scholarly journals Inadequate Sampling Rates Can Undermine the Reliability of Ecological Interaction Estimation

2019 ◽  
Vol 24 (2) ◽  
pp. 48
Author(s):  
Brenno Cabella ◽  
Fernando Meloni ◽  
Alexandre S. Martinez
Keyword(s):  
Population Dynamics ◽  
Slow Rate ◽  
Data Interpretation ◽  
Volterra Model ◽  
Population Cycle ◽  
Cycle Period ◽  
Oscillatory Regime ◽  
Ecological Interaction ◽  
Effect Relationship ◽  
Acquisition Rates

Cycles in population dynamics are abundant in nature and are understood as emerging from the interaction among coupled species. When sampling is conducted at a slow rate compared to the population cycle period (aliasing effect), one is prone to misinterpretations. However, aliasing has been poorly addressed in coupled population dynamics. To illustrate the aliasing effect, the Lotka–Volterra model oscillatory regime is numerically sampled, creating prey–predator cycles. We show that inadequate sampling rates may produce inversions in the cause-effect relationship among other artifacts. More generally, slow acquisition rates may distort data interpretation and produce deceptive patterns and eventually leading to misinterpretations, as predators becoming preys. Experiments in coupled population dynamics should be designed that address the eventual aliasing effect.

scholarly journals Stochastic Delay Population Dynamics under Regime Switching: Permanence and Asymptotic Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Population Dynamics ◽  
Random Environment ◽  
Regime Switching ◽  
Matrix Method ◽  
Volterra Model ◽  
Function Technique ◽  
Stochastic Delay ◽  
Switching Diffusion ◽  
Asymptotic Estimation ◽  
Diffusion In Random Environment

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. Permanence and asymptotic estimations of solutions are investigated by virtue of V-function technique, M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

scholarly journals On a non-standard two-species stochastic competing system and a related degenerate parabolic equation

2020 ◽  
Vol 61 ◽  
pp. C1-C14
Author(s):  
Hidekazu Yoshioka ◽  
Yumi Yoshioka
Keyword(s):  
Differential Equation ◽  
Population Dynamics ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Growth Rates ◽  
Epidemic Model ◽  
Volterra Model ◽  
Sis Epidemic Model ◽  
Sis Epidemic

