Bifurcation analysis in a diffusive Logistic population model with two delayed density-dependent feedback terms

2022 ◽  
Vol 63 ◽  
pp. 103394
Author(s):  
Xiang-Ping Yan ◽  
Cun-Hua Zhang
Keyword(s):  
Bifurcation Analysis ◽  
Population Model ◽  
Density Dependent

scholarly journals An integrated population model for estimating the relative effects of natural and anthropogenic factors on a threatened population of Pacific trout

2019 ◽  
Author(s):  
Mark D. Scheuerell ◽  
Casey P. Ruff ◽  
Joseph H. Anderson ◽  
Eric M. Beamer
Keyword(s):  
At Risk ◽  
Population Model ◽  
Habitat Restoration ◽  
Negative Relationship ◽  
Anthropogenic Factors ◽  
List Type ◽  
Population Demographics ◽  
Density Dependent ◽  
Integrated Population Model ◽  
The North

SummaryAssessing the degree to which at-risk species are regulated by density dependent versus density independent factors is often complicated by incomplete or biased information. If not addressed in an appropriate manner, errors in the data can affect estimates of population demographics, which may obfuscate the anticipated response of the population to a specific action.We developed a Bayesian integrated population model that accounts explicitly for interannual variability in the number of reproducing adults and their age structure, harvest, and environmental conditions. We apply the model to 41 years of data for a population of threatened steelhead troutOncorhynchus mykissusing freshwater flows, ocean indices, and releases of hatchery-born conspecifics as covariates.We found compelling evidence that the population is under strong density dependence, despite being well below its historical population size. In the freshwater portion of the lifecycle, we found a negative relationship between productivity (offspring per parent) and peak winter flows, and a positive relationship with summer flows. We also found a negative relationship between productivity and releases of hatchery conspecifics. In the marine portion of the lifecycle, we found a positive correlation between productivity and the North Pacific Gyre Oscillation. Furthermore, harvest rates on wild fish have been sufficiently low to ensure very little risk of overfishing.Synthesis and applications.The evidence for density dependent population regulation, combined with the substantial loss of juvenile rearing habitat in this river basin, suggests that habitat restoration could benefit this population of at-risk steelhead. Our results also imply that hatchery programs for steelhead need to be considered carefully with respect to habitat availability and recovery goals for wild steelhead. If releases of hatchery steelhead have indeed limited the production potential of wild steelhead, there are likely significant tradeoffs between providing harvest opportunities via hatchery steelhead production, and achieving wild steelhead recovery goals.

Global Bifurcation Analysis of a Population Model with Stage Structure and Beverton–Holt Saturation Function

2015 ◽  
Vol 25 (12) ◽  
pp. 1550170 ◽  
Author(s):  
Li Fan ◽  
Sanyi Tang
Keyword(s):  
Bifurcation Analysis ◽  
Population Model ◽  
Birth Rate ◽  
Global Bifurcation ◽  
Stage Structure ◽  
Phase Portraits ◽  
Approximation Techniques ◽  
Codimension Two ◽  
Codimension One ◽  
Stage Transition

In the present paper, we perform a complete bifurcation analysis of a two-stage population model, in which the per capita birth rate and stage transition rate from juveniles to adults are density dependent and take the general Beverton–Holt functions. Our study reveals a rich bifurcation structure including codimension-one bifurcations such as saddle-node, Hopf, homoclinic bifurcations, and codimension-two bifurcations such as Bogdanov–Takens (BT), Bautin bifurcations, etc. Moreover, by employing the polynomial analysis and approximation techniques, the existences of equilibria, Hopf and BT bifurcations as well as the formulas for calculating their bifurcation sets have been provided. Finally, the complete bifurcation diagrams and associate phase portraits are obtained not only analytically but also confirmed and extended numerically.

