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.     

Extrinsically and intrinsically generated spatial patterns of algal abundance in an experimental stream

Spatial heterogeneity in species abundance arises from both extrinsic (largely abiotic) and intrinsic (largely biotic) processes. The relative importance of these two types of processes can vary across ecological systems and across temporal and spatial scales. Numerous empirical studies have explored spatial patterns resulting from extrinsic and intrinsic processes, however the interaction of these two types of processes can result in complex patterns that are difficult to test. We used a unique model system consisting of periphytic algae grown on agar in an experimental stream to manipulate an extrinsic and an intrinsic process. We manipulated an extrinsic process by varying the spatial arrangement of nutrients creating both heterogeneous and homogeneous environments for the algae. We manipulated an intrinsic process by introducing a snail herbivore to the system. The resulting spatial algal patterns showed that both types of processes were important in producing spatial abundance patterns and that the patterns occurred at two distinct spatial scales in our system. At the scale of the imposed nutrient heterogeneity, algae “tracked” the differences in nutrient supply rates. The snail herbivores both reduced and promoted spatial patterns in algal abundance at different spatial scales reflecting their species-specific foraging behavior. An ability to detect differences in algal abundance allowed the snails to reduce the power of patterns at the scale of the imposed nutrient heterogeneity; however below a spatial scale of approximately 30 mm the snails could no longer detect differences in algal abundance and so foraged randomly. At this spatial scale the spatial heterogeneity in algal abundance increased and the resulting algal patterns were relatively spatially fixed through time. We suggest that this relative constancy may arise in part from a detected weak Allee effect in algal growth rates.     

Construction and analysis of a modular model of caspase activation in apoptosis

Background  

A key physiological mechanism employed by multicellular organisms is apoptosis, or programmed cell death. Apoptosis is triggered by the activation of caspases in response to both extracellular (extrinsic) and intracellular (intrinsic) signals. The extrinsic and intrinsic pathways are characterized by the formation of the death-inducing signaling complex (DISC) and the apoptosome, respectively; both the DISC and the apoptosome are oligomers with complex formation dynamics. Additionally, the extrinsic and intrinsic pathways are coupled through the mitochondrial apoptosis-induced channel via the Bcl-2 family of proteins.     

Capturing escape in infectious disease dynamics

Identifying the causes of interannual variability in disease dynamics is important for understanding and managing epidemics. Traditionally, these causes have been classified as intrinsic (e.g. immunity fluctuations) or extrinsic (e.g. climate forcing); ecologists determine the relative contributions of these factors by applying statistical models to time series of cases. Here we address the problem of isolating the drivers of pathogen dynamics that are influenced by antigenic evolution. Recent findings indicate that many pathogens escape immunity in a punctuated manner; for them, we argue that time series of cases alone will be insufficient to isolate causal drivers. We detail observations that can reveal the presence of punctuated immune escape, and which can be used in new statistical approaches to identify extrinsic and intrinsic regulators of disease.     

Order in spontaneous behavior

Brains are usually described as input/output systems: they transform sensory input into motor output. However, the motor output of brains (behavior) is notoriously variable, even under identical sensory conditions. The question of whether this behavioral variability merely reflects residual deviations due to extrinsic random noise in such otherwise deterministic systems or an intrinsic, adaptive indeterminacy trait is central for the basic understanding of brain function. Instead of random noise, we find a fractal order (resembling Lévy flights) in the temporal structure of spontaneous flight maneuvers in tethered Drosophila fruit flies. Lévy-like probabilistic behavior patterns are evolutionarily conserved, suggesting a general neural mechanism underlying spontaneous behavior. Drosophila can produce these patterns endogenously, without any external cues. The fly's behavior is controlled by brain circuits which operate as a nonlinear system with unstable dynamics far from equilibrium. These findings suggest that both general models of brain function and autonomous agents ought to include biologically relevant nonlinear, endogenous behavior-initiating mechanisms if they strive to realistically simulate biological brains or out-compete other agents.     