We propose and analyse a new stochastic competing two-species population dynamics model. Competing algae population dynamics in river environments, an important engineering problem, motivates this model. The algae dynamics are described by a system of stochastic differential equations with the characteristic that the two populations are competing with each other through the environmental capacities. Unique existence of the uniformly bounded strong solution is proven and an attractor is identified. The Kolmogorov backward equation associated with the population dynamics is formulated and its unique solvability in a Banach space with a weighted norm is discussed. Our mathematical analysis results can be effectively utilized for a foundation of modelling, analysis, and control of the competing algae population dynamics. References S. Cai, Y. Cai, and X. Mao. A stochastic differential equation SIS epidemic model with two correlated brownian motions. Nonlin. Dyn., 97(4):2175–2187, 2019. doi:10.1007/s11071-019-05114-2. S. Cai, Y. Cai, and X. Mao. A stochastic differential equation SIS epidemic model with two independent brownian motions. J. Math. Anal. App., 474(2):1536–1550, 2019. doi:10.1016/j.jmaa.2019.02.039. U. Callies, M. Scharfe, and M. Ratto. Calibration and uncertainty analysis of a simple model of silica-limited diatom growth in the Elbe river. Ecol. Mod., 213(2):229–244, 2008. doi:10.1016/j.ecolmodel.2007.12.015. M. G. Crandall, H. Ishii, and P. L. Lions. User's guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc., 27(1):229–244, 1992. doi:10.1090/S0273-0979-1992-00266-5. N. H. Du and V. H. Sam. Dynamics of a stochastic Lotka–Volterra model perturbed by white noise. J. Math. Anal. App., 324(1):82–97, 2006. doi:10.1016/j.jmaa.2005.11.064. P. Grandits, R. M. Kovacevic, and V. M. Veliov. Optimal control and the value of information for a stochastic epidemiological SIS model. J. Math. Anal. App., 476(2):665–695, 2019. doi:10.1016/j.jmaa.2019.04.005. B. Horvath and O. Reichmann. Dirichlet forms and finite element methods for the SABR model. SIAM J. Fin. Math., 9(2):716–754, 2018. doi:10.1137/16M1066117. J. Hozman and T. Tichy. DG framework for pricing european options under one-factor stochastic volatility models. J. Comput. Appl. Math., 344:585–600, 2018. doi:10.1016/j.cam.2018.05.064. G. Lan, Y. Huang, C. Wei, and S. Zhang. A stochastic SIS epidemic model with saturating contact rate. Physica A, 529(121504):1–14, 2019. doi:10.1016/j.physa.2019.121504. J. L. Lions and E. Magenes. Non-homogeneous Boundary Value Problems and Applications (Vol. 1). Springer Berlin Heidelberg, 1972. doi:10.1007/978-3-642-65161-8. J. Lv, X. Zou, and L. Tian. A geometric method for asymptotic properties of the stochastic Lotka–Volterra model. Commun. Nonlin. Sci. Numer. Sim., 67:449–459, 2019. doi:10.1016/j.cnsns.2018.06.031. S. Morin, M. Coste, and F. Delmas. A comparison of specific growth rates of periphytic diatoms of varying cell size under laboratory and field conditions. Hydrobiologia, 614(1):285–297, 2008. doi:10.1007/s10750-008-9513-y. B. \T1\O ksendal. Stochastic Differential Equations. Springer Berlin Heidelberg, 2003. doi:10.1007/978-3-642-14394-6. O. Oleinik and E. V. Radkevic. Second-order Equations with Nonnegative Characteristic Form. Springer Boston, 1973. doi:10.1007/978-1-4684-8965-1. S. Peng. Nonlinear Expectations and Stochastic Calculus under Uncertainty: with Robust CLT and G-Brownian Motion. Springer-Verlag Berlin Heidelberg, 2019. doi:10.1007/978-3-662-59903-7. T. S. Schmidt, C. P. Konrad, J. L. Miller, S. D. Whitlock, and C. A. Stricker. Benthic algal (periphyton) growth rates in response to nitrogen and phosphorus: parameter estimation for water quality models. J. Am. Water Res. Ass., 2019. doi:10.1111/1752-1688.12797. Y. Toda and T. Tsujimoto. Numerical modeling of interspecific competition between filamentous and nonfilamentous periphyton on a flat channel bed. Landscape Ecol. Eng., 6(1):81–88, 2010. doi:10.1007/s11355-009-0093-4. H. Yoshioka, Y. Yaegashi, Y. Yoshioka, and K. Tsugihashi. Optimal harvesting policy of an inland fishery resource under incomplete information. Appl. Stoch. Models Bus. Ind., 35(4):939–962, 2019. doi:10.1002/asmb.2428.

scholarly journals Parameters of ontogeny and population dynamics modeling of Panagrolaimus detritophagus (Nematoda: Rhabditida) in vitro

2021 ◽  
Vol 325 (1) ◽  
pp. 91-98
Author(s):  
K.S. Polyanina ◽  
A.Y. Ryss
Keyword(s):  
Population Dynamics ◽  
Development Time ◽  
The Body ◽  
Individual Development ◽  
Population Cycle ◽  
Developmental Cycle ◽  
Dynamics Modeling ◽  
Average Life ◽  
Average Life Span

The parameters of individual development and population cycle in in vitro nematodes Panagrolaimus detritophagus were revealed. The nematodes are bacterial feeders and commensals of the cerambycid Monochamus galloprovincialis from the pine Pinus sylvestris; nematodes use beetles as vectors. Mean development time (T) from egg to juvenile is 1–2 days for J2, 3–4 days for J3, and 4–7 days for J4; to adults (G, generation) 7 (6–8) days. In vitro the population cycle is equal to 4 generations and ends with 90% of survival juveniles (J3, day 34). In the growth phase of the population, the proportion of eggs exceeds the proportion of other stages of the developmental cycle: 39±11% for 7 days; 53±10% for 21 days. The average oviposition rate of females is 4.5±1.3/day and only 56±12% of eggs proceed to immediate development (hatching and molting of juveniles). The remaining mass of eggs enter development only after 27 days (4 individual generations). This feature may be considered as a form of delay or a brief diapause at the egg stage. Individual females may accumulate up to 4 synchronous eggs in the body and lay them simultaneously. The average life span of an adult female is 13–20 days. Formulas for the exponential growth of the number of females and the total nematode population have been developed.