Quasi-cycles in crappie populations are forced by interactions among population characteristics and environment

2001 ◽  
Vol 58 (3) ◽  
pp. 594-601 ◽  
Author(s):  
Micheal S Allen ◽  
Leandro E Miranda
Keyword(s):  
Time Series ◽  
Environmental Conditions ◽  
Empirical Data ◽  
Population Model ◽  
Population Characteristics ◽  
Environmental Fluctuation ◽  
Density Dependent ◽  
Stock Recruitment ◽  
Variable Recruitment ◽  
Random Fluctuations

Crappie (Pomoxis spp.) populations have been characterized as cyclic, with strong year-classes recurring at 2- to 4-year intervals. We evaluated the potential for cyclic trends in crappie populations using a population model that included a density-dependent stock recruitment function and random environmental variation. Slow, medium, and fast growth were simulated over 100 years. The model predicted highly variable recruitment that was strongly influenced by environmental fluctuation at low and intermediate stock densities. At high stock density, recruitment was low, even if environmental conditions were favorable. Significant quasi-cycles occurred, but they were not sustained throughout the time series due to random environmental fluctuation. Quasi-cycles occurred because intermediate stock density and favorable environmental conditions occasionally combined to produce a very strong year-class that greatly increased stock density in the following 1–3 years and produced low recruitment, even if environmental conditions were favorable. Empirical data from 32 years of sampling age-0 crappies at Ross Barnett Reservoir showed trends similar to the simulated fluctuations. We conclude that crappie populations likely do not exhibit true cycles but may show quasi-cycles as a result of the interaction between random fluctuations in environment and density-dependent mechanisms. The frequency of such quasi-cycles may be enhanced by rapid growth and high exploitation.

scholarly journals A generic population model for the African tick Rhipicephalus appendiculatus

Parasitology ◽  
1997 ◽  
Vol 115 (3) ◽  
pp. 265-279 ◽  
Author(s):  
S. E. RANDOLPH ◽  
D. J. ROGERS
Keyword(s):  
South Africa ◽  
Population Model ◽  
Egg Production ◽  
Population Analysis ◽  
Rhipicephalus Appendiculatus ◽  
Mortality Factors ◽  
Density Dependent ◽  
Tick Abundance ◽  
Annual Range ◽  
Parameter Values

We present a simulation population model for the African tick Rhipicephalus appendiculatus, based on previous analyses of the mortality factors most closely correlated with observed population changes at 11 sites in equatorial and South Africa. The model incorporates temperature-dependent rates of egg production and development, climate-driven density-independent mortality rates, particularly during the adult-larval stage, and density-dependent regulation of both nymphs and adults. Diapause is also included for tick populations in southern Africa. The model successfully describes both the seasonality and annual range of variation in numbers of each tick stage observed at each of 4 test sites in Uganda, Burundi and South Africa. Sensitivity analysis showed that the final version of the model is robust to 4-fold variation in most parameter values (that were per force based on informed guesses), but is more sensitive to the regression coefficients determining density-dependent interstadial mortality (that were derived from analysis of field data). The model is able to predict the seasonality of ticks from a site in Kenya where a full prior population analysis was not possible because only adults and nymphs had been counted. The model is potentially applicable to other species of ticks, both tropical and temperate, to predict tick abundance and seasonality as risk factors for tick-borne diseases.

scholarly journals Dynamics of Spruce budworms and single species competition models with bifurcation analysis

2020 ◽  
Vol 9 (6) ◽  
pp. 217-222
Author(s):  
Farah Tasnim ◽  
Md. Kamrujjaman
Keyword(s):  
North America ◽  
Mathematical Models ◽  
Bifurcation Analysis ◽  
Population Model ◽  
Choristoneura Fumiferana ◽  
Single Species ◽  
Species Competition ◽  
Numerical Examples ◽  
Competition Models ◽  
Forest Lands

Choristoneura Fumiferana is perilous defoliators of forest lands in North America and many countries in Europe. In this study, we consider mathematical models in ecology, epidemiology and bifurcation studies; the spruce budworm model and the population model with harvesting. The study is designed based on bifurcation analysis. In particular, the results support population thresholds necessary for survival in certain cases. In a series of numerical examples, the outcomes are presented graphically to compare with bifurcation results.

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