Modelling non-additive and nonlinear signals from climatic noise in ecological time series: Soay sheep as an example

Understanding how climate can interact with other factors in determining patterns of species abundance is a persistent challenge in ecology. Recent research has suggested that the dynamics exhibited by some populations may be a non-additive function of climate, with climate affecting population growth more strongly at high density than at low density. However, we lack methodologies to adequately explain patterns in population growth generated as a result of interactions between intrinsic factors and extrinsic climatic variation in non-linear systems. We present a novel method (the Functional Coefficient Threshold Auto-Regressive (FCTAR) method) that can identify interacting influences of climate and density on population dynamics from time-series data. We demonstrate its use on count data on the size of the Soay sheep population, which is known to exhibit dynamics generated by nonlinear and non-additive interactions between density and climate, living on Hirta in the St Kilda archipelago. The FCTAR method suggests that climate fluctuations can drive the Soay sheep population between different dynamical regimes--from stable population size through limit cycles and non-periodic fluctuations.     

Context‐dependent interplays between truncated demographies and climate variation shape the population growth rate of a harvested species

Fisheries ecologists traditionally aimed at disentangling climate and fishing effects from the population dynamics of exploited marine fish stocks. However, recent studies have shown that internal characteristics and external forcing (climate and exploitation) have interactive rather than additive effects. Thought most of these studies explored how demographic truncation induced by exploitation affected the response of recruitment to climate, identifying a general pattern revealed to be difficult as interactions are often case‐specific. Here we compared five exploited stocks of European hake Merluccius merluccius from the Atlantic Ocean and Mediterranean Sea to investigate how the interaction between internal characteristics and external forces affect the variability of the population growth rate and their consequences on recruitment. Our results show that demographic truncation induces a novel population scenario in which the growth rate is maximized when the reproductive stock is younger and less diverse. This scenario is shaped by the climate variability and the fishing pattern. The population growth rate becomes more dependent on the maturation schedule and less on the survival rates. The consequences for the recruitment dynamics are twofold; the effect of density‐dependent regulatory processes decreases while the effect of the density‐independent drivers increases. Our study shows that the interaction between internal characteristics and external forces changes across geographic locations according to 1) the importance of demographic truncation, 2) the influence of the climate on the regional hydrography and 3) the spatiotemporal heterogeneity of the physical environment to which fish life history is adapted.     

Resonance effects and outbreaks in ecological time series

Organismal response to environmental variability is an important aspect of ecological processes. We propose new mechanisms whereby environmental variability can cause cyclic population outbreaks due to the nonlinearity of the organismal response. We consider stage-structured populations that respond to variable environments with variable diapause or dormancy, and in which cyclic changes of the environment induce a resonance-like boost in the population size. If there is also a stochastic component of variation in the environment, the population outbreaks are magnified by the phenomenon of "stochastic resonance". The results show that large population fluctuations may not be due to extrinsic or intrinsic factors alone, but to a nonlinear interaction between the external environment and internal population processes. Indeed, in the presence of such nonlinearities even very small environmental fluctuations can cause massive fluctuations in population size. Our theoretical results may help to explain periodic population cycles and outbreak dynamics found in many infectious diseases and pest species. We also discuss the evolution of the response parameters that regulate diapause or dormancy and promote the outbreak dynamics in variable environments.     

Deciphering the effects of climate on animal populations: diagnostic analysis provides new interpretation of Soay sheep dynamics

Soay sheep on the island of Hirta exhibit periodic population collapses that have been proposed to result from nonlinear interactions between weather, population density, and age structure. Here we employ a diagnostic approach to reanalyze the data from 1985 to 2004 and find that climate mainly affects the equilibrium population size, thus acting as a lateral perturbation. From this, we derive a simple energetic model for a population interacting with its food supply in the presence of variable winter weather. This model explains the strong nonlinearity in the Soay sheep population regulation function and provides a framework for evaluating climatic perturbations. We examined two integrative climatic indexes, one representing effects on forage production and the other representing the severity of winter weather. Results suggest that the latter has the main effect on Soay sheep population dynamics. Models incorporating this variable provided fairly accurate predictions of Soay sheep population fluctuations. The diagnostic approach offers an objective way to develop simple, nonstructured population models that are useful for understanding the causes of population fluctuations and predicting population changes, provided they are based on a careful consideration of the underlying biological and/or ecological mechanisms.     

