Behaviour Of Population Dynamics Research Articles

Moment evolution equations for rational random dynamical systems: an increment decomposition method

Abstract Statistical moments are commonly used tools for exploring the ensemble behavior in gene regulation and population dynamics, where the rational vector fields are particularly ubiquitous, but how to efficiently derive the corresponding moment evolution equations was not much involved. Traditional derivation methods rely on fractional reduction and Itô formula, but it may become extremely complicated if the vector field is described by multivariate fractional polynomials. To resolve this issue, we present a novel incremental decomposition method, by which the rational vector field is divided into two parts: (proper) fractional polynomials and non-fractional polynomials. For the non-fractional polynomial part, we deduce the variation rate of a statistical moment by the Itô formula, but for the fractional polynomial part we acquire the corresponding variation rate by a relation analogous to that between the moment generating function and the distinct statistical moments. As application of the novel technique, the resultant infinite-dimensional moment systems associated with two typical examples are truncated with the schemes of derivative matching closure and the Gaussian moment closure. By comparing the lower-order statistical moments obtained from the closed moment systems with the counterparts obtained from direct simulation, the correctness of the proposed technique is verified. The present study is significant in facilitating the development of moment dynamics towards more complex systems.

The effect of intrinsic decoherence on the dynamics of an Ξ-type qutrit system interacting with a coherent field

This paper solves milburn’s intrinsic noise (IN) model for a 3-level atom of an Ξ-type interacting with a coherent cavity field via multiphoton transitions. Therefore, the effects of the intrinsic noise and the multi-photon interactions are investigated for some quantum phenomena, such as total correlation, entanglement, and atomic inversion. In general, we found that the collapse-revival phenomenon occurs during the oscillatory behaviour of atomic population dynamics. In addition, the birth-death phenomenon is observed in the negativity dynamics. Entropy, negativity, and mutual information have various dynamics. It is found that, as the entropy increases, the negativity and mutual information diminish to stationary levels. When intrinsic noise is considered, all the phenomena of atomic inversion, entropies, negativity and mutual information exhibit high sensitivity to high intrinsic noise values, except the mutual information dynamics, which is more resistant than that of the other quantifiers.

Scaling from optimal behavior to population dynamics and ecosystem function

While behavioral responses of individual organisms can be predicted with optimal foraging theory, the theory of how individual behavior feeds back to population and ecosystem dynamics has not been fully explored. Ecological models of trophic interactions incorporating behavior of entire populations commonly assume either that populations act as one when making decisions, that behavior is slowly varying or that non-linear effects are negligible in behavioral choices at the population scale. Here, we scale from individual optimal behavior to ecosystem structure in a classic tri-trophic chain where both prey and predators adapt their behavior in response to food availability and predation risk. Behavior is modeled as playing the field, with both consumers and predators behaving optimally at every instant basing their choices on the average population behavior. We establish uniqueness of the Nash equilibrium, and find it numerically. By modeling the interactions as playing the field, we can perform instantaneous optimization at the individual level while taking the entire population into account. We find that optimal behavior essentially removes the effect of top-down forcing at the population level, while drastically changing the behavior. Bottom-up forcing is found to increase populations at all trophic levels. These phenomena both appear to be driven by an emerging constant consumption rate, corresponding to a partial satiation. In addition, we find that a Type III functional response arises from a Type II response for both predators and consumers when their behavior follows the Nash equilibrium, showing that this is a general phenomenon. Our approach is general and computationally efficient and can be used to account for behavior in population dynamics with fast behavioral responses.

Moving-habitat models: A numerical approach

As the global climate changes, biological populations have to adapt in place or move in space to stay within their preferred temperature regime. Empirical evidence suggests that shifting speeds of temperature isoclines are location and elevation dependent and may accelerate over time. We present a mathematical tool to study transient behaviour of population dynamics within such moving habitats to discern between populations at high and low risk of extinction. We introduce a system of reaction–diffusion equations to study the impact of varying shifting speeds on the persistence and distribution of a single species. Our model includes habitat dependent movement behaviour and habitat preference of individuals. These assumptions result in a jump in density across habitat types and generalize previous studies. We build and validate a numerical finite difference scheme to solve the resulting equations. Our numerical scheme uses a coordinate system where the location of the moving suitable habitat is fixed in space and a modification of a finite difference scheme to capture the jump in density. We explore a variety of shifting-speed scenarios and contribute insights into the mechanisms that support population persistence through time in shifting habitats. One common finding is that a strong bias for the suitable habitat helps the population persist at faster shifting speeds, yet sustains a smaller total population at slower shifting speeds.

Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates on one side, and transfer which drives the population towards lower birth rates on the other side. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible subpopulations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth–death processes with immigration. For the latter processes, we derive several results of independent interest.

Gene Drives: Dynamics and Regulatory Matters-A Report from the Workshop "Evaluation of Spatial and Temporal Control of Gene Drives," April 4-5, 2019, Vienna.

Gene Drives are regarded as future tools with a high potential for population control. Due to their inherent ability to overcome the rules of Mendelian inheritance, gene drives (GD) may spread genes rapidly through populations of sexually reproducing organisms. A release of organisms carrying a GD would constitute a paradigm shift in the handling of genetically modified organisms because gene drive organisms (GDO) are designed to drive their transgenes into wild populations and thereby increase the number of GDOs. The rapid development in this field and its focus on wild populations demand a prospective risk assessment with a focus on exposure related aspects. Presently, it is unclear how adequate risk management could be guaranteed to limit the spread of GDs in time and space, in order to avoid potential adverse effects in socio‐ecological systems. The recent workshop on the “Evaluation of Spatial and Temporal Control of Gene Drives” hosted by the Institute of Safety/Security and Risk Sciences (ISR) in Vienna aimed at gaining some insight into the potential population dynamic behavior of GDs and appropriate measures of control. Scientists from France, Germany, England, and the USA discussed both topics in this meeting on April 4–5, 2019. This article summarizes results of the workshop.

Kinetic pattern and microbial population dynamic characterization ofEscherichia coliandSalmonella enteritidisin Frankfurter sausage: An experimental and modeling study

AbstractConcerns over the safety of nitrite and its role in the formation of nitrosamines have aroused considerable interest in developing alternative antimicrobial agents to replace nitrite. Plant‐derived antimicrobial agents could serve against food spoilage and pathogens. For the first time in this study, three semiempirical kinetic models, that is, exponential, homographic, andn‐order kinetic models were established to describe the microbiological population pattern and dynamic behavior. TheEscherichia coliandSalmonella enteritidispopulation dynamics were investigated in Frankfurter sausage as a complex food system, contained four different antimicrobial redcurrant extract (RE) concentrations (0, 0.1, 0.2, and 0.4% wt/wt) at two temperatures (4 and 25°C) during 17 days storage. Furthermore, the results were compared with a neuro‐fuzzy system. Although, all three kinetic models showed a reasonable prediction accuracy, homographic kinetic model was the best for predicting antibacterial effects of RE againstE. coli(R2= 0.94–1,= 0.93–0.99,Q‐squared = 0.80–0.89, and RMSE = 0.21–0.68) and then‐order kinetic model did the best in describing the kinetic pattern ofS. enteritidis(R2= 0.97–0.99,= 0.94–0.99,Q‐squared = 0.85–0.93, RMSE = 0.06–0.74). The increase in the RE concentration and temperature resulted in the increase of kinetic parameters of microbial population decline rate and extent for both bacteria, significantly. Furthermore, all the homographic model parameters (except of equilibrium population,p∞) and all the kinetic model parameters withnorder (except of reaction order) the synergistic effect of temperature and concentration was clear. RE at 0.4% concentration induced 0.12 log colony forming unit (CFU)/gE. coliand 0.45 log CFU/gS. enteritidisequilibrium population (p∞) at 17th day of storage at 25°C. Compared toS. enteritidis,E. coliwas more sensitive to RE concentration at both temperatures.Practical applicationsMost formulations of the meat products contain nitrite as a main ingredient to prohibit the pathogenic bacteria growth. The results of the present study showed that all the three studied kinetic models (exponential, homographic, andn‐order kinetic models) appropriately modeled theS. enteritidisandE. colipopulation dynamics. Regarding the statistical parameters,n‐order and homographic kinetic models were found to be the best models for predicting antibacterial effects of RE againstS. enteritidisandE. coli, respectively. Furthermore,E. coliwas more sensitive against RE thanS. enteritidisin Frankfurter sausage samples at 4 and 25°C during 17 days storage. With the increase in the RE concentration at the constant temperature and with the increase in temperature at the constant extract concentration, the decline rate ofE. colipopulation increased significantly (p < .05), while the needed time for 50% reduction decreased; besides,S. enteritidispopulation dynamics showed the increase in the rate and extent of decline, and a decrease in the equilibrium microbial population at these conditions (p < .05). No significant differences were observed between the neuro‐fuzzy system results and semiempirical kinetic models in the prediction of microbiological population dynamic. Nevertheless, the novel semiempirical models presented important biological parameters, which provided a better understanding of the systems biological state than the neuro‐fuzzy system. These results could offer new perspectives in the field of microbiology.

