Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.     

Phenologically-Structured Predator-Prey Dynamics with Temperature Dependence

Studies document the fact that temperature changes strongly affect interactions in many consumer-resource systems through altered, or shifted, phenologies. The mistiming of events, such as migration or emergence times, or the contraction or expansion of development times can upset the normal synchronization and lead to increased or decreased predation events. In this paper, we formulate a continuous time, phenologically-structured model of predator-prey interactions that is driven by temperature variations. It is particularly applicable to arthropod interactions because their development rates are so strongly temperature related. The model takes the form of a system of partial differential-integral equations for the species’ population densities in development-time variables. In special cases, the model is analytically tractable and we find a closed-form solution. By calculating density variations under different temperature regimes, the model gives a quantitative method for assessing the effects of global temperature change on consumer-resource interactions.     

Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.     

The Influence of Hydrologic Residence Time on Lake Carbon Cycling Dynamics Following Extreme Precipitation Events

The frequency and magnitude of extreme events are expected to increase in the future, yet little is known about effects of such events on ecosystem structure and function. We examined how extreme precipitation events affect exports of terrestrial dissolved organic carbon (t-DOC) from watersheds to lakes as well as in-lake heterotrophy in three north-temperate lakes. Extreme precipitation events induced large influxes of t-DOC to our lakes, accounting for 45–58% of the seasonal t-DOC load. These large influxes of t-DOC influenced lake metabolism, resulting in lake net heterotrophy following 67% of the extreme precipitation events across all lakes. Hydrologic residence time (HRT) was negatively related to t-DOC load and heterotrophy; lakes with short HRT had higher t-DOC loads and greater net heterotrophy. The fraction of t-DOC mineralized within each lake following extreme precipitation events generally exhibited a positive relationship with lake HRT, similar to the previous studies of fractions mineralized at annual and supra-annual time scales. Event-associated turnover rate of t-DOC was higher than what is typically reported from laboratory studies and modeling exercises and was also negatively related to lake HRT. This study demonstrates that extreme precipitation events are ‘hot moments’ of carbon load, export, and turnover in lakes and that lake-specific characteristics (for example, HRT) interact with climatic patterns to set rates of important lake carbon fluxes.     

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics

Whereas impacts of predator interference on predator-prey dynamics have received considerable attention, the “inverse” process—foraging facilitation among predators—have not been explored yet. Here we show, via mathematical models, that impacts of foraging facilitation on predator-prey dynamics depend on the way this process is modeled. In particular, foraging facilitation destabilizes predator-prey dynamics when it affects the encounter rate between predators and prey. By contrast, it might have a stabilizing effect if the predator handling time of prey is affected. Foraging facilitation is an Allee effect mechanism among predators and we show that for many parameters, it gives rise to a demographic Allee effect or a critical predator density in need to be crossed for predators to persist. We explore also the effects of predator interference, to make the picture “symmetric” and complete. Predator interference is shown to stabilize predator-prey dynamics once its strength is not too high, and thus corroborates results of others. On the other hand, there is a wide range of model parameters for which predator interference gives rise to three co-occurring co-existence equilibria. Such a multi-equilibrial regime is rather robust as we observe it for all the functional response types we explore. This is a previously unreported phenomenon which we show cannot occur for the Beddington–DeAngelis functional response. An interesting topic for future research thus might be to seek for general conditions on predator functional responses that would produce multiple co-existence equilibria in a predator-prey model.     

Selective Defecation and Selective Foraging: Antiparasite Behavior in Wild Ungulates?

