Populations embedded in trophic communities respond differently to coloured environmental noise

Processes governing species richness in communities exposed to temporal environmental stochasticity: A review and synthesis of modelling approaches

Research into the processes governing species richness has often assumed that the environment is fixed, whereas realistic environments are often characterised by random fluctuations over time. This temporal environmental stochasticity (TES) changes the demographic rates of species populations, with cascading effects on community dynamics and species richness. Theoretical and applied studies have used process-based mathematical models to determine how TES affects species richness, but under a variety of frameworks. Here, we critically review such studies to synthesise their findings and draw general conclusions. We first provide a broad mathematical framework encompassing the different ways in which TES has been modelled. We then review studies that have analysed models with TES under the assumption of negligible interspecific interactions, such that a community is conceptualised as the sum of independent species populations. These analyses have highlighted how TES can reduce species richness by increasing the frequency at which a species becomes rare and therefore prone to extinction. Next, we review studies that have relaxed the assumption of negligible interspecific interactions. To simplify the corresponding models and make them analytically tractable, such studies have used mean-field theory to derive fixed parameters representing the typical strength of interspecific interactions under TES. The resulting analyses have highlighted community-level effects that determine how TES affects species richness, for species that compete for a common limiting resource. With short temporal correlations of environmental conditions, a non-linear averaging effect of interspecific competition strength over time gives an increase in species richness. In contrast, with long temporal correlations of environmental conditions, strong selection favouring the fittest species between changes in environmental conditions results in a decrease in species richness. We compare such results with those from invasion analysis, which examines invasion growth rates (IGRs) instead of species richness directly. Qualitative differences sometimes arise because the IGR is the expected growth rate of a species when it is rare, which does not capture the variation around this mean or the probability of the species becoming rare. Our review elucidates key processes that have been found to mediate the negative and positive effects of TES on species richness, and by doing so highlights key areas for future research.

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase-tipping

Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent work indicates that the changing variability, that is, the amplitude and the temporal autocorrelation of deviations from the mean, may have greater and more imminent impact on ecosystems. In this paper, we demonstrate that changes in climate variability alone could drive cyclic predator-prey ecosystems to extinction via so-called phase-tipping (P-tipping), a new type of instability that occurs only from certain phases of the predator-prey cycle. We construct a mathematical model of a variable climate and couple it to two self-oscillating paradigmatic predator-prey models. Most importantly, we combine realistic parameter values for the Canada lynx and snowshoe hare with actual climate data from the boreal forest. In this way, we demonstrate that critically important species in the boreal forest have increased likelihood of P-tipping to extinction under predicted changes in climate variability, and are most vulnerable during stages of the cycle when the predator population is near its maximum. Furthermore, our analysis reveals that stochastic resonance is the underlying mechanism for the increased likelihood of P-tipping to extinction.

Tipping points in spatial ecosystems driven by short-range correlated noise

Complex spatial systems can experience critical transitions or tippings on crossing a threshold value in their response to stochastic perturbations. While previous studies have well characterized the impact of white noise on tipping, the effect of correlated noise in spatial ecosystems remains largely unexplored. Here, we investigate the effect of both multiplicative and additive Ornstein-Uhlenbeck (OU) correlated noise on the occurrence of critical transitions in spatial ecosystems. We find that decreasing the noise correlation time of OU (exponentially correlated) noise aggravates the chance of critical transitions in spatiotemporal ecological systems. Our results hold good and are supported by the analysis of three well-studied spatial ecological models of varying nonlinearity. We also compute spatial early warning indicators (e.g., spatial variance, spatial skewness, and spatial correlation) to determine their reliability in anticipating tipping points with variations in noise correlation. The indicators of critical transitions exhibit mixed success in forewarning the occurrence of a tipping point, as indicated by the distribution of Kendall's rank correlation.

Intraseasonal predictability of natural phytoplankton population dynamics

It is difficult to make skillful predictions about the future dynamics of marine phytoplankton populations. Here, we use a 22-year time series of monthly average abundances for 198 phytoplankton taxa from Station L4 in the Western English Channel (1992-2014) to test whether and how aggregating phytoplankton into multi-species assemblages can improve predictability of their temporal dynamics. Using a non-parametric framework to assess predictability, we demonstrate that the prediction skill is significantly affected by how species data are grouped into assemblages, the presence of noise, and stochastic behavior within species. Overall, we find that predictability one month into the future increases when species are aggregated together into assemblages with more species, compared with the predictability of individual taxa. However, predictability within dinoflagellates and larger phytoplankton (>12 μm cell radius) is low overall and does not increase by aggregating similar species together. High variability in the data, due to observational error (noise) or stochasticity in population growth rates, reduces the predictability of individual species more than the predictability of assemblages. These findings show that there is greater potential for univariate prediction of species assemblages or whole-community metrics, such as total chlorophyll or biomass, than for the individual dynamics of phytoplankton species.