Climate variation and regional gradients in population dynamics of two hole-nesting passerines

Latitudinal gradients in population dynamics can arise through regional variation in the deterministic components of the population dynamics and the stochastic factors. Here, we demonstrate an increase with latitude in the contribution of a large-scale climate pattern, the North Atlantic Oscillation (NAO), to the fluctuations in size of populations of two European hole-nesting passerine species. However, this influence of climate induced different latitudinal gradients in the population dynamics of the two species. In the great tit the proportion of the variability in the population fluctuations explained by the NAO increased with latitude, showing a larger impact of climate on the population fluctuations of this species at higher latitudes. In contrast, no latitudinal gradient was found in the relative contribution of climate to the variability of the pied flycatcher populations because the total environmental stochasticity increased with latitude. This shows that the population ecological consequences of an expected climate change will depend on how climate affects the environmental stochasticity in the population process. In both species, the effects will be larger in those parts of Europe where large changes in climate are expected.     

Raman Spectral Dynamics of Single Cells in the Early Stages of Growth Factor Stimulation

Cell fates change dynamically in response to various extracellular signals, including growth factors that stimulate differentiation and proliferation. The processes underlying cell-fate decisions are complex and often include large cell-to-cell variations, even within a clonal population in the same environment. To understand the origins of these cell-to-cell variations, we must detect the internal dynamics of single cells that reflect their changing chemical milieu. In this study, we used the Raman spectra of single cells to trace their internal dynamics during the early stages of growth factor stimulation. This method allows nondestructive and inclusive time-series analyses of chemical compositions of the same single cells. Applying a Gaussian mixture model to the major principal components of the single-cell Raman spectra, we detected the dynamics of the chemical states in MCF-7 cancer-derived cells in the absence and presence of differentiation and proliferation factors. The dynamics displayed characteristic variations according to the functions of the growth factors. In the differentiation pathway, the chemical composition changed directionally between multiple states, including both reversible and irreversible state transitions. In contrast, in the proliferation pathway, the chemical composition was homogenized into a single state. The differentiation factor also stimulated fluctuations in the chemical composition, whereas the proliferation factor did not.     

Interactions between local climate and grazing determine the population dynamics of the small herb Viola biflora

Plants of low stature may benefit from the presence of large herbivores through removal of tall competitive neighbours and increased light availability. Accordingly, removal of grazers has been predicted to disfavour small species. In addition to this indirect beneficial effect, the population dynamics of plants is strongly influenced by variation in external conditions such as temperature and precipitation. However, few studies have examined the interaction between large herbivores and inter-annual variation in climate for the population dynamics of small plant species not preferred by herbivores. We studied three populations of the perennial herb Viola biflora exposed to different sheep densities (high, low and zero) for 6 years in a field experiment. Plants were also impacted by invertebrate and small vertebrate herbivores (rodents). Rates of growth were marginally higher at high sheep densities, and during warm summers both survival and growth were higher when sheep were present. Thus, while the height of tall herbs was positively related to July temperature, it was less so in the treatments with sheep, suggesting that sheep reduce the negative effects of interspecific competition for this small herb. Life table response experiment analyses revealed that the population growth rate (λ) was slightly lower in the absence of sheep, but between-year variation in λ was larger than variation among sheep density treatments. λ was negatively related to July temperature, with an additional negative effect of vertebrate grazing frequency (sheep or rodent grazing). The evidence from this 6-year study suggests that the population dynamics of Viola biflora is determined by a complex interplay between climate and grazing by both large and small herbivores.     

