scholarly journals Semi-analytical solutions for the diffusive logistic equation with mixed instantaneous and delayed density dependence

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
H. Y. Alfifi
Keyword(s):  
Density Dependence ◽  
Analytical Solutions ◽  
Logistic Equation ◽  
Delayed Density Dependence ◽  
Diffusive Logistic Equation

scholarly journals Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 888
Author(s):  
Jumpei Inoue ◽  
Kousuke Kuto
Keyword(s):  
Recovery Rate ◽  
Regional Difference ◽  
Total Population ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Logistic Equation ◽  
Sis Model ◽  
Reaction Diffusion Model ◽  
Diffusive Logistic Equation ◽  
Sis Epidemic

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

Geographic variation in population cycles of Canadian muskrats (Ondatra zibethicus)

2000 ◽  
Vol 78 (6) ◽  
pp. 1009-1016 ◽  
Author(s):  
John Erb ◽  
Nils Chr. Stenseth ◽  
Mark S Boyce
Keyword(s):  
Density Dependence ◽  
Trophic Interactions ◽  
Dynamic Properties ◽  
Population Cycles ◽  
Period Length ◽  
Ondatra Zibethicus ◽  
Delayed Density Dependence ◽  
Relative Contribution ◽  
Arctic Regions ◽  
Harvest Data

We investigated the dynamic properties of population cycles in Canadian muskrats (Ondatra zibethicus). Ninety-one historic time series of muskrat-harvest data obtained from the Hudson's Bay Company Archives were analyzed. Most series were 25 years in length (1925–1949) and were distributed primarily throughout five ecozones. For each series, we estimated period length and coefficients for a second-order autoregressive model. Estimated period length varied between 3 and 13 years, with 3- to 5-year periods located in Subarctic-Arctic ecozones. We hypothesize that the 4-year cycles are largely a result of predation by red fox (Vulpes vulpes), which exhibit 4-year cycles in Arctic regions. The remaining ecozones generally averaged 8–9 years in period length. However, the relative contributions of direct and delayed density dependence varied along a latitudinal gradient. We hypothesize that both social and trophic interactions are necessary to produce the observed dynamics, but that shifts in the nature of mink predation were responsible for the changes in the relative contribution of direct and delayed density dependence. Essentially, there is a tension between population-intrinsic and trophic interactions that may bound the length of the cycle.

Population decline in semi-migratory caribou (Rangifer tarandus): intrinsic or extrinsic drivers?

2013 ◽  
Vol 91 (11) ◽  
pp. 820-828 ◽  
Author(s):  
Guillaume Bastille-Rousseau ◽  
James A. Schaefer ◽  
Shane P. Mahoney ◽  
Dennis L. Murray
Keyword(s):  
Density Dependence ◽  
Rangifer Tarandus ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Population Decline ◽  
Negative Relationship ◽  
Population Limitation ◽  
Continental Scale ◽  
Delayed Density Dependence ◽  
Winter Severity

Many populations of caribou (Rangifer tarandus (L., 1758)) across North America, including Newfoundland, are in a state of decline. This phenomenon may reflect continental-scale changes in either the extrinsic or the intrinsic factors affecting caribou abundance. We hypothesized that caribou decline reflected marked resource limitation and predicted that fluctuations should correspond to time-delayed density dependence associated with a decline in range quality and decadal trends in winter severity. By conducting time-series analysis using 12 populations and evaluating correlations between caribou abundance and trends in (i) vegetation available at calving (normalized difference vegetation index, NDVI), (ii) winter weather severity (index of North Atlantic Oscillation, NAO), and (iii) caribou morphometrics, we observed strong evidence of density dependence in population dynamics (i.e., a negative relationship between caribou population size and caribou morphometrics). Caribou population trajectories were time-delayed relative to winter severity, but not relative to calving-ground greenness. These island-wide correlations could not be traced to dispersal between herds, which appears rare at least for adult females. Our results suggest that trends in winter severity may synchronize broad-scale changes in caribou abundance that are driven by time-delayed density dependence, although it remains possible that calving-ground deterioration also may contribute to population limitation in Newfoundland. Our findings provide the basis for additional research into density dependence and caribou population decline.

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