Predator Persistence through Variability of Resource Productivity in Tritrophic Systems

The trophic structure of species communities depends on the energy transfer between trophic levels. Primary productivity varies strongly through time, challenging the persistence of species at higher trophic levels. Yet resource variability has mostly been studied in systems with only one or two trophic levels. We test the effect of variability in resource productivity in a tritrophic model system including a resource, a size-structured consumer, and a size-specific predator. The model complies with fundamental principles of mass conservation and the body-size dependence of individual-level energetics and predator-prey interactions. Surprisingly, we find that resource variability may promote predator persistence. The positive effect of variability on the predator arises through periods with starvation mortality of juvenile prey, which reduces the intraspecific competition in the prey population. With increasing variability in productivity and starvation mortality in the juvenile prey, the prey availability increases in the size range preferred by the predator. The positive effect of prey mortality on the trophic transfer efficiency depends on the biologically realistic consideration of body size-dependent and food-dependent functions for growth and reproduction in our model. Our findings show that variability may promote the trophic transfer efficiency, indicating that environmental variability may sustain species at higher trophic levels in natural ecosystems.

Environmental variability uncovers disruptive effects of species' interactions on population dynamics

How species respond to changes in environmental variability has been shown for single species, but the question remains whether these results are transferable to species when incorporated in ecological communities. Here, we address this issue by analysing the same species exposed to a range of environmental variabilities when (i) isolated or (ii) embedded in a food web. We find that all species in food webs exposed to temporally uncorrelated environments (white noise) show the same type of dynamics as isolated species, whereas species in food webs exposed to positively autocorrelated environments (red noise) can respond completely differently compared with isolated species. This is owing to species following their equilibrium densities in a positively autocorrelated environment that in turn enables species-species interactions to come into play. Our results give new insights into species' response to environmental variation. They especially highlight the importance of considering both species' interactions and environmental autocorrelation when studying population dynamics in a fluctuating environment.

Environmental Variation Generates Environmental Opportunist Pathogen Outbreaks

Many socio-economically important pathogens persist and grow in the outside host environment and opportunistically invade host individuals. The environmental growth and opportunistic nature of these pathogens has received only little attention in epidemiology. Environmental reservoirs are, however, an important source of novel diseases. Thus, attempts to control these diseases require different approaches than in traditional epidemiology focusing on obligatory parasites. Conditions in the outside-host environment are prone to fluctuate over time. This variation is a potentially important driver of epidemiological dynamics and affect the evolution of novel diseases. Using a modelling approach combining the traditional SIRS models to environmental opportunist pathogens and environmental variability, we show that epidemiological dynamics of opportunist diseases are profoundly driven by the quality of environmental variability, such as the long-term predictability and magnitude of fluctuations. When comparing periodic and stochastic environmental factors, for a given variance, stochastic variation is more likely to cause outbreaks than periodic variation. This is due to the extreme values being further away from the mean. Moreover, the effects of variability depend on the underlying biology of the epidemiological system, and which part of the system is being affected. Variation in host susceptibility leads to more severe pathogen outbreaks than variation in pathogen growth rate in the environment. Positive correlation in variation on both targets can cancel the effect of variation altogether. Moreover, the severity of outbreaks is significantly reduced by increase in the duration of immunity. Uncovering these issues helps in understanding and controlling diseases caused by environmental pathogens.

Spatio-temporal environmental correlation and population variability in simple metacommunities

Natural populations experience environmental conditions that vary across space and over time. This variation is often correlated between localities depending on the geographical separation between them, and different species can respond to local environmental fluctuations similarly or differently, depending on their adaptation. How this emerging structure in environmental correlation (between-patches and between-species) affects spatial community dynamics is an open question. This paper aims at a general understanding of the interactions between the environmental correlation structure and population dynamics in spatial networks of local communities (metacommunities), by studying simple two-patch, two-species systems. Three different pairs of interspecific interactions are considered: competition, consumer-resource interaction, and host-parasitoid interaction. While the results paint a relatively complex picture of the effect of environmental correlation, the interaction between environmental forcing, dispersal, and local interactions can be understood via two mechanisms. While increasing between-patch environmental correlation couples immigration and local densities (destabilising effect), the coupling between local populations under increased between-species environmental correlation can either amplify or dampen population fluctuations, depending on the patterns in density dependence. This work provides a unifying framework for modelling stochastic metacommunities, and forms a foundation for a better understanding of population responses to environmental fluctuations in natural systems.

