scholarly journals Dynamics of Planar Systems That Model Stage-Structured Populations

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
N. Lazaryan ◽  
H. Sedaghat
Keyword(s):  
Global Convergence ◽  
Saddle Point ◽  
Structured Populations ◽  
Vital Rates ◽  
Planar System ◽  
Density Dependent ◽  
Planar Systems ◽  
High Level ◽  
Weaker Conditions ◽  
Special Case

We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period two oscillations.

Experiments with a biological material for the closure of incisional hernias

1987 ◽  
Vol 21 (3) ◽  
pp. 195-200 ◽  
Author(s):  
M. Walter ◽  
U. Brenner ◽  
W. Holzmüller ◽  
J. M. Müller
Keyword(s):  
Collagen Type I ◽  
Morphological Properties ◽  
Type I ◽  
Native Structure ◽  
Incisional Hernias ◽  
Small Vessels ◽  
Collagen Implant ◽  
Infiltrating Cells ◽  
High Level ◽  
Special Case

A new preparation process was studied which should allow the implantation of collagen type I in its native structure in reconstructive surgery, in this special case for closure of incisional hernias. As experimental animals we used 30 female Lewis rats. A defect of the anterior abdominal wall measuring 3 cm × 4 cm was closed with our collagen substitute. Biopsies taken after 4, 6 and 8 weeks were examined morphologically. As criteria for revitalization and revascularization we used the type of infiltrating cells, the depth and density of infiltration and the formation of new blood vessels. After 4 weeks the implants were infiltrated by fibroblasts that decreased in density towards the centre. Good revascularization could be seen on the muscle-implant interface. After 6 weeks the density of infiltrating cells had increased markedly even to the centre of the collagen implant. Sporadically small vessels could be seen. Eight weeks after implantation the density of infiltrated cells was at the same high level, and capillary bundles could be seen within the whole implant. We believe that this collagen implant is suitable for the closure of hernias as shown by its physical and morphological properties. In particular it appears to guarantee an earlier and tighter closure of hernias than other materials.

Periodic solutions of planar systems with two delays

1999 ◽  
Vol 129 (5) ◽  
pp. 1017-1032 ◽  
Author(s):  
Shigui Ruan ◽  
Junjie Wei
Keyword(s):  
Neural Network ◽  
Periodic Solutions ◽  
Degree Theory ◽  
Hopf Bifurcations ◽  
Planar System ◽  
Linearized Stability ◽  
Two Delays ◽  
Planar Systems ◽  
Existence Conditions ◽  
Simple Neural Network

In this paper, we consider a planar system with two delays:ẋ1(t) = −a0x1(t) + a1F1 (x1(t − τ1), x2(τ−t2)).ẋ2(t) = −b0x2(t) + b1F2 (x1(t − τ1), x2(t − τxs2)).Firstly, linearized stability and local Hopf bifurcations are studied. Then, existence conditions for non-constant periodic solutions are derived using degree theory methods. Finally, a simple neural network model with two delays is analysed as an example.

scholarly journals Population regulation of territorial species: both site dependence and interference mechanisms matter

2010 ◽  
Vol 278 (1715) ◽  
pp. 2173-2181 ◽  
Author(s):  
Marie Nevoux ◽  
Olivier Gimenez ◽  
Debora Arlt ◽  
Malcolm Nicoll ◽  
Carl Jones ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Regulatory Mechanism ◽  
Site Occupancy ◽  
Integrated Approach ◽  
Vital Rates ◽  
Density Dependent ◽  
Underlying Mechanisms ◽  
A Site ◽  
Site Dependence ◽  
Dependent Processes

Spatial patterns of site occupancy are commonly driven by habitat heterogeneity and are thought to shape population dynamics through a site-dependent regulatory mechanism. When examining this, however, most studies have only focused on a single vital rate (reproduction), and little is known about how space effectively contributes to the regulation of population dynamics. We investigated the underlying mechanisms driving density-dependent processes in vital rates in a Mauritius kestrel population where almost every individual was monitored. Different mechanisms acted on different vital rates, with breeding success regulated by site dependence (differential use of space) and juvenile survival by interference (density-dependent competition for resources). Although territorial species are frequently assumed to be regulated through site dependence, we show that interference was the key regulatory mechanism in this population. Our integrated approach demonstrates that the presence of spatial processes regarding one trait does not mean that they necessarily play an important role in regulating population growth, and demonstrates the complexity of the regulatory process.

scholarly journals Interspecific density-dependent model of predator–prey relationship in the chemostat

2020 ◽  
pp. 2050086
Author(s):  
Tahani Mtar ◽  
Radhouane Fekih-Salem ◽  
Tewfik Sari
Keyword(s):  
Three Dimensional ◽  
Steady States ◽  
Dimensional System ◽  
Planar System ◽  
Predator Species ◽  
Predator Prey ◽  
Density Dependent ◽  
Existence And Stability ◽  
Dependent Growth ◽  
Transcritical Bifurcations

