An R 0 theory for source–sink dynamics with application to Dreissena competition

Krkošek, Martin; Lewis, Mark A.

doi:10.1007/s12080-009-0051-7

Cited by 28 publications

(42 citation statements)

References 62 publications

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“…Here, the concept of a generational invasion "wave" is a useful heuristic, although we could not actually measure a generation of individuals spread out through time. This fact is no less relevant in the case of population-level growth, and the concept of the generational growth rate, R 0 , has proven useful across ecological and epidemiological fields (Cushing and Yicang 1994;Caswell 2001;Heesterbeek 2002;de-Camino-Beck and Lewis 2008;Krkošek and Lewis 2010). We expect the concept of generational spreading speed to do the same in the context of biological (re)invasions.…”

Section: Discussionmentioning

confidence: 99%

“…Others have begun to characterize IDE spreading speeds that incorporate landscape heterogeneity (e.g., Gilbert et al 2014). Another approach is to characterize source-sink dynamics across heterogeneous environments on a generational timescale, assessing whether environmental patches or the environment as a whole generate R 0 1 1 (Krkošek and Lewis 2010). This second approach does not characterize spatial movement, but it does consider invasion potential, and the calculations take a form similar to that we have presented.…”

Section: Discussionmentioning

confidence: 99%

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Generational Spreading Speed and the Dynamics of Population Range Expansion

Bateman

Neubert

Krkošek

et al. 2015

The American Naturalist

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Online enhancement: appendix.abstract: Some of the most fundamental quantities in population ecology describe the growth and spread of populations. Population dynamics are often characterized by the annual rate of increase, l, or the generational rate of increase, R 0 . Analyses involving R 0 have deepened our understanding of disease dynamics and life-history complexities beyond that afforded by analysis of annual growth alone. While range expansion is quantified by the annual spreading speed, a spatial analog of l, an R 0 -like expression for the rate of spread is missing. Using integrodifference models, we derive the appropriate generational spreading speed for populations with complex (stage-structured) life histories. The resulting measure, relevant to locations near the expanding edge of a (re)colonizing population, incorporates both local population growth and explicit spatial dispersal rather than solely growth across a population, as is the case for R 0 . The calculations for generational spreading speed are often simpler than those for annual spreading speed, and analytic or partial analytic solutions can yield insight into the processes that facilitate or slow a population's spatial spread. We analyze the spatial dynamics of green crabs, sea otters, and teasel as examples to demonstrate the flexibility of our methods and the intuitive insights that they afford.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Generational Spreading Speed and the Dynamics of Population Range Expansion

Bateman

Neubert

Krkošek

et al. 2015

The American Naturalist

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“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php space. Following [17], we choose a modified Beverton-Holt density-dependent survival term:…”

Section: Model Formulationmentioning

confidence: 99%

“…These cases suggest that patterns of relative dominance and competitive exclusion among these species may vary over space and time, presumably under the influence of environmental variables. A competition model given by a system of integrodifference equations has been developed to explain interactions of zebra and quagga mussel in lakes [17], but the unidirectional flow conditions of rivers will increase dynamical complexity, which may permit weaker competitors but stronger dispersers to coexist in abundance at upstream locations [22]. As a future effort, we plan to extend our single-species model to a competition model that describes the competing dynamics of zebra and quagga mussels in rivers, assuming that larvae disperse in the drift, and that juveniles and adults compete for resources on the benthos.…”

Section: The Effect Of Flow On the Population Spreadmentioning

confidence: 99%

A Hybrid Continuous/Discrete-Time Model for Invasion Dynamics of Zebra Mussels in Rivers

Huang¹,

Wang²,

Lewis³

2017

SIAM J. Appl. Math.

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Abstract. While some species spread upstream in river environments, not all invasive species are successful in spreading upriver. Here the dynamics of unidirectional water flow found in rivers can play a role in determining invasion success. We develop a continuous-discrete hybrid benthic-drift population model to describe the dynamics of invasive freshwater mussels in rivers. In the model, a reaction-advection-diffusion equation coupled to an ordinary differential equation describes the larval dispersal in the drift until settling to the benthos, while two difference equations describe the population growth on the benthos. We study the population persistence criteria based on three related measures: fundamental niche, source-sink distribution, and net reproductive rate. We calculate the critical domain size in a bounded domain by analyzing a next generation operator. We analyze the upstream and downstream spreading speeds in an unbounded domain. The model is parameterized by available data in the literature. Combining the results of model parameterization and theoretical analysis, we numerically analyze how the interaction between population growth and dispersal, river flow rate, and water temperature affects both persistence and the spread of zebra mussels along a river.

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“…If so, they would spawn earlier in the season, allowing them to outcompete zebra mussels for open space for attachment (Roe & MacIsaac, 1997;Claxton & Mackie, 1998). This could then lead to source-sink metapopulation dynamics and spatial competition, which would influence the distribution and dynamics of zebra mussel and quagga mussel populations in lakes where they co-exist (Krošek & Lewis, 2010).…”

Section: Introductionmentioning

confidence: 99%

Differences in growth and survivorship of zebra and quagga mussels: size matters

et al. 2010

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The zebra mussel (Dreissena polymorpha) and its congener the quagga mussel (Dreissena rostriformis bugensis) are both invaders in freshwater, but have very different invasion histories, with zebra mussels attaining substantially faster rates of spread at virtually all spatial scales. However, in waterbodies where they co-occur, D. r. bugensis can displace D. polymorpha. To determine if the mechanisms for this displacement are associated with different survival and growth, we kept mussels in flow-through tanks for 289 days with two temperature regimes that mimicked the natural surface water (littoral zone) and hypolimnion conditions of Lake Erie. For the littoral zone regime, we used water directly from the surface of Lake Erie (range 4-25°C, average 11.9 ± 0.6°C). For the profundal zone treatment, Lake Erie surface water was chilled to about 6°C (range 5-8°C, average 6.2 ± 0.6°C) for the full duration of the experiment. For each of these temperature regimes, we used three replicate tanks with only zebra mussels present and three replicate tanks with only quagga mussels (150 ind./tank each), and three replicate tanks with both species (75 ind./ tank of each species). Quagga mussels had higher survivorship and grew more than zebra mussels in all treatments. For both species, the size of the mussel entering the winter was critical for survivorship. Larger mussels had a higher survival over the winter in all treatments. For both species, there was a survivorship and growth tradeoff. In the warmer littoral zone treatment both species had higher growth, but lower survival than in the colder profundal zone treatment. Surprisingly, although quagga mussels outperformed zebra mussels, zebra mussel survivorship was better when they were faced with competition by quagga mussels than with just intraspecific competition. In addition, quagga mussels suffered size-specific mortality during the growing season only when facing interspecific competition with zebra mussels. Further experiments are needed to determine the possible mechanisms for these interspecific effects.

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An R 0 theory for source–sink dynamics with application to Dreissena competition

Cited by 28 publications

References 62 publications

Generational Spreading Speed and the Dynamics of Population Range Expansion

Generational Spreading Speed and the Dynamics of Population Range Expansion

A Hybrid Continuous/Discrete-Time Model for Invasion Dynamics of Zebra Mussels in Rivers

Differences in growth and survivorship of zebra and quagga mussels: size matters

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