Mechanistic Analytical Models for Long-Distance Seed Dispersal by Wind

Katul,; Porporato,; Nathan,; Siqueira, Adriano A. G.; Soons,; Poggi,; Horn,; Levin, Levin

doi:10.2307/3473315

Cited by 119 publications

(200 citation statements)

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“…For example, plant height is affected by habitat quality [49], and mechanistic models (e.g. [50]) demonstrate that seed release height strongly affects the dispersal kernel. Here, we have presented a method for deriving the propagation speeds of populations in an IDE model where the kernel, the population projection matrix and their associated parameters take different values in the good and bad patches, but for simplicity, have looked only at examples where the dispersal kernel and parameters are constant throughout the landscape.…”

Section: Discussionmentioning

confidence: 99%

Spreading speeds for stage structured plant populations in fragmented landscapes

Gilbert

White

Bullock

et al. 2014

Journal of Theoretical Biology

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Article (refereed) -postprintGilbert, Mark A.; White, Steven M.; Bullock, James M.; Gaffney, Eamonn A. 2014. Spreading speeds for stage structured plant populations in fragmented landscapes.Contact CEH NORA team at noraceh@ceh.ac.ukThe NERC and CEH trademarks and logos ('the Trademarks') are registered trademarks of NERC in the UK and other countries, and may not be used without the prior written consent of the Trademark owner. Spreading Speeds for Stage Structured Plant Populations in Fragmented Landscapes AbstractLandscape fragmentation has huge ecological and economic implications and affects the spatial dynamics of many plant species. Determining the speed of population spread in fragmented/heterogeneous landscapes is therefore of utmost importance to ecologists. Stage-structured Integrodifference Equations (IDEs) are deterministic models which accurately reflect the life cycles and dispersal patterns for numerous species.Existing approximations to wave-speeds consider only particular kernels, or landscapes in which the scale of variation is much smaller than the dispersal scale. We propose an analytical approximation to the wavespeeds of IDE solutions with periodic landscapes of alternating good and bad patches, where the dispersal scale is greater than the extent of each good patch and where the ratio of the demographic rates in the good and bad patches is given by a small parameter, denoted . We formulate this approximation for the Gaussian and Laplace dispersal kernels and for stage structured and non-stage structured populations, and compare the results against numerical simulations. We find that the approximation is accurate for the landscapes considered, and that the type of dispersal kernel affects the relationship between landscape structure, as classified by landscape period and good patch size, and the spreading speed. This indicates that accurately fitting a kernel to data is important in determining the relationship between landscape structure and spreading speed.

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Section: Discussionmentioning

confidence: 99%

Spreading speeds for stage structured plant populations in fragmented landscapes

Gilbert

White

Bullock

et al. 2014

Journal of Theoretical Biology

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“…The amount of pollen and seed immigration into a population thus depends in the first instance on the dispersal abilities of propagules (in wind-dispersed species particularly on the sink rate of propagules [26,27]) and the spatial distance between the source and the target population. The relationship between dispersal of propagules and space has a mathematical representation, the dispersal curve or dispersal kernel (e.g., [26,28]). The probability of propagule dispersal calculates as a function of space, the effectiveness of adaptations to dispersal-which varies among species-and the activity of vectors (wind, animals, etc.)…”

Section: Gene Flowmentioning

confidence: 99%

Potential Population Genetic Consequences of Habitat Fragmentation in Central European Forest Trees and Associated Understorey Species—An Introductory Survey

Dobeš¹,

Konrad²,

Geburek³

2017

Diversity

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Abstract:Habitat fragmentation threatens the maintenance of genetic diversity of affected populations. Assessment of the risks associated with habitat fragmentation is a big challenge as the change in population genetic diversity is a dynamic process, often acting over long time periods and depending on various characteristics pertaining to both species (life history traits) and their populations (extrinsic characteristics). With this survey, we provide an introductory overview for persons who have to make or are interested in making predictions about the fate of forest-dwelling plant populations which have recently become fragmented and isolated from their main occurrences. We provide a concise introduction to the field of population genetics focusing on terms, processes and phenomena relevant to the maintenance of genetic diversity and vitality of plant populations. In particular the antagonistic effects of gene flow and random genetic drift are covered. A special chapter is devoted to Central European tree species (including the Carpathians) which we treat in detail with reference to an extensive literature survey on population genetic studies assembled from the whole of Europe. We further provide an overview of the population biology of associated understorey species. We conclude with recommended steps to be taken for the evaluation of potential perils of habitat fragmentation or population thinning for the genetics of tree populations. The complexity of effects exerted by life history traits and extrinsic characteristics of populations suggest population genetic development is strongly situation dependent. Therefore, we recommend following a case-by-case approach ideally supported by computer simulations to predict future population genetic development of both trees and associated understorey species.

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“…The ID model with a Gaussian dispersal kernel is essentially equivalent to the classical RD model, in a sense that will be made precise in this paper. Alternative dispersal kernels with heavier tails model the faster and wider spreading observed in many field studies (Bullock and Clarke, 2000;Clark et al, 1999Clark et al, , 2001Katul et al, 2005;Klein et al, 2006;Paradis et al, 2002). This paper proposes a new fractional RD equation…”

Section: Introductionmentioning

confidence: 99%

Fractional Reproduction-Dispersal Equations and Heavy Tail Dispersal Kernels

2007

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Reproduction-Dispersal equations, called reaction-diffusion equations in the physics literature, model the growth and spreading of biological species. IntegroDifference equations were introduced to address the shortcomings of this model, since the dispersal of invasive species is often more widespread than what the classical RD model predicts. In this paper, we extend the RD model, replacing the classical second derivative dispersal term by a fractional derivative of order 1 < α ≤ 2. Fractional derivative models are used in physics to model anomalous super-diffusion, where a cloud of particles spreads faster than the classical diffusion model predicts. This paper also establishes a connection between the new RD model and a corresponding ID equation with a heavy tail dispersal kernel. The general theory developed here accommodates a wide variety of infinitely divisible dispersal kernels that adapt to any scale. Each one corresponds to a generalised RD model with a different dispersal operator. The connection established here between RD and ID equations can also be exploited to generate convergent numerical solutions of RD equations along with explicit error bounds.

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Mechanistic Analytical Models for Long-Distance Seed Dispersal by Wind

Cited by 119 publications

References 0 publications

Spreading speeds for stage structured plant populations in fragmented landscapes

Spreading speeds for stage structured plant populations in fragmented landscapes

Potential Population Genetic Consequences of Habitat Fragmentation in Central European Forest Trees and Associated Understorey Species—An Introductory Survey

Fractional Reproduction-Dispersal Equations and Heavy Tail Dispersal Kernels

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