Weak Allee Effect Research Articles

Existence and stability of almost periodic solutions of nonautonomous competitive systems with weak Allee effect and delays

In this paper, a class of nonautonomous Lotka–Volterra type multispecies competitive systems with weak Allee effect and delays are considered. By using Mawhin’s continuation theorem of coincidence degree theory, we obtain some sufficient conditions for the existence of almost periodic solutions for the Lotka–Volterra system. On the case of no delays of Allee effects, by constructing a suitable Lyapunov function, we get a sufficient condition for the globally attractivity of the almost periodic solution for the Lotka–Volterra system. Moreover, we also present an illustrative example to show the effectiveness of our results.

Three Limit Cycles in a Leslie–Gower Predator-Prey Model with Additive Allee Effect

In this work, a bidimensional continuous-time differential equations system is analyzed which is derived of Leslie-type predator-prey schemes by considering a nonmonotonic functional response and Allee effect on population prey. For the system obtained we describe the bifurcation diagram of limit cycles that appears in the first quadrant, the only quadrant of interest for the sake of realism. We show that, under certain conditions over the parameters, the system allows the existence of three limit cycles: The first two cycles are infinitesimal ones generated by Hopf bifurcation; the third one arises from a homoclinic bifurcation. Furthermore, we give conditions over the parameters such that the model allows long-term extinction or survival of both populations. In particular, the presence of a weak Allee effect does not imply extinction of populations necessarily for our model.

Positive periodic solutions of nonautonomous delay competitive systems with weak Allee effect

This paper considers a nonautonomous Lotka–Volterra type multispecies competitive system with weak Allee effect and delays. The model has the intraspecific competition terms defined by sign changing functions which depend on population density monotonically and time periodically. An existence theorem of positive periodic solutions is established using the coincidence degree theory. Furthermore, for the case of constant delays, a sufficient condition for the positive periodic solution to be globally attractive is proved with the Lyapunov method so that the system attains permanence.

How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses

In Rosenzweig–MacArthur models of predator–prey dynamics, Allee effects in prey usually destabilize interior equilibria and can suppress or enhance limit cycles typical of the paradox of enrichment. We re-evaluate these conclusions through a complete classification of a wide range of Allee effects in prey and predator's functional response shapes. We show that abrupt and deterministic system collapses not preceded by fluctuating predator–prey dynamics occur for sufficiently steep type III functional responses and strong Allee effects (with unstable lower equilibrium in prey dynamics). This phenomenon arises as type III functional responses greatly reduce cyclic dynamics and strong Allee effects promote deterministic collapses. These collapses occur with decreasing predator mortality and/or increasing susceptibility of the prey to fall below the threshold Allee density (e.g. due to increased carrying capacity or the Allee threshold itself). On the other hand, weak Allee effects (without unstable equilibrium in prey dynamics) enlarge the range of carrying capacities for which the cycles occur if predators exhibit decelerating functional responses. We discuss the results in the light of conservation strategies, eradication of alien species, and successful introduction of biocontrol agents.

Persistence in reaction diffusion models with weak allee effect

We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak allele effect type growth, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a heterogeneous bounded region. The existence of multiple steady states is shown, and the global bifurcation diagrams are obtained. Results are applied to a reaction-diffusion model with type II functional response, and also a model with density-dependent diffusion of animal aggregation.

A numerical model to solve single-species invasion problems with Allee effects

The population dynamics problems considered here describe propagation of travelling population fronts that represent either single-species invasion or single-species retreat. The influence of the weak and strong Allee effect is analyzed on the spread of a single species invading organism in a one-dimensional domain. This problem is mathematically modelled by a non-linear advection–diffusion–reaction transport equation, which is numerically solved by using the finite element method. The resulting numerical model is stable and accurate for a wide range of parameters. Some scenarios of single species invasion are investigated so as to evaluate the interaction of travelling population fronts under different parameter values, allowing to derive numerically whether they can reverse or block the species invasion, and to predict the speed of an invasion.

外来巻貝ハブタエモノアラガイの急速な分布拡大_-_1/2の繁殖コストより、低いアリー効果?_-_

外来巻貝ハブタエモノアラガイの急速な分布拡大_-_1/2の繁殖コストより、低いアリー効果?_-_

CONSEQUENCES OF AN ALLEE EFFECT IN THE INVASION OF A PACIFIC ESTUARY BY SPARTINA ALTERNIFLORA

Results from both a spatially explicit stochastic simulation model and a spatially implicit deterministic model show that a weak Allee effect can slow the spread of an invasive plant, Spartina alterniflora, in a Pacific Coast estuary. The mean rate of spread with the Allee effect is ∼19%; removing the Allee effect results in a mean rate of spread of ∼31%. Sensitivity analysis both with and without the Allee effect reveal that seedling establishment, inflorescence density, and outcrossed seed production are key factors determining invasion rate. When there is an Allee effect, the invasion rate is sensitive to variation in self-pollinated seed production. By structuring the population according to density classes instead of the more usual age or stage classes, the deterministic model demonstrates a novel way of representing density dependence and an Allee effect in population biology. This approach could be applied to model the population dynamics of any species that spreads from multiple foci and in which these foci later coalesce.

