N tþ1 ¼ N t exp½rð1 N t =K Þexpðbet Þ:
[Equation I]
where N is the population size, r is the intrinsic growth rate and K the carrying capacity. The distribution of exp(bet) is log-normal with expected value one, when e N(–(bs)2/2, s2). For a specific environmental variable (say, X in the place of e), a multiple regression model with the pgr = ln(Nt+1/Nt) as the response, and Nt and Xt as explanatory variables, corresponds to this model and can be used to estimate the strength of the environmental effect b. Environmental factors can also affect the amount of suitable habitat or intraspecific competition (density dependence). These two features are related: the strength of density dependence determines the carrying capacity in many models (e.g. Equation I). Again, we can consider the environmental effect as being multiplicative. This can be modelled with a temporally varying carrying capacity Kt = Kmexp(bet), where Km is the mean of Kt (Figure Ib). If the environment affects density dependence specifically, the term exp(bet) in Equation I can be replaced with exp(betNt). Here, b can also be estimated using multiple regression with NtXt as an explanatory variable instead of Xt. The environment can influence both pgr and K simultaneously. In statistical detection of environmental effects it is desirable to use models that consider the underlying demographic mechanisms. Investigation of simple correlations between population density and environment can be misleading in many biologically realistic scenarios, such as age-structured populations of semelparous breeders, where the juveniles are subject to environmental forcing [41].
Figure I. Variation in the relationship between population density and per-capita growth according to how the environment affects demography. The environment affects (a) per-capita growth rate ( pgr) or (b) carrying capacity (K, Equation I). The black solid lines represent average relationships and dotted lines show et = 1s. Gray shading indicates log-normal probability distributions of r and K, whereas black dots are their mean values (r = 1.2; K = 250).
overshoots the equilibrium after a perturbation, displaying blue dynamics. The qualitative nature of these dynamics is not altered by different colours of environmental fluctuations [23], which has been experimentally confirmed for undercompensating populations [38,39]. An exactly compensating population is a special case, where the population will closely track the environmental fluctuations and thus express a colour equal to that of the environment [23]. The amplitude of population fluctuations is also affected by environmental colour [29,31–33,42], with direct consequences on extinction risk [30,31,42]. In general, fluctuations in population density are amplified (dampened) in undercompensatory (overcompensatory) single-species populations with increasing environmental reddening [29,31] (Figure 3). Differences in this result that have previously been found under different models for environmental uncertainty (AR- or 1/f -type noise-generating 558
methods, see Box 1) can be understood through differences in the environmental variance rather than in noise colour per se. When age or stage structure is introduced to singlespecies population dynamics, extinction risk becomes dependent on the underlying mechanisms of population renewal; the relationship between density dependence and noise colour also varies with life-history characteristics, such as fecundity and longevity [27,43,44]. Adding structural complexity in the form of life histories potentially breaks down the general relationship between density dependence and noise colour observed in unstructured populations (Figure 3), but more work is required to uncover the extent of general relationships. Differences can arise because there are several possible routes for environmental stochasticity to affect population renewal [44] (e.g. different life stages are affected differently by stochasticity).
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Box 3. Coloured noise in communities Simple community dynamics can be described by the multi-species version of the Ricker model (Equation I): S 1 X N i; tþ1 ¼ N i; t exp r i 1 ai j N j;t expðet þ mi;t Þ; K i j¼1
Figure 3. Preservation of qualitative patterns in the relationship between ensemble P variability ( Ni,t) and environmental reddening with increasing structural complexity in population models. As environmental variation becomes more red (autocorrelation k increases), it interacts with density-dependent feedback to increase or decrease the size of population fluctuations; dependent on whether the intrinsic population dynamics are under- (r = 0.5, Equation I in Box 2; red lines) or over-compensatory (r = 1.8; blue lines), respectively. This relationship holds for single species, single patch populations (dotted lines); single species populations spread over a chain of 25 patches, linked by density-independent stepping-stone dispersal (solid lines; 10% of each patch distributed between the two nearest neighbours following reproduction each generation); or with competitive interactions in a five species community (dashed lines; Equation I in Box 3, aij values drawn randomly from a b distribution with mean 0.1 [p = 1, q = 9]). Results show the mean variance of the simulated ensemble population density based on 200 repetitions run over 200 time-steps for each parameter value. All populations were initiated at their equilibrium density.
In a spatial context, the environmental colour affects population extinction risk through a combination of population variability and synchrony between subpopulations [45,46]. In a homogeneous landscape, increased reddening in the environment increases subpopulation variability (local extinction risk) in undercompensatory populations [47], as well as synchrony between subpopulations (and probability of global extinction). As with single-patch populations, the opposite effect is seen in overcompensatory populations (Figure 3). The situation is different in heterogeneous landscapes, with environmental reddening reducing population persistence time for under- and overcompensatory dynamics [30]. Single-species models have provided a valuable foundation for the impacts of coloured environmental variation. However, it has been unclear if they are adequate in predicting the behaviour of more complex systems, such as those that incorporate species interactions. Species interactions in coloured environments Recent efforts have tried to understand how community organization interacts with coloured environmental variation in affecting population variability. These studies commonly use the Lotka–Volterra community framework to model interspecific competition or predator–prey inter-
[Equation I]
where Ni,t is the density of the ith species at time t, ri is its intrinsic growth rate, Ki its carrying capacity and S is the number of species in the community. Parameter aij gives the per capita effect of species j on the renewal of species i. By changing the sign of a, one can model different types of species interaction (e.g. competition, mutualism or predation) but this should be accompanied by appropriate changes in ri. Variables e and m represent global (common for all species) and species-specific (independent) noise, respectively [52]. Alternatively, the sum of e and m can be considered as one noise term, where the relative strength of e and m results in the realized between species covariance (environmental correlation). Depending on the community structure (a, K and r) and the colour of environmental stochasticity, the similarity in species-specific responses to the environment can have a strong impact upon community dynamics (e.g. Ref. [53]). For example, whereas increasing environmental reddening increases the degree of asynchrony between community members (which can have a destabilizing influence on community biomass [54]), increasing environmental correlation increases between-population synchrony [53].
