Disentangling extrinsic from intrinsic factors in disease dynamics: a nonlinear time series approach with an application to cholera

Alternative explanations for disease and other population cycles typically include extrinsic environmental drivers, such as climate variability, and intrinsic nonlinear dynamics resulting from feedbacks within the system, such as species interactions and density dependence. Because these different factors can interact in nonlinear systems and can give rise to oscillations whose frequencies differ from those of extrinsic drivers, it is difficult to identify their respective contributions from temporal population patterns. In the case of disease, immunity is an important intrinsic factor. However, for many diseases, such as cholera, for which immunity is temporary, the duration and decay pattern of immunity is not well known. We present a nonlinear time series model with two related objectives: the reconstruction of immunity patterns from data on cases and population sizes and the identification of the respective roles of extrinsic and intrinsic factors in the dynamics. Extrinsic factors here include both seasonality and long-term changes or interannual variability in forcing. Results with simulated data show that this semiparametric method successfully recovers the decay of immunity and identifies the origin of interannual variability. An application to historical cholera data indicates that temporary immunity can be long-lasting and decays in approximately 9 yr. Extrinsic forcing of transmissibility is identified to have a strong seasonal component along with a long-term decrease. Furthermore, noise appears to sustain the multiple frequencies in the long-term dynamics. Similar semiparametric models should apply to population data other than for disease.     

Intrinsic and extrinsic drivers of succession: effects of habitat age and season on an aquatic insect community

1. Classic studies of succession, largely dominated by plant community studies, focus on intrinsic drivers of change in community composition, such as inter‐specific competition and changes to the abiotic environment. They often do not consider extrinsic drivers of colonisation, such as seasonal phenology, that can affect community change. 2. Both intrinsic and extrinsic drivers of succession for dipteran communities that occupy ephemeral pools, such as those in artificial containers were investigated. By initiating communities at different times in the season and following them over time, the relative importance of intrinsic (i.e. habitat age) versus extrinsic (i.e. seasonal phenology) drivers of succession were compared. 3. Water‐filled artificial containers were placed in a deciduous forest with 20 containers initiated in each of 3 months. Containers were sampled weekly to assess community composition. Repeated‐measures mixed‐effects analysis of community correspondence analysis (CA) scores enabled us to partition intrinsic and extrinsic effects on succession. Covariates of temperature and precipitation were also tested. 4. Community trajectories (as defined by CA) differed significantly with habitat age and season, indicating that both intrinsic and extrinsic effects influence succession patterns. Comparisons of Akaike Information Criteria corrected for sample sizes (AICcs) showed that habitat age was more important than season for species composition. Temperature and precipitation did not explain composition changes beyond those explained by habitat age and season. 5. Quantification of relative strengths of intrinsic and extrinsic effects on succession in dipteran and other ephemeral communities enables us to disentangle processes that must be understood for predicting changes in community composition.     

Disentangling drivers of spatial autocorrelation in species distribution models

Species distribution models (SDMs) are frequently used to understand the influence of site properties on species occurrence. For robust model inference, SDMs need to account for the spatial autocorrelation of virtually all species occurrence data. Current methods do not routinely distinguish between extrinsic and intrinsic drivers of spatial autocorrelation, although these may have different implications for conservation. Here, we present and test a method that disentangles extrinsic and intrinsic drivers of spatial autocorrelation using repeated observations of a species. We focus on unknown habitat characteristics and conspecific interactions as extrinsic and intrinsic drivers, respectively. We model the former with spatially correlated random effects and the latter with an autocovariate, such that the spatially correlated random effects are constant across the repeated observations whereas the autocovariate may change. We tested the performance of our model on virtual species data and applied it to observations of the corncrake Crex crex in the Netherlands. Applying our model to virtual species data revealed that it was well able to distinguish between the two different drivers of spatial autocorrelation, outperforming models with no or a single component for spatial autocorrelation. This finding was independent of the direction of the conspecific interactions (i.e. conspecific attraction versus competitive exclusion). The simulations confirmed that the ability of our model to disentangle both drivers of autocorrelation depends on repeated observations. In the case study, we discovered that the corncrake has a stronger response to habitat characteristics compared to a model that did not include spatially correlated random effects, whereas conspecific interactions appeared to be less important. This implies that future conservation efforts should primarily focus on maximizing habitat availability. Our study shows how to systematically disentangle extrinsic and intrinsic drivers of spatial autocorrelation. The method we propose can help to correctly identify the main drivers of species distributions.     