Analysis of phenotypic change in relation to climatic drivers in a population of Soay sheep Ovis aries

Climatic change has frequently been identified as a key driver of change in biological communities. These changes can take the form of alterations to population dynamics, phenotypic characters, genetics and the life history of organisms and can have impacts on entire ecosystems. This study presents a novel investigation of how changes in a large scale climatic index, the North Atlantic Oscillation (NAO) can influence population dynamics and phenotypic characters in a population of ungulates. We use an integral projection model combined with actual climate change predictions to project future body size distributions for a population of Soay sheep Ovis aries. The climate change predictions used to direct our model projections were taken from published results of climate models, covering a range of different emissions scenarios. Our model results showed that for positive changes in the mean NAO large population declines occurred simultaneously with increases in mean body weight. The exact direction and magnitude of changes to population dynamics and character distributions were dependent on the greenhouse gas emissions scenario and model used to predict the NAO. This study has demonstrated how integral projection models can use outputs of climate models to direct projections of population dynamics and phenotypic character distributions. This approach allows the results of this study to be placed within current climate change research. The nature of integral projection models means that this methodology can be easily applied to other populations. The model can also be easily updated when new climate change predictions become available, making it a useful tool for understanding potential population level responses to climatic change. Synthesis Understanding how changes in climate affect biological communities is a key component in predicting the future form of populations. Utilising a novel approach that incorporates climatic drivers (in this instance the winter North Atlantic Oscillation) into an integral projection model framework, we predict future Soay sheep dynamics under specific climate change scenarios. Tracking quantitative trait distributions and life history metrics, our results predict declining population size and increasing body weight for an increasingly positive winter North Atlantic Oscillation index, as predicted by climate models. This has important implications for future wildlife management strategies and linking demographic responses to climate change.     

Climate mediated exogenous forcing and synchrony in populations of the oak aphid in the UK

Contemporary population dynamics theory suggests that animal fluctuations in nature are the result of the combined forces of intrinsic and exogenous factors. Weather is the iconic example of an exogenous force. The common approach for analyzing the relationship between population size and climatic variables is by simple correlation or using the climate as an additive covariable in statistical models. Here, we evaluated different functional forms in which climatic variables could influence population dynamics of the oak aphid Tuberculatus annulatus both in each locality and in relation to synchrony between localities. Results indicate that in at least four of eight aphid populations, climate influences population dynamics by modifying the carrying capacity of the system (lateral effect mediated by winter precipitation). Additionally, path analysis showed that synchrony in population dynamics is highly correlated with synchrony in winter precipitation regime, and the spatial scale of both processes is similar, which suggests that this is an example of the Moran effect. Our results show the key effects of precipitation on intra and inter population processes of this aphid. The methods used, mixing population dynamics modelling and test of synchrony, allowed us to connect the direct and indirect effects of exogenous variables into each population with patterns of synchrony inter populations.     

Effect of water temperature and density of juvenile salmonids on growth of young-of-the-year Atlantic salmon Salmo salar

A von Bertalanffy growth model for young-of the-year Atlantic salmon Salmo salar in a small French coastal stream was fitted using water temperatures and densities of juvenile salmonids (S. salar and brown trout Salmo trutta) as covariates influencing daily growth rate. The Bayesian framework was used as a template to integrate prior information from external data sets. The relative influence of the covariates on parr growth was quantified and results showed that growth of S. salar juveniles depended on both water temperatures and densities, but that most of the spatiotemporal variability of growth resulted from local spatiotemporal variations of 0+ age salmonid (S. salar and S. trutta) densities. Further analysis revealed that the fluctuations in young-of-the-year salmonid densities are likely to dominate the effects of potential future warming of water temperature due to climate change. It is concluded that factors that could affect salmonid densities might well have a greater effect on S. salar population dynamics than factors influencing water temperatures.     