actions (Box 3). When scaling up from single-species systems to multi-species communities, network structure can modulate the interaction between noise properties and population processes [48–51]. Species networks can be structured in different ways, depending, for example, on the type, shape and strength of species interactions, species-specific demographic rates and the similarity between species-specific responses to environmental variation. All of these factors can modify the effect of environmental reddening. The observed red spectra of natural populations [55] are a potential consequence of the trophic position of the species [50]. That is, species on top of a food chain should show more red dynamics than those at the bottom because population growth rates decrease with increasing trophic level. The degree of similarity between species-specific responses to environmental forcing (environmental correlation) also influences the colour and variability of population dynamics [54,56–58]. Population autocorrelation tends to increase with environmental reddening independently of the strength of density dependence and environmental correlation, although the degree of change is affected by these features. Whether population variability increases (or decreases) with environmental reddening depends on population density dependence and environmental correlation. Competitive communities are ensembles of species competing for resources at the same trophic level. When such communities are dominated by relatively weak interspecific interactions (considered to be a realistic assumption [59]), their populations respond to environmental reddening in the same way as predicted by single-species population models (Figure 3), independently of environmental correlation between species. If community members interact more strongly, the effect of environmental reddening on overcompensating populations depends on 559
Review environmental correlation; independent responses to the environment increase variability in association with environmental reddening, whereas correlated responses lead to decreased variability [44,56,58,60]. The exact relationship between environmental reddening and population variability further depends on the severity of environmental stochasticity [58], which also has an impact upon between-population synchrony. Population synchrony is decreased by environmental reddening and stronger noise, and increased by increasing environmental correlation [44,58]. Consideration of population synchrony, especially at the community level, is particularly relevant when addressing the impact of environmental stochasticity on biomass stability in communities [54,58]. Trophic interactions can also modify population responses to environmental variation [49,50,54,61]; for example, a simple consumer–resource model echoes results reported for single-species systems [61] (Figure 3). Variability in the resource population (overcompensatory) decreases whereas that in the consumer population (undercompensatory) increases with environmental reddening. In food chains, population colour is reddened up the chain, independently of noise colour, if all species are influenced by stochasticity [49,50]. If only one species is sensitive to environmental fluctuations, this species always has a red spectrum [50]. In general, the population response to environmental reddening is affected by noise amplitude, the focal trophic level and whether the population is directly or indirectly affected by stochasticity [50]. Whether environmental correlation has an effect on these patterns remains an open question. Despite the important role of spatial processes that has been demonstrated for single population models, few studies have considered the effect of coloured noise on model results in metacommunities, where multiple species interact across a spatial network [62]. In open single-patch models, with density-independent immigration, environmental reddening impacts upon biomass stability by decreasing species diversity [18,63]. Biomass stability tends to be affected more by environmental reddening (which increases biomass fluctuations) than by increases in community size (which reduce biomass fluctuations) [18]. The relationship between noise colour and species diversity is sensitive to immigration rate in a competitive metacommunity, such that diversity increases with environmental reddening when immigration rate is low, whereas a high immigration rate leads to the opposite trend [63]. Research on stochastic environmental processes in metacommunities is in its infancy, and future research will show if spatially explicit models will change these predictions. Empirical work is necessary to validate and refine the predictions of theoretical models, but surprisingly few studies exist. Environmental reddening (realized through artificial mortality) decreases population persistence time in experimental, single-species microcosms [64], as expected by theory in undercompensating populations. Examination of open-sink populations of protists (artificial dispersal to low-quality conditions) showed that red 560
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fluctuations in habitat quality can decrease population extinction risk, also matching relevant theoretical predictions [47]. Results from microbial communities indicate that reddened environmental variation increases species diversity [65,66], as compared with white or blue environmental variation. These empirical examples give some early support to theoretical results, but more work is required. As with single-species models, increasing structural complexity is likely to change the above general responses of communities to environmental reddening (Figure 3). Further work is required for a better understanding of the impact of coloured environmental variation on multispecies assemblages. Evolutionary impacts of coloured environments Given the importance of the colour of environmental variation for population fluctuations, environmental colour will also have important effects on evolutionary processes [5]. In practice, it will directly affect the prevalence and duration of genetic bottleneck effects (i.e. periods of stronger genetic drift). Currently, understanding of how environmental reddening might influence the interplay of ecological and evolutionary processes is limited [67–70] and few studies have considered evolution through ecological dynamics in coloured environments [71,72]. Resolving the interaction of ecological and evolutionary dynamics will be crucial to understand fully the potential influence of global climate change on existing species and communities. In theory, temporal structure is likely to be an important aspect of environmental variability that contributes to shaping age- and stage-specific patterns of survival probabilities in nature [69]. Reddened environmental variation can lead to sustained reductions in population size, eventually resulting in a loss of genetic variance, which substantially reduces the ability of the population to respond to future selective challenges [73]. This can cause a population to lag behind the optimum phenotype, increasing the risk of extinction [73]. By contrast, positively autocorrelated changes in the optimum phenotype allow for increased additive genetic variance, which in turn enables the mean phenotype of a population to track the optimum more closely (compared with white or blue environments [74]) reducing evolutionary load [total genetic load on a population is defined as the expected loss of mean Malthusian fitness (intrinsic population growth rate; Ref. [68]) owing to genetic and evolutionary factors] [68]. Additive genetic variance is most effective in reducing the total load when populations exhibit highly reddened fluctuations and high variance. Moreover, no empirical data exist to date to validate these predictions. Evolutionary change also has inevitable effects on longterm population dynamics. Population performance is likely to lag continuously behind the optimum, depending on the adaptive capacity of a species [73]. Changes in fitness could, in practice, be expressed as evolving intrinsic growth rates or density-dependent effects. This could result in covariation between environment, population dynamics and evolution, which cannot be understood by modelling these components separately. This topic has been neglected owing to the tradition of considering
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Box 4. Environmental variation in quantitative genetics Environmental variation is likely to affect the phenotype of individuals in several ways that are worth considering when looking at the effects of environmental colour. Phenotypic variation in a quantitative trait can be partitioned between its genetic and environmental components as Equation I [76]: V P ¼ V G þ V E þ V GE þ 2COV ðG; EÞ;
[Equation I]
where VG and VE represent the components of variance in phenotype resulting from genetic and environmental effects, respectively. VGE is the non-additive interaction between genotypic and environmental effects. An example of such genetically determined individually varying responses (reaction norms) to given conditions is antibiotic resistance in bacteria. COV(G, E) is the covariance between genotypic and environmental sources of variances. Such covariation can arise, for example, through genetically determined habitat preferences if the habitats show variable microclimates. In the context of evolutionary models, eventual evolution of all these aspects should also be considered. Covariation between population dynamics and environmental fluctuations boost or dampen population variability depending on the sign of this covariation [31]. Similarly, covariation between genotypes and environmental effects can inflate or reduce variation in a quantitative character depending on whether genetic and environmental influences reinforce or oppose one another [76]. This implies that spatio-temporal autocorrelation in environmental variation is likely to influence patterns of phenotypic variation. The spatial dimension appears to be particularly important for population genetics. For example, dispersal into new habitats can rapidly change the genetic makeup of populations during range expansion owing to strong genetic drift on the edge of expansion [77]. Dispersal can also lead to local allele fixation [75] and temporal environmental reddening can increase genetic diversity in a spatial network in connection with genetic drift [71], in contrast with earlier results from models incorporating serially uncorrelated white noise. Environmental and spatial autocorrelation have both been shown to affect the evolution of density-dependent dispersal [72], which can influence overall genetic differentiation in a population.
