scholarly journals Population dynamics of mutualism and intraspecific density dependence: howθ-logistic density dependence affects mutualistic positive feedback

2017 ◽  
Author(s):  
Christopher M. Moore ◽  
Samantha A. Catella ◽  
Karen C. Abbott
Keyword(s):  
Population Growth ◽  
Density Dependence ◽  
Logistic Growth ◽  
Positive Interactions ◽  
Linear Interaction ◽  
Mutualistic Interaction ◽  
Classic Theory ◽  
Sign Change ◽  
Interaction Term ◽  
Intraspecific Density Dependence

AbstractMutualism describes the biological phenomenon where two or more species are reciprocally beneficial, regardless of their ecological intimacy or evolutionary history. Classic theory shows that mutualistic benefit must be relatively weak, or else it overpowers the stabilizing influence of intraspecific competition and leads to unrealistic, unbounded population growth. Interestingly, the conclusion that strong positive interactions lead to runaway population growth is strongly grounded in the behavior of a single model. This model ― the Lotka-Volterra competition model with a sign change to generate mutualism rather than competition between species ― assumes logistic growth of each species plus a linear interaction term to represent the mutualism. While it is commonly held that the linear interaction term is to blame for the model’s unrealistic behavior, we show here that a linear mutualism added to aθ-logistic model of population growth can prevent unbounded growth. We find that when density dependence is decelerating, the benefit of mutualism at equilibrium is greater than when density dependence is accelerating. Although there is a greater benefit, however, decelerating density dependence tends to destabilize populations whereas accelerating density dependence is always stable. We interpret these findings tentatively, but with promise for the understanding of the population ecology of mutualism by generating several predictions relating growth rates of mutualist populations and the strength of mutualistic interaction.

Density-Dependent Population Growth

2020 ◽  
pp. 29-46
Author(s):  
Michael J. Fogarty ◽  
Jeremy S. Collie
Keyword(s):  
Population Density ◽  
Population Growth ◽  
Density Dependence ◽  
Multiple Equilibria ◽  
Dynamical Behavior ◽  
Logistic Growth ◽  
Density Dependent ◽  
Per Capita ◽  
Discrete Time Models ◽  
Complex Dynamical Behavior

The observation that no population can grow indefinitely and that most populations persist on ecological timescales implies that mechanisms of population regulation exist. Feedback mechanisms include competition for limited resources, cannibalism, and predation rates that vary with density. Density dependence occurs when per capita birth or death rates depend on population density. Density dependence is compensatory when the population growth rate decreases with population density and depensatory when it increases. The logistic model incorporates density dependence as a simple linear function. A population exhibiting logistic growth will reach a stable population size. Non-linear density-dependent terms can give rise to multiple equilibria. With discrete time models or time delays in density-dependent regulation, the approach to equilibrium may not be smooth—complex dynamical behavior is possible. Density-dependent feedback processes can compensate, up to a point, for natural and anthropogenic disturbances; beyond this point a population will collapse.

scholarly journals Role of prey and intraspecific density dependence on the population growth of an avian top predator

2014 ◽  
Vol 60 ◽  
pp. 1-6 ◽  
Author(s):  
Javier Fernandez-de-Simon ◽  
Francisco Díaz-Ruiz ◽  
Francesca Cirilli ◽  
Francisco S. Tortosa ◽  
Rafael Villafuerte ◽  
...  
Keyword(s):  
Population Growth ◽  
Density Dependence ◽  
Top Predator ◽  
Intraspecific Density Dependence

scholarly journals The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

2018 ◽  
Author(s):  
Emanuel A. Fronhofer ◽  
Lynn Govaert ◽  
Mary I. O’Connor ◽  
Sebastian J. Schreiber ◽  
Florian Altermatt
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Level ◽  
Logistic Growth ◽  
Population Densities ◽  
Density Regulation ◽  
Logistic Growth Model ◽  
Regulation Functions ◽  
Consumer Resource ◽  
Population Growth Models

AbstractThe logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

scholarly journals Psi-Caputo Logistic Population Growth Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abu Asbeh
Keyword(s):  
Population Growth ◽  
Fractional Derivative ◽  
Carrying Capacity ◽  
Chinese Population ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Growth Equation ◽  
Uniqueness Of The Solution ◽  
Better Than

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α  = 1.6455.

