Population growth models from a detailed historical perspective

2014 ◽  
Author(s):  
Nathan Keyfitz
Keyword(s):  
Population Growth ◽  
Historical Perspective ◽  
Growth Models ◽  
Population Growth Models

scholarly journals The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

2018 ◽  
Author(s):  
Emanuel A. Fronhofer ◽  
Lynn Govaert ◽  
Mary I. O’Connor ◽  
Sebastian J. Schreiber ◽  
Florian Altermatt
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Level ◽  
Logistic Growth ◽  
Population Densities ◽  
Density Regulation ◽  
Logistic Growth Model ◽  
Regulation Functions ◽  
Consumer Resource ◽  
Population Growth Models

AbstractThe logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Stability in terms of two measures for population growth models with impulsive perturbations

2020 ◽  
Vol 13 (06) ◽  
pp. 2050051
Author(s):  
Zhinan Xia ◽  
Qianlian Wu ◽  
Dingjiang Wang
Keyword(s):  
Differential Equations ◽  
Population Growth ◽  
Ordinary Differential Equations ◽  
Trivial Solution ◽  
Growth Models ◽  
Two Measures ◽  
Impulsive Perturbations ◽  
The Stability ◽  
Generalized Ordinary Differential Equations ◽  
Population Growth Models

In this paper, we establish some criteria for the stability of trivial solution of population growth models with impulsive perturbations. The working tools are based on the theory of generalized ordinary differential equations. Here, the conditions concerning the functions are more general than the classical ones.

Application of population growth models based on cumulative size to pecan aphids

2006 ◽  
Vol 11 (4) ◽  
pp. 425-449 ◽  
Author(s):  
James H. Matis ◽  
Thomas R. Kiffe ◽  
Timothy I. Matis ◽  
Douglass E. Stevenson
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Growth Models

Deterministic Population Growth Models

1971 ◽  
Vol 78 (8) ◽  
pp. 841 ◽  
Author(s):  
W. G. Costello ◽  
H. M. Taylor
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Growth Models

Population processes allowing emigration of families

1984 ◽  
Vol 21 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Abebe Tessera
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Death Process ◽  
Population Processes ◽  
The Individual ◽  
Population Growth Models ◽  
Birth Death

In the familiar immigration–birth–death process the events of immigration, birth and death relate to the individual. There are processes in which the whole family and not just an individual migrates. Such population growth models are studied in some detail.

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