scholarly journals Ecological theory of mutualism: Robust patterns of stability and thresholds in two-species population models

2021 ◽  
Author(s):  
Kayla Hale ◽  
Fernanda Valdovinos
Keyword(s):  
Population Dynamics ◽  
Ecosystem Services ◽  
Dynamic Theory ◽  
Theoretical Work ◽  
Competitive Interactions ◽  
Low Density ◽  
Allee Effects ◽  
Levels Of Detail ◽  
Generalized Framework ◽  
Species Population

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, comparatively lagged behind that of trophic and competitive interactions, leading to the impression that ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Yet, over the last 90 years, abundant theoretical work has accumulated, ranging from abstract to detailed. Here, we review and synthesize historical models of two-species mutualisms. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms tend to exhibit stable coexistence at high density and destabilizing thresholds at low density. These dynamics emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density-dependence in intraspecific processes, interspecific processes, or both. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. Our synthesis suggests that there exists a robust population dynamic theory of mutualism that can make general predictions.

scholarly journals Ecological theory of mutualism: Qualitative patterns in two-species population models

2021 ◽  
Author(s):  
Kayla Hale ◽  
Fernanda Valdovinos
Keyword(s):  
Population Dynamics ◽  
Ecosystem Services ◽  
Dynamic Theory ◽  
Competitive Interactions ◽  
Low Density ◽  
Allee Effects ◽  
Stable Coexistence ◽  
Levels Of Detail ◽  
Generalized Framework ◽  
Species Population

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, has comparatively lagged behind that of trophic and competitive interactions. Consequently, ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Here, we review historical models of two-species mutualisms from over the last 90 years. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms exhibit stable coexistence at high density and destabilizing thresholds at low density. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. The dynamics of stable coexistence and thresholds in partner density emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density dependence in intraspecific, interspecific, or both. These results suggest that there exists a robust population dynamic theory of mutualism that can make general predictions.

scholarly journals Ecological theory of mutualism: Models generalizing across different mechanisms

2020 ◽  
Author(s):  
Kayla R. S. Hale ◽  
Daniel P. Maes ◽  
Fernanda S. Valdovinos
Keyword(s):  
Population Dynamics ◽  
Ecosystem Services ◽  
Population Dynamic ◽  
Dynamic Models ◽  
Historical Context ◽  
Ecological Theory ◽  
Population Level ◽  
Competitive Interactions ◽  
Specific Density ◽  
Generalized Framework

AbstractMutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, has comparatively lagged behind that of trophic and competitive interactions. Consequently, ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Here, we propose extensible models for two-species mutualisms focusing on nutritional, protection, and transportation mechanisms and evaluate the population-level consequences of those mechanisms. We introduce a novel theoretical framework that highlights characteristic dynamics when the effects of mutualism are directly dependent or independent of recipient density and when they saturate due to inter- or intra-specific density-dependence. We end by integrating our work into the broader historical context of population-dynamic models of mutualism and conclude that a general ecological theory of mutualism exists.

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.

scholarly journals A MICRO-LEVEL ‘CONSUMER APPROACH’ TO SPECIES POPULATION DYNAMICS

2008 ◽  
Vol 20 (1) ◽  
pp. 7-59 ◽  
Author(s):  
THOMAS CHRISTIAANS ◽  
THOMAS EICHNER ◽  
RÜDIGER PETHIG
Keyword(s):  
Population Dynamics ◽  
Species Population ◽  
Micro Level

Allee effects on population dynamics with delay

2008 ◽  
Vol 37 (1) ◽  
pp. 65-74 ◽  
Author(s):  
C. Çelik ◽  
H. Merdan ◽  
O. Duman ◽  
Ö. Akın
Keyword(s):  
Population Dynamics ◽  
Allee Effects

scholarly journals Evidence for an Allee effect in a declining fur seal population

