On the effects of carrying capacity and intrinsic growth rate on single and multiple species in spatially heterogeneous environments

We first consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r ( x ) for intrinsic growth rate and K ( x ) for carrying capacity. When r ( x ) and K ( x ) are proportional, i.e., r = c K , it is proved by Lou (J Differ Equ 223(2):400–426, 2006...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical biology 2020-08, Vol.81 (2), p.403-433
Main Authors: Guo, Qian, He, Xiaoqing, Ni, Wei-Ming
Format: Article
Language:English
Subjects:
Applications of Mathematics
Carrying capacity
Competition
Diffusion rate
Dispersal
Dispersion
Growth rate
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Population
Population ecology
Spatial distribution
Species
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We first consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r ( x ) for intrinsic growth rate and K ( x ) for carrying capacity. When r ( x ) and K ( x ) are proportional, i.e., r = c K , it is proved by Lou (J Differ Equ 223(2):400–426, 2006) that a population diffusing at any rate will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. This paper studies another case when r ( x ) is a constant, i.e., independent of K ( x ). In such case, a striking result is that for any dispersal rate, the logistic equation with spatially heterogeneous resources will always support a total population strictly smaller than the total carrying capacity at equilibrium, which is just opposite to the case r = c K . These two cases of single species models also lead to two different forms of Lotka–Volterra competition-diffusion systems. We then examine the consequences of the aforementioned difference on the two forms of competition systems. We find that the outcome of the competition in terms of the dispersal rates and spatial distributions of resources for the two forms of competition systems are again quite different. Our results indicate that in heterogeneous environments, the correlation between r ( x ) and K ( x ) has more profound impacts in population ecology than we had previously expected, at least from a mathematical point of view.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-020-01507-9