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

2015 ◽  
Vol 2 (6) ◽  
pp. 150034 ◽  
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.

scholarly journals Experimental demonstration of an Allee effect in microbial populations

2016 ◽  
Vol 12 (4) ◽  
pp. 20160070 ◽  
Author(s):  
RajReni B. Kaul ◽  
Andrew M. Kramer ◽  
Fred C. Dobbs ◽  
John M. Drake
Keyword(s):  
Allee Effect ◽  
Vibrio Fischeri ◽  
Microbial Populations ◽  
Critical Threshold ◽  
Initial Population ◽  
Positive Density ◽  
Allee Effects ◽  
Low Carbon ◽  
Positive Density Dependence ◽  
The Relationship

Microbial populations can be dispersal limited. However, microorganisms that successfully disperse into physiologically ideal environments are not guaranteed to establish. This observation contradicts the Baas-Becking tenet: ‘Everything is everywhere, but the environment selects’. Allee effects, which manifest in the relationship between initial population density and probability of establishment, could explain this observation. Here, we experimentally demonstrate that small populations of Vibrio fischeri are subject to an intrinsic demographic Allee effect. Populations subjected to predation by the bacterivore Cafeteria roenbergensis display both intrinsic and extrinsic demographic Allee effects. The estimated critical threshold required to escape positive density-dependence is around 5, 20 or 90 cells ml −1 under conditions of high carbon resources, low carbon resources or low carbon resources with predation, respectively. This work builds on the foundations of modern microbial ecology, demonstrating that mechanisms controlling macroorganisms apply to microorganisms, and provides a statistical method to detect Allee effects in data.

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

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.

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

2021 ◽  
pp. 2150037
Author(s):  
Jia Liu
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Spatially Homogeneous ◽  
Fear Effects

In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

Population growth and density dependence

2019 ◽  
pp. 63-80
Author(s):  
Gary G. Mittelbach ◽  
Brian J. McGill
Keyword(s):  
Population Growth ◽  
Density Dependence ◽  
Growth Model ◽  
Species Interactions ◽  
Single Species ◽  
Positive Density ◽  
Allee Effects ◽  
Species Population ◽  
Exponential Growth Model ◽  
Single Species Population

This chapter reviews the basic mathematics of population growth as described by the exponential growth model and the logistic growth model. These simple models of population growth provide a foundation for the development of more complex models of species interactions covered in later chapters on predation, competition, and mutualism. The second half of the chapter examines the important topic of density-dependence and its role in population regulation. The preponderance of evidence for negative density-dependence in nature is reviewed, along with examples of positive density dependence (Allee effects). The study of density dependence in single-species populations leads naturally to the concept of community-level regulation, the idea that species richness or the total abundance of individuals in a community may be regulated just like abundance in a single-species population. The chapter concludes with a look at the evidence for community regulation in nature and a discussion of its importance.

Prompt Leak Detection for High Pressure Feedwater Heaters

2002 ◽  
Author(s):  
Steven A. Kidwell
Keyword(s):  
High Pressure ◽  
Local Level ◽  
High Flow ◽  
First Year ◽  
Collateral Damage ◽  
Flow Conditions ◽  
Unit Load ◽  
Single Tube ◽  
Drain Flow ◽  
High Level

I. THE NEED. A. In high pressure feedwater heaters, a tube leak quickly claims several neighboring tubes as collateral victims. B. Prompt detection of the initial leak would save the neighboring tubes from damage and preclude a potential turbine water induction incident. II. EXAMPLE. A. A Midwest generating station replaced 12 old high pressure heaters. The new heaters contained 304N SS tubes. In one of the new heaters, an unknown localized contaminant caused a single tube leak within the first year. This single leak went undetected until several surrounding tubes were lost due to impingement from the initial leak. And even the conservatively sized normal and emergency drains were overwhelmed, causing the heater to trip on high level. III. CAPABILITY OF SMART LEVEL CONTROLS. A. There are three known possibilities that would cause high drain-flow conditions in a feedwater heater. 1. High Unit Load. 2. The upstream feedwater heater is out of service. 3. A tube leak. B. Traditional Local level controls can sense high flow conditions, but cannot tell why. Most systems will alarm the opening of the emergency drain valve, but by that time, the collateral tube damage is usually severe. “Smart” Level Controls have the capability to distinguish between these conditions, thus allowing it to give early notification of a tube leak, before collateral damage becomes severe.

scholarly journals Farmers’ spatial behaviour, demographic density dependence and the spread of Neolithic agriculture in Central Europe

2015 ◽  
Vol 42 ◽  
Author(s):  
Serge Svizzero
Keyword(s):  
Density Dependence ◽  
Central Europe ◽  
Allee Effect ◽  
Indigenous Populations ◽  
Allee Effects ◽  
Spatial Behaviour ◽  
Neolithic Agriculture ◽  
Agglomeration Effects ◽  
Spread Of Agriculture ◽  
Demic Diffusion