Selective defecation and selective foraging are two potential antiparasite behaviors used by grazing ungulates to reduce infection by fecal–oral transmitted parasites. While there is some evidence that domestic species use these strategies, less is known about the occurrence and efficacy of these behaviors in wild ungulates. In this study, I examined whether wild antelope use selective defecation and selective foraging strategies to reduce exposure to gastrointestinal nematode parasites. By quantifying parasite levels in the environment in relation to the defecation patterns of three species, dik‐dik (Madoqua kirkii), Grant's gazelle (Gazella granti), and impala (Aepyceros melampus), I found that nematode larval concentrations in pasture were higher in the vicinity of clusters of feces (dung middens) compared to single fecal pellet groups or dung‐free areas. In addition, experimental feeding trials in free‐ranging dik‐dik showed that individuals selectively avoided feeding near concentrations of feces. Given that increased parasite contamination was found in the immediate vicinity of fecal clusters, fecal avoidance could help reduce host consumption of parasites and may therefore be an effective antiparasite behavior for certain species. On the other hand, while the concentration of parasite larvae in the vicinity of middens coupled with host avoidance of these areas during grazing could reduce host contact with parasites, results showing a positive correlation between the number of middens in a habitat and larval abundance at control sites suggest that dung middens might increase and not decrease overall host exposure to parasites. If this is the case, dung midden formation may not be a viable antiparasite strategy.     

Size-Dependent Axonal Bouton Dynamics following Visual Deprivation In Vivo

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The Dynamics of Turing Patterns for Morphogen-Regulated Growing Domains with Cellular Response Delays

Since its conception in 1952, the Turing paradigm for pattern formation has been the subject of numerous theoretical investigations. Experimentally, this mechanism was first demonstrated in chemical reactions over 20 years ago and, more recently, several examples of biological self-organisation have also been implicated as Turing systems. One criticism of the Turing model is its lack of robustness, not only with respect to fluctuations in the initial conditions, but also with respect to the inclusion of delays in critical feedback processes such as gene expression. In this work we investigate the possibilities for Turing patterns on growing domains where the morphogens additionally regulate domain growth, incorporating delays in the feedback between signalling and domain growth, as well as gene expression. We present results for the proto-typical Schnakenberg and Gierer–Meinhardt systems: exploring the dynamics of these systems suggests a reconsideration of the basic Turing mechanism for pattern formation on morphogen-regulated growing domains as well as highlighting when feedback delays on domain growth are important for pattern formation.     

Methanol Accelerates DMPC Flip-Flop and Transfer: A SANS Study on Lipid Dynamics

Methanol is a common solubilizing agent used to study transmembrane proteins/peptides in biological and synthetic membranes. Using small angle neutron scattering and a strategic contrast-matching scheme, we show that methanol has a major impact on lipid dynamics. Under increasing methanol concentrations, isotopically distinct 1,2-dimyristoyl-sn-glycero-3-phosphocholine large unilamellar vesicle populations exhibit increased mixing. Specifically, 1,2-dimyristoyl-sn-glycero-3-phosphocholine transfer and flip-flop kinetics display linear and exponential rate enhancements, respectively. Ultimately, methanol is capable of influencing the structure-function relationship associated with bilayer composition (e.g., lipid asymmetry). The use of methanol as a carrier solvent, despite better simulating some biological conditions (e.g., antimicrobial attack), can help misconstrue lipid scrambling as the action of proteins or peptides, when in actuality it is a combination of solvent and biological agent. As bilayer compositional stability is crucial to cell survival and protein reconstitution, these results highlight the importance of methanol, and solvents in general, in biomembrane and proteolipid studies.     

Erratum to: Attractor Dynamics and Thermodynamic Analogies in the Cerebral Cortex: Synchronous Oscillation,the Background EEG,and the Regulation of Attention

Ongoing changes in attention and cognition depend upon cortical/subcortical interactions, which select sequences of different spatial patterns of activation in the cortex.     

Evolutionary Behaviour,Trade-Offs and Cyclic and Chaotic Population Dynamics

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.     

Global Dynamics of an In-host Viral Model with Intracellular Delay

The dynamics of a general in-host model with intracellular delay is studied. The model can describe in vivo infections of HIV-I, HCV, and HBV. It can also be considered as a model for HTLV-I infection. We derive the basic reproduction number R ₀ for the viral infection, and establish that the global dynamics are completely determined by the values of R ₀. If R ₀≤1, the infection-free equilibrium is globally asymptotically stable, and the virus are cleared. If R ₀>1, then the infection persists and the chronic-infection equilibrium is locally asymptotically stable. Furthermore, using the method of Lyapunov functional, we prove that the chronic-infection equilibrium is globally asymptotically stable when R ₀>1. Our results shows that for intercellular delays to generate sustained oscillations in in-host models it is necessary have a logistic mitosis term in target-cell compartments.     