Behavioural asymmetry affects escape performance in a teleost fish

Escape performance is fundamental for survival in fish and most other animals. While previous work has shown that both intrinsic (e.g. size, shape) and extrinsic (e.g. temperature, hypoxia) factors can affect escape performance, the possibility that behavioural asymmetry may affect timing and locomotor performance in startled fish is largely unexplored. Numerous studies have found a relationship between brain lateralization and performance in several cognitive tasks. Here, we tested the hypothesis that behavioural lateralization may affect escape performance in a teleost, the shiner perch Cymatogaster aggregata. Escape responses were elicited by mechanical stimulation and recorded using high-speed video (250 Hz). A number of performance variables were analysed, including directionality, escape latency, turning rate and distance travelled within a fixed time. A lateralization index was obtained by testing the turning preference of each subject in a detour test. While lateralization had no effect on escape directionality, strongly lateralized fish showed higher escape reactivity, i.e. shorter latencies, which were associated with higher turning rates and longer distances travelled. Therefore, lateralization is likely to result in superior ability to escape from predator attacks, since previous work has shown that escape timing, turning rate and distance travelled are among the main determinants of escape success.     

Offspring size–number tradeoffs and food quality feedbacks impact population dynamics in a Daphnia–algae system

Population fluctuations can be affected by both extrinsic (e.g. weather patterns, food availability) and intrinsic (e.g. life‐history) factors. A key life‐history tradeoff is the production of offspring size versus number, ranging from many small offspring to few large offspring. Models show that this life‐history tradeoff in offspring size and number, through maturation time, can have significant impacts on population dynamics. However, few manipulative experiments have been conducted that can isolate life‐history effects from impacts of extrinsic factors in consumer–resource systems. We experimentally tested the effect of an offspring size–number tradeoff on population stability and food availability in a consumer–resource system. Using Daphnia pulex, we created a shift from many, small offspring being produced to fewer, larger offspring. Two sets of experiments were performed to examine the interaction of an extrinsic factor (light levels) and intrinsic population structure on dynamics, and we controlled for the ingestion pressure on algal prey at the time of the manipulation. We predicted that the tradeoff would impact internal consumer population characteristics, including biasing the stage structure towards adults, increasing adult size, and increasing average population‐level reproduction. This adult‐dominated stage structure was predicted to then lead to instability and a low quantity–high quality food state. Under all light levels, the manipulated populations became dominated by large adults. Contrary to predictions, the amplitudes of fluctuations in Daphnia biomass were lower in populations shifted to few–large offspring, representing higher stability in these populations. Furthermore, in high light conditions, a stable low Daphnia – high algae biomass (low food quality) state was observed in few–large offspring treatments but not in control (many–small offspring) treatments. Our results show a strong link between light levels as an extrinsic factor and the life‐history tradeoff of consumer offspring size versus number that impacts consumer–resource population dynamics through feedbacks with resource quality.     

Optimal Feedback Strength for Noise Suppression in Autoregulatory Gene Networks

Autoregulatory feedback loops, where the protein expressed from a gene inhibits or activates its own expression are common gene network motifs within cells. In these networks, stochastic fluctuations in protein levels are attributed to two factors: intrinsic noise (i.e., the randomness associated with mRNA/protein expression and degradation) and extrinsic noise (i.e., the noise caused by fluctuations in cellular components such as enzyme levels and gene-copy numbers). We present results that predict the level of both intrinsic and extrinsic noise in protein numbers as a function of quantities that can be experimentally determined and/or manipulated, such as the response time of the protein and the level of feedback strength. In particular, we show that for a fixed average number of protein molecules, decreasing response times leads to attenuation of both protein intrinsic and extrinsic noise, with the extrinsic noise being more sensitive to changes in the response time. We further show that for autoregulatory networks with negative feedback, the protein noise levels can be minimal at an optimal level of feedback strength. For such cases, we provide an analytical expression for the highest level of noise suppression and the amount of feedback that achieves this minimal noise. These theoretical results are shown to be consistent and explain recent experimental observations. Finally, we illustrate how measuring changes in the protein noise levels as the feedback strength is manipulated can be used to determine the level of extrinsic noise in these gene networks.     

