Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control

Vaidya, Naveen K.; Wu, Jianhong

doi:10.1007/s11538-007-9278-x

Cited by 12 publications

(11 citation statements)

References 20 publications

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“…For the reasons discussed above, there are no reliable budworm consumption estimates for budworm densities under 100 000 per hectare. Nevertheless, it is generally accepted that bird predation exerts its greatest influence on budworm at endemic population levels (George and Mitchell 1948;Morris et al 1958;Morris 1963c;Crawford et al 1983;Crawford and Jennings 1989;Vaidya and Wu 2008).…”

Section: ) Evening Grosbeakmentioning

confidence: 99%

“…A number of mathematical models have been developed to simulate the temporal and spatial patterns of spruce budworm outbreaks (e.g., Clark et al 1979;Holling 1978;Jones 1979;Ludwig et al 1978;Morris 1963b;Mott 1963;Royama et al 2005;Stedinger 1984;Vaidya and Wu 2008). Most of the data for these models derive from the New Brunswick Green River Project described in Morris (1963a).…”

Section: ) Evening Grosbeakmentioning

confidence: 99%

“…Near the beginning of a spruce budworm outbreak at Black Sturgeon Lake in Ontario (1978-83), bird densities increased on average by about 33% per year, whereas budworm densities increased by about 358% per year (Holmes et al 2009 and unpublished data). However, although it may not be the primary cause of budworm oscillations, bird predation probably does play a role in determining the mean level of those oscillations (Royama 1984;Vaidya and Wu 2008).…”

Section: ) Evening Grosbeakmentioning

confidence: 99%

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A review of the interaction between forest birds and eastern spruce budworm

Venier

Holmes

2010

Environ. Rev.

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The eastern spruce budworm, Choristoneura fumiferana Clem., (hereafter budworm) is responsible for the largest areas of insect-caused disturbance in North America, and as such, is an important part of spruce–fir forest change and succession. The insectivorous forest bird community shows large and rapid responses to budworm outbreaks. There is good evidence that there are budworm-linked species (bay-breasted, Cape May, and Tennessee warblers) that respond to budworm outbreak much more strongly and consistently than other species, probably through increased productivity of local populations when budworm are abundant. There also appears to be a more widespread positive bird community response to budworm outbreak that involves many more species. The response is evident in local and regional scale studies, but individual species’ responses across studies are not always consistent, probably because of the relatively small number of studies conducted in a wide variety of contexts. Budworm outbreaks provide a short-term increase in food supply for birds, but also result in longer-term habitat change due to budworm-induced defoliation and tree mortality. Birds appear to influence budworm cycles, mostly at endemic population levels, through predation of large larvae and pupae. There are good arguments suggesting that bird predation is not the primary cause of budworm oscillations, but may play a role in determining the mean level of oscillations. Climate change is expected to change the bird–budworm relationship through changes in fire regimes, spruce–fir distributions, bird distributions, and budworm and bird phenology.

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Section: ) Evening Grosbeakmentioning

confidence: 99%

Section: ) Evening Grosbeakmentioning

confidence: 99%

Section: ) Evening Grosbeakmentioning

confidence: 99%

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A review of the interaction between forest birds and eastern spruce budworm

Venier

Holmes

2010

Environ. Rev.

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“…We consider the above birth functions due to their wide use in the field of mathematical biology, especially, for the cases q = 1 in b 1 (u), q = 2 in b 2 (u) and q = 1 in b 3 (u), see also [26]. 4).…”

Section: Remark 44mentioning

confidence: 99%

Population dynamics with age-dependent diffusion and death rates

Al-Jararha

2013

Eur. J. Appl. Math

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Link to this article: http://journals.cambridge.org/abstract_S0956792513000028How to cite this article: M. AL-JARARHA and CHUNHUA OU (2013). Population dynamics with age-dependent diffusion and death rates.In this paper we investigate the population dynamics of a species with age structure in the case where the diffusion and death rates of the matured population are both age-dependent. We develop a new application of the age-structure technique in terms of an integral equation. For unbounded spatial domains, we study the existence of travelling waves, whilst in bounded domains, we investigate the existence of positive steady-state solutions and their stability.Population dynamics with age-dependent diffusion and death rates 473 where u m and u are the population density of the mature and the immature populations, f(u m ) and g(u m ) are the birth and death functions, D I (a) and μ I (a) are the diffusion and death rates of the immature population, and D m and d m are age independent diffusion and death rates of the mature population. They investigated the existence of travelling wave solutions of this model, when the spatial domain is the whole real line R. When the spatial domain is bounded, the above model was studied by Xu and Zhao in [28] and by Jin and Zhao in [11] where they investigated the existence of steady-state solutions. Also, with a slight modification, these types of models have been recently studied by many mathematicians. For example, Al-Omari and Gourley [1], Gourley and Kuang in [4], Gourley and So in [5], Gourley, So, and Wu in [6] and Ou and Wu in [18]. Overall, all these papers study the models with a crucial assumption that the diffusion and death rates of the mature population are constants so that equation (1.4) can be easily derived. Actually, all models above seem to fail if D m (a) and d m (a) are not constants, because equation (1.4) is not valid anymore if both D m (a) and d m (a) are age-dependent.Biologically, it is more realistic to include the age effects in the mathematical models during the whole life of the species. For example, women in the age between 15-40 years have higher birth rate and lower death rate. Another example is the predation of animals; the predation could be heavier on some certain age groups of mature population, which makes the death rate depend on the age. In epidemiology, it is also important to consider the death rate of mature population to be age-dependent. Indeed, the disease may have different infection rates for different age groups of mature population. An example of this is the sexually-transited diseases (STDs), which spread through mature individuals; most AIDS cases occur in young adults. This causes a variation in the death rate amongst the different age of the mature individuals. Therefore, it is natural and more realistic to consider the diffusion and death rates to be age-dependent during all the life time.In this paper, we aim to investigate the populations dynamics for this case (agedependent in the whole life). Therefore, we consider the...

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“…As is well known, since the spruce budworm population site model [1] has been proposed and was accepted by numerous scholars, during the last decade, spruce budworm population models have been extensively investigated both in theory and applications, such as for protection of spruce trees and development of a strategy for spruce budworm population control [1][2][3][4][5][6][7][8][9][10][11][12][13]. For example, in [2], the authors considered the following standard structured partial differential model of the budworm population:…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

Muhammadhaji

Halik

2021

Journal of Function Spaces

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A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.

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Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control

Cited by 12 publications

References 20 publications

A review of the interaction between forest birds and eastern spruce budworm

A review of the interaction between forest birds and eastern spruce budworm

Population dynamics with age-dependent diffusion and death rates

Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

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