Patterns of temporal community turnover are spatially synchronous across boreal lakes

1. Ecosystems are often exposed to broad‐scale environmental change, which can potentially synchronise community dynamics and biodiversity trends. Detection of temporal coherence may, however, depend on the metrics used and their sensitivity to detect change, requiring several lines of evidence to elucidate the full range of temporal responses to environmental change. 2. Here, we tested whether the patterns of synchrony among littoral invertebrate communities of Swedish lakes over 20 years (1988–2007) differed when analysed using univariate (taxon richness, evenness, Shannon diversity and total abundance) or multivariate (temporal turnover in community composition) metrics. We included both culturally acidified and circumneutral lakes to examine whether anthropogenic stress influenced the patterns of synchrony. 3. Average total abundance, taxon richness and temporal turnover in community composition changed monotonically with time, while evenness and Shannon diversity fluctuated around a long‐term mean. However, among‐lake variability was high, resulting in a weak temporal coherence. Only trends of temporal turnover changed synchronously across lakes, irrespective of their acidification history. 4. Spatially synchronous trends in turnover across lakes were correlated with increasing water colour and decreasing sulphate concentrations, showing the importance of regional drivers of spatiotemporal coherence. 5. Our results underpin an increasing body of evidence that the detection of diversity patterns varies among metrics that ignore (taxon richness, evenness, Shannon diversity) or consider (turnover) species identities. More generally, our results suggest that community‐level studies of synchrony are suitable for elucidating the role of intrinsic versus extrinsic factors in mediating complex community assembly processes in the long term. This, in turn, contributes to our understanding of temporal patterns of biodiversity.     

Investigating a network model of word generation with positron emission tomography.

By using positron emission tomography (PET) we examined the biological validity of a network model describing changes in cerebral activity associated with intrinsic and extrinsic word generation. The production of words not specified by an extrinsic stimulus constitutes willed or intrinsic generation. Perceiving a heard word is an example of extrinsic generation. The model incorporates three neuronal systems: a pool that stores word representations in a distributed fashion, an afferent system conveying sensory input to the pool and a modulating system that alters the responsivity of neurons in the pool. Simulations based on the model suggested that intrinsic generation would be associated with low activity in the pool, consequent on reduced modulation, and extrinsic generation with high activity. We measured cerebral activity with PET during intrinsic (verbal fluency) and extrinsic (responding to heard words) word generation and found this pattern of changes in the left superior temporal region. We were able to designate this region the site of the distributed word store and implicate the left dorsolateral prefrontal cortex (DLPFC) as the source of modulation. The relation between the superior temporal gyrus and DLPFC was shown by examining the correlation between the two regions in terms of cerebral activity. We conclude that the left DLPFC is responsible for modulating the responsivity of a neural system in the superior temporal gyrus and is the probable mediator of changes in attentional and intentional states that underlies the intrinsic generation of words.     

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 and extrinsic regulators of developmental timing: from miRNAs to nutritional cues

A fundamental challenge in biology is to understand the reproducibility of developmental programs between individuals of the same metazoan species. This developmental precision reflects the meticulous integration of temporal control mechanisms with those that specify other aspects of pattern formation, such as spatial and sexual information. The cues that guide these developmental events are largely intrinsic to the organism but can also include extrinsic inputs, such as nutrition or temperature. This review discusses the well-characterized developmental timing mechanism that patterns the C. elegans epidermis. Components of this pathway are conserved, and their links to developmental time control in other species are considered, including the temporal patterning of the fly nervous system. Particular attention is given to the roles of miRNAs in developmental timing and to the emerging mechanisms that link developmental programs to nutritional cues.     

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.     

