Pattern formation of a predator-prey system with Ivlev-type functional response

In this paper, we investigate the spatial pattern formation of a predator-prey system with prey-dependent functional response Ivlev-type and reaction-diffusion. The Hopf bifurcation of the model is discussed, and the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained. Based on this, we perform the spiral and the chaotic spiral patterns via numerical simulation, i.e., the evolution process of the system with the initial conditions which was small amplitude random perturbation around the steady state. For the sake of learning the pattern formation of the model further, we perform three categories of unsymmetric initial condition, and find that with these special initial conditions the system can emerge not only spiral pattern but also target pattern and so on, and the effect of these special conditions on the formation of spatial patterns is less and less with more and more iterations but the effect does not decay forever. This indicates that for prey-dependent type predator-prey system, pattern formations do depend on the initial conditions, while for predator-dependent type they do not.     

Kelvin–Helmholtz Instability as a Boundary-Value Problem

The Kelvin–Helmholtz (KH) instability is traditionally viewed as an initial-value problem, wherein wave perturbations of a two-layer shear flow grow over time into billows and eventually generate vertical mixing. Yet, the instability can also be viewed as a boundary-value problem. In such a framework, there exists an upstream condition where a lighter fluid flows over a denser fluid, wave perturbations grow downstream to eventually overturn some distance away from the point of origin. As the reverse of the traditional problem, this flow is periodic in time and exhibits instability in space. A natural application is the mixing of a warmer river emptying into a colder lake or reservoir, or the salt-wedge estuary. This study of the KH instability from the perspective of a boundary-value problem is divided into two parts. Firstly, the instability theory is conducted with a real frequency and complex horizontal wavenumber, and the main result is that the critical wavelength at the instability threshold is longer in the boundary-value than in the initial-value situation. Secondly, mass, momentum and energy budgets are performed between the upstream, unmixed state on one side, and the downstream, mixed state on the other, to determine under which condition mixing is energetically possible. Cases with a rigid lid and free surface are treated separately. And, although the algebra is somewhat complicated, both end results are identical to the criterion for complete mixing in the initial-value problem.     

Prey-predator dynamics in rotifers: density-dependent consequences of spatial heterogeneity due to surface attachment

Classical models of prey-predator interactions assume that per capita prey consumption is dependent on prey density alone and that prey consumption (functional response) and consumer proliferation (numerical response) operate on the same timescales and without time lags. Several modifications have been proposed for resolving this timescale discrepancy, including variants where the functional response depends on both prey and predator densities. A microcosm system with the rotifer Brachionus 'Nevada' feeding on the prasinophyte Tetraselmis sp. showed significant (P < 0.0005) increases in steady-state biomasses of both prey and predators with increasing carrying capacity (represented by total phosphorus of the growth medium), which is inconsistent with predictions based on the traditional prey-only-dependent functional response. We provide data indicating that surfaces where the predator can attach provide a high-quality habitat for rotifers, which can result in a predator-dependent functional response. We also show that partitioning between the attached and free-swimming habitats was fast compared to the timescale of the numerical response. When attached to surfaces, rotifers maximized net energy gain by avoiding the high cost of swimming and by increased food capture due to reduced viscous drag. A mathematical model with prey-dependent functional response and wall-attached and free-swimming fractions of the population describes our data adequately. We discuss the implications of this finding for extrapolating microcosm experiments to systems with other surface-to-volume ratios, and to what extent our findings may apply to other popular model organisms for prey-predator interaction.     

Clustering of aerosols in atmospheric turbulent flow

A mechanism of formation of small-scale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution due to the clustering instability, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. In this paper a theoretical approach proposed in Elperin et al. (2002) Phys Rev E 66:036302 is further developed and applied to investigate the mechanisms of formation of small-scale aerosol inhomogeneities in the atmospheric turbulent flow. The theory of the particle clustering instability is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is much smaller than the correlation time at the integral scale of turbulence. We determined the criterion of the clustering instability for the Stokes number larger than 1. We discussed applications of the analyzed effects to the dynamics of aerosols and droplets in the atmospheric turbulent flow.     

Qualitative analysis of generalized volterra models

Generalized Volterra models are analyzed qualitatively to provide some information concerning their applicability as ecological-model estimators. For the general two-population system (including prey-predator, competitive, and other cases), the stability of the equilibrium points and other properties of the phase representation are investigated. For n-population systems, stability analysis is carried out mainly by means of several Liapunov functions. The persistence (or global stability of nontrivial equilibrium) of n-population systems is investigated, leading to an interaction-exclusion principle which implies restrictions on the interaction structure of the system, especially in the case of trophic systems.     

