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.     

Latency and quarantine vs. backward bifurcation

Two models are presented which can show a backward bifurcation. The possibilities are analyzed whether latency, quarantine, vaccine efficacy, and other parameters of the models can affect the appearance of a backward bifurcation. Explicit conditions on the parameters are given for the backward bifurcation to be present, to be reduced, or to disappear.     

When rate maximization is impulsive

Although optimal foraging theory predicts that natural selection should favor animal behaviors that maximize long-term rate of gain, behaviors observed in the laboratory tend to be impulsive. In binary-choice experiments, despite the long-term gain of each alternative, animals favor short handling times. Most explanations of this behavior suggest that there is hidden rationality in impulsiveness. Instead, we suggest that simultaneous and mutually exclusive binary-choice encounters are often unnatural and thus immune to the effects of natural selection. Using a simulation of an imperfect forager, we show how a simple strategy (i.e., an intuitive model of animal behavior) that maximizes long-term rate of gain under natural conditions appears to be impulsive under operant laboratory conditions. We then show how the accuracy of this model can be verified in the laboratory by biasing subjects with a short pre-experiment ad libitum high-quality feeding period. We also show a similar behavioral mechanism results in diet preferences that are qualitatively consistent with the digestive rate model of foraging (i.e., foraging under digestive rate constraints).     

Using the maximum principle of impulse control for ecology-economical models

In this work we present mathematical models for population of single cohort and homogeneous animals. Investigating these mathematical models, we determine structure of optimal impulsive control which used maximum principle for optimal processes with impulse control.     

Dynamics of free-living nitrogen-fixing bacterial populations in antagonistic conditions

The survival of free-living nitrogen-fixing microbial populations in the natural ecosystem is crucial for the system maintenance and productivity due to the unique role of these organisms in the global biogeochemical cycle of nitrogen.The dynamics of a nitrogen-fixing microbial population grown at various conditions in a chemostat, together with a competitive (for the common resources) population, was studied through bifurcation analysis of a mathematical model of the system. When the carbon source is found in abundance in the feed, then the competition for this nutrient is low. High amounts of ammonium nitrogen (a substance that inhibits growth of the nitrogen-fixing population) are assimilated for the growth needs of both populations. Under these conditions the nitrogen-fixing population can survive (alone or together with its competitor) in a wide range of parameter values and operating conditions and in some cases nitrogenase synthesis occurs.When the inflow medium contains low carbon substrate concentrations, high competition occurs for this nutrient. In these conditions the nitrogen-fixing population can survive only if it has the competitive advantage over its competitor. However, if the inflow medium contains high ammonium concentrations, the nitrogen-fixing population is inhibited and loses its competitive advantage. Under these conditions, only nitrogen-fixing populations, which are able to establish amensalistic interactions can survive in the system.     

Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations

Many biological populations are subject to periodically changing environments such as years with or without fire, or rotation of crop types. The dynamics and management options for such populations are frequently investigated using periodic matrix models. However the analysis is usually limited to long-term results (asymptotic population growth rate and its sensitivity to perturbations of vital rates). In non-periodic matrix models it has been shown that long-term results may be misleading as populations are rarely in their stable structure. We therefore develop methods to analyze transient dynamics of periodic matrix models. In particular, we show how to calculate the effects of perturbations on population size within and at the end of environmental cycles. Using a model of a weed population subject to a crop rotation, we show that different cyclic permutations produce different patterns of sensitivity of population size and different population sizes. By examining how the starting environment interacts with the initial conditions, we explain how different patterns arise. Such understanding is critical to developing effective management and monitoring strategies for populations subject to periodically recurring environments.     

Cannibalism in an age-structured predator–prey system

The effect of cannibalism on an age-structured predator–prey system is studied. Three stable equilibrium states are found. Using a Hopf bifurcation analysis, it is found that the non washout steady state looses its stability as the cannibalism attack rate increases past a bifurcation point S_c. The dependence of the bifurcation point on the other parameters in the model is found. It is shown that the trajectory of the solution spirals in for attack rates S<S_c and exhibits limit cycle behavior for S>S_c.     