Population dynamics of large and small mammals

We offer an evaluation of the Caughley and Krebs hypothesis that small mammals are more likely than large mammals to possess intrinsic population regulating mechanisms. Based on the assumption that intrinsic regulation will be manifest via direct density-dependent feedbacks, and extrinsic regulation via delayed density-dependent feedbacks, we fit autoregressive models to 30 time series of abundance for large and small mammals to characterize their dynamics. Delayed feedbacks characterizing extrinsic mechanisms, such as trophic-level interactions, were detected in most time series, including both small and large mammals. Spectral analyses indicated that the effect of such delayed feedbacks on the variability in population growth rates differed with body size, with large mammals exhibiting predominantly reddened and whitened spectra in contrast with predominantly blue spectra for small mammals. Large mammals showed less variance and more stable dynamics than small mammals, consistent with, among other factors, differences in their potential population growth rates. Patterns of population dynamics in small versus large mammals contradicted those predicted by the Caughley and Krebs hypothesis.     

Causality and persistence in ecological systems: a nonparametric spectral granger causality approach

Abstract Directionality in coupling, defined as the linkage relating causes to their effects at a later time, can be used to explain the core dynamics of ecological systems by untangling direct and feedback relationships between the different components of the systems. Inferring causality from measured ecological variables sampled through time remains a formidable challenge further made difficult by the action of periodic drivers overlapping the natural dynamics of the system. Periodicity in the drivers can often mask the self-sustained oscillations originating from the autonomous dynamics. While linear and direct causal relationships are commonly addressed in the time domain, using the well-established machinery of Granger causality (G-causality), the presence of periodic forcing requires frequency-based statistics (e.g., the Fourier transform), able to distinguish coupling induced by oscillations in external drivers from genuine endogenous interactions. Recent nonparametric spectral extensions of G-causality to the frequency domain pave the way for the scale-by-scale decomposition of causality, which can improve our ability to link oscillatory behaviors of ecological networks to causal mechanisms. The performance of both spectral G-causality and its conditional extension for multivariate systems is explored in quantifying causal interactions within ecological networks. Through two case studies involving synthetic and actual time series, it is demonstrated that conditional G-causality outperforms standard G-causality in identifying causal links and their concomitant timescales.     

How Stochasticity Influences Leading Indicators of Critical Transitions

Many complex systems exhibit critical transitions. Of considerable interest are bifurcations, small smooth changes in underlying drivers that produce abrupt shifts in system state. Before reaching the bifurcation point, the system gradually loses stability (‘critical slowing down’). Signals of critical slowing down may be detected through measurement of summary statistics, but how extrinsic and intrinsic noises influence statistical patterns prior to a transition is unclear. Here, we consider a range of stochastic models that exhibit transcritical, saddle-node and pitchfork bifurcations. Noise was assumed to be either intrinsic or extrinsic. We derived expressions for the stationary variance, autocorrelation and power spectrum for all cases. Trends in summary statistics signaling the approach of each bifurcation depend on the form of noise. For example, models with intrinsic stochasticity may predict an increase in or a decline in variance as the bifurcation parameter changes, whereas models with extrinsic noise applied additively predict an increase in variance. The ability to classify trends of summary statistics for a broad class of models enhances our understanding of how critical slowing down manifests in complex systems approaching a transition.     

