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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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Spread of a population with two dispersal abilities.Parameter values are  A–C: Population size at different time with the initial populations  The colours red, green and black correspond to the type-1, type-2 and total population size respectively. D: A break of slope was observed in the population range. Initial propagules are  (solid line) and  (dashed line).
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pone-0103409-g001: Spread of a population with two dispersal abilities.Parameter values are A–C: Population size at different time with the initial populations The colours red, green and black correspond to the type-1, type-2 and total population size respectively. D: A break of slope was observed in the population range. Initial propagules are (solid line) and (dashed line).

Mentions: When the initial propagule contains two types of individuals, the number of the fast disperser type 2 individuals remained low at the initial phase, while the total population consisted mainly of type 1 individuals, similar to the composition in the initial propagules (Fig. 1A). The type 2 individuals gradually reached the expanding front through spatial sorting (Fig. 1B) and then increased in numbers, with the type 1 individuals compressed back to the range core (comparing Fig. 1B with Fig. 1C). A breaking point of slope was observed during the range expansion (Fig. 1D), indicating a type II bi-phase expansion. The time lag to the breaking point decreased when more type 2 individuals were in the initial propagule but the asymptotic rate of spread was not affected by the propagule composition (Fig. 1D).


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

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

Spread of a population with two dispersal abilities.Parameter values are  A–C: Population size at different time with the initial populations  The colours red, green and black correspond to the type-1, type-2 and total population size respectively. D: A break of slope was observed in the population range. Initial propagules are  (solid line) and  (dashed line).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0103409-g001: Spread of a population with two dispersal abilities.Parameter values are A–C: Population size at different time with the initial populations The colours red, green and black correspond to the type-1, type-2 and total population size respectively. D: A break of slope was observed in the population range. Initial propagules are (solid line) and (dashed line).
Mentions: When the initial propagule contains two types of individuals, the number of the fast disperser type 2 individuals remained low at the initial phase, while the total population consisted mainly of type 1 individuals, similar to the composition in the initial propagules (Fig. 1A). The type 2 individuals gradually reached the expanding front through spatial sorting (Fig. 1B) and then increased in numbers, with the type 1 individuals compressed back to the range core (comparing Fig. 1B with Fig. 1C). A breaking point of slope was observed during the range expansion (Fig. 1D), indicating a type II bi-phase expansion. The time lag to the breaking point decreased when more type 2 individuals were in the initial propagule but the asymptotic rate of spread was not affected by the propagule composition (Fig. 1D).

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