Confounding environmental colour and distribution shape leads to underestimation of population extinction risk

The colour of environmental variability influences the size of population fluctuations when filtered through density dependent dynamics, driving extinction risk through dynamical resonance. Slow fluctuations (low frequencies) dominate in red environments, rapid fluctuations (high frequencies) in blue environments and white environments are purely random (no frequencies dominate). Two methods are commonly employed to generate the coloured spatial and/or temporal stochastic (environmental) series used in combination with population (dynamical feedback) models: autoregressive [AR(1)] and sinusoidal (1/f) models. We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models. Increasing variability of sample Skewness and Kurtosis and decreasing mean Kurtosis of these series alter the frequency distribution shape of the realised values of the coloured stochastic processes. These changes in distribution shape alter patterns in the probability of single and series of extreme conditions. We show that the reduced extinction risk for undercompensating (slow growing) populations in red environments previously predicted with traditional 1/f methods is an artefact of changes in the distribution shapes of the environmental series. This is demonstrated by comparison with coloured series controlled to be normally distributed using spectral mimicry. Changes in the distribution shape that arise using traditional methods lead to underestimation of extinction risk in normally distributed, red 1/f environments. AR(1) methods also underestimate extinction risks in traditionally generated red environments. This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations. We must let the characteristics of known natural environmental covariates (e.g., colour and distribution shape) guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.

When can we trust our model predictions? Unearthing structural sensitivity in biological systems

It is well recognized that models in the life sciences can be sensitive to small variations in their model functions, a phenomenon known as ‘structural sensitivity’. Conventionally, modellers test for sensitivity by varying parameters for a specific formulation of the model functions, but models can show structural sensitivity to the choice of functional representations used: a particularly concerning problem when system processes are too complex, or insufficiently understood, to theoretically justify specific parameterizations. Here we propose a rigorous test for the detection of structural sensitivity in a system with respect to the local stability of equilibria, the main idea being to project infinite dimensional function space onto a finite dimensional space by considering the local properties of the model functions. As an illustrative example, we use our test to demonstrate structural sensitivity in the seminal Rosenzweig–MacArthur predator–prey model, and show that the conventional parameter-based approach can fail to do so. We also consider some implications that structural sensitivity has for ecological modelling: we argue that when the model exhibits structural sensitivity but experimental results remain consistent it may indicate that there is a problem with the model construction, and that in some cases trying to find an ‘optimal’ parameterization of a model function may simply be impossible when the model exhibits structural sensitivity. Finally, we suggest that the phenomenon of structural sensitivity in biological models may help explain the irregular oscillations often observed in real ecosystems.

The strength of species interactions modifies population responses to environmental variation in competitive communities

The life-history parameters of most living organisms are modified by fluctuations in environmental conditions. The impact of environmental autocorrelation on population persistence is well understood in single species systems. However, in multi-species communities the impact of stochasticity is complicated by the possibility of different species having differing intrinsic responses to the environment (environmental correlation). Previous work has shown that whether increasing between-species environmental correlation stabilises population fluctuations or not, depends on an interaction between density-dependence and environmental autocorrelation. Here we derive analytical conditions for how this interaction in turn depends on the strength of interspecific competition. Under relatively weak between-species interactions, increasing environmental autocorrelation always dampens population fluctuations, while increasing autocorrelation destabilises strongly interacting populations. In contrast, under intermediate interaction strengths, increasing autocorrelation destabilises (stabilises) population dynamics when populations respond independently (similarly) to environmental fluctuations. These results apply to a wide range of competitive communities and also have some relevance to consumer-resource systems. The results presented here help us better understand population responses to environmental fluctuations under different conditions.

Resonance of plankton communities with temperature fluctuations

The interplay between intrinsic population dynamics and environmental variation is still poorly understood. It is known, however, that even mild environmental noise may induce large fluctuations in population abundances. This is due to a resonance effect that occurs in communities on the edge of stability. Here, we use a simple predator-prey model to explore the sensitivity of plankton communities to stochastic environmental fluctuations. Our results show that the magnitude of resonance depends on the timescale of intrinsic population dynamics relative to the characteristic timescale of the environmental fluctuations. Predator-prey communities with an intrinsic tendency to oscillate at a period T are particularly responsive to red noise characterized by a timescale of τ = T/2π. We compare these theoretical predictions with the timescales of temperature fluctuations measured in lakes and oceans. This reveals that plankton communities will be highly sensitive to natural temperature fluctuations. More specifically, we demonstrate that the relatively fast temperature fluctuations in shallow lakes fall largely within the range to which rotifers and cladocerans are most sensitive, while marine copepods and krill will tend to resonate more strongly with the slower temperature variability of the open ocean.