Mathematical models for invasive species management: Grey squirrel control on Anglesey

Jones, Hannah; White, Andy; Lurz, Peter W. W.; Shuttleworth, Craig M.

doi:10.1016/j.ecolmodel.2017.05.020

Cited by 17 publications

(32 citation statements)

References 27 publications

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“…The healthy red squirrels also follow a logistic growth in which, for the very same reasons just outlined, the intraspecific competition is confined only to their healthy similars. Note that the two carrying capacities of the grey and red squirrels are assumed to be different, respectively E and K, because in suitable habitats, the grey squirrel can live at higher densities (e.g., 1.45-2.99 individuals /ha, up to 7-10 or even more than 10 ind./ha [34][35][36][37]) than the red squirrel, whose densities are usually lower than 1-2 ind./ha [7,27,30,31,[38][39][40][41][42]. Furthermore, their net reproductive rates differ, r and s, respectively [43].…”

Section: The Modelmentioning

confidence: 99%

“…This can occur if it comes in contact with an infected consimilar at rate λ, which is modeled by the fourth term, or also at rate β by the interaction with a grey individual, which is always an asymptomatic carrier, as stated earlier, the last term of the second equation. Rates of viral shedding from infected grey and red squirrels may be different [45], but a transmission rate of 3.27 between and within each species was obtained by matching model and field data on the seroprevalence in the U.K. [27,46]. Note that we take the interspecific transmission term to be in a rational form because the squirrels are mainly residing in a fixed place, for which their interactions with possible neighbors are limited.…”

Section: The Modelmentioning

confidence: 99%

“…These values are obtained from the literature, mainly from [27,51]. Instead, the natural plus disease-related mortality for the red squirrels and the weight of the two populations are arbitrarily assumed:…”

Section: Study Of the Ecosystem Behaviormentioning

confidence: 99%

“…Note that the natural plus disease-related mortality µ is chosen at a high value in view of the high virulence and lethality of the epidemics, for the red squirrels. In addition, note that the literature [27,43,51] reports that some of them vary in the following suitable ranges:…”

Section: Study Of the Ecosystem Behaviormentioning

confidence: 99%

“…In particular, this paper attempts a different approach than other current research in the field [25,27]. While these models include space in the model formulation and tend to be more specific (e.g., [27] for the Anglesey peninsula in U.K.), here we try to concentrate on a more ample view. The main aim is indeed to obtain more general results and to possibly provide an indication of how to approach the invasion problem in different scenarios.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels

et al. 2018

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A model for the interactions of the invasive grey squirrel species as asymptomatic carriers of the poxvirus with the native red squirrel is presented and analyzed. Equilibria of the dynamical system are assessed, and their sensitivity in terms of the ecosystem parameters is investigated through numerical simulations. The findings are in line with both field and theoretical research. The results indicate that mainly the reproduction rate of the alien population should be drastically reduced to repel the invasion, and to achieve disease eradication, actions must be performed to reduce the intraspecific transmission rate; also, the native species mortality plays a role: if grey squirrels are controlled, increasing it may help in the red squirrel preservation, while the invaders vanish; on the contrary, decreasing it in favorable situations, the coexistence of the two species may occur. Preservation or restoration of the native red squirrel requires removal of the grey squirrels or keeping them at low values. Wildlife managers should exert a constant effort to achieve a harsh reduction of the grey squirrel growth rate and to protect the remnant red squirrel population.

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Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Section: Study Of the Ecosystem Behaviormentioning

confidence: 99%

Section: Study Of the Ecosystem Behaviormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels

et al. 2018

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Brown Treesnake Mortality After Aerial Application of Toxic Baits

et al. 2021

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Quantitative evaluation of control tools for managing invasive species is necessary to assess overall effectiveness and individual variation in treatment susceptibility. Invasive brown treesnakes (Boiga irregularis) on Guam have caused severe ecological and economic effects, pose a risk of accidental introduction to other islands, and are the greatest impediment to the reestablishment of extirpated native fauna. An aerial delivery system for rodent‐based toxic baits can reduce brown treesnake abundance and heterogeneity among individuals may influence bait attraction or toxicant susceptibility. Previous baiting trials have either been simulated aerial treatments or relied on slightly different bait capsule compositions and the results of aerial delivery of toxic baits under operational conditions may not be directly comparable. We monitored 30 radio‐tagged adult snakes (990–1,265 mm snout‐vent length) during an aerial baiting operation in a 55‐ha area using transmitters equipped with accelerometers and receivers programed to display a status code indicating mortality if a snake failed to move for >24 hours. We used known‐fate models to estimate mortality and evaluate a priori hypotheses explaining differences in mortality based on size, sex, and treatment effects. Eleven radio‐tagged snakes died in the aerial baiting treatment period (0.37, 95% CI = 0.21–0.55) and no individuals (0.00, 95% CI = 0.00–0.04) died during the non‐treatment period. Our data provide strong evidence for an additive size‐based treatment effect on mortality, with smaller adults (0.59, 95% CI = 0.35–0.80) exhibiting higher mortality than larger snakes (0.14, 95% CI = 0.02–0.37) but did not support a sex effect on mortality. The high mortality of snakes during the treatment period indicates that aerial baiting can reduce brown treesnake abundance, but further refinement or use in combination with other removal tools may be necessary to overcome size‐based differences in susceptibility and achieve eradication. © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.

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Model-based predictive control for the regulation of the golden mussel Limnoperna fortunei (Dunker, 1857)

Ávila-Simas¹,

Morato

Reynalte‐Tataje

et al. 2019

Ecological Modelling

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Mathematical models for invasive species management: Grey squirrel control on Anglesey

Cited by 17 publications

References 27 publications

Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels

Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels

Brown Treesnake Mortality After Aerial Application of Toxic Baits

Model-based predictive control for the regulation of the golden mussel Limnoperna fortunei (Dunker, 1857)

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