Unconstrained Population Growth for Single Species

2018 ◽  
pp. 13-32
Keyword(s):  
Population Growth ◽  
Single Species

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.

DYNAMICS OF A NONAUTONOMOUS SYSTEM WITH IMPULSIVE OUTPUT

2008 ◽  
Vol 01 (02) ◽  
pp. 225-238 ◽  
Author(s):  
YUANSHUN TAN ◽  
FENGMEI TAO ◽  
LANSUN CHEN
Keyword(s):  
Population Growth ◽  
Growth Model ◽  
Single Species ◽  
Nonautonomous System ◽  
Nonautonomous Equation

In this paper, an impulsive exploitation of single species modelled by a general nonautonomous equation is considered. The persistence of the population can be obtained under sufficiently weak conditions and also be distinguished from conditions that cause extinction. These attributes resemble corresponding features of the related autonomous population growth model and improve the results of [6–8].

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.

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