The objective of this study is to analyze a model of competition for one resource in the chemostat with general interspecific density-dependent growth rates, taking into account the predator–prey relationship. This relationship is characterized by the fact that the prey species promotes the growth of the predator species which in turn inhibits the growth of the first species. The model is a three-dimensional system of ordinary differential equations. With the same dilution rates, the model can be reduced to a planar system where the two models have the same local and even global behavior. The existence and stability conditions of all steady states of the reduced model in the plane are determined according to the operating parameters. Using the nullcline method, we present a geometric characterization of the existence and stability of all equilibria showing the multiplicity of coexistence steady states. The bifurcation diagrams illustrate that the steady states can appear or disappear only through saddle-node or transcritical bifurcations. Moreover, the operating diagrams describe the asymptotic behavior of this system by varying the control parameters and show the effect of the inhibition of predation on the emergence of the bistability region and the reduction until the disappearance of the coexistence region by increasing this inhibition parameter.

scholarly journals Harvesting can stabilize population fluctuations and buffer the impacts of climate change

2021 ◽  
Author(s):  
Bart Peeters ◽  
Vidar GrØtan ◽  
Marlène Gamelon ◽  
Vebjørn Veiberg ◽  
Aline Magdalena Lee ◽  
...  
Keyword(s):  
Life Histories ◽  
Resource Competition ◽  
Extinction Risk ◽  
Population Models ◽  
Environmental Stochasticity ◽  
Environmental Drivers ◽  
Population Fluctuations ◽  
Vital Rates ◽  
Density Dependent ◽  
Environmental Perturbations

Harvesting can magnify the destabilizing effects of environmental perturbations on population dynamics and, thereby, increase extinction risk. However, population-dynamic theory predicts that impacts of harvesting depend on the type and strength of density-dependent regulation. Here, we used population models for a range of life histories and an empirical reindeer case study to show that harvesting can actually buffer populations against environmental perturbations. This occurs because of density-dependent environmental stochasticity, where negative environmental impacts on vital rates are amplified at high population density due to intra-specific resource competition. Simulations from our population models show that even low levels of proportional harvesting may prevent overabundance, thereby dampening population fluctuations and reducing the risk of population collapse and quasi-extinction induced by environmental perturbations. Thus, depending on the species’ life history and the strength of density-dependent environmental drivers, harvesting can improve population resistance to increased climate variability and extreme weather expected under global warming.

Demographic processes in socially structured populations

2021 ◽  
pp. 341-350
Author(s):  
Maria Paniw ◽  
Gabriele Cozzi ◽  
Stefan Sommer ◽  
Arpat Ozgul
Keyword(s):  
Population Dynamics ◽  
Social Groups ◽  
Population Models ◽  
Structured Populations ◽  
Model Complexity ◽  
Vital Rates ◽  
Integral Projection Model ◽  
Projection Model ◽  
Structured Population Models ◽  
Structured Population

In socially structured animal populations, vital rates such as survival and reproduction, are affected by complex interactions among individuals of different social ranks and among social groups. Due to this complexity, mechanistic approaches to model vital rates may be preferred over commonly used structured population models. However, mechanistic approaches come at a cost of increased modelling complexity, computational requirements, and reliance on simulated metrics, while structured population models are analytically tractable. This chapter compares different approaches to modelling population dynamics of socially structured populations. It first simulates individual-based data based on the life cycle of a hypothetical cooperative breeder and then projects population dynamics using a matrix population model (MPM), an integral projection model (IPM), and an individual-based model (IBM). The authors demonstrate that, when projecting population size or structure, the relatively simpler MPM can outperform both the IPM and IBM. However, mechanistic details parametrised in the more complex IBM are required to accurately project interactions within social groups. The R scripts in this chapter provide a roadmap to both simulate data that best describe a socially structured system and assess the level of model complexity needed to capture the dynamics of the system.

Predicting the effects of climate change on bird population dynamics

2019 ◽  
pp. 74-90
Author(s):  
Bernt-Erik Sæther ◽  
Steinar Engen ◽  
Marlène Gamelon ◽  
Vidar Grøtan
Keyword(s):  
Climate Change ◽  
Population Dynamics ◽  
Population Size ◽  
Environmental Stochasticity ◽  
Population Estimates ◽  
Parameter Estimates ◽  
Vital Rates ◽  
Statistical Sense ◽  
High Level ◽  
Avian Populations

