The dynamics of collembolan populations: a matrix model of single species population growth

1977 ◽  
Vol 55 (2) ◽  
pp. 314-324 ◽  
Author(s):  
Barry C. Longstaff
Keyword(s):  
Population Growth ◽  
Matrix Model ◽  
Size Structure ◽  
Single Species ◽  
Deterministic Models ◽  
Damped Oscillations ◽  
Species Population ◽  
Population Sizes ◽  
Set Up ◽  
Single Species Population

The construction of a matrix model for the growth of populations of soil Collembola is described. Data from four replicate cultures of each of two species kept under laboratory conditions were modelled in the form of difference equations, which took into account the size structure of the populations. These equations were set up so as to effect a Leslie-type matrix model. The effect of density upon population growth rate was incorporated into the model in the form of a density-related function for fecundity.The success of the modelling procedures was varied with some of the models accurately predicting both the pattern of population growth and the population sizes at successive time intervals, whilst others only showed the trends. The deterministic models of each of the replicates for each species were combined to produce a stochastic model for that species. These also met with mixed success. The equilibrium values for the deterministic models were calculated and their stability properties examined. The models for both species predict a stable equilibrium approached by a series of damped oscillations.

scholarly journals STUDY OF SINGLE-SPECIES POPULATION MODELS

2020 ◽  
pp. 161-166
Author(s):  
Marthak Rutu
Keyword(s):  
Spatial Heterogeneity ◽  
Environmental Effects ◽  
Age Structure ◽  
Single Species ◽  
Research Paper ◽  
Population Models ◽  
Deterministic Models ◽  
One Dimensional ◽  
Species Population ◽  
Single Species Population

In this research paper one dimensional population models developed centuries ago shows that growth and/decay of single homogeneous populations But environmental effects spatial heterogeneity or age-structure deterministic models prevailing single species population models.

scholarly journals Coarse, Medium or Fine? A Quantum Mechanics Approach to Single Species Population Dynamics

2020 ◽  
Author(s):  
Olcay Akman ◽  
Leon Arriola ◽  
Aditi Ghosh ◽  
Ryan Schroeder
Keyword(s):  
Population Dynamics ◽  
Quantum Mechanics ◽  
Single Species ◽  
Stable Equilibrium Point ◽  
Ode Model ◽  
Deterministic Models ◽  
Species Population ◽  
Quantum Approach ◽  
Single Species Population ◽  
Quantum Framework

AbstractStandard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the possibility of searching for “black–swan” events. In other words, using the more sophisticated quantum approach, we may be able to make quantitative statements about rare events that have significant ramifications to the dynamical system.

Population growth and density dependence

2019 ◽  
pp. 63-80
Author(s):  
Gary G. Mittelbach ◽  
Brian J. McGill
Keyword(s):  
Population Growth ◽  
Density Dependence ◽  
Growth Model ◽  
Species Interactions ◽  
Single Species ◽  
Positive Density ◽  
Allee Effects ◽  
Species Population ◽  
Exponential Growth Model ◽  
Single Species Population

This chapter reviews the basic mathematics of population growth as described by the exponential growth model and the logistic growth model. These simple models of population growth provide a foundation for the development of more complex models of species interactions covered in later chapters on predation, competition, and mutualism. The second half of the chapter examines the important topic of density-dependence and its role in population regulation. The preponderance of evidence for negative density-dependence in nature is reviewed, along with examples of positive density dependence (Allee effects). The study of density dependence in single-species populations leads naturally to the concept of community-level regulation, the idea that species richness or the total abundance of individuals in a community may be regulated just like abundance in a single-species population. The chapter concludes with a look at the evidence for community regulation in nature and a discussion of its importance.

scholarly journals A white-box model of population growth

2014 ◽  
Author(s):  
Lev V. Kalmykov ◽  
Vyacheslav L. Kalmykov
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Complex Systems ◽  
Population Growth ◽  
Single Species ◽  
Black Box ◽  
Box Model ◽  
Holistic Approaches ◽  
Species Population ◽  
Single Species Population