Improving the Modeling of Disease Data from the Government Surveillance System: A Case Study on Malaria in the Brazilian Amazon

The study of the effect of large-scale drivers (e.g., climate) of human diseases typically relies on aggregate disease data collected by the government surveillance network. The usual approach to analyze these data, however, often ignores a) changes in the total number of individuals examined, b) the bias towards symptomatic individuals in routine government surveillance, and; c) the influence that observations can have on disease dynamics. Here, we highlight the consequences of ignoring the problems listed above and develop a novel modeling framework to circumvent them, which is illustrated using simulations and real malaria data. Our simulations reveal that trends in the number of disease cases do not necessarily imply similar trends in infection prevalence or incidence, due to the strong influence of concurrent changes in sampling effort. We also show that ignoring decreases in the pool of infected individuals due to the treatment of part of these individuals can hamper reliable inference on infection incidence. We propose a model that avoids these problems, being a compromise between phenomenological statistical models and mechanistic disease dynamics models; in particular, a cross-validation exercise reveals that it has better out-of-sample predictive performance than both of these alternative models. Our case study in the Brazilian Amazon reveals that infection prevalence was high in 2004–2008 (prevalence of 4% with 95% CI of 3–5%), with outbreaks (prevalence up to 18%) occurring during the dry season of the year. After this period, infection prevalence decreased substantially (0.9% with 95% CI of 0.8–1.1%), which is due to a large reduction in infection incidence (i.e., incidence in 2008–2010 was approximately one fifth of the incidence in 2004–2008).We believe that our approach to modeling government surveillance disease data will be useful to advance current understanding of large-scale drivers of several diseases.     

Inference for nonlinear epidemiological models using genealogies and time series

Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.     

Lymphocyte Sensitization in Asthma with Special Reference to Nature and Identity of Intrinsic Form

Studies of lymphocyte sensitization in patients with asthma showed that the intrinsic and extrinsic forms of the disease fell into two distinct groups. Intrinsic disease showed a general sensitization to a number of non-specific antigens, while the extrinsic form had only slight elevation above normal values. These findings suggest that intrinsic asthma results from a defect of general immunity, whereas extrinsic asthma is a specific sensitization.     

Backward bifurcations and multiple equilibria in epidemic models with structured immunity

Many disease pathogens stimulate immunity in their hosts, which then wanes over time. To better understand the impact of this immunity on epidemiological dynamics, we propose an epidemic model structured according to immunity level that can be applied in many different settings. Under biologically realistic hypotheses, we find that immunity alone never creates a backward bifurcation of the disease-free steady state. This does not rule out the possibility of multiple stable equilibria, but we provide two sufficient conditions for the uniqueness of the endemic equilibrium, and show that these conditions ensure uniqueness in several common special cases. Our results indicate that the within-host dynamics of immunity can, in principle, have important consequences for population-level dynamics, but also suggest that this would require strong non-monotone effects in the immune response to infection. Neutralizing antibody titer data for measles are used to demonstrate the biological application of our theory.     

Multiscale model of CRISPR-induced coevolutionary dynamics: diversification at the interface of Lamarck and Darwin

The CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is a recently discovered type of adaptive immune defense in bacteria and archaea that functions via directed incorporation of viral and plasmid DNA into host genomes. Here, we introduce a multiscale model of dynamic coevolution between hosts and viruses in an ecological context that incorporates CRISPR immunity principles. We analyze the model to test whether and how CRISPR immunity induces host and viral diversification and the maintenance of many coexisting strains. We show that hosts and viruses coevolve to form highly diverse communities. We observe the punctuated replacement of existent strains, such that populations have very low similarity compared over the long term. However, in the short term, we observe evolutionary dynamics consistent with both incomplete selective sweeps of novel strains (as single strains and coalitions) and the recurrence of previously rare strains. Coalitions of multiple dominant host strains are predicted to arise because host strains can have nearly identical immune phenotypes mediated by CRISPR defense albeit with different genotypes. We close by discussing how our explicit eco-evolutionary model of CRISPR immunity can help guide efforts to understand the drivers of diversity seen in microbial communities where CRISPR systems are active.     

Dinamica dei sistemi a Cymodocea nodosa,Zostera marina e Zostera noltii nel Mediterraneo

Abstract

Data on geographical and depth distribution, sediment granulometry, salinity, biomass variability, below/aboveground biomass ratio, and reproductive strategies of seagrass communities in the Mediterranean Sea were analysed to describe their dynamics patterns.

Notwithstanding their different latitudinal distribution, they have a similar seasonal biomass variability, deriving both from extrinsic forcing (e.g. light and temperature) and intrinsic species-specific components (e.g. reproduction pattern), these latter being responsible for their different structure and seasonal dynamics.     