Biological interactions and environmental effects in the economics of pest control

The problem of pest control is tackled in a context of an ecosystem that consists of prey-predator populations with human interaction through pesticide application. The control, aimed at reducing pest damage, results in two undesirable external effects: reduction of beneficial predator population and environmental contamination. The untapped natural equilibrium is compared with equilibrium resulting from decentralized and centralized economic decision making. It is shown that, under certain conditions, myopic decision rules increase rather than decrease the pest damage. The “user cost” (or benefit) is shown to be crucial in determining the optimal centralized policy, and its relations to the various components of the system are analyzed. The components of the user cost are analyzed to determine the level of taxes or subsidies that will yield the optimal policy.     

Kelvin–Helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries

The temporal stability of a parallel shear flow of miscible fluid layers of different density and viscosity is investigated through a linear stability analysis and direct numerical simulations. The geometry and rheology of this Newtonian fluid mixing can be viewed as a simplified model of the behavior of mudflow at the bottom of estuaries for suspension studies. In this study, focus is on the stability and transition to turbulence of an initially laminar configuration. A parametric analysis is performed by varying the values of three control parameters, namely the viscosity ratio, the Richardson and Reynolds numbers, in the case of initially identical thickness of the velocity, density and viscosity profiles. The range of parameters has been chosen so as to mimic a wide variety of real configurations. This study shows that the Kelvin–Helmholtz instability is controlled by the local Reynolds and Richardson numbers of the inflection point. In addition, at moderate Reynolds number, viscosity stratification has a strong influence on the onset of instability, the latter being enhanced at high viscosity ratio, while at high Reynolds number, the influence is less pronounced. In all cases, we show that the thickness of the mixing layer (and thus resuspension) is increased by high viscosity stratification, in particular during the non-linear development of the instability and especially pairing processes. This study suggests that mud viscosity has to be taken into account for resuspension parameterizations because of its impact on the inflection point Reynolds number and the viscosity ratio, which are key parameters for shear instabilities.     

Biomonitoring insecticide pollution using non-target soil microarthropods

The scope of biomonitoring insecticide pollution in soil is discussed with the help of field and laboratory findings on the density, prey-predator ratio and fecundity of non-target microarthropod fauna. Field experiments were conducted in small plots with mustard, wheat and lady's finger crops and insecticides namely heptachlor 20EC (3.25 kg ai/ha = 16.25 lit/ha) and endosulfan 35EC (0.875 kg ai/ha = 2.5 lit/ha) applied at the seedling stages. Soil microarthropod population estimated at fortnightly intervals in the treated and untreated control plots revealed a general trend of adverse effect of the insecticides, prominently on the density and relative abundance of major prey groups like Collembola and Acari leading to notable decline in prey-predator ratio. Comparison of the percentage reductions of major taxonomic and trophic groups between pre-treatment and post-treatment intervals also demonstrated the ill effect of both heptachlor and endosulfan, notably on Collembola and the prey category. In the laboratory the survival success and fecundity of Cyphoderus javanus (Collembola) and Archegozetes longisetosus (Acari) were compared by exposing freshly emerged adults to sub-lethal concentrations of heptachlor and endosulfan for varying durations. The untreated control sets recorded high fecundity for both C. javanus and A. longisetosus, but chronic toxicity of the insecticides on adults confined to the treated soil resulted into very low fecundity. Even short duration exposure to heptachlor and endosulfan treated soil for 24 or 72 hours only was found to delay the egg-laying and decrease the fecundity of both the species. It is concluded that population responses and reproductive sensitivity in non-target soil microarthropods are potential eco-toxicological parameters for detecting pesticide pollution in soil and for ecological health assessment since the results are based on the bioactivity of toxicants.     

Genetic profile of overweight and obese school-age children

Obesity is associated with overproduction of free radicals that promotes genotoxicity and could be measured as micronuclei (MN) and nuclear abnormalities (NA) in buccal mucosa cells. The frequency of MN and NA in buccal mucosa cells from overweight and obesity school-age children was determined. In a cross-sectional study, four anthropometric parameters were obtained from each child and one buccal mucosa sample was collected from each child. The slides were stained with orcein and fast green and microscopically analyzed for MN and NA. Twenty overweight and obesity school-age children (7–11 years old) from three schools located at the metropolitan area of Guadalajara were selected to form three groups with 20 children each, according to the weight features as follows: (1) normal weight; (2) overweight; and (3) obesity. No marked differences were found between groups for frequency of MN and NA. Genotoxicity, as indicated by increase in binucleated (BN) cells, was found in children within both overweight and obese groups exposed to passive tobacco smoke. There was no evidence of genetic instability in overweight and obese school-age children and no associations between body weight and genotoxicity markers found.     