population genetics separately from population dynamics. However, recent advances show promise of an integrated theory [71,75] (Box 4). Prospects Models and empirical work have provided insight into some general eco-evolutionary patterns caused by coloured environmental variation. There is a recent trend towards being more mechanistic in the assumptions about stochasticity (this being the case in theoretical, experimental and statistical population studies). To move understanding forward of the true impact of coloured environmental variation in eco-evolutionary patterns, future research must explicitly consider how the environment will affect populations. For example, Box 2 presents an approach to modelling densitydependent and -independent environmental effects. The Ricker model (Box 2) can also be reformulated in terms of birth and death rates that can be independently subjected to environmental stochasticity [78]. We can improve our ability to make quantitative predictions of dynamical patterns (e.g. extinction risk) by accounting for other potentially important mechanisms of stochasticity, such as demographic stochasticity and heterogeneity in vital rates [79]. We now highlight three more specific directions where further investigation will enhance our understanding of the interplay between natural systems and coloured environmental variation.
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Interaction between ecological and evolutionary dynamics Perhaps the greatest theoretical challenge is to merge the two fields of population ecology and population genetics, which combine to drive the evolutionary trajectory of species. Models that integrate population genetics and dynamics (e.g. dependence on frequency and density) will enable researchers to address questions about the mechanisms of species adaptation to fluctuating environments and how the colour of these fluctuations influences this process. Early progress indicates that environmental colour will interact with genetic drift; environmental reddening has been shown to reinforce genetic differentiation across a spatially structured landscape [71]. The next step is to ask if selective changes in the gene pool could also be affected by different regimes of environmental variation. Community structure, environmental correlation and spatial structure Previous work combining community dynamics and environmental autocorrelation has concentrated on simple communities where species tend to be equivalent in their demographic traits and their species-specific responses to environmental stochasticity. Results from these simple communities will help to understand those from more complex models. Directions for further research include: relaxing overly simplistic assumptions in competitive systems (e.g. looking at non-uniform covariance patterns in between-species responses to environmental variation); exploring the relationship between noise colour and patterns in environmental correlation within and between trophic levels; investigating other functional forms in species interactions; and considering systems with nonequilibrium dynamics [80]. A related challenge is to unravel how populations and communities respond to dispersal and spatially autocorrelated environmental fluctuations. Empirical challenges Most time-series of natural populations consist of proxies or correlates of population densities, not exact population counts or densities. Ignoring observation error in statistical investigation of these systems is known to bias the estimated strength of density dependence [81] and, potentially, the effects of environmental factors [82]. To empirically assess how environmental colour affects population dynamics (Figure 3), not only must the relevant environmental factors be appropriately recognized and quantified, but the level of compensation (density dependence) must also be estimated correctly. More precise statistical estimates of density dependence [81] and environmental effects [82] can be achieved using state-space models, separating process and observation error in empirical time-series. Another empirical challenge related to combining ecological and evolutionary dynamics is statistical investigation of these systems using multiple sources of data. Time-series of population densities and quantitative traits (or allele frequencies) potentially contain synergistic information about each other. Low population size can result in rapid evolution owing to genetic drift (‘bottlenecks’); strong selection in a quantitative trait might result in population 561
Review decrease owing to loss of poorly adapted individuals. Statistical models for these purposes must usually be explicit about mechanisms of biological and data observation processes, and be tailored for each specific situation. Such specific (and sometimes complicated) hierarchical models can be technically difficult to evaluate. At present, Bayesian statistics using Markov Chain Monte Carlo simulation provides the easiest framework for constructing and fitting such models [83]. Conclusions The interplay between internal population dynamics, community structure [48,56] and external noise processes [23] produces various responses in population dynamics. One general result, observed in single-species models and simple generalizations of such, including spatial and interspecific interactions, is that reddening of environmental variation increases (decreases) the amplitude of population fluctuations in systems with undercompensatory (overcompensatory) dynamics (Figure 3). The structure of density-dependent feedbacks and the strength and colour of environmental variation interact to modify the impact of environmental variation on population fluctuations. Other factors affecting the impact of coloured environmental variation include differential (e.g. species- or stagespecific) responses to temporal disturbances, species identities in food webs and spatial structuring of populations. One implication is that observed spectra in population time-series tell little about the relative contribution of the internal and external factors impacting upon these populations [41,53], without considering the biotic and abiotic interactions that modify population responses. Development and application of stronger statistical methods, accounting for observation error (state-space models) and integrating several potentially synergistic sources of data (Bayesian methods) is needed to disentangle empirically the mechanisms behind population behaviour. Future challenges are encouraged to concentrate on understanding responses to the environment at the level of the individual. This will be followed by building across levels of organization to understand how interactions within and between species and within and between population patches will modify changes to the environment. For example, how food webs with different structures respond to coloured noise and how explicit spatial structure can alter the dynamics of single species or communities from those observed in single patch systems. In addition, the environmental covariance structure within a community also remains an undeveloped area for future research. A major current concern in population ecology is how local and global processes in the climate will change in the future. Complex natural systems can show unexpected responses if the natural disturbance regimes are altered by human activities. Further investigation of the impact of coloured environmental variation is urgently required, to understand how natural populations will respond to long- and shortterm changes in the biotic and abiotic environment. Acknowledgements We dedicate this article to our colleague, teacher and friend Esa Ranta. We thank Jouni Laakso, Justin Travis and two anonymous reviewers for 562
Trends in Ecology and Evolution Vol.24 No.10 comments that helped to improve the manuscript. A.L. and M.S.F. received funding from the Nordic Centre of Excellence EcoClim project and Helsinki University. L.R. was funded by the Jenny and Antti Wihuri Foundation.