Forcing Versus Feedback: Epidemic Malaria and Monsoon Rains in Northwest India

Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing.     

Unravelling insect declines: can space replace time?

Temporal trends in insect numbers vary across studies and habitats, but drivers are poorly understood. Suitable long-term data are scant and biased, and interpretations of trends remain controversial. By contrast, there is substantial quantitative evidence for drivers of spatial variation. From observational and experimental studies, we have gained a profound understanding of where insect abundance and diversity is higher—and identified underlying environmental conditions, resource change and disturbances. We thus propose an increased consideration of spatial evidence in studying the causes of insect decline. This is because for most time series available today, the number of sites and thus statistical power strongly exceed the number of years studied. Comparisons across sites allow quantifying insect population risks, impacts of land use, habitat destruction, restoration or management, and stressors such as chemical and light pollution, pesticides, mowing or harvesting, climatic extremes or biological invasions. Notably, drivers may not have to change in intensity to have long-term effects on populations, e.g. annually repeated disturbances or mortality risks such as those arising from agricultural practices. Space-for-time substitution has been controversially debated. However, evidence from well-replicated spatial data can inform on urgent actions required to halt or reverse declines—to be implemented in space.     

Explaining ecological shifts: the roles of temperature and primary production in the long‐term dynamics of benthic faunal composition

Predicting the ecological consequences of environmental change requires that we can identify the drivers of long‐term ecological variation. Biological assemblages can exhibit abrupt deviations from temporal trends, potentially resulting in irreversible shifts in species composition over short periods of time. Such dynamics are hypothesised to occur as gradual forcing eventually causes biological thresholds to be crossed, but could also be explained by biota simply tracking abrupt changes to their environment. Here, we modelled temporal variation in a North Sea benthic faunal assemblage over a 40‐year period (1972–2012) to test for changes to temporal trends of biota and determine whether they could be explained by underlying patterns in sea temperature and primary production. These extrinsic factors were postulated to influence community dynamics through their roles in determining and sustaining the metabolic demands of organisms, respectively. A subset of mainly large and long‐lived taxa (those loaded on the first principal component of taxa densities) exhibited two significant changes to their temporal trends, which culminated in a shift in assemblage composition. These changes were explained by an increase in pelagic primary production, and hence detrital food input to the seabed, but were unrelated to variation in sea temperature. A second subset of mainly small and short‐lived taxa (those loaded on the second principal component) did not experience any significant changes to their temporal trends, as enhanced pelagic primary production appeared to mitigate the impact of warming on these organisms. Our results suggest that abrupt ecological shifts can occur as biota track underlying variation in extrinsic factors, in this case primary production. Changes to the structure of ecosystems may therefore be predictable based on environmental change projections.     

Intrinsic fluctuations, robustness, and tunability in signaling cycles

Covalent modification cycles (e.g., phosphorylation-dephosphorylation) underlie most cellular signaling and control processes. Low molecular copy number, arising from compartmental segregation and slow diffusion between compartments, potentially renders these cycles vulnerable to intrinsic chemical fluctuations. How can a cell operate reliably in the presence of this inherent stochasticity? How do changes in extrinsic parameters lead to variability of response? Can cells exploit these parameters to tune cycles to different ranges of stimuli? We study the dynamics of an isolated phosphorylation cycle. Our model shows that the cycle transmits information reliably if it is tuned to an optimal parameter range, despite intrinsic fluctuations and even for small input signal amplitudes. At the same time, the cycle is sensitive to changes in the concentration and activity of kinases and phosphatases. This sensitivity can lead to significant cell-to-cell response variability. It also provides a mechanism to tune the cycle to transmit signals in various amplitude ranges. Our results show that signaling cycles possess a surprising combination of robustness and tunability. This combination makes them ubiquitous in eukaryotic signaling, optimizing signaling in the presence of fluctuations using their inherent flexibility. On the other hand, cycles tuned to suppress intrinsic fluctuations can be vulnerable to changes in the number and activity of kinases and phosphatases. Such trade-offs in robustness to intrinsic and extrinsic fluctuations can influence the evolution of signaling cascades, making them the weakest links in cellular circuits.