Sustained dynamic transience in a Lotka-Volterra competition model system for grassland species

Theoretical approaches, such as the Lotka-Volterra framework, enable predictions about long term species coexistence based on stability criteria, but generally assume temporal constancy of system equations and parameters. In real world systems, temporal variability may interfere with the attainment of stable states. Managed grassland ecosystems in Northwestern Europe experience structural periodic fluctuations in environmental conditions: the seasons. In addition, periodic disturbances such as cutting are very common. Here we show, using a Lotka-Volterra system applied to grassland species with empirically derived parameters, that seasonal variability can result in a time dependent equilibrium and redirection of displacement processes.Parameter estimates differed between species and - in most cases - between the seasons. As a result, five of the fifteen tested species combinations had different outcomes of species interactions between seasons. This indicates that systems remain in dynamic transience over the year as the equilibrium changes and the species composition of the system follows the equilibrium without ever attaining it. The non-attainment of the steady state enables coexistence of species even if there is competitive exclusion in one of the seasons. For three of the fifteen species combinations, cutting frequency affected the long-term coexistence patterns. Cutting resets the biomass of competing species and favours during regrowth those species that have a high growth rate, which can alter species coexistence in comparison to a Lotka-Volterra model without cutting. The Lotka-Volterra framework with seasonally changing empirical parameters predicts coexistence as a possible outcome of systems that in component seasons are characterised by exclusion, and vice versa.     

Control targets for the management of biological systems

Attention is focused on biological systems which are describable in terms of ordinary differential equations subject to human control inputs. The concept of an isochronal system is introduced in order to include systems for which the differential equations are valid only over regularly reoccurring time intervals.It is assumed that the control inputs are to be chosen so that an integral cost function of the state of the system, the control used, current time, and the time interval of the control program is minimized. Problems associated with minimizing this cost function over an infinitely long time interval is then considered. Difficulties inherent with minimizing a cost integral on an infinite time interval are shown to be avoided by minimizing an average of the cost function over an unknown but periodic time interval. Under proper circumstance, the optimal control program for the average cost function is either identical to or a good approximation to the optimal control program for the original cost function over an infinitely long time interval.Necessary conditions are obtained for minimizing an average cost function over an unspecified time interval subject to the system equations. For a given problem the necessary conditions will yield but a single system trajectory in the state space. For management purposes this trajectory may be thought of as a target to which the system should be driven and maintained.A number of examples illustrate the use of the necessary conditions to obtain control targets. Certain problems associated with the stability of the target solutions are illustrated with the examples.     

Assessing area-specific relative risks from large forest fire size in Canada

The evaluation of area-specific risks for large fires is of great policy relevance to fire management and prevention. When analyzing data for the burned areas of large fires in Canada, we found that there are dramatic patterns that cannot be adequately modelled by traditional hierarchical modelling assuming spatial autocorrelation. In this paper, we use the robust locally weighted scatterplot smoothing (LOESS) technique to remove spatial and temporal trends; and we account for periodical cycles by employing the relevant periodic functions as covariates in a hierarchical Gamma mixed effects model. Based on the results of this generalized multilevel analysis of large fire size, we provide an area-specific relative risks ranking system for Canada and confirm that lightning tends to cause more severe damage in terms of fire size than human factor. A diagnostic check on the modelling shows that large fires data are reasonably modelled using this combination of semiparametric and mixed effects modelling approaches.     

A Comparison of Logging Systems and Bat Diversity in the Neotropics

Abstract:  Evaluating logging systems to determine which are most compatible with the maintenance of biodiversity is of prime importance if tropical forests are to be managed in a sustainable way. Bats are model taxa for this purpose. Two different logging systems are used in the natural forest of the Victoria-Mayaro Forest Reserve in Trinidad: open range and periodic block. Open range is a continuous harvesting system and, in common with most methods used to log tropical forests worldwide, has few harvest controls other than girth limits for selected species. Periodic block is a polycyclic system, with felling based on ecological criteria assumed to be compatible with the maintenance of biodiversity. To compare the effects of periodic block and open-range systems on biodiversity, we determined bat species richness and abundance in each system and in primary forest. We caught bats in mist nets set at ground level and in the canopy and in harp traps. In total 1959 individuals representing 38 species were captured. Species richness was similar among primary forest and logged forest habitats, although bat diversity was lower in logged forest. The distributions of bat species abundance did not differ significantly between logged forest and primary forest. We found, however, that both logging systems lead to a decrease in gleaning animalivores and an increase in frugivores. The increase in frugivores was likely the result of an increase in the abundance of bat-dispersed pioneer fruiting plants in logged forest. Bats of periodic-block-managed forest were more similar to those of primary forest than those of forest logged using the open-range system, indicating that the periodic-block system is more compatible with the maintenance of bat diversity. Our results support the suggestion that the measured use of tropical forests can largely be compatible with biodiversity conservation.     