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.

scholarly journals Dynamics and Management of Rising Outbreak Spruce Budworm Populations

Forests ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 748 ◽  
Author(s):  
Jacques Régnière ◽  
Barry Cooke ◽  
Ariane Béchard ◽  
Alain Dupont ◽  
Pierre Therrien
Keyword(s):  
Population Growth ◽  
Density Dependence ◽  
Natural Enemies ◽  
Choristoneura Fumiferana ◽  
Regional Scale ◽  
Adult Emergence ◽  
Spruce Budworm ◽  
Migration Activity ◽  
Larval Stages ◽  
The Impact

Management of spruce budworm, Choristoneura fumiferana (Clem.), outbreak spread requires understanding the demographic processes occurring in low, but rising populations. For the first time, detailed observations were made in the early stages of outbreak development. We sampled populations over a three-year period in both treated and untreated populations in the Lower St-Lawrence region of Quebec, Canada, and measured the density-dependence of survival and population growth rates, and the impact of natural enemies and insecticides. Insecticides tested were Bacillus thuringiensis (Berliner 1915) and tebufenozide. We recorded strong density-dependence of survival between early larval stages and adult emergence, explained largely by the variation of natural enemy impacts and overcrowding. We also observed inverse density-dependence of apparent fecundity: net immigration into lower-density populations and net emigration from the higher, linked to a threshold of ~25% defoliation. Because of high migration rates, none of the 2013 treatments reduced egg populations at the end of summer. However lower migration activity in 2014 allowed population growth to be reduced in treated plots. This evidence lends support to the conclusion that, for a budworm population to increase to outbreak density, it must be elevated via external perturbations, such as immigration, above a threshold density of ~4 larvae per branch tip (L4). Once a population has increased beyond this threshold, it can continue growing and itself become a source of further spread by moth migration. These findings imply that populations can be brought down by insecticide applications to a density where mortality from natural enemies can keep the reduced population in check, barring subsequent immigration. While we recognize that other factors may occasionally cause a population to exceed the Allee threshold and reach outbreak level, the preponderance of immigration implies that if all potential sources of significant numbers of moths are reduced on a regional scale by insecticide applications, a widespread outbreak can be prevented, stopped or slowed down by reducing the supply of migrating moths.

VORTEX: a computer simulation model for population viability analysis

1993 ◽  
Vol 20 (1) ◽  
pp. 45 ◽  
Author(s):  
RC Lacy
Keyword(s):  
Computer Simulation ◽  
Population Growth ◽  
Simulation Model ◽  
Density Dependence ◽  
Carrying Capacity ◽  
Population Viability Analysis ◽  
Simulation Modelling ◽  
Population Viability ◽  
Reproductive Age ◽  
Viability Analysis

Population Viability Analysis (PVA) is the estimation of extinction probabilities by analyses that incorporate identifiable threats to population survival into models of the extinction process. Extrinsic forces, such as habitat loss, over-harvesting, and competition or predation by introduced species, often lead to population decline. Although the traditional methods of wildlife ecology can reveal such deterministic trends, random fluctuations that increase as populations become smaller can lead to extinction even of populations that have, on average, positive population growth when below carrying capacity. Computer simulation modelling provides a tool for exploring the viability of populations subjected to many complex, interacting deterministic and random processes. One such simulation model, VORTEX, has been used extensively by the Captive Breeding Specialist Group (Species Survival Commission, IUCN), by wildlife agencies, and by university classes. The algorithms, structure, assumptions and applications of VORTEX are described in this paper. VORTEX models population processes as discrete, sequential events, with probabilistic outcomes. VORTEX simulates birth and death processes and the transmission of genes through the generations by generating random numbers to determine whether each animal lives or dies, to determine the number of progeny produced by each female each year, and to determine which of the two alleles at a genetic locus are transmitted from each parent to each offspring. Fecundity is assumed to be independent of age after an animal reaches reproductive age. Mortality rates are specified for each pre-reproductive age-sex class and for reproductive-age animals. Inbreeding depression is modelled as a decrease in viability in inbred animals. The user has the option of modelling density dependence in reproductive rates. As a simple model of density dependence in survival, a carrying capacity is imposed by a probabilistic truncation of each age class if the population size exceeds the specified carrying capacity. VORTEX can model linear trends in the carrying capacity. VORTEX models environmental variation by sampling birth rates, death rates, and the carrying capacity from binomial or normal distributions. Catastrophes are modelled as sporadic random events that reduce survival and reproduction for one year. VORTEX also allows the user to supplement or harvest the population, and multiple subpopulations can be tracked, with user-specified migration among the units. VORTEX outputs summary statistics on population growth rates, the probability of population extinction, the time to extinction, and the mean size and genetic variation in extant populations. VORTEX necessarily makes many assumptions. The model it incorporates is most applicable to species with low fecundity and long lifespans, such as mammals, birds and reptiles. It integrates the interacting effects of many of the deterministic and stochastic processes that have an impact on the viability of small populations, providing opportunity for more complete analysis than is possible by other techniques. PVA by simulation modelling is an important tool for identifying populations at risk of extinction, determining the urgency of action, and evaluating options for management.

