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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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Rate of spread of a mixed population.Parameter values are . Diamonds: Instantaneous rate of spread. Circles: Average rate of spread. Solid black line: Predicted asymptotic rate of spread. Solid red line: predicted instantaneous rate of spread (Eq (10)). The rate of spread predicted by a single population model is shown by the dashed line.
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pone-0103409-g005: Rate of spread of a mixed population.Parameter values are . Diamonds: Instantaneous rate of spread. Circles: Average rate of spread. Solid black line: Predicted asymptotic rate of spread. Solid red line: predicted instantaneous rate of spread (Eq (10)). The rate of spread predicted by a single population model is shown by the dashed line.

Mentions: We observed two distinct phases during the range expansion. The instantaneous rate of spread increased with time in the first phase (e.g. in the first 40 generations of the simulated population in Fig. 5), followed by a constant rate of spread in the second phase. Numerical simulations further suggested that the instantaneous rate of spread can be estimated by the mean dispersal ability of the population at the advancing range front (Fig. 5). Specifically, the instantaneous rate of spread c*(t) can be approximated as the rate of spread of a single species with the kernel :(10)where is the mean dispersal ability at the front of the invasion at time t. Furthermore, following the same procedure as for the scenario with two dispersal abilities (section 3.1), we found that both the instantaneous and average rate of spread approached a same asymptotic rate of spread:(11)where is the maximal dispersal ability in the population.


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

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

Rate of spread of a mixed population.Parameter values are . Diamonds: Instantaneous rate of spread. Circles: Average rate of spread. Solid black line: Predicted asymptotic rate of spread. Solid red line: predicted instantaneous rate of spread (Eq (10)). The rate of spread predicted by a single population model is shown by the dashed line.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0103409-g005: Rate of spread of a mixed population.Parameter values are . Diamonds: Instantaneous rate of spread. Circles: Average rate of spread. Solid black line: Predicted asymptotic rate of spread. Solid red line: predicted instantaneous rate of spread (Eq (10)). The rate of spread predicted by a single population model is shown by the dashed line.
Mentions: We observed two distinct phases during the range expansion. The instantaneous rate of spread increased with time in the first phase (e.g. in the first 40 generations of the simulated population in Fig. 5), followed by a constant rate of spread in the second phase. Numerical simulations further suggested that the instantaneous rate of spread can be estimated by the mean dispersal ability of the population at the advancing range front (Fig. 5). Specifically, the instantaneous rate of spread c*(t) can be approximated as the rate of spread of a single species with the kernel :(10)where is the mean dispersal ability at the front of the invasion at time t. Furthermore, following the same procedure as for the scenario with two dispersal abilities (section 3.1), we found that both the instantaneous and average rate of spread approached a same asymptotic rate of spread:(11)where is the maximal dispersal ability in the population.

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