Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

AbstractWe present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death, and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

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Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0350 ◽

2020 ◽

Vol 476 (2241) ◽

pp. 20200350

Author(s):

Nabil T. Fadai ◽

Stuart T. Johnston ◽

Matthew J. Simpson

Keyword(s):

Population Dynamics ◽

Cell Biology ◽

Allee Effect ◽

Local Density ◽

Growth Models ◽

Logistic Growth ◽

Allee Effects ◽

Individual Level ◽

Modelling Framework ◽

Global Population

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

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The influence of density in population dynamics with strong and weak Allee effect

Journal of the Egyptian Mathematical Society ◽

10.1186/s42787-021-00114-x ◽

2021 ◽

Vol 29 (1) ◽

Author(s):

Kamrun Nahar Keya ◽

Md. Kamrujjaman ◽

Md. Shafiqul Islam

Keyword(s):

Population Dynamics ◽

Allee Effect ◽

Global Bifurcation ◽

Reaction Diffusion ◽

Logistic Growth ◽

Allee Effects ◽

Reaction Diffusion Model ◽

Positive Steady States ◽

The Stability ◽

The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

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Population dynamics with threshold effects give rise to a diverse family of Allee effects

10.1101/2020.04.02.021741 ◽

2020 ◽

Author(s):

Nabil T. Fadai ◽

Matthew J. Simpson

Keyword(s):

Cell Biology ◽

Growth Models ◽

Critical Density ◽

Threshold Effect ◽

Logistic Growth ◽

Threshold Effects ◽

Allee Effects ◽

Growth Mechanisms ◽

Local Growth ◽

Local Threshold

AbstractThe Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.

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Excitable and Nonexcitable Population Dynamics

Food Webs (MPB-50) ◽

10.23943/princeton/9780691134178.003.0004 ◽

2011 ◽

Author(s):

Kevin S. McCann

Keyword(s):

Population Dynamics ◽

Growth Rates ◽

Growth Models ◽

Population Models ◽

Logistic Growth ◽

Population Growth Rates ◽

Discrete Equations ◽

Sustained Oscillations ◽

Continuous Models ◽

Per Capita

This chapter examines the dynamics of basic population models, with a particular focus on the general biological conditions under which population dynamics are stabilized, or destabilized, by increased population growth rates. Three classes of population models are discussed in relation to excitable and nonexcitable interactions: continuous logistic growth models, discrete equations, and continuous models with stage-structured lags. The chapter shows how increasing per capita growth rates tend to stabilize population models as a result of excitable interactions; that is, when dynamic trajectories monotonically approach an equilibrium after a localized perturbation. However, lags in population models tend to give rise to dynamics with oscillatory decays to equilibrium or sustained oscillations around the carrying capacity. Such oscillatory decays or sustained oscillations are only further destabilized by increased growth or production rates. The chapter concludes with a review of empirical evidence for excitable dynamics.

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Population dynamics of marine fishes at low abundance

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f2012-055 ◽

2012 ◽

Vol 69 (7) ◽

pp. 1150-1163 ◽

Cited By ~ 57

Author(s):

David M. Keith ◽

Jeffrey A. Hutchings

Keyword(s):

Population Dynamics ◽

Population Growth ◽

Gadus Morhua ◽

Atlantic Cod ◽

Growth Models ◽

Analytical Techniques ◽

Allee Effects ◽

Fisheries Science ◽

Offspring Production ◽

Per Capita

The recovery of depleted species depends on their population dynamics at low abundance. Classical population growth models, applied widely in fisheries science, assume that per capita offspring production increases as abundance declines (compensation). However, slow or absent recovery by many depleted fishes might reflect unexpectedly weak compensation or the presence of Allee effects (depensation). Using meta-analytical techniques to describe reproductive dynamics, we find considerable variability among 207 exploited marine fish stocks (104 species) in how standardized per capita population growth changes with abundance. Although many species exhibit strong compensatory dynamics (negative density dependence), others show much weaker compensation than expected, and some exhibit evidence of an Allee effect, such as Atlantic cod ( Gadus morhua ) and Alaskan walleye pollock ( Theragra chalcogramma ). As data at low levels of abundance become increasingly available, it appears that compensation, while strong in some species, is comparatively weak or nonexistent in others, thus providing an explanation for why the recovery of some depleted stocks, despite reductions in exploitation, has been considerably less than what classic models of population growth would otherwise suggest.

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Faculty Opinions recommendation of Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.13371997.14742108 ◽

2011 ◽

Author(s):

Vlastimil Krivan ◽

Ludek Berec

Keyword(s):

Population Dynamics ◽

Density Dependence ◽

Population Abundance ◽

Global Population

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Global Population Dynamics Drive the Phases of the Great Divergence and Convergence

SSRN Electronic Journal ◽

10.2139/ssrn.2389005 ◽

2014 ◽

Author(s):

Andrey Korotayev ◽

Jonas J. Nazimoff Shaende ◽

Jack A. Goldstone

Keyword(s):

Population Dynamics ◽

Great Divergence ◽

Global Population

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A cryptic Allee effect: spatial contexts mask an existing fitness–density relationship

Royal Society Open Science ◽

10.1098/rsos.150034 ◽

2015 ◽

Vol 2 (6) ◽

pp. 150034 ◽

Cited By ~ 4

Author(s):

Akira Terui ◽

Yusuke Miyazaki ◽

Akira Yoshioka ◽

Shin-ichiro S. Matsuzaki

Keyword(s):

Allee Effect ◽

Local Level ◽

Freshwater Mussel ◽

Fertilization Rate ◽

Positive Density ◽

Allee Effects ◽

Flow Conditions ◽

Conspecific Density ◽

Sperm Density ◽

Density Relationship

Current theories predict that Allee effects should be widespread in nature, but there is little consistency in empirical findings. We hypothesized that this gap can arise from ignoring spatial contexts (i.e. spatial scale and heterogeneity) that potentially mask an existing fitness–density relationship: a ‘cryptic’ Allee effect. To test this hypothesis, we analysed how spatial contexts interacted with conspecific density to influence the fertilization rate of the freshwater mussel Margaritifera laevis . This sessile organism has a simple fertilization process whereby females filter sperm from the water column; this system enabled us to readily assess the interaction between conspecific density and spatial heterogeneity (e.g. flow conditions) at multiple spatial levels. Our findings were twofold. First, positive density-dependence in fertilization was undetectable at a population scale (approx. less than 50.5 m 2 ), probably reflecting the exponential decay of sperm density with distance from the sperm source. Second, the Allee effect was confirmed at a local level (0.25 m 2 ), but only when certain flow conditions were met (slow current velocity and shallow water depth). These results suggest that spatial contexts can mask existing Allee effects.

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