Benefits of memory for the evolution of tag-based cooperation in structured populations

We study the effects of working memory capacity and network rewiring probability on the evolution of cooperation in the standard and modified versions of an agent-based model of tag-mediated altruism. In our evolutionary model, computational agents populate a large complex network, engage into multiplayer Prisoner’s Dilemma-like interactions, and reproduce sexually. Agents carry discernible phenotypic traits subject to mutation, memorize their own experiences, and employ different strategies when interacting with different types of co-players. Choices made are selected from a pool of two conditional and two unconditional strategies, depending on the available memory contents and phenotypic similarity among interactors. For the dominating strategy in our standard model version, we found a strong dependence of cooperation on network structure and a weak one on memory, whereas in the modified version, the structural effect was weaker than that of memory. Most importantly, we found that the previously reported decline of cooperation in memory-based models, typically observed at a high memory capacity, is now prevented with the help of tags. This suggests that the evolutionary advantages of memory capacity limits may be far more complex than previously assumed. For much smaller systems, we observed a quasi-symmetric alternation of the two winning groups of strategists. This result provides an example of ingroup biased interactions that are characterized by bursts of intra-tag cooperation interspersed with periods of unconditional transient altruism. Such switches of strategies may represent a boosting mechanism necessary for the emergence and stability of global altruism in its early evolutionary stages.     

A derivation of the statistical characteristics of forest fires

The analysis of large data sets concerning fires in various forested areas of the world has pointed out that burned areas can often be described by different power-law distributions for small, medium and large fires and that a scaling law for the time intervals separating successive fires is fulfilled. The attempts of deriving such statistical laws from purely theoretical arguments have not been fully successful so far, most likely because important physical and/or biological factors controlling forest fires were not taken into account. By contrast, the two-layer spatially extended forest model we propose in this paper encapsulates the main characteristics of vegetational growth and fire ignition and propagation, and supports the empirically discovered statistical laws. Since the model is fully deterministic and spatially homogeneous, the emergence of the power and scaling laws does not seem to necessarily require meteorological randomness and geophysical heterogeneity, although these factors certainly amplify the chaoticity of the fires. Moreover, the analysis suggests that the existence of different power-laws for fires of various scale might be due to the two-layer structure of the forest which allows the formation of different kinds of fires, i.e. surface, crown, and mixed fires.     

A Bayesian approach to evaluating site impairment

In the United States, each state is required to list water resources that are declared to be impaired under guidelines set by the Clean Water Act. Measurements are typically collected on a number of chemical constituents and compared with a standard. If there are too many measurements exceeding the standard, then the site is declared impaired. The approach is non-statistical but similar to a Binomial test. The Binomial approach would convert the measurements to binary data then test if the proportion exceeding the standard is excessive. Both methods convert measurements to binary values hence exclude potentially important information in the data. We present a statistical approach using a Bayesian model that uses the raw data instead of the binary transformed data. The population distribution of a family of location-scale parameter models is studied under the model. Posterior distributions from the Bayesian analysis are used in the decision-making process and error probabilities for the Bayesian and the Binomial approaches are compared for a normal population.     

A population model for the peach fruit moth, Carposina sasakii Matsumura (Lepidoptera: Carposinidae), in a Korean orchard system

A population model for the peach fruit moth, Carposina sasakii Matsumura, was constructed to understand the population dynamics of this pest species and to develop an effective management strategy for various orchard (apple, peach, apple + peach) systems. The model was structured by the five developmental stages of C. sasakii: egg, larva, pupa, larval-cocoon (overwintering larva), and adult. The model consisted of a series of component models: (1) a bimodal spring adult emergence model, (2) an adult oviposition model, (3) stage emergence models of eggs, larvae, and pupae, (4) a larval survival rate model in fruits, (5) a larval-cocoon formation model, and (6) an insecticide effect model. Simulations using the model described the typical patterns of C. sasakii adult abundance in various orchard systems well, and was specific to the composition of host plants: three adult abundance peaks (first peak, mid-season peak, and last peak) a year with decreased peaks after the first peak in monoculture orchards of late apple, two adult peaks a year with a much higher last peak in monoculture orchards of early peach, and three adult peaks a year with much higher later peaks in mixed orchards of late apple and early peach. The average deviation between model outputs and actual records for first and second adult peak dates was 2.8 and 3.9 d, respectively, in simulations without an insecticide effect. The deviation decreased when insecticide effects were incorporated into the model. We also performed a sensitivity analysis of our model, and suggest possible applications of the model.     