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Ecological and evolutionary dynamics under coloured environmental variation Lasse Ruokolainen, Andreas Linde´n, Veijo Kaitala and Mike S. Fowler Integrative Ecology Unit, Department of Biological and Environmental Sciences, PO Box 65 (Viikinkaari 1), FIN-00014 University of Helsinki, Finland
Environmental variation is a ubiquitous component of individual, population and community processes in the natural world. Here, we review the consequences of spatio-temporally autocorrelated (coloured) environmental variation for ecological and evolutionary population dynamics. In single-species population models, environmental reddening increases (decreases) the amplitude of fluctuations in undercompensatory (overcompensatory) populations. This general result is also found in structurally more complex models (e.g. with space or species interactions). Environmental autocorrelation will also influence evolutionary dynamics as the changing environment is filtered through ecological dynamics. In the context of long-term environmental change, it becomes crucial to understand the potential impacts of different regimes of environmental variation at different scales of organization, from genes to species to communities. Natural populations exist in fluctuating environments Organisms in the natural world are constantly buffeted by exogenous forces that lead to changes in their population density. The term ‘environmental stochasticity’ reflects the unpredictability of the environment, generally encompassing a broad spectrum of variables that can change over time and space, affecting the birth, death and migration processes of individuals within a population. Typical examples of these variables include climatic factors, availability of light, nutrients and food, and water salinity. Recent changes in global climatic conditions [1] raise questions about the consequences of large-scale climatic forcing on ecosystems. Evidence is accumulating of unexpected responses to environmental perturbations and to human activities in ecosystems [2,3], particularly in combination with the loss and fragmentation of habitats [4]. In 1996, Halley [5] highlighted the importance of considering the temporal structure of environmental timeseries in ecological and evolutionary modelling. As well as changes in features such as the mean and variance of a stochastic variable, he pointed out that temporal structure was apparent in various natural and human-induced timeseries. Here, we review the progress that has been made in the fields of ecology and evolutionary biology since Halley’s ‘call to arms’. Corresponding author: Ruokolainen, L. ([email protected]).
The temporal structure (i.e. colour) of a time-series can be characterized in several ways, including the frequency spectrum and autocorrelation structure (Box 1). We focus on the impact of coloured noise [5,6] on ecological dynamics across different levels of organizational complexity and examine the effect of coloured noise in evolutionary dynamics. We highlight the need for more attention to be paid to examining the importance of environmental colour in the interaction between ecological and evolutionary dynamics. In general, natural environmental variation is thought to be positively autocorrelated (pink or red in colour) [11], that is, consecutive observations in a time-series are expected to be similar [12]. However, it is possible that long-term climate change will change natural regimes of environmental fluctuations [13,14], which might hamper predictions of population and community responses to environmental changes. This has consequences for the management of natural populations, including commercial fisheries, conservation projects, forestry, pest control and hunting. In addition, it can be difficult to predict population and community responses to environmental fluctuations if the mechanism (i.e. how environmental variables translate into population dynamical processes) is unknown [15]. How different environmental scenarios affect community stability depends on species demography [16], between-species interactions and community size [17,18], and the ecological role of community members [19]. As we discuss here, these issues call for a more detailed understanding of the underlying dynamical mechanisms in natural communities. The temporal structure of environmental variation in natural systems Many climatic variables have temporally reddened spectra and marine time-series are, in general, more reddened than terrestrial ones [11,20]; this is because large water bodies can buffer much of the rapid variation present in terrestrial locations [11]. Despite this generality, climatic processes that exhibit blue-shifted temporal dynamics do exist, such as the El Nin˜o Southern Oscillation with lags of 12–24 months [21]. The colour of an environmental variable depends on the timescale considered [22] (Figure 1); thus, this should be chosen carefully with respect to the life cycle of the focal organisms. The temporal structure of physical environments can also have anthropogenic causes. A simple example comes from the regulation of
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Box 1. Models of coloured environments Temporal environmental variation is usually modelled as a coloured process [5,6], in analogy with visible light, where different dominant frequencies in a stochastic time-series correspond to different colours. In blue noise, changes occur rapidly (high frequencies dominate), red indicates slow changes (low frequencies dominate), whereas no frequencies dominate in white noise. Such processes are most frequently modelled in the time domain using discrete time autoregressive (AR) processes, but can alternatively be considered in the frequency domain using sinusoidal (1/f) processes [5]. An AR process, describing an environmental variable e, can be modelled as (Equation I) [6]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi etþ1 ¼ ket þ vt 1 k2 ; [Equation I] where v is a random standard normal variable. Owing to the square root term, the variance of e will remain at unity, independent of its autocorrelation (k) [7,8]. The process produces blue noise when k < 0, red noise when k > 0, and white noise when k = 0 (Figure I).