Grasshopper (Orthoptera: Acrididae) communities respond to fire,bison grazing and weather in North American tallgrass prairie: a long-term study

Because both intrinsic and extrinsic factors influence insect population dynamics, operating at a range of temporal and spatial scales, it is difficult to assess their contributions. Long-term studies are ideal for assessing the relative contributions of multiple factors to abundance and community dynamics. Using data spanning 25 years, we investigate the contributions of weather at annual and decadal scales, fire return interval, and grazing by bison to understand the dynamics of abundance and community composition in grasshopper assemblages from North American continental grassland. Each of these three primary drivers of grassland ecosystem dynamics affects grasshopper population and community dynamics. Negative feedbacks in abundances, as expected for regulated populations, were observed for all feeding guilds of grasshoppers. Abundance of grasshoppers did not vary in response to frequency of prescribed burns at the site. Among watersheds that varied with respect to controlled spring burns and grazing by bison, species composition of grasshopper assemblages responded significantly to both after 25 years. However, after more than 20 years of fire and grazing treatments, the number of years since the last fire was more important than the managed long-term fire frequency per se. Yearly shifts in species composition (1983–2005), examined using non-metric multidimensional scaling and fourth-corner analysis, were best explained by local weather events occurring early in grasshopper life cycles. Large-scale patterns were represented by the Palmer Drought Severity Index and the North Atlantic Oscillation (NAO). The NAO was significantly correlated with annual mean frequencies of grasshoppers, especially for forb- and mixed-feeding species. Primary grassland drivers—fire, grazing and weather—contributing both intrinsic and extrinsic influences modulate long-term fluctuations in grasshopper abundances and community taxonomic composition. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Absence of cue-recruitment for extrinsic signals: sounds, spots, and swirling dots fail to influence perceived 3D rotation direction after training

The visual system can learn to use information in new ways to construct appearance. Thus, signals such as the location or translation direction of an ambiguously rotating wire frame cube, which are normally uninformative, can be learned as cues to determine the rotation direction. This perceptual learning occurs when the formerly uninformative signal is statistically associated with long-trusted visual cues (such as binocular disparity) that disambiguate appearance during training. In previous demonstrations, the newly learned cue was intrinsic to the perceived object, in that the signal was conveyed by the same image elements as the object itself. Here we used extrinsic new signals and observed no learning. We correlated three new signals with long-trusted cues in the rotating cube paradigm: one crossmodal (an auditory signal) and two within modality (visual). Cue recruitment did not occur in any of these conditions, either in single sessions or in ten sessions across as many days. These results suggest that the intrinsic/extrinsic distinction is important for the perceptual system in determining whether it can learn and use new information from the environment to construct appearance. Extrinsic cues do have perceptual effects (e.g. the "bounce-pass" illusion and McGurk effect), so we speculate that extrinsic signals must be recruited for perception, but only if certain conditions are met. These conditions might specify the age of the observer, the strength of the long-trusted cues, or the amount of exposure to the correlation.     

Song complexity is associated with habitat quality in an upland passerine

Understanding the influence of intrinsic (genetic and morphological) and extrinsic (geographical, environmental and social) factors on the performance and spatial differentiation of sexual signals, such as bird song, can help identify behavioural indicators of individual quality, habitat degradation and social environment. We used the Iberian Bluethroat Luscinia svecica azuricollis, a migratory bird that breeds in fragmented landscapes dominated by shrublands, as a case study to: (1) assess how a set of acoustic indicators of song performance are driven by intrinsic and extrinsic factors; and (2) contrast deterministic (adaptations to the environmental context and morphological constraints) vs. stochastic (differentiation by geographical isolation) explanations for song differentiation patterns. We explored acoustic indicators of song performance (spectral, temporal and song complexity) in relation to parameters related to genetic structure, body size, habitat type, habitat quality (assessed through a spatially explicit modelling approach) and social context (population abundance and songbird community composition). Then, we explored the contribution of genetic, geographical and environmental dissimilarity to song diversification across space. Our results highlight an association of song spectral variables with genetic structure and a significant connection between song complexity and duration with habitat quality. We found no relationship between social features and acoustic variables, or between song differentiation and genetic or geographical distances. There was, however, a correlation between song differentiation and environmental dissimilarity. We recommend the consideration of song complexity as an indicator of habitat quality.