Within-tree life process models of the southern pine beetle, dendroctonus frontalis

This paper develops models of gallery construction, emergence and re-emergence for use in a general population dynamics model of the southern pine beetle, Dendroctonuc frontalis Zimmermann. Models of these processes were originally developed from laboratory data, and are extended here to account for fluctuating temperatures and variable attack densities under field conditions. The resulting models were tested using data from three natural populations (infestations) from east Texas. These tests reveal that the laboratory-derived models closely predict the timing and length of gallery, and the timing of emergence and re-emergence in the field.     

A novel hybrid model for water quality prediction based on VMD and IGOA optimized for LSTM

● A novel VMD-IGOA-LSTM model has proposed for the prediction of water quality. ● Improved model quickly converges to the global optimal fitness and remains stable. ● The prediction accuracy of water quality parameters is significantly improved. Water quality prediction is vital for solving water pollution and protecting the water environment. In terms of the characteristics of nonlinearity, instability, and randomness of water quality parameters, a short-term water quality prediction model was proposed based on variational mode decomposition (VMD) and improved grasshopper optimization algorithm (IGOA), so as to optimize long short-term memory neural network (LSTM). First, VMD was adopted to decompose the water quality data into a series of relatively stable components, with the aim to reduce the instability of the original data and increase the predictability, then each component was input into the IGOA-LSTM model for prediction. Finally, each component was added to obtain the predicted values. In this study, the monitoring data from Dayangzhou Station and Shengmi Station of the Ganjiang River was used for training and prediction. The experimental results showed that the prediction accuracy of the VMD-IGOA-LSTM model proposed was higher than that of the integrated model of Ensemble Empirical Mode Decomposition (EEMD), the integrated model of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Nonlinear Autoregressive Network with Exogenous Inputs (NARX), Recurrent Neural Network (RNN), as well as other models, showing better performance in short-term prediction. The current study will provide a reliable solution for water quality prediction studies in other areas.     

Field observations on the emergence rhythm of the Norway lobsterNephrops norvegicus,using different methods

The emergence ofNephrops norvegicus (L.) from their burrows was studied on several fishing grounds around Scotland at 28 to 62 m depth. Various methods were used: sampling by trawl and baited creels, observations by television and time-lapse cameras. Peak emergence generally occurred around dusk and dawn. In shallow water (30 m) there was also a significant level of activity during the intervening night period. Day/night variations in the size composition of catches suggest that relatively more time is spent out of the burrow with increasing size. There was good agreement between the various methods employed, suggesting that trawl and camera avoidance has little influence on the pattern of emergence observed. The use of bait in some experiments confirmed that emergence is essentially a feeding activity.     

An inverse ecosystem model of year-to-year variations with first order approximation to the annual mean fluxes

Ecosystems exhibit nonlinear dynamics that are often difficult to capture in models. Consequently, linearization is commonly applied to remove some of the uncertainties associated with the nonlinear terms. However, since the true model is unknown and the operating point to linearize the model about is uncertain, developing linear ecosystems models is non-trivial. To develop a linear ecosystem model, we assume that the annual mean state of an ecosystem is a minor bias from the long-term mean state. A first order approximation inverse model to govern the year-to-year dynamics of ecosystems whose characteristic time scales are less than 1 year is developed, through theoretically formulation, on the basis of steady state analysis, time scale separation and nondimensionalization. The approach is adept at predicting year-to-year variations and to tracking system response to changes in environmental drivers when compared to data generated with a standard nonlinear NPZD model.     

Fuzzy modelling of chlorophyll production in a Brazilian upwelling system

In the context of coastal management the aim of this paper is to present the development of a fuzzy model through the application of a Genetic algorithm in order to select the most appropriate set of variables and improve our understanding with a set of rules. The case studied is the chlorophyll response as bioindicator of ecological status in the Northeast coastal upwelling system of Rio de Janeiro state, Southeastern of Brazil. The prediction of the fuzzy model has shown an improved performance when compared to the traditional approaches as Multiple Regression modelling. The results show that the set of inferred rules can assess three different water masses. Despite the increased occurrence of upwelling is observed in spring–summer period and some instability of the model, it is able to forecast some chlorophyll peaks. We conclude that the sampling frequency is crucial to reach a better performance.