Modelling population dynamics of seabirds: importance of the effects of climate fluctuations on breeding proportions

Environmental factors and their interactions are likely to have shaped specific breeding and survival strategies in top predators. Understanding how climatic factors affect populations requires detailed investigation of the demographic parameters and population modelling. Here, we focus on the modelling of a southern fulmar population over a 39 year period in Terre Adélie, Antarctica, using Leslie matrix models to understand from a prospective and retrospective point of view, how vital rates and their variations, affect the cyclic population dynamics. The elasticity of population growth rate to adult survival was very high (0.95), as predicted by a slow–fast continuum in avian life histories. However, adult survival varied little between years (mean±SD: 0.92±0.07), and could not explain the strong fluctuations observed in the number of breeders and chicks. The high temporal fluctuations of the proportion of breeders (0.57±0.22) and breeding success (0.70±0.14) had the strongest impact on population dynamics, despite their weak elasticities (0.05). Before the 1980s, population fluctuations were mainly explained by a direct impact of sea-ice extent (SIE) anomalies during summer (by a threshold effect) on the proportion of breeders. After 1980s, 3 years periodic population fluctuations were best predicted by 3 years cyclic variations in the proportion of breeders. SIE showed a marked change of periodicity during the 1980s, and SIE during winter fluctuated with a 3 years periodicity during 1980–1995. The marked change in population dynamics, through a change of the variations of the proportion of breeders, may be explained in the light of a regime shift that probably occurred around the 1980s, and which affected the sea ice environment, the availability of prey, and thus the demographic parameters and population dynamics of southern fulmars.     

Visibility of the environmental noise modulating population dynamics

Characterizing population fluctuations and their causes is a major theme in population ecology. The debate is on the relative merits of density-dependent and density-independent effects. One paradigm (revived by the research on global warming and its relation to long-term population data) states that fluctuations in population densities can often be accounted for by external noise. Several empirical models have been suggested to support this view. We followed this by assuming a given population skeleton dynamics (Ricker dynamics and second-order autoregressive dynamics) topped off with noise composed of low- and high-frequency components. Our aim was to determine to what extent the modulated population dynamics correlate with the noise signal. High correlations (with time-lag -1) were observed with both model categories in the region of stable dynamics, but not in the region of periodic or complex dynamics. This finding is not very sensitive to low-frequency noise. High correlations throughout the entire range of dynamics are only achievable when the impact of the noise is very high. Fitted parameter values of skeleton dynamics modulated with noise are prone to err substantially. This casts doubt as to what degree the underlying dynamics are any more recognizable after being modulated by the external noise.     

Impact of temperature shifts on the joint evolution of seed dormancy and size

Seed dormancy and size are two important life‐history traits that interplay as adaptation to varying environmental settings. As evolution of both traits involves correlated selective pressures, it is of interest to comparatively investigate the evolution of the two traits jointly as well as independently. We explore evolutionary trajectories of seed dormancy and size using adaptive dynamics in scenarios of deterministic or stochastic temperature variations. Ecological dynamics usually result in unbalanced population structures, and temperature shifts or fluctuations of high magnitude give rise to more balanced ecological structures. When only seed dormancy evolves, it is counter‐selected and temperature shifts hasten this evolution. Evolution of seed size results in the fixation of a given strategy and evolved seed size decreases when seed dormancy is lowered. When coevolution is allowed, evolutionary variations are reduced while the speed of evolution becomes faster given temperature shifts. Such coevolution scenarios systematically result in reduced seed dormancy and size and similar unbalanced population structures. We discuss how this may be linked to the system stability. Dormancy is counter‐selected because population dynamics lead to stable equilibrium, while small seeds are selected as the outcome of size‐number trade‐offs. Our results suggest that unlike random temperature variation between generations, temperature shifts with high magnitude can considerably alter population structures and accelerate life‐history evolution. This study increases our understanding of plant evolution and persistence in the context of climate changes.     