SiQAD: A Design and Simulation Tool for Atomic Silicon Quantum Dot Circuits

This paper introduces SiQAD, a computer-aided design tool enabling the rapid design and simulation of atomic silicon dangling bond quantum dot patterns capable of computational logic. Several simulation tools are included, each able to inform the designer on various aspects of their designs: a ground-state electron configuration finder, a non-equilibrium electron dynamics simulator, and an electric potential landscape solver with clocking electrode support. Simulations have been compared against past experimental results to inform the electron population estimation and dynamic behavior. New logic gates suitable for this platform have been designed and simulated, and a clocked wire has been demonstrated. This work paves the way for the exploration of the vast and fertile design space of atomic silicon dangling bond quantum dot circuits.

Memory and adaptive behavior in population dynamics: anti-predator behavior as a case study.

Memory allows organisms to forecast the future on the basis of experience, and thus, in some form, is important for the development of flexible adaptive behavior by animal communities. To model memory, we use the concept of hysteresis, which mathematically is described by the Preisach operator. As a case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows us to naturally incorporate essential features of an adaptive system and memory. Our analysis and simulations show that a system with memory can have a continuum of equilibrium states with non-trivial stability properties. The main factor that determines the actual equilibrium state to which a trajectory converges is the maximal number achieved by the population of predator along this trajectory.

Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion

This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a) to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b) we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of our model; (c) the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival) may lead to extinction of the population.

Global qualitative analysis of a non-smooth Gause predator–prey model with a refuge

The present paper aims to provide a detailed qualitative analysis of a non-smooth Gause predator–prey model. In this model, the saturating functional response function with a discontinuity at a critical prey density was employed to show the effects of a prey refuge on the population dynamic behavior. Analysis of this model revealed rich dynamics including locally (or globally) stable canard cycles, a locally (globally) stable pseudo-equilibrium, unbounded trajectories in which both populations go to infinity or the prey goes to infinity and the predator dies out eventually. The main purpose of the present work is to carry out a completely qualitative analysis for this model. In particular, two sets of sufficient conditions drive both populations to approach infinity and the sufficient and necessary conditions for all of the other main results are presented.

Population Dynamics of Pathogens with Multiple Host Species

Pathogens that can infect multiple host species will have different dynamics than pathogens that are restricted to a single species of host. This article examines the conditions for establishment and long-term population dynamic behavior of pathogens that infect multiple species of hosts. The article attempts to address three major questions in this area: First, under which conditions will increases in the diversity of host species buffer infectious disease outbreaks, and under which conditions will host diversity amplify disease outbreaks? Second, under what conditions is it possible to control an infectious agent by focusing control against only one host species? Third, what role does host species diversity play in maintaining pathogen persistence? The answers to these questions supply some important general insights into the role that biodiversity plays in buffering humans and other species against new and emerging pathogens.

