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Spatial assortment of mixed propagules explains the acceleration of range expansion.

Ramanantoanina A, Ouhinou A, Hui C - PLoS ONE (2014)

Bottom Line: Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread.We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate.Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.

View Article: PubMed Central - PubMed

Affiliation: Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Matieland, South Africa; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Muizenberg, South Africa.

ABSTRACT
Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.

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Evolution of the mean dispersal ability and expected dispersal kernels.(A–B) Mean dispersal ability: During the invasion, the dispersal ability at the front is higher than the dispersal ability at the core of the invasion. The region in blue indicates habitats that have not been invaded at each generation. (C–D): The expected dispersal kernel at the core of the invasion (in black) is narrower than that at the front of the invasion (blue). In both cases, the expected dispersal kernel (full circles) can be approximated by the kernel associated to the mean dispersal ability (Eq (8) and Eq (9)) (Solid lines). Figures (A,C) and (B,D) were obtained using Gaussian and Laplace dispersal kernels respectively.
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pone-0103409-g004: Evolution of the mean dispersal ability and expected dispersal kernels.(A–B) Mean dispersal ability: During the invasion, the dispersal ability at the front is higher than the dispersal ability at the core of the invasion. The region in blue indicates habitats that have not been invaded at each generation. (C–D): The expected dispersal kernel at the core of the invasion (in black) is narrower than that at the front of the invasion (blue). In both cases, the expected dispersal kernel (full circles) can be approximated by the kernel associated to the mean dispersal ability (Eq (8) and Eq (9)) (Solid lines). Figures (A,C) and (B,D) were obtained using Gaussian and Laplace dispersal kernels respectively.

Mentions: When a number of n dispersal abilities were present in the initial propagule, the process of spatial sorting gradually pushed fast dispersers to the advancing range front while compressing slow dispersers to the range core (Fig. 3). Spatial sorting was also detected by calculating the mean dispersal ability which kept increasing while expanding (Fig. 4A–B). The expected dispersal kernel has a fatter tail at the range front than at the range core (Fig. 4C–D); that is, individuals at the front are more likely to travel longer distances than individuals from the range core. Importantly, the expected dispersal kernel was found closely related to the dispersal kernel corresponding to the mean dispersal ability. Consequently, for the expected Gaussian dispersal kernel can be approximated as,(8)and the expected Laplace dispersal kernel can be approximated as,(9)where is the mean dispersal ability at location y and time t.


Spatial assortment of mixed propagules explains the acceleration of range expansion.

Ramanantoanina A, Ouhinou A, Hui C - PLoS ONE (2014)

Evolution of the mean dispersal ability and expected dispersal kernels.(A–B) Mean dispersal ability: During the invasion, the dispersal ability at the front is higher than the dispersal ability at the core of the invasion. The region in blue indicates habitats that have not been invaded at each generation. (C–D): The expected dispersal kernel at the core of the invasion (in black) is narrower than that at the front of the invasion (blue). In both cases, the expected dispersal kernel (full circles) can be approximated by the kernel associated to the mean dispersal ability (Eq (8) and Eq (9)) (Solid lines). Figures (A,C) and (B,D) were obtained using Gaussian and Laplace dispersal kernels respectively.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126666&req=5

pone-0103409-g004: Evolution of the mean dispersal ability and expected dispersal kernels.(A–B) Mean dispersal ability: During the invasion, the dispersal ability at the front is higher than the dispersal ability at the core of the invasion. The region in blue indicates habitats that have not been invaded at each generation. (C–D): The expected dispersal kernel at the core of the invasion (in black) is narrower than that at the front of the invasion (blue). In both cases, the expected dispersal kernel (full circles) can be approximated by the kernel associated to the mean dispersal ability (Eq (8) and Eq (9)) (Solid lines). Figures (A,C) and (B,D) were obtained using Gaussian and Laplace dispersal kernels respectively.
Mentions: When a number of n dispersal abilities were present in the initial propagule, the process of spatial sorting gradually pushed fast dispersers to the advancing range front while compressing slow dispersers to the range core (Fig. 3). Spatial sorting was also detected by calculating the mean dispersal ability which kept increasing while expanding (Fig. 4A–B). The expected dispersal kernel has a fatter tail at the range front than at the range core (Fig. 4C–D); that is, individuals at the front are more likely to travel longer distances than individuals from the range core. Importantly, the expected dispersal kernel was found closely related to the dispersal kernel corresponding to the mean dispersal ability. Consequently, for the expected Gaussian dispersal kernel can be approximated as,(8)and the expected Laplace dispersal kernel can be approximated as,(9)where is the mean dispersal ability at location y and time t.

Bottom Line: Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread.We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate.Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.

View Article: PubMed Central - PubMed

Affiliation: Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Matieland, South Africa; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Muizenberg, South Africa.

ABSTRACT
Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.

Show MeSH
Related in: MedlinePlus