Combined effect of ENSO and SAM on the population dynamics of the invasive yellowjacket wasp in central Chile

The population dynamics of the yellowjacket wasp (Vespula germanica Fabricus) in central Chile were analyzed for the first time. Using a simple Ricker logistic model and adding the effects of local weather variables (temperature and precipitation) and large-scale climate phenomena as El Niño Southern Oscillation (ENSO) and the Southern Annular Mode (SAM), we modeled the interannual fluctuations in nest density. The best model according to the Bayesian information criterion (BIC) included 1-year-lag negative feedback combined with the positive additive effects of ENSO and SAM. According to this model, yellowjacket nest density was favored by warm and dry winters, which probably influenced the survival of overwintering queens. Large-scale climatic variables [Southern Oscillation Index (SOI) and SAM] described the effect of exogenous factors in wasp fluctuations better than local weather variables did. Our results emphasize the usefulness of climate indices and simple theoretical-based models in insect ecological research.     

Population dynamics of a South American rodent: seasonal structure interacting with climate,density dependence and predator effects

Understanding the role of interactions between intrinsic feedback loops and external climatic forces is one of the central challenges within the field of population ecology. For rodent dynamics, the seasonal structure of the environment necessitates changes between two stages: reproductive and non-reproductive. Nevertheless, the interactions between seasonality, climate, density dependence and predators have been generally ignored. We demonstrate that direct climate effects, the nonlinear effect of predators and the nonlinear first-order feedback embedded in a seasonal structure are key elements underlying the large and irregular fluctuations in population numbers exhibited by a small rodent in a semi-arid region of central Chile. We found that factors influencing population growth rates clearly differ between breeding and non-breeding seasons. In addition, we detected nonlinear density dependencies as well as nonlinear and differential effects of generalist and specialist predators. Recent climatic changes may account for dramatic perturbations of the rodent's population dynamics. Changes in the predator guild induced by climate are likely to result, through the food web, in a large impact on small rodent demography and population dynamics. Assuming such interactions to be typical of ecological systems, we conclude that appropriate predictions of the ecological consequences of climate change will depend on having an in-depth understanding of the community-weather system.     

Bayesian Inference on the Effect of Density Dependence and Weather on a Guanaco Population from Chile

Understanding the mechanisms that drive population dynamics is fundamental for management of wild populations. The guanaco (Lama guanicoe) is one of two wild camelid species in South America. We evaluated the effects of density dependence and weather variables on population regulation based on a time series of 36 years of population sampling of guanacos in Tierra del Fuego, Chile. The population density varied between 2.7 and 30.7 guanaco/km², with an apparent monotonic growth during the first 25 years; however, in the last 10 years the population has shown large fluctuations, suggesting that it might have reached its carrying capacity. We used a Bayesian state-space framework and model selection to determine the effect of density and environmental variables on guanaco population dynamics. Our results show that the population is under density dependent regulation and that it is currently fluctuating around an average carrying capacity of 45,000 guanacos. We also found a significant positive effect of previous winter temperature while sheep density has a strong negative effect on the guanaco population growth. We conclude that there are significant density dependent processes and that climate as well as competition with domestic species have important effects determining the population size of guanacos, with important implications for management and conservation.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. II. Application to human lysozyme.

The dynamic structure of a protein, human lysozyme, is determined by the normal mode refinement of X-ray crystal structure. This method uses the normal modes of both internal and external motions to distinguish the real internal dynamics from the external terms such as lattice disorder, and gives an anisotropic and concerted picture of atomic fluctuations. The refinement is carried out with diffraction data of 5.0 to 1.8 A resolution, which are collected on an imaging plate. The results of the refinement show: (1) Debye-Waller factor consists of two parts, highly anisotropic internal fluctuations and almost isotropic external terms. The former is smaller than the latter by a factor of 0.72 in the scale of B-factor. Therefore, the internal dynamics cannot be recognized directly from the apparent electron density distribution. (2) The internal fluctuations show basically similar features as those predicted by the normal mode analysis, with almost the same amplitude and a similar level of anisotropy. (3) Correlations of fluctuations are detected between two lobes forming the active site cleft, which move simultaneously in opposite directions. This corresponds to the hinge-bending motion of lysozyme.     