An alternative for AR-processes is sinusoidal (1/f) processes [5]. In general, this can be used for theoretical studies as an alternative for white noise. Sinusoidal noise (1/f) time-series can be generated by summing random-phase (uf) sine waves following the power law amplitude = 1/fb/2, where f is the frequency and b is the spectral exponent [9], giving Equation II Ft ¼
n=2 X f ¼1
1 f
b=2
sin
2p ft þuf ; n
[Equation II]
where t is the time unit and n is period length. b < 0 generates blue noise (Figure Ia), b = 0 results in white noise (Figure Ib) and b > 0 leads to reddened noise. Depending on the value of parameter b, 1/f noise can be called pink (Figure Ic), brown, or black (Figure Id) [10]. The autocorrelation (k) or the spectral exponent (b) can both be estimated from natural time-series (e.g. Figure Ie). The estimated colour is likely to be biased towards white in variables containing measurement error because such errors are usually temporally uncorrelated.
Figure I. Models of coloured environments. (a–d) Typical coloured noise time-series, generated using autoregressive (Equation I, darker lines) or 1/f methods (Equation II, lighter lines): (e) The annual North Atlantic Oscillation (NAO) index from 1822 to 2000 is approximately white. Autocorrelation coefficients (k) and spectral exponents (b) for time-series are embedded in the figure. In (e), these statistics are estimated from the NAO time-series, whereas in (a–d) they represent parameters in Equations I and II.
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Figure 2. Anthropogenic action leading to variation in the colour of environmental conditions. (a) Temporal variation in the water level (m above sea level) at Lokka reservoir (67849’ N, 27844’ E) in northern Finland during 1968–2008. The surface area of the lake varies between 216 m2 and 418 m2 owing to regulation of the water level. Until mid-1981 (red line), autocorrelation in water-level variation was significantly positive (k = 0.72); since then (black line), the variation has had zero autocorrelation (estimates based on samples taken every fourth month). This switch is due to a change in the regulation pattern. Data provided by Finnish National Environmental Institute (SYKE). (b) Three of the most important fish species in the Lokka reservoir. The breeding success of two of these species [(i) white fish (Coregonus lavaretus) and (ii) pike (Esox lucius)] depends on shallow water habitats, thus regulation of the water level will affect the amount of available breeding habitat. The third species is perch (Perca fluviatilis) (iii). Reproduced with permission from the Finnish Game and Fisheries Research Institute. Figure 1. Dependence of observed temporal autocorrelation on the scale and period of investigation, as well as on chance (sampling effects). The sample autocorrelation coefficients (k) for the North Atlantic Oscillation (NAO) are estimated with sliding time-windows of varying length. The (a) annual NAO (from 1822 to 2008) and (b) monthly NAO (1993–2008) are considered. The investigated time period is defined by the time of the first observation (X-axis; unit year) and time-series length [Y-axis; the time-units are (a) year and (b) month]. Different colours refer to different sample autocorrelations; blue indicates k < 0, whereas red indicates k > 0.
water level at the Lokka reservoir in northern Finland (Figure 2a), which leads to variation in the available habitat volume of economically significant fish species (Figure 2b). Increases in the frequency and severity of extreme climatic events have been predicted [1], which will also change the colour of environmental variables in the future. The general patterns of temporal structure in biotic and abiotic environmental factors might also differ from each other [23]. For example, mast seeding events [24] can create blue-shifted resource environments for granivorous animals. As we discuss next, coloured environmental variation can interact with population processes, with
important consequences for the resulting population dynamical patterns. Single-species populations in coloured environments The behaviour of unstructured single-species population models in coloured environments has been studied intensively [6,7,25–36]. Much of the research has concentrated on the risk of population extinction under different environmental conditions, which generally involves considering the colour and/or variance of population fluctuations over time. The observed responses depend on model assumptions; for example, how population demography is influenced by the environment [15,37] (Box 2). However, one general pattern that emerges is that noise colour interacts with density dependence to produce the observed response [23,32]. A population with undercompensating growth reacts slowly to environmental changes (i.e. has reddened dynamics) [32]. By contrast, an overcompensating population rapidly 557
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Box 2. How does environment affect population demography? In population models, environment variation is often assumed to affect individuals equally, through the rates of reproduction, mortality or dispersal. One modelling approach is to alter the percapita growth rate ( pgr) by multiplying the deterministic model prediction with exp(bet) [40], where et is environment at time t and b is its effect (Figure I). For example, in the Ricker model, we would have Equation I: N tþ1 ¼ N t exp½rð1 N t =K Þexpðbet Þ:
[Equation I]
where N is the population size, r is the intrinsic growth rate and K the carrying capacity. The distribution of exp(bet) is log-normal with expected value one, when e N(–(bs)2/2, s2). For a specific environmental variable (say, X in the place of e), a multiple regression model with the pgr = ln(Nt+1/Nt) as the response, and Nt and Xt as explanatory variables, corresponds to this model and can be used to estimate the strength of the environmental effect b. Environmental factors can also affect the amount of suitable habitat or intraspecific competition (density dependence). These two features are related: the strength of density dependence determines the carrying capacity in many models (e.g. Equation I). Again, we can consider the environmental effect as being multiplicative. This can be modelled with a temporally varying carrying capacity Kt = Kmexp(bet), where Km is the mean of Kt (Figure Ib). If the environment affects density dependence specifically, the term exp(bet) in Equation I can be replaced with exp(betNt). Here, b can also be estimated using multiple regression with NtXt as an explanatory variable instead of Xt. The environment can influence both pgr and K simultaneously. In statistical detection of environmental effects it is desirable to use models that consider the underlying demographic mechanisms. Investigation of simple correlations between population density and environment can be misleading in many biologically realistic scenarios, such as age-structured populations of semelparous breeders, where the juveniles are subject to environmental forcing [41].
