An empirically based model for latitudinal gradient in vole population dynamics

Vole dynamics in northern Europe exhibit a well-defined geographical gradient, with oscillatory populations being confined to high latitudes. It has been proposed that oscillations in northern vole populations are driven by their interaction with specialist predators (weasels), while the more southern rodent populations are relatively stable because of regulation by generalist predators. We tested this generalist/specialist predation hypothesis by constructing an empirically based model for vole population dynamics, estimating its parameters, and making predictions about the quantitative pattern of the latitudinal shift in vole dynamics. Our results indicated that the model accurately predicted the latitudinal shift in the amplitude and periodicity of population fluctuations. Moreover, the model predicted that vole dynamics should shift from stable to chaotic as latitude is increased, a result in agreement with nonlinear time-series analysis of the data. The striking success of the model at predicting the shifts in amplitude and stability along the geographical gradient in northern Europe provides strong support for the key role of specialist and generalist predators in vole population dynamics.     

Disentangling demographic co‐effects of predation and pollution on population dynamics

In nature species react to a variety of endogenous and exogenous ecological factors. Understanding the mechanisms by which these factors interact and drive population dynamics is a need for understanding and managing ecosystems. In this study we assess, using laboratory experiments, the effects that the combinations of two exogenous factors exert on the endogenous structure of the population dynamics of a size‐structured population of Daphnia. One exogenous factor was size‐selective predation, which was applied on experimental populations through simulating: 1) selective predation on small prey, 2) selective predation on large prey and 3) non‐selective predation. The second exogenous factor was pesticide exposure, applied experimentally in a quasi‐continuous regime. Our analysis combined theoretical models and statistical testing of experimental data for analyzing how the density dependence structure of the population dynamics was shifted by the different exogenous factors. Our results showed that pesticide exposure interacted with the mode of predation in determining the endogenous dynamics. Populations exposed to the pesticide and to either selective predation on newborns or selective predation on adults exhibited marked nonlinear effects of pesticide exposure. However, the specific mechanisms behind such nonlinear effects were dependent on the mode of size‐selectivity. In populations under non‐selective predation the pesticide exposure exerted a weak lateral effect. The ways in which endogenous process and exogenous factors may interact determine population dynamics. Increases in equilibrium density results in higher variance of population fluctuations but do not modify the stability properties of the system, while changes in the maximum growth rate induce changes in the dynamic regimes and stability properties of the population. Future consideration for research includes the consequences of the seasonal variation in the composition and activity of the predator assembly in interaction with the seasonal variation in exposure to agrochemicals on freshwater population dynamics.     

Overcompensatory population dynamic responses to environmental stochasticity

1. To quantify the interactions between density-dependent, population regulation and density-independent limitation, we studied the time-series dynamics of an experimental laboratory insect microcosm system in which both environmental noise and resource limitation were manipulated. 2. A hierarchical Bayesian state-space approach is presented through which it is feasible to capture all sources of uncertainty, including observation error to accurately quantify the density dependence operating on the dynamics. 3. The regulatory processes underpinning the dynamics of two different bruchid beetles (Callosobruchus maculatus and Callosobruchus chinensis) are principally determined by environmental conditions, with fluctuations in abundance explained in terms of changes in overcompensatory dynamics and stochastic processes. 4. A general, stochastic population model is developed to explore the link between abundance fluctuations and the interaction between density dependence and noise. Taking account of time-lags in population regulation can substantially increase predicted population fluctuations resulting from underlying noise processes.     

How much complexity is needed to describe the fluctuations observed in dengue hemorrhagic fever incidence data?

Different extensions of the classical single-strain SIR model for the host population, motivated by modeling dengue fever epidemiology, have reported a rich dynamic structure including deterministic chaos which was able to mimic the large fluctuations of disease incidences. A comparison between the basic two-strain dengue model, which already captures differences between primary and secondary infections including temporary cross-immunity, with the four-strain dengue model, that introduces the idea of competition of multiple strains in dengue epidemics shows that the difference between first and secondary infections drives the rich dynamics more than the detailed number of strains to be considered in the model structure. Chaotic dynamics were found to happen in the same parameter region of interest, for both the two and the four-strain models, able to describe the fluctuations observed in empirical data and shows a qualitatively good agreement between empirical data and model simulation. The predictability of the system does not change significantly when considering two or four strains, i.e. both models present a positive dominant Lyapunov exponent giving approximately the same prediction horizon in time series. Since the law of parsimony favors the simplest of two competing models, the two-strain model would be the better candidate to be analyzed, as well the best option for estimating all initial conditions and the few model parameters based on the available incidence data.     