Background. Integration of reductionist and holistic approaches is one of the great challenges for mathematical modeling. Mathematical models of complex systems are divided into black-box, white-box and grey-box types. A black-box model is completely nonmechanistic as internal mechanisms of a modeled complex system are hidden. A white-box model demonstrates direct mechanisms of functioning of a complex system. It holistically shows all events at microlevel, mesolevel and macrolevel of a modeled system at all stages of its dynamics. Earlier we have used the white-box modeling for verification and reformulation of the competitive exlusion principle. Here we investigate our white-box model of single-species population dynamics. This is fundamentally important because most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka-Volterra models. Methods. Our white-box model of single-species population growth is a purely logical deterministic individual-based cellular automata model. A biological prototype of the model is a vegetative propagation of rhizomatous lawn grasses. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We also investigate different size and structure of the habitat and two types of fecundity. Results. We have created and investigated a logical white-box model of an ecosystem with one species. This model demonstrates mechanisms of the S-shaped and double S-shaped population growth. We have investigated population growth limited by different factors, in particular by resources, habitat structure, intraspecific competition, lifetime of individuals, regeneration time and fecundity of individuals. We have compared the S-shaped curves with J-shaped curves of population growth. Conclusion. We present a basic white-box model of population dynamics which combines reductionist and holistic approaches. Integration of reductionist and holistic approaches is provided by the simultaneous modeling of both part-whole and cause-effect relations in complex system. We consider this holystic multi-level white-box modeling approach as a method of artificial intelligence which works as hyper-logical automatic deductive inference that provides direct mechanistic insights into complex systems. The white-box modeling by logical deterministic cellular automata is a perspective way for investigation not only of population dynamics but also of any complex systems.

scholarly journals A white-box model of population growth

2014 ◽  
Author(s):  
Lev V. Kalmykov ◽  
Vyacheslav L. Kalmykov
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Complex Systems ◽  
Population Growth ◽  
Single Species ◽  
Black Box ◽  
Box Model ◽  
Holistic Approaches ◽  
Species Population ◽  
Single Species Population

Background. Integration of reductionist and holistic approaches is one of the great challenges for mathematical modeling. Mathematical models of complex systems are divided into black-box, white-box and grey-box types. A black-box model is completely nonmechanistic as internal mechanisms of a modeled complex system are hidden. A white-box model demonstrates direct mechanisms of functioning of a complex system. It holistically shows all events at microlevel, mesolevel and macrolevel of a modeled system at all stages of its dynamics. Earlier we have used the white-box modeling for verification and reformulation of the competitive exlusion principle. Here we investigate our white-box model of single-species population dynamics. This is fundamentally important because most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka-Volterra models. Methods. Our white-box model of single-species population growth is a purely logical deterministic individual-based cellular automata model. A biological prototype of the model is a vegetative propagation of rhizomatous lawn grasses. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We also investigate different size and structure of the habitat and two types of fecundity. Results. We have created and investigated a logical white-box model of an ecosystem with one species. This model demonstrates mechanisms of the S-shaped and double S-shaped population growth. We have investigated population growth limited by different factors, in particular by resources, habitat structure, intraspecific competition, lifetime of individuals, regeneration time and fecundity of individuals. We have compared the S-shaped curves with J-shaped curves of population growth. Conclusion. We present a basic white-box model of population dynamics which combines reductionist and holistic approaches. Integration of reductionist and holistic approaches is provided by the simultaneous modeling of both part-whole and cause-effect relations in complex system. We consider this holystic multi-level white-box modeling approach as a method of artificial intelligence which works as hyper-logical automatic deductive inference that provides direct mechanistic insights into complex systems. The white-box modeling by logical deterministic cellular automata is a perspective way for investigation not only of population dynamics but also of any complex systems.

scholarly journals Two Positive Periodic Solutions for a Neutral Delay Model of Single-Species Population Growth with Harvesting

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hui Fang
Keyword(s):  
Population Growth ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Single Species ◽  
Delay Model ◽  
Positive Periodic Solutions ◽  
Neutral Delay ◽  
Species Population ◽  
Single Species Population

By coincidence degree theory fork-set-contractive mapping, this paper establishes a new criterion for the existence of at least two positive periodic solutions for a neutral delay model of single-species population growth with harvesting. An example is given to illustrate the effectiveness of the result.

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