Climate variation strongly influences fluctuations in size of avian populations. In this chapter, we show that it is difficult to predict how the abundance of birds will respond to climate change. A major reason for this is that most available time series of fluctuations in population size are in a statistical sense short, thus often resulting in large uncertainties in parameter estimates. We therefore argue that reliable population predictions must be based on models that capture how climate change will affect vital rates as well as including other processes (e.g. density-dependences) known to affect the population dynamics of the species in question. Our survey of examples of such forecast studies show that reliable predictions necessarily contain a high level of uncertainty. A major reason for this is that avian population dynamics are strongly influenced by environmental stochasticity, which is for most species, irrespective of their life history, the most important driver of fluctuations in population size. Credible population predictions must therefore assess the effects of such uncertainties as well as biases in population estimates.

scholarly journals Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations

2017 ◽  
Vol 114 (44) ◽  
pp. 11582-11590 ◽  
Author(s):  
Russell Lande ◽  
Steinar Engen ◽  
Bernt-Erik Sæther
Keyword(s):  
Life History ◽  
Population Growth ◽  
Density Dependence ◽  
Population Size ◽  
Structured Populations ◽  
Environmental Stochasticity ◽  
Trade Off ◽  
Density Dependent ◽  
Fluctuating Environment ◽  
Stochastic Demography

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, N, exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, r0 and K, and the environmental variance in population growth rate, σe2. Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, θ, measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes E[Nθ]=[1−σe2/(2r0)]Kθ. This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher r0 versus higher K. However, selection also acts to decrease σe2, so the simple life-history trade-off between r- and K-selection may be obscured by additional trade-offs between them and σe2. Under the classical logistic model of population growth with linear density dependence (θ=1), life-history evolution in a fluctuating environment tends to maximize the average population size.

scholarly journals Can't live with them, can't live without them? Balancing mating and competition in two-sex populations

2017 ◽  
Vol 284 (1865) ◽  
pp. 20171999 ◽  
Author(s):  
Aldo Compagnoni ◽  
Kenneth Steigman ◽  
Tom E. X. Miller
Keyword(s):  
Sex Ratio ◽  
Mating Success ◽  
Sex Ratios ◽  
Structured Populations ◽  
Allee Effects ◽  
Mate Finding ◽  
Frequency Dependent ◽  
Density Dependent ◽  
Positive Effects ◽  
Demographic Processes

Two-sex populations are usually studied through frequency-dependent models that describe how sex ratio affects mating, recruitment and population growth. However, in two-sex populations, mating and recruitment should also be affected by density and by its interactions with the sex ratio. Density may have positive effects on mating (Allee effects) but negative effects on other demographic processes. In this study, we quantified how positive and negative inter-sexual interactions balance in two-sex populations. Using a dioecious grass ( Poa arachnifera ), we established experimental field populations that varied in density and sex ratio. We then quantified mating success (seed fertilization) and non-mating demographic performance, and integrated these responses to project population-level recruitment. Female mating success was positively density-dependent, especially at female-biased sex ratios. Other demographic processes were negatively density-dependent and, in some cases, frequency-dependent. Integrating our experimental results showed that mate-finding Allee effects dominated other types of density-dependence, giving rise to recruitment that increased with increasing density and peaked at intermediate sex ratios, reflecting tension between seed initiation (greater with more females) and seed viability (greater with more males). Our results reveal, for the first time, the balance of positive and negative inter-sexual interactions in sex-structured populations. Models that account for both density- and sex ratio dependence, particularly in mating, may be necessary for understanding and predicting two-sex population dynamics.

Melnikov-Type Chaos of Planar Systems with Two Discontinuities

2015 ◽  
Vol 25 (02) ◽  
pp. 1550027 ◽  
Author(s):  
Jose Castro ◽  
Joaquin Alvarez
Keyword(s):  
Equilibrium Point ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Approximate Model ◽  
Discontinuous System ◽  
Planar System ◽  
Sign Function ◽  
Nonsmooth Systems ◽  
Planar Systems ◽  
Chaotic Nature

In this paper, the chaotic behavior of a driven planar system with two discontinuous terms and a pseudo-equilibrium point in the intersection of the discontinuity surfaces is analyzed. This scenario is not covered by smooth techniques of chaos analysis or other techniques like the extension of Melnikov's method for nonsmooth systems. In consequence, we propose to use an approximate model of the discontinuous system for which this technique can be applied, and compare the responses of both systems, the discontinuous and the approximate, when this last model is close, in a certain way, to the discontinuous system. One of the discontinuous terms, given by a sign function, is approximated by a saturation with high slope at the equilibrium point. Some conditions that determine the chaotic behavior of the approximate system are formally established, and the convergence of its chaotic orbits to some orbits of the discontinuous system, when the slope of the approximation is large enough, is shown. In particular, we show the similarity of the dynamical behavior of both systems where a chaotic behavior can be displayed, for a parameter region determined by the application of the Melnikov technique to nonsmooth systems. A comparison of the Feigenbaum diagrams, for a parameter range obtained from the application of this technique, shows the similarity of their dynamics and the chaotic nature of the discontinuous system.

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