Exploring the drivers of wildlife population dynamics from insufficient data by Bayesian model averaging

A long-standing interest in ecology and wildlife management is to find drivers of wildlife population dynamics because it is crucial for implementing the effective wildlife management. Recent studies have demonstrated the usefulness of state-space modeling for this purpose, but we often confront the lack of the necessary time-series data. This is particularly common in wildlife management because of limited funds or early stage of data collection. In this study, we proposed a Bayesian model averaging technique in a state-space modeling framework for identifying the drivers of wildlife population dynamics from limited data. To exemplify the utility of Bayesian model averaging for wildlife management, we illustrate here the population dynamics of wild boars Sus scrofa in Chiba prefecture, central Japan. Despite the fact that our data are limited in both temporal and spatial resolution, Bayesian model averaging revealed the potential influence of bamboo forests and abandoned agricultural fields on wild boar population dynamics, and largely enhanced model predictability compared to the full model. Although Bayesian model averaging is not commonly used in ecology and wildlife management, our case study demonstrated that it may help to find influential drivers of wildlife population dynamics and develop a better management plan even from limited time-series data.     

Scaling up: how do exogenous fluctuations in individual-based resource competition models re-emerge in aggregated stochastic population models?

In applied population dynamics the choice of stochastic per capita growth function has implications for population viability analyses, management recommendations, and pest control. This model choice is often based on statistical criteria, mathematical tractability or personal preferences, and general ecological guidelines are either too vague or entirely missing. To identify such guidelines, it is important to understand how exogenous and endogenous factors interact at the individual level and re-emerge at the aggregated population level. We therefore study different types of resource competition (contest vs. scramble competition) and different types of exogenous fluctuations (food and weather fluctuations) at the individual level in a simple individual-based simulation model. We statistically fit the resulting time series to find out (1) which functional form of the growth function (‘hyperbolic’ or ‘exponential’) better describes contest and scramble competition and (2) whether the pattern of population fluctuations resulting from the simulations can be assigned to vertical, lateral or nonlinear perturbations in the stochastic growth function (a classification scheme suggested by Royama 1992, Analytical Population Dynamics, Chapman and Hall, London). We found that the same type of competition can result in ‘hyperbolic’ or ‘exponential’ functional forms, depending on the type of exogenous fluctuations. So it is the interplay between exogenous variability and endogenous resource competition that affects model performance. In contrast to the widespread assumption of vertical (additive) perturbations, our findings highlight the importance of (non-additive) lateral and nonlinear perturbations and their combinations with vertical perturbations. The choice of the stochastic growth function should therefore consider not only statistical criteria but also ecological guidelines. We derive such ecological guidelines from our analysis.     

Population dynamics of two small pelagic fish in the central-south area off Chile: delayed density-dependence and biological interaction

It is widely believed that environmental variability is the main cause for fluctuations in commercially exploited small pelagic fish populations around the world. Nevertheless, density-dependent factors also can drive population dynamics. In this paper, we analyzed thirteen years of a relative abundance index of two clupeoids fish populations coexisting in the central-south area off Chile, namely the common sardine, Strangomera bentincki, and anchovy, Engraulis ringens. We applied the classical diagnostic tools of time series analysis to the observed time-series. Also, the realized per capita population growth rate was studied with the aim of detecting the feedback structure that is characterizing the population dynamics of the two species. The analysis suggests that population fluctuations of the two species have an important density-dependent component, displaying first-order (direct density-dependent) and second-order (delayed density-dependent) simultaneously. The density-dependent component explained 70.5 and 55.6 % of the realized per capita population growth rate of common sardine and anchovy, respectively. The deterministic skeleton model showed an asymptotic convergence to equilibrium density. In presence of a stochastic environment, fluctuations were reproduced for the species showing a component of fluctuation with a period of 4 year. The intrinsic dynamics of each species is typical of interacting species resulting from trophic interactions. It is postulated that the second-order dynamics of S. bentincki and E. ringens in central-south Chile, may be the result from interactions with a specialist predator (the fishing fleet), interacting with exogenous environmental factors.     

Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep

The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant degree of nonlinear RRI dynamics in all subjects. A parametric model, consisting of a nonlinear delayed-feedback system with stochastic noise as the perturbing input, was employed to estimate the relative contributions of linear and nonlinear deterministic dynamics in the data. Both infant groups showed similar proportional contributions in linear, nonlinear, and stochastic dynamics. However, approximate entropy, correlation dimension, and nonlinear prediction error were all decreased in active versus quiet sleep; in addition, the parametric model revealed a doubling of the linear component and a halving of the nonlinear contribution to overall heart rate variability. Spectral analysis indicated a shift in relative power toward lower frequencies. We conclude that 1) RRI dynamics in infants with PCE and normal controls are similar; and 2) in both groups, sympathetic dominance during active sleep produces primarily periodic low-frequency oscillations in RRI, whereas in quiet sleep vagal modulation leads to RRI fluctuations that are broadband and dynamically more complex.     

Non-linear feedback processes and a latitudinal gradient in the climatic effects determine green spruce aphid outbreaks in the UK

The role of climatic fluctuations in determining the dynamics of insect populations has been a classical problem in population ecology. Here, we use long-term annual data on green spruce aphid populations at nine localities in the UK for determining the importance of endogenous processes, local weather and large-scale climatic factors. We rely on diagnostic and modelling tools from population dynamic theory to analyse these long-term data and to determine the role of the North Atlantic Oscillation (NAO) and local weather as exogenous factors influencing aphid dynamics. Our modelling suggests that the key elements determining population fluctuations in green spruce aphid populations in the UK are the strong non-linear feedback structure, the high potential for population growth and the effects of winter and spring weather. The results indicate that the main effect of the NAO on green spruce aphid populations is operating through the effect of winter temperatures on the maximum per capita growth rate (R_m). In particular, we can predict quite accurately the occurrence of an outbreak by using a simple logistic model with weather as a perturbation effect. However, model predictions using different climatic variables showed a clear geographical signature. The NAO and winter temperature were best for predicting observed dynamics toward the southern localities, while spring temperature was a much better predictor of aphid dynamics at northern localities. Although aphid species are characterized by complex life-cycles, we emphasize the value of simple and general population dynamic models in predicting their dynamics.     

Population dynamics of two rodent species in agro-ecosystems of central Argentina: intra-specific competition,land-use,and climate effects

Understanding the role of feedback structure (endogenous processes) and exogenous (climatic and environmental) factors in shaping the dynamics of natural populations is a central challenge within the field of population ecology. We attempted to explain the numerical fluctuations of two sympatric rodent species in agro-ecosystems of central Argentina using Royama’s theoretical framework for analyzing the dynamics of populations influenced by exogenous climatic forces. We found that both rodent species show a first-order negative feedback structure, suggesting that these populations are regulated by intra-specific competition (limited by food, space, or enemy-free space). In Akodon azarae endogenous structure seems to be very strongly influenced by human land-use represented by annual minimum normalized difference vegetation index (NDVI), with spring and summer rainfall having little influence upon carrying capacity. Calomys venustus’ population dynamics, on the other hand, seem to be more affected by local climate, also with spring and summer rainfall influencing the carrying capacity of the environment, but combined with spring mean temperature. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Generalizations of the Moran effect explaining spatial synchrony in population fluctuations

The Moran effect for populations separated in space states that the autocorrelations in the population fluctuations equal the autocorrelation in environmental noise, assuming the same linear density regulation in all populations. Here we generalize the Moran effect to include also nonlinear density regulation with spatial heterogeneity in local population dynamics as well as in the effects of environmental covariates by deriving a simple expression for the correlation between the sizes of two populations, using diffusion approximation to the theta-logistic model. In general, spatial variation in parameters describing the dynamics reduces population synchrony. We also show that the contribution of a covariate to spatial synchrony depends strongly on spatial heterogeneity in the covariate or in its effect on local dynamics. These analyses show exactly how spatial environmental covariation can synchronize fluctuations of spatially segregated populations with no interchange of individuals even if the dynamics are nonlinear.     