Large-Time Behavior in Population Dynamics with Offspring Production at Fixed Ages, Child Care, and Spatial Dispersal

We present a density-dependent population dynamics model with age-dependence, child care, and spatial dispersal. The population consists of the young (under maternal care), juvenile, and adult (producing offsprings at fixed ages or of post-reproductive age) classes. Death moduli of the juvenile and adult individuals are decomposed into two-term sums. The first sum represents the death rate by natural causes and by those that do not depend on the population spatial density, while the other one describes the environmental influence depending on the spatial density of the juvenile and adult individuals. The steady-state and a class of separable solutions are considered, and the large-time behavior of separable solutions is analyzed for the stationary vital rates. The asymptotic behavior of nondispersing semelparous species is also examined.

The role of habitat selection behavior in population dynamics: source–sink systems and ecological traps

Ecological traps, poor‐quality habitat that nonetheless attract individuals, have been observed in both natural and human‐altered settings. Until recently, ecological traps were considered a kind of source–sink system, but source–sink theory does not model maladaptive habitat choice, and therefore cannot accurately represent ecological traps or predict their population‐level consequences. Although recent models of ecological traps addressed this problem, they used patch‐based models containing only two habitats that were very different from one another, but were internally homogeneous. These sorts of patch models may not apply to many real populations, and using them for populations in landscapes with mosaic or gradient habitat structures may be misleading. I developed models that treat source–sink dynamics and ecological traps as special cases of a single process, in which the attractiveness and quality of the habitat are separate variables that can be either positively or negatively related, and in which habitat quality varies continuously throughout the landscape. As expected, sinks are less detrimental to populations than ecological traps, in which preferential use of poor habitat elevates extinction risk. Furthermore, ecological traps may be undetected, and may even appear to be sources, when population sizes are large, but may still prevent recovery in spite of the availability of high‐quality habitat when populations drop below threshold levels. Conservation biologists do not routinely consider the possibility that apparent sinks are actually traps, but since traps should be associated with the rapidly changing and novel habitat characteristics primarily produced by human activities, ecological traps should be considered an important and potentially widespread conservation concern.

Effect of environment partitioning on the survival and coexistence of autocatalytic replicators.

The paradigm of cubic autocatalytic replicators with decay in coupled isothermal continuous stirred tank reactors is selected as a model to study complex behavior in population dynamics of sexually reproducing species in a heterogenous environment. It is shown that, even a setup with single species in two coupled environments may have regions in parameter space that result in chaotic behavior, hence segregation in the environment causes complexity in the system dynamics. Furthermore, partitioning is found to lead to emergence phenomena exemplified by steady states not obtainable in the equivalent homogeneous system. These phenomena are illustrated through case studies involving single or multiple species. Results show that the coupled environments can host species, that would not survive should the coupling be removed.

Frequency-dependent predation by birds at edges and interiors of woodland

Structural variations between edge and interior areas within forest fragments may bring about differences in food availability that may influence the selective behaviour of predators and prey population dynamics. The purpose of this paper was to assess patterns of artificial prey selection by wild birds (House Sparrow Passer domesticus and Rock Dove Columba livid) between edge and interior areas of woodland, taking into account differences in prey frequency (10% of one food type and 90% of the other) and density (30 baits/m-2 and 50 baits/m-2). Experiments were conducted at 24 plots in 3 forest fragments in the city of Madrid, Spain. Selectivity did not vary among parks or between densities. However, selectivity did vary with the frequency and location of baits, showing an anti-apostatic trend (baits were preferred at low rather than at high frequencies) that was more pronounced at interiors than at edges. Two possible factors that may account for stronger anti-apostatic selection at edges are the higher densities of predators and pedestrians found there. However, there are many other possible explanations, and no specific conclusion can be supported with the current data. The results of this study also point out that site heterogeneity should be taken into account in the experimental design of future studies on frequency-dependent food selection by wild birds, particularly in fragmented landscapes.