Disease prevention and resistance in social insects: modeling the survival consequences of immunity,hygienic behavior,and colony organization

Understanding the origin of disease resistance in social insects is difficult due to the lack of well-established phylogenies of presocial and eusocial species and the absence of extant basal and intermediate forms. Moreover, comprehensive accounts of infection-control traits in social insect lineages are not available. Therefore, to explore the evolution of pathogen control in social insects we used cellular automata models to analyze the efficacy of immunity and nest hygiene, which we assumed were basal traits, and allogrooming, which likely followed the transition to eusociality, and their interactions with colony demography and patterns of worker spatial distribution. Models showed that nest hygiene provided an immediate survival benefit and that immunity lowered overall disease susceptibility under both constant and periodic exposure scenarios. Allogrooming increased survivorship in chronically challenged colonies but also increased pathogen transmission rates under conditions of periodic exposure. Colonies having demographies biased towards young or old individuals had slightly higher mortality than those with heterogeneous demographies. The distribution of older individuals relative to the nest center had no significant effect on susceptibility and provided only a minor survival advantage. Models indicated that nest hygiene and immunity function on different temporal scales and can interact with demography to lower disease risks. Our results suggest how infection control systems in social insects could have been built upon the inducible immune defenses and nest hygienic behaviors of solitary and presocial ancestors and served as important preadaptations to manage disease exposure and transmission in colonies of eusocial species.     

Analytical discussions on species extinction in competitive communities due to habitat destruction

An improvement of a metapopulation model is developed and used to analyze the behaviors of abundant and extinct species in the system analytically. By approximating the direct effect rate of habitat destructions on individual species using differentiable functions, the model enables us to discuss the equilibrium and stability of the system. Special cases of the habitat destruction functions, constant, piecewise linear, exponential and periodic functions, are discussed analytically and numerically. The conditions for system stability are also given.     

Queen number, queen cycling and queen loss: the evolution of complex multiple queen societies in the social wasp genus Ropalidia

Complex, highly integrated societies have evolved from simpler societies repeatedly, and the social insects provide an excellent model system for understanding increasing complexity and integration. In the paper wasps, large societies, known as swarm-founding, have evolved repeatedly from smaller societies, known as independent-founding. Swarm-founding colonies have many more queens than independent-founding colonies, which should dramatically reduce relatedness, posing a challenge to cooperation. However, in each instance, swarm-founding species have also evolved a cyclical pattern of queen reduction which elevates relatedness despite high queen numbers. The genus Ropalidia provides an excellent system in which to study the transition to swarm-founding because it has both independent and swarm-founding species. We studied the Australian independent-founding wasp Ropalidia revolutionalis to better understand the evolution of multiple queens and their periodic reductions in swarm-founding wasps. Using microsatellite genetic markers we genotyped queens, workers and brood from 37 colonies and found that while most colonies had a single queen, three of the colonies had multiple queens at or immediately prior to the time of collection. An additional seven colonies had had multiple co-occurring queens earlier in the season. We also found that colonies experienced many queen losses, and that founding queens were gradually lost until they were replaced by a new cohort of daughter queens in many colonies. This pattern is similar to the periodic reductions and replacements in swarm-founding wasps and suggests that multiple queens and queen cycling evolved relatively early in the shift to swarm-founding in Ropalidia.Communicated by R. Page     

Morphological diversity of Struvite crystals produced by Myxococcus Coralloides and Myxococcus Xanthus

We studied the morphological diversity of struvite crystals produced by Myxococcus coralloides and Myxococcus xanthus in different culture conditions. We discussed the similarities of these crystals with the struvite morphology studied previously following the theory of the periodic bond chains.     

Incorporating dormancy in dynamic microbial community models

Biogeochemical activity in natural and engineered systems depends on the abundances, functional capabilities and physiological states of the indigenous microorganisms. Typically, only a fraction of the microbial population is active at any given time. As environmental conditions change, previously active microorganisms may switch to an inactive or dormant state, while dormant ones may become active. Here, we present an extended modeling concept for the growth and decay of microorganisms that explicitly accounts for their ability to switch between active and dormant states. The equations describing the switching between physiological states are implemented into a biogeochemical reaction simulator. The model was used to reproduce published data from two laboratory experiments in which microorganisms were subjected to intermittent substrate supply or reactivated after a prolonged period of starvation. Parameter values obtained from the simulation of these experiments were used for subsequent sensitivity analyses and for the simulation of hypothetical scenarios. Results for hypothetical microbial communities consisting of two competing species exposed to periodic feeding imply that, under certain conditions, an effective dormancy-reactivation strategy may have a competitive advantage over a fast growth strategy. That is, organisms that can switch rapidly in response to fluctuations in external conditions may outcompete fast-growing organisms. Furthermore, certain combinations of growth and dormancy strategies may lead to the long-term coexistence of the two competing species. Overall, the simulated population dynamics show that dormancy is an important feature of microbial communities, which can lead to complex responses to environmental fluctuations.     