Since the early 1970s, the demic diffusion model is the cornerstone of the migrationist approach of the European neolithization. It considers the latter as a slow, gradual and unintentionally process. During the last decade its relevance has been challenged by the observed variability of the spread, such as the extreme one exhibited by the LBK expansion in Central Europe. To account for it, migration - which is usually explained by exogenous push-pull factors - must rather be viewed as the result of farmers’ spatial behaviour. We adopt this approach and highlight the influence on farmers’ location choice of agglomeration effects and Allee effect in settled areas, an influence which also leads to define migration endogenously. Both effects – which find support in archaeological records - exhibit demographic density dependence and help to explain an observed but counter-intuitive result. Indeed, a high demographic density is associated with a slower rate of expansion of farming; this may result from strong agglomeration and Allee effects which hinder – or even stop - the migratory spread of agriculture. Farmers’ cooperation with indigenous populations are leading to acculturation of the latter and therefore may reduce the influence of both effects, fostering farmers’ migration.

scholarly journals Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Ankit Kumar ◽  
Balram Dubey
Keyword(s):  
Allee Effect ◽  
Threshold Value ◽  
Prey Population ◽  
Predator Population ◽  
Allee Effects ◽  
Normal Form Theory ◽  
Delayed Systems ◽  
Gestation Delay ◽  
The Status ◽  
Manifold Theory

This study proposes two prey–predator models with strong and weak Allee effects in prey population with Crowley–Martin functional response. Further, gestation delay of the predator population is introduced in both the models. We discussed the boundedness, local stability and Hopf-bifurcation of both nondelayed and delayed systems. The stability and direction of Hopfbifurcation is also analyzed by using Normal form theory and Center manifold theory. It is shown that species in the model with strong Allee effect become extinct beyond a threshold value of Allee parameter at low density of prey population, whereas species never become extinct in weak Allee effect if they are initially present. It is also shown that gestation delay is unable to avoiding the status of extinction. Lastly, numerical simulation is conducted to verify the theoretical findings. 

scholarly journals Genetic Allee effects and their interaction with ecological Allee effects

2016 ◽  
Author(s):  
Meike J. Wittmann ◽  
Hanna Stuis ◽  
Dirk Metzler
Keyword(s):  
Population Size ◽  
Inbreeding Depression ◽  
Survival Probability ◽  
Allee Effect ◽  
Extinction Risk ◽  
List Type ◽  
Small Populations ◽  
Allee Effects ◽  
Deleterious Mutations ◽  
Lethal Equivalents

SummaryIt is now widely accepted that genetic processes such as inbreeding depression and loss of genetic variation can increase the extinction risk of small populations. However, it is generally unclear whether extinction risk from genetic causes gradually increases with decreasing population size or whether there is a sharp transition around a specific threshold population size. In the ecological literature, such threshold phenomena are called “strong Allee effects” and they can arise for example from mate limitation in small populations.In this study, we aim to a) develop a meaningful notion of a “strong genetic Allee effect”, b) explore whether and under what conditions such an effect can arise from inbreeding depression due to recessive deleterious mutations, and c) quantify the interaction of potential genetic Allee effects with the well-known mate-finding Allee effect.We define a strong genetic Allee effect as a genetic process that causes a population’s survival probability to be a sigmoid function of its initial size. The inflection point of this function defines the critical population size. To characterize survival-probability curves, we develop and analyze simple stochastic models for the ecology and genetics of small populations.Our results indicate that inbreeding depression can indeed cause a strong genetic Allee effect, but only if individuals carry sufficiently many deleterious mutations (lethal equivalents) on average and if these mutations are spread across sufficiently many loci. Populations suffering from a genetic Allee effect often first grow, then decline as inbreeding depression sets in, and then potentially recover as deleterious mutations are purged. Critical population sizes of ecological and genetic Allee effects appear to be often additive, but even superadditive interactions are possible.Many published estimates for the number of lethal equivalents in birds and mammals fall in the parameter range where strong genetic Allee effects are expected. Unfortunately, extinction risk due to genetic Allee effects can easily be underestimated as populations with genetic problems often grow initially, but then crash later. Also interactions between ecological and genetic Allee effects can be strong and should not be neglected when assessing the viability of endangered or introduced populations.

scholarly journals When higher carrying capacities lead to faster propagation

2018 ◽  
Author(s):  
Marjorie Haond ◽  
Thibaut Morel-Journel ◽  
Eric Lombaert ◽  
Elodie Vercken ◽  
Ludovic Mailleret ◽  
...  
Keyword(s):  
Carrying Capacity ◽  
Invasion Biology ◽  
Reaction Diffusion Equations ◽  
Positive Density ◽  
Allee Effects ◽  
Demographic Stochasticity ◽  
Positive Dependence ◽  
Density Dependent ◽  
Temporal Models ◽  
Density Dependent Dispersal

AbstractThis preprint has been reviewed and recommended by Peer Community In Ecology (https://dx.doi.org/10.24072/pci.ecology.100004). Finding general patterns in the expansion of natural populations is a major challenge in ecology and invasion biology. Classical spatio-temporal models predict that the carrying capacity (K) of the environment should have no influence on the speed (v) of an expanding population. We tested the generality of this statement with reaction-diffusion equations, stochastic individual-based models, and microcosms experiments with Trichogramma chilonis wasps. We investigated the dependence between K and v under different assumptions: null model (Fisher-KPP-like assumptions), strong Allee effects, and positive density-dependent dispersal. These approaches led to similar and complementary results. Strong Allee effects, positive density-dependent dispersal and demographic stochasticity in small populations lead to a positive dependence between K and v. A positive correlation between carrying capacity and propagation speed might be more frequent than previously expected, and be the rule when individuals at the edge of a population range are not able to fully drive the expansion.

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

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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