Mate-finding allee effect in spruce budworm population dynamics

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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A METHOD FOR REARING THE LARVAL STAGES OF THE EASTERN SPRUCE BUDWORM, CHORISTONEURA FUMIFERANA CLEMENS (LEPIDOPTERA: TORTRICIDAE), FOR PHYSIOLOGICAL STUDIES

The Canadian Entomologist ◽

10.4039/ent1221271-11 ◽

1990 ◽

Vol 122 (6) ◽

pp. 1271-1272 ◽

Cited By ~ 3

Author(s):

Hemendra Mulye ◽

Roger Gordon

Keyword(s):

Population Dynamics ◽

North America ◽

Choristoneura Fumiferana ◽

Insect Pest ◽

Spruce Budworm ◽

Forest Pest ◽

Forest Insect ◽

Larval Stages ◽

Eastern Spruce Budworm ◽

Physiological Studies

The eastern spruce budworm, Choristoneura fumiferana Clemens, is the most widely distributed and destructive forest insect pest in North America. Although much is known about the ecology, population dynamics, and impact of C. fumiferana on tree growth (Sanders et al. 1985), there is very little information available on the physiology of this forest pest. Physiological studies are crucial to the development of novel strategies for spruce budworm control.

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Natural variation in balsam fir foliar components of dietary importance to spruce budworm

Canadian Journal of Forest Research ◽

10.1139/x77-007 ◽

1977 ◽

Vol 7 (1) ◽

pp. 47-53 ◽

Cited By ~ 9

Author(s):

G. G. Shaw ◽

C. H. A. Little

Keyword(s):

Population Dynamics ◽

Natural Variation ◽

Spruce Budworm ◽

Balsam Fir ◽

Total Sugars ◽

Caloric Value ◽

Seasonal Trends ◽

Geographical Variations ◽

Foliar Concentrations ◽

Foliar Concentration

Year-to-year, geographical, and local variations in foliar concentrations of crude fat, nitrogen, total sugars, and starch and in foliar caloric value were determined for maturing, current-year needles of balsam fir (Abiesbalsamea L.). All except geographical variations proved to be statistically significant. Seasonal trends of chemical concentrations in maturing needles were in agreement with previous findings.Much of the variation in foliar caloric value could be explained by changes in foliar concentration of crude fat.Year-to-year changes in foliar nutrients may influence spruce budworm population dynamics.

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The interaction between dispersal, the Allee effect and scramble competition affects population dynamics

Ecological Modelling ◽

10.1016/s0304-3800(01)00417-3 ◽

2002 ◽

Vol 148 (2) ◽

pp. 153-168 ◽

Cited By ~ 56

Author(s):

Rampal Etienne ◽

Bregje Wertheim ◽

Lia Hemerik ◽

Petra Schneider ◽

James Powell

Keyword(s):

Population Dynamics ◽

Allee Effect ◽

Scramble Competition

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Population dynamics with spatial structure and an Allee effect

10.1101/2020.06.26.173153 ◽

2020 ◽

Author(s):

Anudeep Surendran ◽

Michael Plank ◽

Matthew Simpson

Keyword(s):

Population Dynamics ◽

Spatial Structure ◽

Short Range ◽

Allee Effect ◽

Mean Field ◽

Mean Field Approximation ◽

Continuum Approximation ◽

Spatial Moment ◽

Mean Field Models ◽

The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

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A logistic two-sex model with mate-finding Allee effect

Involve a Journal of Mathematics ◽

10.2140/involve.2019.12.1343 ◽

2019 ◽

Vol 12 (8) ◽

pp. 1343-1355

Author(s):

Elizabeth Anderson ◽

Daniel Maxin ◽

Jared Ott ◽

Gwyneth Terrett

Keyword(s):

Allee Effect ◽

Mate Finding

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

Royal Society Open Science ◽

10.1098/rsos.140075 ◽

2014 ◽

Vol 1 (2) ◽

pp. 140075 ◽

Cited By ~ 10

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.

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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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