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

Andriamihaja Ramanantoanina,Aziz Ouhinou,Cang Hui

doi:10.1371/journal.pone.0103409

Andriamihaja Ramanantoanina, Aziz Ouhinou + Show 1 more

Open Access

https://doi.org/10.1371/journal.pone.0103409

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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.

Highlights

The ability to estimate the rate of spread of an invasive species is important for the success of its management and control [1]
Models based on partial differential equations, the reaction-diffusion (RD) model, assume a normal distribution of species’ dispersal distances and yield a wpideffiffilffiffiyffiffiused formula which depicts a constant rate of spread (c~2 rD, where r and D denote the intrinsic growth and diffusion rates, respectively) [2,3,4]
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)

Summary

Introduction

The ability to estimate the rate of spread of an invasive species is important for the success of its management and control [1]. We present a mathematical model that uses integrodifference equations to incorporate individuals with different dispersal abilities in the initial propagule. The new formulae of the instantaneous and asymptotic rates of spread derived from this model include rates of growth and dispersal as in the formula for linear expansion, and parameters depicting the propagule size, its compopsitffiffiiffioffiffiffin and the process of spatial sorting.

Results

Conclusion