Speeds of invasion in a model with strong or weak Allee effects

We study an invasion model based on a reaction–diffusion equation with an Allee effect. We use a special, piecewise-linear, population growth rate. This function allows us to obtain traveling wave solutions and to compute wave speeds for a full range of Allee effects, including weak Allee effects. Some investigators claim that linearization fails to give the correct speed of invasion if there is an Allee effect. We show that the minimum speed for a sufficiently weak Allee may, in fact, be the same as that derived by means of linearization.

The Relation of Density of Population to Rate of Reproduction in Paramecium caudatum

Previous articleNext article No AccessThe Relation of Density of Population to Rate of Reproduction in Paramecium caudatumWalburga A. PetersenWalburga A. Petersen Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 2, Number 2Apr., 1929 Article DOIhttps://doi.org/10.1086/physzool.2.2.30151355 Views: 35Total views on this site Citations: 21Citations are reported from Crossref Journal History This article was published in Physiological Zoology (1928-1998), which is continued by Physiological and Biochemical Zoology (1999-present). PDF download Crossref reports the following articles citing this article:Paulina A. Arancibia, Peter J. Morin Network topology and patch connectivity affect dynamics in experimental and model metapopulations, Journal of Animal Ecology 91, no.22 (Dec 2021): 496–505.https://doi.org/10.1111/1365-2656.13647Wenjie Xu, Xianxian Li, Yapeng Li, Yunfei Sun, Lu Zhang, Yuan Huang, Zhou Yang Rising temperature more strongly promotes low-abundance Paramecium to remove Microcystis and degrade microcystins, Environmental Pollution 291 (Dec 2021): 118143.https://doi.org/10.1016/j.envpol.2021.118143Mei-Hui Wang, Mark Kot Speeds of invasion in a model with strong or weak Allee effects, Mathematical Biosciences 171, no.11 (May 2001): 83–97.https://doi.org/10.1016/S0025-5564(01)00048-7J.M. Cushing Oscillations in age-structured population models with an Allee effect, Journal of Computational and Applied Mathematics 52, no.1-31-3 (Jul 1994): 71–80.https://doi.org/10.1016/0377-0427(94)90349-2P. 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Oesting The effect of homotypic conditioning of water on the growth of fishes, and chemical studies of the factors involved, Journal of Experimental Zoology 68, no.22 (Jul 1934): 183–213.https://doi.org/10.1002/jez.1400680203W. C. ALLEE RECENT STUDIES IN MASS PHYSIOLOGY 1, Biological Reviews 9, no.11 (Jan 1934): 1–48.https://doi.org/10.1111/j.1469-185X.1934.tb00872.xTheo L. Jahn Studies on the oxidation-reduction potential of protozoan cultures, Protoplasma 20, no.11 (Oct 1933): 90–104.https://doi.org/10.1007/BF02674816Thomas Park Studies In Population Physiology. II. Factors regulating initial growth of Tribolium confusum populations, Journal of Experimental Zoology 65, no.11 (Apr 1933): 17–42.https://doi.org/10.1002/jez.1400650103Ralph M. Buchsbaum Size of explant and volume of medium in tissue cultures, Journal of Experimental Zoology 63, no.22 (Oct 1932): 483–508.https://doi.org/10.1002/jez.1400630212 The effect of population density upon rate of reproduction with special reference to insects, Proceedings of the Royal Society of London. Series B, Containing Papers of a Biological Character 111, no.773773 (Jan 1997): 437–454.https://doi.org/10.1098/rspb.1932.0067Tracy M. Sonneborn Genetic studies on stenostomum incaudatum (Nov. spec.). I. The nature and origin of differences among individuals formed during vegetative reproduction, Journal of Experimental Zoology 57, no.11 (Aug 1930): 57–108.https://doi.org/10.1002/jez.1400570104W. C. Allee Studies in animal aggregations: Mass protection from hypotonic sea-water for Procerodes, a marine turbellarian, with total electrolytes controlled, Journal of Experimental Zoology 54, no.33 (Nov 1929): 349–381.https://doi.org/10.1002/jez.1400540302