Warming effects in the western Antarctic Peninsula ecosystem: the role of population dynamic models for explaining and predicting penguin trends

The western Antarctica Peninsula and Scotia Sea ecosystems appear to be driven by complex links between climatic variables, primary productivity, krill and Avian predators. There are several studies reporting statistical relationships between climate, krill and Penguin population size. The Adélie (Pygoscelis adeliae), Chinstrap (P. antarctica) and Gentoo (P. papua) penguins appear to be influenced by interannual variability in sea-ice extent and krill biomass. In this paper we developed simple conceptual models to decipher the role of climate and krill fluctuations on the population dynamics of these three Pygoscelis penguin species inhabiting the Antarctic Peninsula region. Our results suggest that the relevant processes underlying the population dynamics of these penguin species at King George Island (South Shetland Islands) are intra-specific competition and the combined effects of krill abundance and sea-ice cover. Our results using population theoretical models appear to support that climate change, specifically regional warming on the western Antarctic Peninsula, represents a major driver. At our study site, penguins showed species-specific responses to climate change. While Chinstrap penguins were only influenced by krill abundance, the contrasting population trends of Adélie and Gentoo penguins appear to be better explained by the “sea-ice hypothesis”. We think that proper population dynamic modeling and theory are essential for deciphering and proposing the ecological mechanisms underlying dynamics of these penguin populations.     

Climate and spatio-temporal variation in the population dynamics of a long distance migrant, the white stork

1. A central question in ecology is to separate the relative contribution of density dependence and stochastic influences to annual fluctuations in population size. Here we estimate the deterministic and stochastic components of the dynamics of different European populations of white stork Ciconia ciconia. We then examined whether annual changes in population size was related to the climate during the breeding period (the 'tap hypothesis' sensu Saether, Sutherland & Engen (2004, Advances in Ecological Research, 35, 185 209) or during the nonbreeding period, especially in the winter areas in Africa (the 'tube hypothesis'). 2. A general characteristic of the population dynamics of this long-distance migrant is small environmental stochasticity and strong density regulation around the carrying capacity with short return times to equilibrium. 3. Annual changes in the size of the eastern European populations were correlated by rainfall in the wintering areas in Africa as well as local weather in the breeding areas just before arrival and in the later part of the breeding season and regional climate variation (North Atlantic Oscillation). This indicates that weather influences the population fluctuations of white storks through losses of sexually mature individuals as well as through an effect on the number of individuals that manages to establish themselves in the breeding population. Thus, both the tap and tube hypothesis explains climate influences on white stork population dynamics. 4. The spatial scale of environmental noise after accounting for the local dynamics was 67 km, suggesting that the strong density dependence reduces the synchronizing effects of climate variation on the population dynamics of white stork. 5. Several climate variables reduced the synchrony of the residual variation in population size after accounting for density dependence and demographic stochasticity, indicating that these climate variables had a synchronizing effect on the population fluctuations. In contrast, other climatic variables acted as desynchronizing agents. 6. Our results illustrate that evaluating the effects of common environmental variables on the spatio-temporal variation in population dynamics require estimates and modelling of their influence on the local dynamics.     

Biological filtering of correlated environments: towards a generalised Moran theorem

Many species from diverse taxa are known to display synchronous fluctuations across vast geographical ranges. It is often thought that climate factors influencing the growth of conspecific populations are correlated over large distances and hence produce the synchronous population dynamics – an effect known as the Moran effect. However, for species embedded in a food web the Moran effect needs not necessarily influence the focal species directly, but can act indirectly through other species. Such an indirect synchronization can also occur in an age-structured population, where the correlated environment of one age-class causes synchronous fluctuations of another. Here, we investigate this indirect Moran effect. We find first of all that synchrony is readily transferred through food webs or between age classes, which complicates the identification of the underlying synchronizing factor. Secondly, we find puzzling cases, where synchrony is enhanced as it is filtered through a food web or between age-classes. Our results also apply to systems of different species, but with closely matching dynamics.