Figure I. Variation in the relationship between population density and per-capita growth according to how the environment affects demography. The environment affects (a) per-capita growth rate ( pgr) or (b) carrying capacity (K, Equation I). The black solid lines represent average relationships and dotted lines show et = 1s. Gray shading indicates log-normal probability distributions of r and K, whereas black dots are their mean values (r = 1.2; K = 250).
overshoots the equilibrium after a perturbation, displaying blue dynamics. The qualitative nature of these dynamics is not altered by different colours of environmental fluctuations [23], which has been experimentally confirmed for undercompensating populations [38,39]. An exactly compensating population is a special case, where the population will closely track the environmental fluctuations and thus express a colour equal to that of the environment [23]. The amplitude of population fluctuations is also affected by environmental colour [29,31–33,42], with direct consequences on extinction risk [30,31,42]. In general, fluctuations in population density are amplified (dampened) in undercompensatory (overcompensatory) single-species populations with increasing environmental reddening [29,31] (Figure 3). Differences in this result that have previously been found under different models for environmental uncertainty (AR- or 1/f -type noise-generating 558
methods, see Box 1) can be understood through differences in the environmental variance rather than in noise colour per se. When age or stage structure is introduced to singlespecies population dynamics, extinction risk becomes dependent on the underlying mechanisms of population renewal; the relationship between density dependence and noise colour also varies with life-history characteristics, such as fecundity and longevity [27,43,44]. Adding structural complexity in the form of life histories potentially breaks down the general relationship between density dependence and noise colour observed in unstructured populations (Figure 3), but more work is required to uncover the extent of general relationships. Differences can arise because there are several possible routes for environmental stochasticity to affect population renewal [44] (e.g. different life stages are affected differently by stochasticity).
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Box 3. Coloured noise in communities Simple community dynamics can be described by the multi-species version of the Ricker model (Equation I): S 1 X N i; tþ1 ¼ N i; t exp r i 1 ai j N j;t expðet þ mi;t Þ; K i j¼1
Figure 3. Preservation of qualitative patterns in the relationship between ensemble P variability ( Ni,t) and environmental reddening with increasing structural complexity in population models. As environmental variation becomes more red (autocorrelation k increases), it interacts with density-dependent feedback to increase or decrease the size of population fluctuations; dependent on whether the intrinsic population dynamics are under- (r = 0.5, Equation I in Box 2; red lines) or over-compensatory (r = 1.8; blue lines), respectively. This relationship holds for single species, single patch populations (dotted lines); single species populations spread over a chain of 25 patches, linked by density-independent stepping-stone dispersal (solid lines; 10% of each patch distributed between the two nearest neighbours following reproduction each generation); or with competitive interactions in a five species community (dashed lines; Equation I in Box 3, aij values drawn randomly from a b distribution with mean 0.1 [p = 1, q = 9]). Results show the mean variance of the simulated ensemble population density based on 200 repetitions run over 200 time-steps for each parameter value. All populations were initiated at their equilibrium density.
In a spatial context, the environmental colour affects population extinction risk through a combination of population variability and synchrony between subpopulations [45,46]. In a homogeneous landscape, increased reddening in the environment increases subpopulation variability (local extinction risk) in undercompensatory populations [47], as well as synchrony between subpopulations (and probability of global extinction). As with single-patch populations, the opposite effect is seen in overcompensatory populations (Figure 3). The situation is different in heterogeneous landscapes, with environmental reddening reducing population persistence time for under- and overcompensatory dynamics [30]. Single-species models have provided a valuable foundation for the impacts of coloured environmental variation. However, it has been unclear if they are adequate in predicting the behaviour of more complex systems, such as those that incorporate species interactions. Species interactions in coloured environments Recent efforts have tried to understand how community organization interacts with coloured environmental variation in affecting population variability. These studies commonly use the Lotka–Volterra community framework to model interspecific competition or predator–prey inter-
[Equation I]
where Ni,t is the density of the ith species at time t, ri is its intrinsic growth rate, Ki its carrying capacity and S is the number of species in the community. Parameter aij gives the per capita effect of species j on the renewal of species i. By changing the sign of a, one can model different types of species interaction (e.g. competition, mutualism or predation) but this should be accompanied by appropriate changes in ri. Variables e and m represent global (common for all species) and species-specific (independent) noise, respectively [52]. Alternatively, the sum of e and m can be considered as one noise term, where the relative strength of e and m results in the realized between species covariance (environmental correlation). Depending on the community structure (a, K and r) and the colour of environmental stochasticity, the similarity in species-specific responses to the environment can have a strong impact upon community dynamics (e.g. Ref. [53]). For example, whereas increasing environmental reddening increases the degree of asynchrony between community members (which can have a destabilizing influence on community biomass [54]), increasing environmental correlation increases between-population synchrony [53].
