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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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Propagule pressure and the median rate of spread.Theoretical (left) and computed (right) median of the asymptotic rate of spread for , A:  and B: . The computed median was obtained from 15 simulations for each set of parameter values.
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pone-0103409-g006: Propagule pressure and the median rate of spread.Theoretical (left) and computed (right) median of the asymptotic rate of spread for , A: and B: . The computed median was obtained from 15 simulations for each set of parameter values.

Mentions: As the dispersal abilities of the individuals were randomly drawn from the lognormal distribution, , the maximal dispersal ability is a random number. Let be the random variable of the maximal dispersal ability in the initial propagules of size . The cumulative distribution function of can be given as, , where is the cumulative distribution function of the lognormal distribution, , where erf(·) stands for the Gaussian error function. By solving with respect to d we can obtain the median of :(12)For Gaussian dispersal kernels with propagules having multiple dispersal abilities, the asymptotic rate of spread is, thus, given by:(13)This formula for the median asymptotic rate of spread was tested by solving Eq.(2) numerically for different propagule size U0 and propagule diversity σ. For each pair of U0 and σ the median of the asymptotic rate of spread from 15 simulations was calculated and compared with Eq.(13). Evidently, as the propagule diversity σ approaches zero (i.e. all individuals have an equal dispersal ability) the asymptotic rate of spread becomes independent of the propagule size, whereas increasing either propagule size or propagule diversity will result in a faster spreading rate (Fig. 6).


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

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

Propagule pressure and the median rate of spread.Theoretical (left) and computed (right) median of the asymptotic rate of spread for , A:  and B: . The computed median was obtained from 15 simulations for each set of parameter values.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0103409-g006: Propagule pressure and the median rate of spread.Theoretical (left) and computed (right) median of the asymptotic rate of spread for , A: and B: . The computed median was obtained from 15 simulations for each set of parameter values.
Mentions: As the dispersal abilities of the individuals were randomly drawn from the lognormal distribution, , the maximal dispersal ability is a random number. Let be the random variable of the maximal dispersal ability in the initial propagules of size . The cumulative distribution function of can be given as, , where is the cumulative distribution function of the lognormal distribution, , where erf(·) stands for the Gaussian error function. By solving with respect to d we can obtain the median of :(12)For Gaussian dispersal kernels with propagules having multiple dispersal abilities, the asymptotic rate of spread is, thus, given by:(13)This formula for the median asymptotic rate of spread was tested by solving Eq.(2) numerically for different propagule size U0 and propagule diversity σ. For each pair of U0 and σ the median of the asymptotic rate of spread from 15 simulations was calculated and compared with Eq.(13). Evidently, as the propagule diversity σ approaches zero (i.e. all individuals have an equal dispersal ability) the asymptotic rate of spread becomes independent of the propagule size, whereas increasing either propagule size or propagule diversity will result in a faster spreading rate (Fig. 6).

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