Forced oscillations in a windkessel model

Volume elasticity of the arterial system and its component parts is developed starting from a Windkessel^*-model, which is defined in 4 points. Emphasis is laid on the simplicity of the derived equations and accessibility to experimental verification. The theory is an extension of earlier work achieved by Wetterer and Pieper (1953), who introduced an essentially physical method for the indirect determination of volume elasticity in situ, by creating forced sinusoidal oscillations in the arterial system, using a special pump operated at a considerably lower frequency than the mean heart frequency. The elegance of both experimental technique and the derived equations incited us to investigate the mathematical foundation and possible generalization of the method.     

Forced oscillations in a windkessel model

Volume elasticity of the arterial system and its component parts is developed starting from a Windkessel^*-model, which is defined in 4 points. Emphasis is laid on the simplicity of the derived equations and accessibility to experimental verification. The theory is an extension of earlier work achieved by Wetterer and Pieper (1953), who introduced an essentially physical method for the indirect determination of volume elasticity in situ, by creating forced sinusoidal oscillations in the arterial system, using a special pump operated at a considerably lower frequency than the mean heart frequency. The elegance of both experimental technique and the derived equations incited us to investigate the mathematical foundation and possible generalization of the method.     

Limited emigration from an outbreak of a forest pest insect

Population density and individual dispersal behaviour affect species' distribution dynamics. Population densities vary over time, and some species occasionally increase to very high numbers, for example during outbreaks. In such situations, populations are expected to expand into new areas as a result of density-dependent dispersal which sometimes even results in range expansion. A local population of the northern pine processionary moth Thaumetopoea pinivora has recently reached outbreak densities at the edge of its northern range at the southern tip of Gotland Island in the Baltic Sea. We first investigated whether the outbreak had resulted in establishment of populations in suitable habitats on Gotland Island outside the outbreak area. Six small populations were found that could potentially have originated from the outbreak area. However, data from 12 microsatellite markers strongly suggest that these populations did not originate from the recent outbreak. Genetic variability was not reduced in these small, isolated populations, and there were several unique alleles, indicating instead a different population history and that there has been no recent range expansion. In addition, there was apparent genetic isolation by geographic distance, implying that despite the high density of the outbreak population, significant gene flow has not occurred.     

Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model

This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models.     

Implications of early production in an invasive forest pest

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Chaotic oscillations in a simple collapsible-tube model.

A steady flow through a segment of externally pressurized, collapsible tube can become unstable to a wide variety of self-excited oscillations of the internal flow and tube walls. A simple, one-dimensional model of the conventional laboratory apparatus, which has been shown previously to predict steady flows and multiple modes of oscillation, is investigated numerically here. Large amplitude oscillations are shown to have a relaxation structure, and the nonlinear interaction between different modes is shown to give rise to quasiperiodic and apparently aperiodic behavior. These predictions are shown to compare favorably with experimental observations.     

Model‐specification uncertainty in future forest pest outbreak

Climate change will modify forest pest outbreak characteristics, although there are disagreements regarding the specifics of these changes. A large part of this variability may be attributed to model specifications. As a case study, we developed a consensus model predicting spruce budworm (SBW, Choristoneura fumiferana [Clem.]) outbreak duration using two different predictor data sets and six different correlative methods. The model was used to project outbreak duration and the uncertainty associated with using different data sets and correlative methods (=model‐specification uncertainty) for 2011–2040, 2041–2070 and 2071–2100, according to three forcing scenarios (RCP 2.6, RCP 4.5 and RCP 8.5). The consensus model showed very high explanatory power and low bias. The model projected a more important northward shift and decrease in outbreak duration under the RCP 8.5 scenario. However, variation in single‐model projections increases with time, making future projections highly uncertain. Notably, the magnitude of the shifts in northward expansion, overall outbreak duration and the patterns of outbreaks duration at the southern edge were highly variable according to the predictor data set and correlative method used. We also demonstrated that variation in forcing scenarios contributed only slightly to the uncertainty of model projections compared with the two sources of model‐specification uncertainty. Our approach helped to quantify model‐specification uncertainty in future forest pest outbreak characteristics. It may contribute to sounder decision‐making by acknowledging the limits of the projections and help to identify areas where model‐specification uncertainty is high. As such, we further stress that this uncertainty should be strongly considered when making forest management plans, notably by adopting adaptive management strategies so as to reduce future risks.     

Canards for a reduction of the Hodgkin-Huxley equations

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Stomatal oscillations in adult forest trees in natural environment

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Travelling waves of resistance in a bi-trophic pest adaptation model

We consider a reaction-diffusion system for spatial spread of pest resistance to host plant resistance genes which is based on the Lotka-Volterra predator-prey equations, with logistic growth of the resource level and a diffusion term added to account for spatial spread of the pest. The model is phenotype specific, in which a pest subpopulation's fitness comes down to a balance between its resource assimilation rate and its respiration rate. We derive an expression for the rate of spatial spread of the resistant pest types from an initial point source, and discuss its relevance for adaptive pest resistance management strategies. Using results for an analogous single-species reaction-diffusion model in heterogeneous media, we consider the likely impact of pest-susceptible plant refugia on the speed of the travelling wave of resistant pests, and simultaneously the expected trade-off, in terms of crop yield decrease, when refugia are included. We also explore the possibility that resistance breaking by the pest population is not an inevitable phenomenon, particularly when refugia of the appropriate size are used.     