Multi-Annual Fluctuations in Reconstructed Historical Time-Series of a European Lobster (Homarus gammarus) Population Disappear at Increased Exploitation Levels

Through the history of ecology, fluctuations of populations have been a dominating topic, and endogenous causes of fluctuations and oscillations have been recognized and studied for more than 80 years. Here we analyzed an historical dataset, covering more than 130 years, of European lobster (Homarus gammarus) catches. The data shows periodic fluctuations, which are first dampened and then disappear over time. The disappearance of the periodicity coincided with a substantial increase in fishing effort and the oscillations have not reappeared in the time series. The shifting baseline syndrome has changed our perception of not only the status of the stock, but also the regulating pressures. We describe the transition of a naturally regulated lobster population into a heavily exploited fisheries controlled stock. This is shown by the incorporation of environmental and endogenous processes in generalized additive models, autocorrelation functions and periodicity analyses of time-series.     

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.     

Intrinsically generated coloured noise in laboratory insect populations

What are the mechanisms responsible for generating the erratic fluctuations observed in natural populations? This question has been at the centre of a long debate in contemporary ecology. The irregularities in the patterns of population abundance were initially mostly attributed to environmental factors. In the mid-1970s, however, it was proposed that these fluctuations may be generated intrinsically, by the underlying nonlinearities inherent in population processes. More recently, the focus of this argument has turned increasingly towards the statistical properties of population fluctuations, with many studies showing that ecological systems tend to be dominated by low-frequency or long-term dynamics, termed ''red'' noise. Currently, the source of the ''redness'' in ecological time-series is hotly debated, with the general consensus being that environmental variables are the major driving force. Here we show that three classic laboratory populations known to display irregular fluctuations also have reddened spectra. Furthermore, the dynamics of these populations show very well-defined generic scaling properties in the form of power laws. These results imply that long-term influences in ecological systems can be the product of intrinsic dynamics.     

Concordant population dynamics of Lepidoptera herbivores in a forest ecosystem

It is frequently assumed that population fluctuations are largely independent within a community of trophically‐similar species, but this need not be so. If population fluctuations are partly synchronized or concordant, this will produce interannual variability in the community's aggregate abundance and generate temporal variance in ecosystem structure. We studied the community of Lepidoptera inhabiting northern hardwood forests in New Hampshire, USA, to evaluate the hypothesis that fluctuations in consumer communities can arise from concordant dynamics of constituent populations. Interannual comparisons of moth abundances for >75 species sampled at three sites over four years revealed that concordant dynamics contribute strongly to interannual variability in the abundance of consumers. A conspicuous decline in community abundance from 2004 to 2005 was the result of predominantly negative population growth rates of the component species, while an increase in community abundance from 2006 to 2007 was the result of predominantly positive population growth rates. Population dynamics most strongly linked species that feed in the early season (perhaps due to shared responses to climatic effects), but not species that might share natural enemies or host plants. The observed concordant dynamics introduced conspicuous temporal variation in the abundance of primary consumers relative to plants and secondary consumers, thereby altering the forest's trophic structure. Such variance in the aggregate abundance of forest primary consumers could generate time‐lagged fluctuations in abundances of secondary consumers and will generally have important consequences for ecosystem properties and processes that are nonlinear functions of consumer abundance, such as plant community structure and nutrient cycling.     

Population cycles in voles and lemmings: state of the science and future directions

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Second-order feedback and climatic effects determine the dynamics of a small rodent population in a temperate forest of South America

 The multiannual cyclic fluctuations exhibited by arvicoline rodents in the Northern Hemisphere have attracted the attention of population ecologists. However, despite the abundant information on small rodent dynamics in South America, there are no studies reporting cyclic population dynamics. Here, we report evidence of cyclic population dynamics in a South American small rodent, the longhaired field mouse (Abrothrix longipilis) from southern temperate forests in Chile. The time-series analyses showed that longhaired field mice dynamics are better represented by a second-order autoregressive model characterized by 3-year cyclic dynamics. The 3-year cycles are clearly shown in the autocorrelation factor (ACF) pattern and in the dominant frequency of the spectral analysis. In addition, we determined nonlinear effects of the Antarctic Oscillation Index (AAOI). The results shown here pointed out that we need the integration of studies about cyclic small rodent populations from the different continents and beyond the Northern Hemisphere to resolve the enigma underlying the cyclic population dynamics exhibited by many small rodent species. Received: September 19, 2002 / Accepted: February 4, 2003