2021 ◽  
Vol 288 (1947) ◽  
Author(s):  
Rebecca Nagel ◽  
Claire Stainfield ◽  
Cameron Fox-Clarke ◽  
Camille Toscani ◽  
Jaume Forcada ◽  
...  
Keyword(s):  
Time Series Data ◽  
Poor Quality ◽  
Weight Of Evidence ◽  
Series Data ◽  
Low Density ◽  
Allee Effects ◽  
Wild Populations ◽  
Fur Seal ◽  
Parallel Body ◽  
Pup Mortality

Allee effects play an important role in the dynamics of many populations and can increase the risk of local extinction. However, some authors have questioned the weight of evidence for Allee effects in wild populations. We therefore exploited a natural experiment provided by two adjacent breeding colonies of contrasting density to investigate the potential for Allee effects in an Antarctic fur seal ( Arctocephalus gazella ) population that is declining in response to climate change-induced reductions in food availability. Biometric time-series data were collected from 25 pups per colony during two consecutive breeding seasons, the first of which was among the worst on record in terms of breeding female numbers, pup birth weights and foraging trip durations. In previous decades when population densities were higher, pup mortality was consistently negatively density dependent, with rates of trauma and starvation scaling positively with density. However, we found the opposite, with higher pup mortality at low density and the majority of deaths attributable to predation. In parallel, body condition was depressed at low density, particularly in the poor-quality season. Our findings shed light on Allee effects in wild populations and highlight a potential emerging role of predators in the ongoing decline of a pinniped species.

scholarly journals Impacts of predator-mediated interactions along a climatic gradient on the population dynamics of an alpine bird

2020 ◽  
Author(s):  
Diana E. Bowler ◽  
Mikkel A. J. Kvasnes ◽  
Hans C. Pedersen ◽  
Brett K. Sandercock ◽  
Erlend B. Nilsen
Keyword(s):  
Population Dynamics ◽  
Species Interactions ◽  
Climatic Conditions ◽  
Boreal Ecosystems ◽  
Prey Switching ◽  
Predator Prey ◽  
Classic Theory ◽  
Species Population ◽  
Cyclic Dynamics ◽  
Ground Nesting

AbstractAccording to classic theory, species’ population dynamics and distributions are less influenced by species interactions under harsh climatic conditions compared to under more benign climatic conditions. In alpine and boreal ecosystems in Fennoscandia, the cyclic dynamics of rodents strongly affect many other species, including ground-nesting birds such as ptarmigan. According to the ‘alternative prey hypothesis’ (APH), the densities of ground-nesting birds and rodents are positively associated due to predator-prey dynamics and prey-switching. However, it remains unclear how the strength of these predator-mediated interactions change along a climatic harshness gradient in comparison with the effects of climatic variation. We built a hierarchical Bayesian model to estimate the sensitivity of ptarmigan populations to interannual variation in climate and rodent occurrence across Norway during 2007–2017. Ptarmigan abundance was positively linked with rodent occurrence, consistent with the APH. Moreover, we found that rodent dynamics had stronger effects on ptarmigan in colder regions. Our study highlights how species interactions play an important role for the population dynamics of species at higher latitudes and suggests that they can become even more important in the most climatically harsh regions.

scholarly journals Coarse, Medium or Fine? A Quantum Mechanics Approach to Single Species Population Dynamics

2020 ◽  
Author(s):  
Olcay Akman ◽  
Leon Arriola ◽  
Aditi Ghosh ◽  
Ryan Schroeder
Keyword(s):  
Population Dynamics ◽  
Quantum Mechanics ◽  
Single Species ◽  
Stable Equilibrium Point ◽  
Ode Model ◽  
Deterministic Models ◽  
Species Population ◽  
Quantum Approach ◽  
Single Species Population ◽  
Quantum Framework

AbstractStandard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the possibility of searching for “black–swan” events. In other words, using the more sophisticated quantum approach, we may be able to make quantitative statements about rare events that have significant ramifications to the dynamical 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.

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