A note on the collection of associated behavioural data with biopsy samples during cetacean assessment cruises

Understanding the influence of social organisation on the distribution, abundance and genetic structure of cetacean populations is critical in developing better predictive models for management. Field data on cetacean social organisation are far more valuable when collected and analysed together with genetic data from biopsy samples and environmental information (e.g. oceanographic patterns, prey availability). Traditionally, however, studies of cetacean social behaviour and studies of cetacean population dynamics have been conducted independently (Tillman and Donovan, 1986). To integrate these fields, this paper recommends that multi-disciplinary cetacean assessment surveys collect biopsy and associated behavioural data for each sample taken (the minimum data being group size, number of animals biopsied and age class). Examples of sampling forms, outlining the desired information, are provided. Understanding of cetacean stock structure and the processes affecting stock differentiation will best come from a combined genetic, social, ecological and oceanographic approach.

Models for mating disruption by means of pheromone for insect pest control

AbstractModels are presented to investigate the population dynamic behavior of a pest population with the release of pheromone for mating disruption. Three mechanisms of mating disruption are considered: (i) confusion of males, (ii) competition with female pheromone trails yielding false trail following, (iii) emigration of males prior to mating. In addition, several refinements to confusion are considered. Confusion and emigration of males were found to be very similar both quantitatively and dynamically; also, a combination of both mechanisms was very little more efficient than either one separately. False trail following is difficult to compare with the other two, since competition with wild females is involved and thus the total population size enters the equations. Density dependence of the action of pheromones results in some cases in which mating disruption cannot control the pest population. Similarly, aggregation of the pest population decreases the efficiency of the method unless the pheromone action is density independent. Delayed mating of females makes control easier, and may constitute one mechanism for mating disruption.

Asymptotic Behavior in Age-Dependent Population Dynamics with Hereditary Renewal Law

This paper is concerned with the age dependent population dynamics where the renewal law involves hereditary effects. The first section is devoted to a model of Von Foerster type (i.e., a single species linear model). The second section is devoted to the same model with spatial spread. Both models are studied by means of the Laplace transform applied to a convolution integral equation (renewal equation). Actually in the model with diffusion we convert the equation to an abstract differential equation on a Banach space. The semigroup approach combined with a spectral mapping argument allow us to use the Laplace transform also in this case. An asymptotic expansion as in the classical Von Foerster model is obtained.

Possible Role of Behavior in Regulating Greater Prairie Chicken Populations

This paper presents data on reproductive behavior gathered during a 5-year study of greater prairie chickens (Tympanuchus cupido pinnatus) in northeastern Kansas. Data were collected by direct observation and by radio-telemetry on a 6,000-acre study area. Numbers of male prairie chickens on booming grounds decreased between March and May each year. Only about 50 percent of the males were territory-owners on booming grounds during the peak of mating activity. The fate of the non-booming males was unknown. Aggressive behavior was evident in groups of females visiting booming grounds during the height of the mating season. Dominant females prevented or at least delayed the mating of subordinate females. Three instances of greater prairie chicken renesting were observed; one bird renested twice. There were two peaks of mating activity, the second may have reflected renesting activity. Success of six nests begun before May 1 was 66 percent while that for 13 nests begun after May 1 was only 8 percent. Inter-booming ground movements of both males and females indicated that booming ground areas could not be considered separate gene pools. Courtship display patterns of male greater prairie chickens have been extensively described (Breckenridge 1929, Hamerstrom 1941, Schwartz 1945, Hamerstrom and Hamerstrom 1960, Robel 1964). Essentially no data are available on the preand postnesting behavior of female greater prairie chickens. During an intensive study of prairie chickens in Kansas, data were acquired which may be helpful in determining the role of behavior in population dynamics of 1Contribution No. 1059 Division of Biology, Kansas Agricultural Experiment Station, Kansas State University, Manhattan, 66502. prairie chickens. This paper presents some pertinent behavioral data collected between 1964 and 1968. I am indebted to J. Cebula, N. Silvy, C. Viers, and P. Watt, former graduate students at Kansas State University, who assisted in collecting much of the data presented in this paper. John and the late Grover Simpson, owners of the property on which this study was conducted, provided unlimited cooperation. This study was supported in part by grants from the National Institutes of Health, National Science Foundation, and the Penrose Fund of the American Philosophical Society. This content downloaded from 157.55.39.112 on Wed, 29 Jun 2016 05:33:20 UTC All use subject to http://about.jstor.org/terms REGULATION OF PRAIRIE CHICKEN POPULATIONS * Robel 307