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

Wang, Mei-Hui; Kot, Mark

doi:10.1016/s0025-5564(01)00048-7

Cited by 243 publications

(176 citation statements)

References 37 publications

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“…One major difference in the presence of an Allee effect is that a population may retreat, that is, its 'invasion' speed can be negative. For model (1) in a homogeneous landscape, the sign of the speed can be determined by the sign of the integral K 0 f (u) du, where K is the carrying capacity [31]. For the cubic nonlinearity, negative speeds arise when a > 1/2 in Equation (2).…”

Section: Discussionmentioning

confidence: 99%

“…Spatially extended populations require a minimum initial spatial range occupied to successfully invade a region when a strong Allee effect is present [13,14]. In addition, Allee effects negatively affect the rate of spatial spread [13,31]. Patchy invasion can also occur when Allee effects are present in predator-prey systems and systems with viral infection [9,20].…”

Section: Introductionmentioning

confidence: 99%

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Allee effects and population spread in patchy landscapes

Maciel

Lutscher

2015

Journal of Biological Dynamics

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Invasion of alien species is one of the major threats for natural community structures, potentially leading to high economic and environmental costs. In this work, we study through a reaction-diffusion model the dynamics of an invasion in a heterogeneous environment and in the presence of a strong Allee effect. We model space as an infinite landscape consisting of periodically alternating favourable and unfavourable patches. In addition, we consider that at the interface between patch types individuals may show preference for more favourable regions. Using homogenization techniques and a classical result for spread with Allee effect in homogeneous landscapes, we derive approximate expressions for the spread speed. When compared with numerical simulations, these expressions prove to be very accurate even beyond the expected small-scale heterogeneity limit of homogenization. We demonstrate how rates of spatial spread depend on demographic and movement parameters as well as on the landscape properties.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Allee effects and population spread in patchy landscapes

Maciel

Lutscher

2015

Journal of Biological Dynamics

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“…The spatial dynamics of such variants were first described in the evolutionary genetics literature by Bazykin (1969) and Barton (1979a) and in the mathematics literature by Aronson and Weinberger (1975). These dynamics are similar to the population dynamics of invasive species with (strong) Allee effects, namely, species that decline at low densities, so that populations tend to increase only above a critical density threshold (Wang and Kot 2001;Taylor and Hastings 2005). These genetic and ecological systems are "bistable," possessing two locally stable equilibria: one at zero frequency or density and another at high frequency or density.…”

Section: Introductionmentioning

confidence: 96%

Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects

Barton

Turelli

2011

The American Naturalist

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400

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. abstract: Unlike unconditionally advantageous "Fisherian" variants that tend to spread throughout a species range once introduced anywhere, "bistable" variants, such as chromosome translocations, have two alternative stable frequencies, absence and (near) fixation. Analogous to populations with Allee effects, bistable variants tend to increase locally only once they become sufficiently common, and their spread depends on their rate of increase averaged over all frequencies. Several proposed manipulations of insect populations, such as using Wolbachia or "engineered underdominance" to suppress vector-borne diseases, produce bistable rather than Fisherian dynamics. We synthesize and extend theoretical analyses concerning three features of their spatial behavior: rate of spread, conditions to initiate spread from a localized introduction, and wave stopping caused by variation in population densities or dispersal rates. Unlike Fisherian variants, bistable variants tend to spread spatially only for particular parameter combinations and initial conditions. Wave initiation requires introduction over an extended region, while subsequent spatial spread is slower than for Fisherian waves and can easily be halted by local spatial inhomogeneities. We present several new results, including robust sufficient conditions to initiate (and stop) spread, using a one-parameter cubic approximation applicable to several models. The results have both basic and applied implications. The University of Chicago Press and

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“…A ''strong'' Allee effect results in negative per capita rate of growth when population density drops below a threshold. A ''weak'' Allee effect, as can be the case with long-lived adults, causes a depressed per capita rate of growth at low population density, but it never becomes negative (27,28). A lack of mating opportunities among sparse or widely spaced individuals can result in an Allee effect and a slowing of the invasion (27)(28)(29).…”

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confidence: 99%

Pollen limitation causes an Allee effect in a wind-pollinated invasive grass ( Spartina alterniflora )

Davis

Taylor

Lambrinos

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

187

155

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It is usually assumed that pollen availability does not limit reproduction in wind-pollinated plants. Little evidence either supporting or contradicting this assumption exists, despite the importance of seed production to population persistence and growth. We investigated the role of pollen limitation in an invasive estuarine grass (Spartina alterniflora), with a manipulative pollen supplementation and exclusion experiment in areas of high population density and at the low-density leading edge of the invasion. We also quantified pollen deposition rates on stigmas and pollen traps along a windward to leeward gradient. We found pollen impoverishment at the low-density leading edge of a large invasion, causing an 8-fold reduction in seed set. We found 9-fold more pollen on stigmas of high-density plants than on those of lowdensity plants. Pollen deposition rates on stigmas and traps did not increase downwind of low-density plants but did increase downwind of high-density plants and dropped off precipitously across a gap that lacked pollen donors. The delay of appreciable numbers of seed caused by pollen limitation persists for decades until vegetative growth coalesces plants into continuous meadows, and this Allee effect has slowed the rate of spread of the invasion.

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

Cited by 243 publications

References 37 publications

Allee effects and population spread in patchy landscapes

Allee effects and population spread in patchy landscapes

Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects

Pollen limitation causes an Allee effect in a wind-pollinated invasive grass ( Spartina alterniflora )

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