Microenvironmental influences of apoptosis in vivo and in vitro

The apoptosis program of physiological cell death elicits a range of non-phlogistic homeostatic mechanisms—“recognition, response and removal”—that regulate the microenvironments of normal and diseased tissues via multiple modalities operating over short and long distances. The molecular mechanisms mediate intercellular signaling through direct contact with neighboring cells, release of soluble factors and production of membrane-delimited fragments (apoptotic bodies, blebs and microparticles) that allow for interaction with host cells over long distances. These processes effect the selective recruitment of mononuclear phagocytes and the specific activation of both phagocytic and non-phagocytic cells. While much evidence is available concerning the mechanisms underlying the recognition and responses of phagocytes that culminate in the engulfment and removal of apoptotic cell bodies, relatively little is yet known about the non-phagocytic cellular responses to the apoptosis program. These responses regulate inflammatory and immune cell activation as well as cell fate decisions of proliferation, differentiation and death. Here, we review current knowledge of these processes, considering especially how apoptotic cells condition the microenvironments of normal and malignant tissues. We also discuss how apoptotic cells that persist in the absence of phagocytic clearance exert inhibitory effects over their viable neighbors, paying particular attention to the specific case of cell cultures and highlighting how new cell-corpse-clearance devices—Dead-Cert^® Nanoparticles—can significantly improve the efficacy of cell cultures through effective removal of non-viable cells in the absence of phagocytes in vitro.     

Mathematical Study of the Role of Gametocytes and an Imperfect Vaccine on Malaria Transmission Dynamics

A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite) in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features. It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by ℛ₀), is less than unity. Further, it has a unique endemic equilibrium if ℛ₀>1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by ℛ_vac) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine if ℛ_vac is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level of gametocyte is critically important to the malaria burden in the community.     

Impacts of Incubation Delay on the Dynamics of an Eco-Epidemiological System—A Theoretical Study

Parasite and predator play significant role in trophic interaction, productivity and stability of an ecosystem. In this paper, we have studied a host-parasite-predator interaction that incorporates incubation delay. How the qualitative and quantitative behaviors of the system alter with the incubation delay have been discussed both from mathematical and biological point of views. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate, there exists a threshold value of the delay above which the system is unstable and below which the system is stable leading to the persistence of all the species. Also, the instability arising from the incubation delay may be controlled if somehow the growth rate of predator population is increased. Numerical studies have also been performed to illustrate different analytical findings. Research is supported by UGC, India; F No. 32-173/2006(SR).     

DROIDS 1.20: A GUI-Based Pipeline for GPU-Accelerated Comparative Protein Dynamics

Traditional informatics in comparative genomics work only with static representations of biomolecules (i.e., sequence and structure), thereby ignoring the molecular dynamics (MD) of proteins that define function in the cell. A comparative approach applied to MD would connect this very short timescale process, defined in femtoseconds, to one of the longest in the universe: molecular evolution measured in millions of years. Here, we leverage advances in graphics-processing-unit-accelerated MD simulation software to develop a comparative method of MD analysis and visualization that can be applied to any two homologous Protein Data Bank structures. Our open-source pipeline, DROIDS (Detecting Relative Outlier Impacts in Dynamic Simulations), works in conjunction with existing molecular modeling software to convert any Linux gaming personal computer into a “comparative computational microscope” for observing the biophysical effects of mutations and other chemical changes in proteins. DROIDS implements structural alignment and Benjamini-Hochberg-corrected Kolmogorov-Smirnov statistics to compare nanosecond-scale atom bond fluctuations on the protein backbone, color mapping the significant differences identified in protein MD with single-amino-acid resolution. DROIDS is simple to use, incorporating graphical user interface control for Amber16 MD simulations, cpptraj analysis, and the final statistical and visual representations in R graphics and UCSF Chimera. We demonstrate that DROIDS can be utilized to visually investigate molecular evolution and disease-related functional changes in MD due to genetic mutation and epigenetic modification. DROIDS can also be used to potentially investigate binding interactions of pharmaceuticals, toxins, or other biomolecules in a functional evolutionary context as well.     

Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein–Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.