Dynamics of a chemostat with three competitive hydrogen oxidizing denitrifying microbial populations and their efficiency for denitrification

In this work, competition for two nitrogen resources (nitrate-, nitrite-nitrogen) between three hydrogen oxidizing denitrifying populations (Acidovorax sp. strain Ic3 (X₁), Paracoccus sp. strain Ic1 (X₂), and Acinetobacter sp. strain Ic2 (X₃)) was examined. The dynamics of three systems of microbial populations (system I: X₁ − X₃, system II: X₂ − X₃, and system III: X₁ − X₂ − X₃), grown in a chemostat, was studied using bifurcation analysis. The chemostat is the most common type of biological reactor used for the study of microbial growth under controlled conditions. The effect of the operating parameters (i.e., dilution rate and feed nitrate nitrogen concentration) on the long-term behavior of the systems showed that X₃ was the predominant population for a wide range of combinations of dilution rate and feed nitrate nitrogen concentration. Also, coexistence of two populations (X₂X₃, X₁X₃) was observed. The results of the bifurcation analysis were also used to determine the denitrification rate and the nitrite nitrogen accumulation for each of the three systems as a function of the dilution rate (up to 0.17 h⁻¹) and the feed nitrate nitrogen concentration (up to 300 mg/L). The highest denitrification rate was achieved by system I (28 mg/Lh). A comparison between the three systems showed that the nitrite nitrogen concentration in system I was less than the one in system III, while the two systems gave similar denitrification rates. The second system had the greatest accumulation of nitrites with the lowest denitrification rate.     

Interaction of alongshore sediment transport and habitat conditions at Laguna La Mancha, Veracruz, Mexico

The habitats of La Mancha Lagoon, located midway along the coast of Veracruz, Mexico, are responding to the change of sediment supply reaching its primary inlet at the Gulf of Mexico. Until several decades ago, an abundant alongshore supply of sediment created a periodic opening and closing of the La Mancha inlet. The hydrologic regime of the lagoon consisted of raised water level and lower salinity during the closures, whereas the open inlet favored lower water level, higher salinity, and sediment accumulation in the flood tidal delta. Currently, diminished alongshore sediment supply has affected the inlet morphology and the discharge regime. Associated with the reduced sediment supply, the inlet is open longer in its periodic cycle, the water level variation is reduced, the salinity contrasts are reduced, and the rate of sedimentation in the flood-tide delta is increased. This combination of alterations to the inlet area is changing the flooding regime and affecting the conditions in a very well-developed mangrove habitat at the lagoon margins as well as conditions within the aqueous portions of the lagoon. Management options produce a conflict between supporting the direction of change or preserving the existing habitats.     

Dynamic compartment approach for modelling regimes of carbon cycle functioning in bog ecosystems

Svirezhev's method of dynamic model design by a given “storage-flow” diagram [Svirezhev Y.M., 1997. On some general properties of trophic networks. Ecol. Model. 99, 7–17] is developed and used for investigating dynamic regimes of carbon cycle functioning in a typical boreal transitional bog ecosystem. Ecosystems are often represented by static “storage-flow” diagrams reflecting their structure and matter or energy transfer between components at fixed time moments. Using the data of such diagrams aggregated in ecological field studies one can construct a dynamic model of the ecosystem to predict its future behaviour and to estimate a response to external perturbations—natural and human. Stability of both current equilibrium and possible alternative steady states and more complicated attractors are studied under two types of parameter perturbation: CO₂ atmospheric concentration increase initiated by greenhouse effect, and change in the rate of carbon output from dead organic matter and litter which depends on the water table level and possible peat excavation. Calculation of bifurcation curves gives areas in the parameter space where stable functioning of carbon cycle is provided. Steady states can be interpreted as raised bog, meadow, forest and fen. CO₂ concentration increase leads the current state of transitional bog to loose stability with appearance of oscillatory dynamics and further evolution to the chaotic attractor. The model is rich by chaotic solutions serving as transition regimes between regular steady and periodic attractors. Another chaotic regime is formed from forest equilibrium and exists in the same area of phase space where current equilibrium is stable.     

Evaluation of some competition indices for the construction of Lebanon cedar (Cedrus libani A. Rich.) stand models

The purpose of this research is to test the precision of some published competition indices of Lebanon cedar (Cedrus libani A. Rich.) for the estimation of future periodic diameter increment of individual trees. Twenty- nine published competition indices were tested, using fifteen separate sets of data and their pooled values, collected from various stand age and site quality classes Lebanon cedar at Antalya. Temporary sample plots were taken in Elmali-Qamkuyusu (9 sample plots) and Finike-Pinarcik (6 sample plots) in 2001. Every plot was stem mapped (x and y coordinate system), diameter (dbh), total height, crown length, crown diameter and 10-year radial increment were recorded for trees greater than 4 cm in dbh. Then, in order to evaluate these competition indices for the prediction of the periodic diameter increment of the individual trees. Three linear models have been constructed for each competition index. It was found that the competition indices (Daniels et al., 1986; Biging and Dobbertin, 1995; Pukkala and Kolstr?m, 1987; Hegyi, 1974) with larger influence-zone areas produce better results.