actions (Box 3). When scaling up from single-species systems to multi-species communities, network structure can modulate the interaction between noise properties and population processes [48–51]. Species networks can be structured in different ways, depending, for example, on the type, shape and strength of species interactions, species-specific demographic rates and the similarity between species-specific responses to environmental variation. All of these factors can modify the effect of environmental reddening. The observed red spectra of natural populations [55] are a potential consequence of the trophic position of the species [50]. That is, species on top of a food chain should show more red dynamics than those at the bottom because population growth rates decrease with increasing trophic level. The degree of similarity between species-specific responses to environmental forcing (environmental correlation) also influences the colour and variability of population dynamics [54,56–58]. Population autocorrelation tends to increase with environmental reddening independently of the strength of density dependence and environmental correlation, although the degree of change is affected by these features. Whether population variability increases (or decreases) with environmental reddening depends on population density dependence and environmental correlation. Competitive communities are ensembles of species competing for resources at the same trophic level. When such communities are dominated by relatively weak interspecific interactions (considered to be a realistic assumption [59]), their populations respond to environmental reddening in the same way as predicted by single-species population models (Figure 3), independently of environmental correlation between species. If community members interact more strongly, the effect of environmental reddening on overcompensating populations depends on 559
Review environmental correlation; independent responses to the environment increase variability in association with environmental reddening, whereas correlated responses lead to decreased variability [44,56,58,60]. The exact relationship between environmental reddening and population variability further depends on the severity of environmental stochasticity [58], which also has an impact upon between-population synchrony. Population synchrony is decreased by environmental reddening and stronger noise, and increased by increasing environmental correlation [44,58]. Consideration of population synchrony, especially at the community level, is particularly relevant when addressing the impact of environmental stochasticity on biomass stability in communities [54,58]. Trophic interactions can also modify population responses to environmental variation [49,50,54,61]; for example, a simple consumer–resource model echoes results reported for single-species systems [61] (Figure 3). Variability in the resource population (overcompensatory) decreases whereas that in the consumer population (undercompensatory) increases with environmental reddening. In food chains, population colour is reddened up the chain, independently of noise colour, if all species are influenced by stochasticity [49,50]. If only one species is sensitive to environmental fluctuations, this species always has a red spectrum [50]. In general, the population response to environmental reddening is affected by noise amplitude, the focal trophic level and whether the population is directly or indirectly affected by stochasticity [50]. Whether environmental correlation has an effect on these patterns remains an open question. Despite the important role of spatial processes that has been demonstrated for single population models, few studies have considered the effect of coloured noise on model results in metacommunities, where multiple species interact across a spatial network [62]. In open single-patch models, with density-independent immigration, environmental reddening impacts upon biomass stability by decreasing species diversity [18,63]. Biomass stability tends to be affected more by environmental reddening (which increases biomass fluctuations) than by increases in community size (which reduce biomass fluctuations) [18]. The relationship between noise colour and species diversity is sensitive to immigration rate in a competitive metacommunity, such that diversity increases with environmental reddening when immigration rate is low, whereas a high immigration rate leads to the opposite trend [63]. Research on stochastic environmental processes in metacommunities is in its infancy, and future research will show if spatially explicit models will change these predictions. Empirical work is necessary to validate and refine the predictions of theoretical models, but surprisingly few studies exist. Environmental reddening (realized through artificial mortality) decreases population persistence time in experimental, single-species microcosms [64], as expected by theory in undercompensating populations. Examination of open-sink populations of protists (artificial dispersal to low-quality conditions) showed that red 560
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fluctuations in habitat quality can decrease population extinction risk, also matching relevant theoretical predictions [47]. Results from microbial communities indicate that reddened environmental variation increases species diversity [65,66], as compared with white or blue environmental variation. These empirical examples give some early support to theoretical results, but more work is required. As with single-species models, increasing structural complexity is likely to change the above general responses of communities to environmental reddening (Figure 3). Further work is required for a better understanding of the impact of coloured environmental variation on multispecies assemblages. Evolutionary impacts of coloured environments Given the importance of the colour of environmental variation for population fluctuations, environmental colour will also have important effects on evolutionary processes [5]. In practice, it will directly affect the prevalence and duration of genetic bottleneck effects (i.e. periods of stronger genetic drift). Currently, understanding of how environmental reddening might influence the interplay of ecological and evolutionary processes is limited [67–70] and few studies have considered evolution through ecological dynamics in coloured environments [71,72]. Resolving the interaction of ecological and evolutionary dynamics will be crucial to understand fully the potential influence of global climate change on existing species and communities. In theory, temporal structure is likely to be an important aspect of environmental variability that contributes to shaping age- and stage-specific patterns of survival probabilities in nature [69]. Reddened environmental variation can lead to sustained reductions in population size, eventually resulting in a loss of genetic variance, which substantially reduces the ability of the population to respond to future selective challenges [73]. This can cause a population to lag behind the optimum phenotype, increasing the risk of extinction [73]. By contrast, positively autocorrelated changes in the optimum phenotype allow for increased additive genetic variance, which in turn enables the mean phenotype of a population to track the optimum more closely (compared with white or blue environments [74]) reducing evolutionary load [total genetic load on a population is defined as the expected loss of mean Malthusian fitness (intrinsic population growth rate; Ref. [68]) owing to genetic and evolutionary factors] [68]. Additive genetic variance is most effective in reducing the total load when populations exhibit highly reddened fluctuations and high variance. Moreover, no empirical data exist to date to validate these predictions. Evolutionary change also has inevitable effects on longterm population dynamics. Population performance is likely to lag continuously behind the optimum, depending on the adaptive capacity of a species [73]. Changes in fitness could, in practice, be expressed as evolving intrinsic growth rates or density-dependent effects. This could result in covariation between environment, population dynamics and evolution, which cannot be understood by modelling these components separately. This topic has been neglected owing to the tradition of considering
Review
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Box 4. Environmental variation in quantitative genetics Environmental variation is likely to affect the phenotype of individuals in several ways that are worth considering when looking at the effects of environmental colour. Phenotypic variation in a quantitative trait can be partitioned between its genetic and environmental components as Equation I [76]: V P ¼ V G þ V E þ V GE þ 2COV ðG; EÞ;
[Equation I]
where VG and VE represent the components of variance in phenotype resulting from genetic and environmental effects, respectively. VGE is the non-additive interaction between genotypic and environmental effects. An example of such genetically determined individually varying responses (reaction norms) to given conditions is antibiotic resistance in bacteria. COV(G, E) is the covariance between genotypic and environmental sources of variances. Such covariation can arise, for example, through genetically determined habitat preferences if the habitats show variable microclimates. In the context of evolutionary models, eventual evolution of all these aspects should also be considered. Covariation between population dynamics and environmental fluctuations boost or dampen population variability depending on the sign of this covariation [31]. Similarly, covariation between genotypes and environmental effects can inflate or reduce variation in a quantitative character depending on whether genetic and environmental influences reinforce or oppose one another [76]. This implies that spatio-temporal autocorrelation in environmental variation is likely to influence patterns of phenotypic variation. The spatial dimension appears to be particularly important for population genetics. For example, dispersal into new habitats can rapidly change the genetic makeup of populations during range expansion owing to strong genetic drift on the edge of expansion [77]. Dispersal can also lead to local allele fixation [75] and temporal environmental reddening can increase genetic diversity in a spatial network in connection with genetic drift [71], in contrast with earlier results from models incorporating serially uncorrelated white noise. Environmental and spatial autocorrelation have both been shown to affect the evolution of density-dependent dispersal [72], which can influence overall genetic differentiation in a population.