scholarly journals Hyperchaos from a Model of Coupled Stratosphere-Troposphere Dynamics

2017 ◽  
Vol 27 (02) ◽  
pp. 1730007 ◽  
Author(s):  
Susheel Adusumilli ◽  
Robert A. Van Gorder
Keyword(s):  
Energy Transfer ◽  
Time Evolution ◽  
Physical Problem ◽  
Coupled Systems ◽  
Dimensional System ◽  
Linear Interaction ◽  
Precise Form ◽  
Small Coupling ◽  
Interaction Term ◽  
Smooth Dynamics

We present a six-dimensional system describing coupled troposphere-stratosphere dynamics which takes the form of two coupled Lorenz-84 systems (one for each of the troposphere and stratosphere) involving thermal forcing terms. The systems are coupled through a linear interaction term, which permits energy transfer between both troposphere and stratosphere layers. While other six-dimensional systems giving hyperchaos and multiscroll attractors have been found in the literature, the coupled systems given here arise naturally from the physical problem. In particular, the resulting six-dimensional system constitutes a physically interesting model where the stratosphere-troposphere dynamics are coupled to one another (rather than just coupling the troposphere dynamics to the stratosphere, while keeping the time evolution of the stratosphere independent). This model gives bounded dynamics and for some parameters exhibits chaos or hyperchaos. Interestingly, there are parameter regimes for which the dynamics go directly between periodic orbits and hyperchaos, bypassing an intermediate chaos step. The precise form of the coupling between the two Lorenz-84 systems is found to strongly influence the solution behavior. We find that even small coupling from the stratosphere back to the troposphere can destabilize the system and yield hyperchaotic dynamics, while for other parameter sets this coupling can instead yield smooth dynamics in both regions.

scholarly journals Increased natural mortality at low abundance can generate an Allee effect in a marine fish

2014 ◽  
Vol 1 (2) ◽  
pp. 140075 ◽  
Author(s):  
Anna Kuparinen ◽  
Jeffrey A. Hutchings
Keyword(s):  
Population Dynamics ◽  
Population Growth ◽  
Density Dependence ◽  
Gadus Morhua ◽  
Allee Effect ◽  
Population Regulation ◽  
Atlantic Cod ◽  
Adult Mortality ◽  
Natural Mortality ◽  
Density Dependent

Negative density-dependent regulation of population dynamics promotes population growth at low abundance and is therefore vital for recovery following depletion. Inversely, any process that reduces the compensatory density-dependence of population growth can negatively affect recovery. Here, we show that increased adult mortality at low abundance can reverse compensatory population dynamics into its opposite—a demographic Allee effect. Northwest Atlantic cod ( Gadus morhua ) stocks collapsed dramatically in the early 1990s and have since shown little sign of recovery. Many experienced dramatic increases in natural mortality, ostensibly attributable in some populations to increased predation by seals. Our findings show that increased natural mortality of a magnitude observed for overfished cod stocks has been more than sufficient to fundamentally alter the dynamics of density-dependent population regulation. The demographic Allee effect generated by these changes can slow down or even impede the recovery of depleted populations even in the absence of fishing.

Sign in / Sign up

Export Citation Format

Share Document