scholarly journals Investigating Lotka-Volterra model using computer simulation

2020 ◽  
Vol 3 (10) ◽  
Author(s):  
F. Kunis ◽  
M. Dimitrov
Keyword(s):  
Computer Simulation ◽  
Population Dynamics ◽  
Numerical Solution ◽  
Fourth Order ◽  
Real Data ◽  
Volterra Model ◽  
Predator Prey ◽  
Prey System ◽  
Two Populations ◽  
Over Time

In this project we study the Lotka-Volterra model, also known as the model describing the population dynamics in the Predator-prey system. This model describes the interaction of the two species and also the development of their populations over time. We simulate this model using the fourth-order Runge-Kutta algorithm. This is the most widely used method for numerical solution of ordinary differential equations. Based on the obtained program, we simulated two populations and traced their behavior over time. We optimized the parameters and managed to obtain results that are very close to real data for such populations.

Two New Competition Indexes on the Basis of Lotka-Volterra Competition Model

2013 ◽  
Author(s):  
Huayong Zhang ◽  
Tousheng Huang ◽  
Liming Dai
Keyword(s):  
Population Dynamics ◽  
Equilibrium Point ◽  
Interspecific Competition ◽  
Competition Model ◽  
Volterra Model ◽  
Dynamics Analysis ◽  
Competitive Process ◽  
Stability Of Equilibrium ◽  
The Stability ◽  
Strength Of Competition

In this research, two competition indexes, competing capacity and competing tensor, are brought forward to better understand the interspecific competition between species. With the employment of the two indexes, the competitive process in Lotka-Volterra model can be described much clearly. The strength of competition for a species is divided into three competition grades according to the competing tensor. In the interspecific competition, when two species are in different competition grades, the weak species will be excluded; when two species are in the same grade, the coexistent equilibrium will present. Two cases are studied with the methods by employing the two indexes. In the second case, the stability of equilibrium point is determined by the competing tensor. The new indexes have shown potential in population dynamics analysis.

Multiannual fluctuations in precipitation and population dynamics of the montane vole, Microtus montanus

1988 ◽  
Vol 66 (10) ◽  
pp. 2128-2132 ◽  
Author(s):  
Aelita J. Pinter
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Critical Time ◽  
Significant Negative Correlation ◽  
Population Cycle ◽  
Spring Precipitation ◽  
Density Peak ◽  
Microtus Montanus ◽  
Population Peak ◽  
North Western

The montane vole, Microtus montanus, exhibits multiannual fluctuations in population density in northwestern Wyoming. Multiannual fluctuations in precipitation during May were also observed in the area. For data from the past 19 years, there is a significant negative correlation (r = −0.61, p < 0.01) between precipitation during May and vole population dynamics. Furthermore, there was a correlation between cycle phases of May precipitation and of population density. Peak precipitation in May (1970, 1974, 1977, 1980, 1984) was correlated in the same year with the decline phase in the population cycle. A trough in the May precipitation cycle (1969, 1973, 1976, 1979, 1983, 1985) was correlated in the same year with a population peak. It is hypothesized that spring precipitation may contribute to the population dynamics of Microtus montanus in north-western Wyoming by influencing the survival and reproductive success of these rodents at a critical time, the onset of the breeding season.

Sparse generalized Laguerre-Volterra model of neural population dynamics

2009 ◽  
Author(s):  
Dong Song ◽  
R.H.M. Chan ◽  
V.Z. Marmarelis ◽  
R.E. Hampson ◽  
S.A. Deadwyler ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Volterra Model ◽  
Neural Population

scholarly journals Discrete Competitive Lotka–Volterra Model with Controllable Phase Volume

Systems ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 17
Author(s):  
Anzhelika Voroshilova ◽  
Jeff Wafubwa
Keyword(s):  
Population Dynamics ◽  
Phase Space ◽  
Discrete Model ◽  
Dynamic Properties ◽  
Volterra Model ◽  
Volterra Equations ◽  
Stable Marriage ◽  
Stable Marriage Problem ◽  
Phase Space Volume ◽  
Space Volume