population genetics separately from population dynamics. However, recent advances show promise of an integrated theory [71,75] (Box 4). Prospects Models and empirical work have provided insight into some general eco-evolutionary patterns caused by coloured environmental variation. There is a recent trend towards being more mechanistic in the assumptions about stochasticity (this being the case in theoretical, experimental and statistical population studies). To move understanding forward of the true impact of coloured environmental variation in eco-evolutionary patterns, future research must explicitly consider how the environment will affect populations. For example, Box 2 presents an approach to modelling densitydependent and -independent environmental effects. The Ricker model (Box 2) can also be reformulated in terms of birth and death rates that can be independently subjected to environmental stochasticity [78]. We can improve our ability to make quantitative predictions of dynamical patterns (e.g. extinction risk) by accounting for other potentially important mechanisms of stochasticity, such as demographic stochasticity and heterogeneity in vital rates [79]. We now highlight three more specific directions where further investigation will enhance our understanding of the interplay between natural systems and coloured environmental variation.
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Interaction between ecological and evolutionary dynamics Perhaps the greatest theoretical challenge is to merge the two fields of population ecology and population genetics, which combine to drive the evolutionary trajectory of species. Models that integrate population genetics and dynamics (e.g. dependence on frequency and density) will enable researchers to address questions about the mechanisms of species adaptation to fluctuating environments and how the colour of these fluctuations influences this process. Early progress indicates that environmental colour will interact with genetic drift; environmental reddening has been shown to reinforce genetic differentiation across a spatially structured landscape [71]. The next step is to ask if selective changes in the gene pool could also be affected by different regimes of environmental variation. Community structure, environmental correlation and spatial structure Previous work combining community dynamics and environmental autocorrelation has concentrated on simple communities where species tend to be equivalent in their demographic traits and their species-specific responses to environmental stochasticity. Results from these simple communities will help to understand those from more complex models. Directions for further research include: relaxing overly simplistic assumptions in competitive systems (e.g. looking at non-uniform covariance patterns in between-species responses to environmental variation); exploring the relationship between noise colour and patterns in environmental correlation within and between trophic levels; investigating other functional forms in species interactions; and considering systems with nonequilibrium dynamics [80]. A related challenge is to unravel how populations and communities respond to dispersal and spatially autocorrelated environmental fluctuations. Empirical challenges Most time-series of natural populations consist of proxies or correlates of population densities, not exact population counts or densities. Ignoring observation error in statistical investigation of these systems is known to bias the estimated strength of density dependence [81] and, potentially, the effects of environmental factors [82]. To empirically assess how environmental colour affects population dynamics (Figure 3), not only must the relevant environmental factors be appropriately recognized and quantified, but the level of compensation (density dependence) must also be estimated correctly. More precise statistical estimates of density dependence [81] and environmental effects [82] can be achieved using state-space models, separating process and observation error in empirical time-series. Another empirical challenge related to combining ecological and evolutionary dynamics is statistical investigation of these systems using multiple sources of data. Time-series of population densities and quantitative traits (or allele frequencies) potentially contain synergistic information about each other. Low population size can result in rapid evolution owing to genetic drift (‘bottlenecks’); strong selection in a quantitative trait might result in population 561
Review decrease owing to loss of poorly adapted individuals. Statistical models for these purposes must usually be explicit about mechanisms of biological and data observation processes, and be tailored for each specific situation. Such specific (and sometimes complicated) hierarchical models can be technically difficult to evaluate. At present, Bayesian statistics using Markov Chain Monte Carlo simulation provides the easiest framework for constructing and fitting such models [83]. Conclusions The interplay between internal population dynamics, community structure [48,56] and external noise processes [23] produces various responses in population dynamics. One general result, observed in single-species models and simple generalizations of such, including spatial and interspecific interactions, is that reddening of environmental variation increases (decreases) the amplitude of population fluctuations in systems with undercompensatory (overcompensatory) dynamics (Figure 3). The structure of density-dependent feedbacks and the strength and colour of environmental variation interact to modify the impact of environmental variation on population fluctuations. Other factors affecting the impact of coloured environmental variation include differential (e.g. species- or stagespecific) responses to temporal disturbances, species identities in food webs and spatial structuring of populations. One implication is that observed spectra in population time-series tell little about the relative contribution of the internal and external factors impacting upon these populations [41,53], without considering the biotic and abiotic interactions that modify population responses. Development and application of stronger statistical methods, accounting for observation error (state-space models) and integrating several potentially synergistic sources of data (Bayesian methods) is needed to disentangle empirically the mechanisms behind population behaviour. Future challenges are encouraged to concentrate on understanding responses to the environment at the level of the individual. This will be followed by building across levels of organization to understand how interactions within and between species and within and between population patches will modify changes to the environment. For example, how food webs with different structures respond to coloured noise and how explicit spatial structure can alter the dynamics of single species or communities from those observed in single patch systems. In addition, the environmental covariance structure within a community also remains an undeveloped area for future research. A major current concern in population ecology is how local and global processes in the climate will change in the future. Complex natural systems can show unexpected responses if the natural disturbance regimes are altered by human activities. Further investigation of the impact of coloured environmental variation is urgently required, to understand how natural populations will respond to long- and shortterm changes in the biotic and abiotic environment. Acknowledgements We dedicate this article to our colleague, teacher and friend Esa Ranta. We thank Jouni Laakso, Justin Travis and two anonymous reviewers for 562
Trends in Ecology and Evolution Vol.24 No.10 comments that helped to improve the manuscript. A.L. and M.S.F. received funding from the Nordic Centre of Excellence EcoClim project and Helsinki University. L.R. was funded by the Jenny and Antti Wihuri Foundation.
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