Note on asocial populations dispersing in two dimensions

Bradford, Emma L.; Philip, J. R.

doi:10.1016/0022-5193(70)90116-5

Cited by 15 publications

(6 citation statements)

References 3 publications

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“…The effect of dispersal (diffusion) in one‐dimensional RD models is to dilute the population at any given location thereby reducing density and resulting in higher initial densities necessary to overcome the Allee effect than in the corresponding non‐spatial models (in which diffusion is zero) (Bradford & Philip 1970b). Two dimensional RD models predict critical densities even higher than found in one‐dimensional models (Bradford & Philip 1970a; Soboleva et al. 2003).…”

Section: Theoretical Consequences Of Allee Effects In Invasionsmentioning

confidence: 75%

“…The most prevalent is that of mate shortage in sexually reproducing species (Dennis 1989; Boukal & Berec 2002). Early work refers to Allee effects as the absence of cooperation (sometimes called disoperation), or simply asociality in sexually reproducing species (Odum & Allee 1954; Philip 1957; Bradford & Philip 1970a,b). Other mechanisms include sex ratio changes, asynchrony in reproductive timing of potential mates, sexual selection, more effective predator avoidance in large groups, obligate cooperation and many others.…”

Section: Introductionmentioning

confidence: 99%

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Allee effects in biological invasions

2005

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Understanding the dynamics of small populations is obviously important for declining or rare species but is also particularly important for invading species. The Allee effect, where fitness is reduced when conspecific density is low, can dramatically affect the dynamics of biological invasions. Here, we summarize the literature of Allee effects in biological invasions, revealing an extensive theory of the consequences of the Allee effect in invading species and some empirical support for the theory. Allee effects cause longer lag times, slower spread and decreased establishment likelihood of invasive species. Expected spatial ranges, distributions and patterns of species may be altered when an Allee effect is present. We examine how the theory can and has been used to detect Allee effects in invasive species and we discuss how the presence of an Allee effect and its successful or unsuccessful detection may affect management of invasives. The Allee effect has been shown to change optimal control decisions, costs of control and the estimation of the risk posed by potentially invasive species. Numerous ways in which the Allee effect can influence the efficacy of biological control are discussed.

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Section: Theoretical Consequences Of Allee Effects In Invasionsmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Allee effects in biological invasions

2005

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“…Early work investigated the impact of movement on population dynamics in the presence of an Allee effect using reaction–diffusion models (Bradford & Philip ,b). The authors investigated steady state solutions on a finite spatial domain and found that to achieve population persistence, the peak of the steady state solution must be larger than the non‐spatial Allee threshold.…”

Section: Introductionmentioning

confidence: 99%

The minimum founding population in dispersing organisms subject to strong Allee effects

Goodsman

Lewis

2016

Methods Ecol Evol

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Summary1. Dispersal can push population density below strong Allee thresholds ensuring the demise of small founding populations. As a result, for isolated populations of dispersing organisms, the minimum founding population size that enables establishment can be quite different from the Allee threshold. 2. We derive an expression for the minimum founding population size for a general integrodifference equation model of a dispersing population with a strong Allee effect. We demonstrate the utility of the general model by using it to approximate minimum founding populations for the mountain pine beetle. 3. The minimum founding population of the general model increases linearly with the mean squared displacement of the dispersing organism. Transient dynamics of the general model suggest that population density at the point of introduction will often decrease before increasing, even when the minimum founding population size is exceeded. 4. Calculation of minimum founding population sizes may prove useful for predicting invasion success based on propagule size and for maximizing the success of species reintroductions when strong Allee effects exist.

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“…Unfortunately, investigators in the topic have an Allee effect of their own, so to speak: old papers on the topic are hard to find, and several recent modeling studies have missed earlier related work. Models of Allee effects have a rich but sporadic history dating back to Volterra (highlights before 1990 include Volterra 1938, Kostitzin 1940, Odum and Allee 1954, Philip 1957, Mosimann 1958, Klomp et al 1964, Bradford and Philip 1970a,b, Hsu and Frederickson 1975, Kuno 1978, Asmussen 1979, Gerritson 1980, Dennis 1981, 1989a, Dennis and Patil 1984, Jacobs 1984, Hopf and Hopf 1985, Lande 1987, Cushing 1988).…”

mentioning

confidence: 99%

Allee effects in stochastic populations

Dennis

2002

Oikos

301

296

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Dennis, B. 2002. Allee effects in stochastic populations. -Oikos 96: 389-401.The Allee effect, or inverse density dependence at low population sizes, could seriously impact preservation and management of biological populations. The mounting evidence for widespread Allee effects has lately inspired theoretical studies of how Allee effects alter population dynamics. However, the recent mathematical models of Allee effects have been missing another important force prevalent at low population sizes: stochasticity. In this paper, the combination of Allee effects and stochasticity is studied using diffusion processes, a type of general stochastic population model that accommodates both demographic and environmental stochastic fluctuations. Including an Allee effect in a conventional deterministic population model typically produces an unstable equilibrium at a low population size, a critical population level below which extinction is certain. In a stochastic version of such a model, the probability of reaching a lower size a before reaching an upper size b, when considered as a function of initial population size, has an inflection point at the underlying deterministic unstable equilibrium. The inflection point represents a threshold in the probabilistic prospects for the population and is independent of the type of stochastic fluctuations in the model. In particular, models containing demographic noise alone (absent Allee effects) do not display this threshold behavior, even though demographic noise is considered an "extinction vortex". The results in this paper provide a new understanding of the interplay of stochastic and deterministic forces in ecological populations.

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Note on asocial populations dispersing in two dimensions

Cited by 15 publications

References 3 publications

Allee effects in biological invasions

Allee effects in biological invasions

The minimum founding population in dispersing organisms subject to strong Allee effects

Allee effects in stochastic populations

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