Modelling the biological invasion of<i>Carcinus maenas</i>(the European green crab)

Marculis, Nathan G.; Lui, Roger

doi:10.1080/17513758.2015.1115563

Cited by 17 publications

(12 citation statements)

References 33 publications

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“…The simplification of a uniform settling rate of larvae in our model has also recently been used in modeling green crab population dynamics [ 52 ]. Other forms of probability distributions for settlement rate include Gaussian when settlement is normally distributed during the settlement period (i.e., with a main event in the middle of the period) [ 27 ], peaked when there is a one-time particularly strong settlement event at some point during the settlement period [ 53 , 54 ], decay when settlement is initially high and decreases over time [ 55 ], and, more generally, gamma when there is one main settlement event which could be modeled any time during the settlement period [ 56 ].…”

Section: Discussionmentioning

confidence: 99%

Stochastic dispersal increases the rate of upstream spread: A case study with green crabs on the northwest Atlantic coast

et al. 2017

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Dispersal heterogeneity is an important process that can compensate for downstream advection, enabling aquatic organisms to persist or spread upstream. Our main focus was the effect of year-to-year variation in larval dispersal on invasion spread rate. We used the green crab, Carcinus maenas, as a case study. This species was first introduced over 200 years ago to the east coast of North America, and once established has maintained a relatively consistent spread rate against the dominant current. We used a stage-structured, integro-difference equation model that couples a demographic matrix for population growth and dispersal kernels for spread of individuals within a season. The kernel describing larval dispersal, the main dispersive stage, was mechanistically modeled to include both drift and settlement rate components. It was parameterized using a 3-dimensional hydrodynamic model of the Gulf of St Lawrence, which enabled us to incorporate larval behavior, namely vertical swimming. Dispersal heterogeneity was modeled at two temporal scales: within the larval period (months) and over the adult lifespan (years). The kernel models variation within the larval period. To model the variation among years, we allowed the kernel parameters to vary by year. Results indicated that when dispersal parameters vary with time, knowledge of the time-averaged dispersal process is insufficient for determining the upstream spread rate of the population. Rather upstream spread is possible over a number of years when incorporating the yearly variation, even when there are only a few “good years” featured by some upstream dispersal among many “bad years” featured by only downstream dispersal. Accounting for annual variations in dispersal in population models is important to enhance understanding of spatial dynamics and population spread rates. Our developed model also provides a good platform to link the modeling of larval behavior and demography to large-scale hydrodynamic models.

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Section: Discussionmentioning

confidence: 99%

Stochastic dispersal increases the rate of upstream spread: A case study with green crabs on the northwest Atlantic coast

et al. 2017

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“…Therefore, the type of averaging done in modeling or experimental studies needs to be considered carefully. 23 The simplification of a uniform settling rate of larvae in our model has also recently been used in modeling green crab population dynamics [52]. Other forms of probability distributions for settlement rate include Gaussian when settlement is normally distributed during the settlement period (i.e., with a main event in the middle of the period) [27], peaked when there is a one-time particularly strong settlement event at some point during the settlement period [53,54], decay when settlement is initially high and decreases over time [55], and, more generally, gamma when there is one main settlement event which could be modeled any time during the settlement period [56].…”

Section: Other Considerations and Future Workmentioning

confidence: 99%

Stochastic dispersal increases the rate of upstream spread: a case study with green crabs on the northwest Atlantic coast

Gharouni¹,

Barbeau

Chassé

et al. 2017

Preprint

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Dispersal heterogeneity is an important process that can compensate for downstream advection, enabling aquatic organisms to persist or spread upstream. Our main focus was the effect of year-to-year variation in larval dispersal on invasion spread rate. We used the green crab, Carcinus maenas, as a case study. This species was first introduced over 200 years ago to the east coast of North America, and once established has maintained a relatively consistent spread rate against the dominant current. We used a stage-structured, integro-difference equation model that couples a demographic matrix for population growth and dispersal kernels for spread of individuals within a season. The kernel describing larval dispersal, the main dispersive stage, was mechanistically modeled to include both drift and settlement rate components. It was parameterized using a 3-dimensional hydrodynamic model of the Gulf of St Lawrence, which enabled us to incorporate larval behavior, namely vertical swimming. Dispersal heterogeneity was modeled at two temporal scales: within the larval period (months) and over the adult lifespan (years). The kernel models variation within the larval period. To model the variation among years, we allowed the kernel parameters to vary by year. Results indicated that when dispersal parameters vary with time, knowledge of the time-averaged dispersal process is insufficient for determining the upstream spread rate of the population. Rather upstream spread is possible over a number of years when incorporating the yearly variation, even when there are only a few "good years" featured by some upstream dispersal among many "bad years" featured by only downstream dispersal. Accounting for annual variations in dispersal in population models is important to enhance understanding of spatial dynamics and population spread rates. Our developed model also provides a good platform to link the modeling of larval behavior and demography to largescale hydrodynamic models.PLOS ONE | https://doi.org/10.1371/journal.pone

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“…and it is linearly determined [10,15,32,33]. Hence, the explicit expressions (19,20) give the spreading speed for the Ricker and logistic functions even when r > 1.…”

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confidence: 95%

Spreading Phenomena in Integrodifference Equations with Nonmonotone Growth Functions

Bourgeois¹,

LeBlanc²,

Lutscher³

2018

SIAM J. Appl. Math.

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Integrodifference equations are discrete-time cousins of reaction-diffusion equations. Like their continuous-time counterparts, they are used to model spreading phenomena in ecology and other sciences. Unlike their continuous-time counterparts, even scalar integrodifference equations can exhibit non-monotone dynamics. Few authors studied the existence of spreading speeds and travelling waves in the non-monotone case; previous numerical simulations indicated the existence of travelling two-cycles. Our numerical observations indicate the presence of several spreading speeds and multiple travelling wave profiles in these equations. We generalize the concept of a spreading speed to encompass this situation and prove the existence of such generalized spreading speeds and associated travelling waves in the corresponding second-iterate operator. Our numerical simulations let us conjecture that these spreading speeds could be linearly determined. We prove the existence of bistable travelling waves in a related second-iterate operator. We relate our results to the existence of stacked waves and to dynamical stabilization.

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Modelling the biological invasion ofCarcinus maenas(the European green crab)

Cited by 17 publications

References 33 publications

Stochastic dispersal increases the rate of upstream spread: A case study with green crabs on the northwest Atlantic coast

Stochastic dispersal increases the rate of upstream spread: A case study with green crabs on the northwest Atlantic coast

Stochastic dispersal increases the rate of upstream spread: a case study with green crabs on the northwest Atlantic coast

Spreading Phenomena in Integrodifference Equations with Nonmonotone Growth Functions

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