The simulation of population dynamics and social processes is of great interest in nonlinear systems. Recently, many scholars have paid attention to the possible applications of population dynamics models, such as the competitive Lotka–Volterra equation, in economic, demographic and social sciences. It was found that these models can describe some complex behavioral phenomena such as marital behavior, the stable marriage problem and other demographic processes, possessing chaotic dynamics under certain conditions. However, the introduction of external factors directly into the continuous system can influence its dynamic properties and requires a reformulation of the whole model. Nowadays most of the simulations are performed on digital computers. Thus, it is possible to use special numerical techniques and discrete effects to introduce additional features to the digital models of continuous systems. In this paper we propose a discrete model with controllable phase-space volume based on the competitive Lotka–Volterra equations. This model is obtained through the application of semi-implicit numerical methods with controllable symmetry to the continuous competitive Lotka–Volterra model. The proposed model provides almost linear control of the phase-space volume and, consequently, the quantitative characteristics of simulated behavior, by shifting the symmetry of the underlying finite-difference scheme. We explicitly show the possibility of introducing almost arbitrary law to control the phase-space volume and entropy of the system. The proposed approach is verified through bifurcation, time domain and phase-space volume analysis. Several possible applications of the developed model to the social and demographic problems’ simulation are discussed. The developed discrete model can be broadly used in modern behavioral, demographic and social studies.

Stochastic structure and nonlinear dynamics of food webs: qualitative stability in a Lotka-Volterra cascade model

1990 ◽  
Vol 240 (1299) ◽  
pp. 607-627 ◽  
Keyword(s):  
Population Dynamics ◽  
Food Webs ◽  
Trophic Structure ◽  
Three Dimensional ◽  
Cascade Model ◽  
Volterra Model ◽  
Critical Surface ◽  
Dimensional Parameter ◽  
Globally Asymptotically Stable ◽  
Number Of Species

Two competing models currently offer to explain empirical regularities observed in food webs. The Lotka-Volterra model describes population dynamics; the cascade model describes trophic structure. In a real ecological community, both population dynamics and trophic structure are important. This paper proposes and analyses a new hybrid model that combines population dynamics and trophic structure: the Lotka-Volterra cascade model (LVCM). The LVCM assumes the population dynamics of the Lotka-Volterra model when the interactions between species are shaped by a refinement of the cascade model. A critical surface divides the three-dimensional parameter space of the LVCM into two regions. In one region, as the number of species becomes large, the limiting probability that the LVCM is qualitatively globally asymptotically stable is positive. In the region on the other side of the critical surface, and on the critical surface itself, this limiting probability is zero. Thus the LVCM displays an ecological phase transition: gradual changes in the probabilities of various kinds of population dynamical interactions related to feeding can have sharp effects on a community’s qualitative stability. The LVCM shows that an inverse proportionality between connectance and the number of species, and a direct proportionality between the number of links and the number of species, as observed in data on food webs, need not be directly connected with the qualitative global asymptotic stability or instability of population dynamics. Empirical testing of the LVCM will require field data on the population dynamical effects of feeding relations.

A NUMERICAL STUDY ON PREDATOR PREY MODEL

2012 ◽  
Vol 09 ◽  
pp. 347-353
Author(s):  
MOHAMED FARIS LAHAM ◽  
ISTHRINAYAGY KRISHNARAJAH ◽  
ABDUL KADIR JUMAAT
Keyword(s):  
Stochastic Processes ◽  
Numerical Study ◽  
Spatial Models ◽  
Euler Method ◽  
Volterra Model ◽  
Population Cycle ◽  
Stochastic Representation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Spatial Models

Stochastic spatial models are becoming a popular tool for understand the ecological and evolution of ecosystem problems. We consider the predator prey interactions in term of stochastic representation of this Lotka-Volterra model and explore the use of stochastic processes to extinction behavior of the interacting populations. Here, we present simulation of stochastic processes of continuous time Lotka-Volterra model. Euler method has been used to solve the predator prey system. The trajectory spiral graph has been plotted based on obtained solution to show the population cycle of predator as a function of time.

Sign in / Sign up

Export Citation Format

Share Document