基于发生指数的中国森林生物灾害趋势与突变特征

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Self-sustained oscillations of electric potential in a model membrane

A model membrane constructed from a Millipore filter, whose pores are filled with dioleyl phosphate molecules, exhibits a self-oscillation of the electric potential with a period of about a few seconds in the presence of a salt-concentration difference, pressure difference and/or electric current across the filter. In this paper, the effects of chemicals such as KCl, CaCl2, pH and sucrose on the self-oscillation are investigated experimentally. These chemical substances are shown to alter the characteristic properties as the frequency of oscillation. Theoretical consideration of electrochemical interaction between these substances and DOPH molecules gives a fairly good explanation of the observed results.     

Organizing centres and symbolic dynamic in the study of mixed-mode oscillations generated by models of biological autocatalytic processes

The organization of the complex mixed-mode oscillations generated, in a three-dimensional variable space, by an autocatalytic process formalized as a cubic monomial is analyzed. The generation of the temporal patterns is elucidated by complementary approaches dealing with the three-variable differential continuous system itself and with successive discrete applications modelling its first return map. The extent to which the underlying bifurcation structures could constitute a fingerprint of autocatalytic processes is discussed in connection with the modelling of biological systems.     

Cytoplasmic calcium oscillations: a two pool model

Cytosolic calcium oscillations induced by a wide range of agonists, particularly those which stimulate phosphoinositide metabolism, are the result of a periodic release of stored calcium. The formation of inositol 1,4,5 trisphosphate (Ins(1,4,5)P3) seems to play an important role because it can initiate this periodic behaviour when injected or perfused into a variety of cells. A two pool model has been developed to explain how Ins(1,4, 5)P3 sets up these calcium oscillations. It is proposed that Ins(1,4,5)P3 acts through its specific receptor to create a constant influx of primer calcium (Ca2+p) made up of calcium released from the Ins(1,4,5)P3-sensitive pool (ISCS) together with an influx of external calcium. This Ca2+p fails to significantly elevate cytosolic calcium because it is rapidly sequestered by the Ins(1,4,5)P3-insensitive (IICS) stores of calcium distributed throughout the cytosol. Once the latter have filled, they are triggered to release their stored calcium through a process of calcium-induced calcium release to give a typical calcium spike (Ca2+s). In many cells, each Ca2+s begins at a discrete initiation site from which it then spreads through the cell as a wave. The two pool model can account for such waves if it is assumed that calcium released from one IICS diffused across to excite its neighbours thereby setting up a self-propagating wave based on calcium-induced calcium release.     

A comparison of presence-only analytical techniques and their application in forest pest modeling

Insect pests are natural disturbance agents that can significantly alter the structure and composition of forested landscapes, and thus impact their ability to provide critical ecosystem services. Predicting population levels of pest species has become crucial for the management of healthy forests, and species distribution modeling techniques may assist with predictions. Due to the nature of sampling in pest assessments there is often a lack of absence data which requires practitioners to rely on presence-only information. Modeling approaches have been developed for presence-only data but have not been tested for pest species that have major impacts on forest ecosystems. Our research objectives were to compare species distribution models for traditional techniques (i.e., generalized linear and additive models) and contemporary machine learning algorithms (i.e., maximum entropy, random forest, gradient boosted decision trees, and extreme gradient boosting), as well as assess how varying background points influence model performance. True presence-absence data and presences combined with background point data at one, two, three, and ten times the number of presences were compared. Comparisons were done using a comprehensive dataset from 2405 survey plots that assessed the presence and absence of non-native Sirex woodwasp (Sirex noctilio Fabricius) collected in pine plantations in Chile. Contemporary machine learning techniques (>84% average accuracy) outperformed traditional modeling techniques (<82% average accuracy) when utilizing true presence-absence data. For presence-background point models, accuracy tended to increase as the number of background points increased, except for generalized additive models and MaxEnt which had relatively similar performances. Generalized linear models, MaxEnt, and random forest substantially underperformed as compared to other modeling frameworks when using background point data. Gradient boosting and extreme gradient boosting had the highest prediction accuracies when combined with background points (74–81% depending on the number of background points) and may provide valuable alternative analyses to traditional techniques for presence-only data that contain complex correlations and interactions. Increasing the precision of these models, while reducing the inherent biases due to data structure, will allow for more informed forest pest management. This is becoming increasingly important, as changes in population and outbreak dynamics and the introduction of invasive species are projected to increase in the coming decades, partially due to global climate change and increased international trade and travel.     

Synchronized oscillations in the visual cortex — a synergetic model

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Social predation by ants as a mortality source for an arboreal gregarious forest pest

Biocontrol of caterpillars by ants is highly variable, and we investigate how the strength of the trophic relationship between ants and an important outbreaking forest pest depends on phenological synchrony and on social foraging. We test the hypothesis that early spring foraging by ants, coupled with eusocial recruitment behavior, could undermine the caterpillar's strategies to achieve either enemy-free space or predator satiation.We use a series of field surveys and experiments in trembling aspen stands (Populus tremuloides) in the boreal forest of eastern Canada to assess the role of ants in early-instar mortality of the outbreaking, gregarious forest tent caterpillar (Malacosoma disstria). We also investigate individual-level mechanisms related to phenology and social behavior that underlie the effectiveness of ants as biocontrol on caterpillars. Our results show that ants climb trees early in the spring and harvest young forest tent caterpillars, suggesting that early phenology does not provide an entirely enemy-free space for caterpillars. Our findings further show that recruitment-based social foraging enables ants to deplete groups of gregarious prey, suggesting that these eusocial insects are particularly effective at generating predation pressure on gregarious herbivores since they do not satiate easily. Finally, a manipulative predator exclusion experiment confirms that ant predation is a significant mortality source for early-instar forest tent caterpillars. Taken together, these results suggest that phenology and sociality could modulate the role of ants as effective caterpillar predators and thus showcase the importance of considering natural history and behavioral traits when studying trophic interactions and their role in population dynamics.     

Theta oscillations by synaptic excitation in a neocortical circuit model

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